Finite Group Databasebeta

← #31027883

Subgroups — #31027883

Order 17152.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22565609C211yesmaximal, characteristic
2#22565607C211yesmaximal, characteristic
3#22565601C211yesmaximal, characteristic
4#22565599C211yesmaximal, characteristic
5#22565578C211yesmaximal, characteristic
6#22565420C211yesmaximal, characteristic
7#22565239C211yesmaximal, characteristic
8#22565193C211yesmaximal, characteristic
9#22564779C211yesmaximal, characteristic
10#22564777C211yesmaximal, characteristic
11#22564753C211yesmaximal, characteristic
12#22564751C211yesmaximal, characteristic
13#22564065C211yesmaximal, characteristic
14#22564063C211yesmaximal, characteristic
15#22563980C211yesmaximal, characteristic
16#22563978C211yesmaximal, characteristic
17#22563517C211yesmaximal, characteristic
18#22563516C211yesmaximal, characteristic
19#22563516C211yesmaximal, characteristic
20C4×#14524042C211yesmaximal, characteristic
21C4×#14524042C211yesmaximal, characteristic
22C4×#14524042C211yesmaximal, characteristic
23C4×#14524033C211yesmaximal, characteristic
24C4×#14524033C211yesmaximal, characteristic
25#22562685C211yesmaximal, characteristic
26#22562685C211yesmaximal, characteristic
27#22562681C211yesmaximal, characteristic
28#22562681C211yesmaximal, characteristic
29C4×#14524008C211yesmaximal, characteristic
30C4×#14524008C211yesmaximal, characteristic
31C67×#2402C211yesmaximal, characteristic
32C2×#14524042C2211yescharacteristic
33C2×#14524042C2211yescharacteristic
34C2×#14524042C2211yescharacteristic
35C2×#14524033C2211yescharacteristic
36C2×#14524033C2211yescharacteristic
37C2×C4×Dic134C2211yescharacteristic
38C2×C4×Dic134C2211yescharacteristic
39C2×C4×Dic134C2211yescharacteristic
40C2×C4×Dic134C2211yescharacteristic
41C2×#14524008C2211yescharacteristic
42C2×#14524008C2211yescharacteristic
43C2×#14524008C2211yescharacteristic
44C2×#14524008C2211yescharacteristic
45#16863338C2211yescharacteristic
46#16863338C2211yescharacteristic
47#16863337C2211yescharacteristic
48#16863337C2211yescharacteristic
49#16863337C2211yescharacteristic
50#16863337C2211yescharacteristic
51#16863336C2211yescharacteristic
52#16863336C2211yescharacteristic
53#16863335C2211yescharacteristic
54#16863335C2211yescharacteristic
55#16863334C2211yescharacteristic
56#16863334C2211yescharacteristic
57#16863330C2211yescharacteristic
58#16863330C2211yescharacteristic
59#16863329C2211yescharacteristic
60#16863329C2211yescharacteristic
61#16863329C2211yescharacteristic
62#16863329C2211yescharacteristic
63#16863328C2211yescharacteristic
64#16863328C2211yescharacteristic
65#16863327C2211yescharacteristic
66#16863327C2211yescharacteristic
67#16863326C2211yescharacteristic
68#16863326C2211yescharacteristic
69#16863300C2211yescharacteristic
70#16863300C2211yescharacteristic
71#16863300C2211yescharacteristic
72#16863300C2211yescharacteristic
73#16863300C2211yescharacteristic
74#16863300C2211yescharacteristic
75#16863300C2211yescharacteristic
76#16863300C2211yescharacteristic
77#16863300C2211yescharacteristic
78#16863300C2211yescharacteristic
79#16863300C2211yescharacteristic
80#16863300C2211yescharacteristic
81#16863300C2211yescharacteristic
82#16863300C2211yescharacteristic
83#16863295C2211yescharacteristic
84#16863295C2211yescharacteristic
85#16863295C2211yescharacteristic
86#16863293C2211yescharacteristic
87#16863293C2211yescharacteristic
88#16863293C2211yescharacteristic
89#16863293C2211yescharacteristic
90#16863293C2211yescharacteristic
91#16863293C2211yescharacteristic
92#16863293C2211yescharacteristic
93#16863293C2211yescharacteristic
94#16863293C2211yescharacteristic
95#16863293C2211yescharacteristic
96#16863293C2211yescharacteristic
97#16863293C2211yescharacteristic
98#16863292C2211yescharacteristic
99#16863292C2211yescharacteristic
100#16863292C2211yescharacteristic
101#16863291C2211yescharacteristic
102#16863291C2211yescharacteristic
103#16863291C2211yescharacteristic
104#16863291C2211yescharacteristic
105#16863291C2211yescharacteristic
106#16863291C2211yescharacteristic
107#16863283C2211yescharacteristic
108#16863283C2211yescharacteristic
109#16863283C2211yescharacteristic
110#16863283C2211yescharacteristic
111#16863282C2211yescharacteristic
112#16863282C2211yescharacteristic
113#16863281C2211yescharacteristic
114#16863281C2211yescharacteristic
115#16863281C2211yescharacteristic
116#16863281C2211yescharacteristic
117#16863281C2211yescharacteristic
118#16863281C2211yescharacteristic
119#16863279C2211yescharacteristic
120#16863279C2211yescharacteristic
121#16863279C2211yescharacteristic
122#16863279C2211yescharacteristic
123#16863278C2211yescharacteristic
124#16863278C2211yescharacteristic
125#16863277C2211yescharacteristic
126#16863277C2211yescharacteristic
127#16863277C2211yescharacteristic
128#16863277C2211yescharacteristic
129#16863277C2211yescharacteristic
130#16863277C2211yescharacteristic
131#16863265C2211yescharacteristic
132#16863265C2211yescharacteristic
133#16863265C2211yescharacteristic
134#16863260C2211yescharacteristic
135#16863260C2211yescharacteristic
136C4⋊C4×Dic67C2211yescharacteristic
137C4⋊C4×Dic67C2211yescharacteristic
138C4⋊C4×Dic67C2211yescharacteristic
139C4⋊C4×Dic67C2211yescharacteristic
140C4×Dic67⋊C4C2211yescharacteristic
141C4×Dic67⋊C4C2211yescharacteristic
142C4×Dic67⋊C4C2211yescharacteristic
143C4×Dic67⋊C4C2211yescharacteristic
144C4×Dic67⋊C4C2211yescharacteristic
145C4×Dic67⋊C4C2211yescharacteristic
146C4×Dic67⋊C4C2211yescharacteristic
147C4×Dic67⋊C4C2211yescharacteristic
148C4×Dic67⋊C4C2211yescharacteristic
149C4×Dic67⋊C4C2211yescharacteristic
150C4×Dic67⋊C4C2211yescharacteristic
151C4×Dic67⋊C4C2211yescharacteristic
152C4×C4⋊Dic67C2211yescharacteristic
153C4×C4⋊Dic67C2211yescharacteristic
154C4×C4⋊Dic67C2211yescharacteristic
155C4×C4⋊Dic67C2211yescharacteristic
156#16863247C2211yescharacteristic
157#16863247C2211yescharacteristic
158#16863247C2211yescharacteristic
159#16863247C2211yescharacteristic
160#16863247C2211yescharacteristic
161#16863247C2211yescharacteristic
162#16863247C2211yescharacteristic
163#16863247C2211yescharacteristic
164#16863242C2211yescharacteristic
165#16863242C2211yescharacteristic
166#16863242C2211yescharacteristic
167C42×Dic67C2211yescharacteristic
168C42×Dic67C2211yescharacteristic
169C42×Dic67C2211yescharacteristic
170C42×Dic67C2211yescharacteristic
171C42×Dic67C2211yescharacteristic
172#400×C67C2211yescharacteristic
173#400×C67C2211yescharacteristic
174#400×C67C2211yescharacteristic
175#400×C67C2211yescharacteristic
176#398×C67C2211yescharacteristic
177#398×C67C2211yescharacteristic
178#398×C67C2211yescharacteristic
179#398×C67C2211yescharacteristic
180C4×C4⋊C4×C67C2211yescharacteristic
181C4×C4⋊C4×C67C2211yescharacteristic
182C4×C4⋊C4×C67C2211yescharacteristic
183C4×C4⋊C4×C67C2211yescharacteristic
184C4×C4⋊C4×C67C2211yescharacteristic
185C4×C4⋊C4×C67C2211yescharacteristic
186#376×C67C2211yescharacteristic
187C22×Dic134C2311yescharacteristic
188C22×Dic134C2311yescharacteristic
189C22×Dic134C2311yescharacteristic
190C22×Dic134C2311yescharacteristic
191#14524042—24no—
192#14524042—24no—
193#14524042—24no—
194#14524033—24no—
195#14524033—24no—
196C4×Dic134—24no—
197C4×Dic134—24no—
198C4×Dic134—24no—
199C4×Dic134Q818yescomplemented
200#14524008—24no—
201#14524008—24no—
202#14524008—24no—
203#14524008—24no—
204C2×C4⋊Dic67C2311yescharacteristic
205C2×C4⋊Dic67C2311yescharacteristic
206C2×C4⋊Dic67C2311yescharacteristic
207C2×C4⋊Dic67C2311yescharacteristic
208C2×C4⋊Dic67C2311yescharacteristic
209C2×C4⋊Dic67C2311yescharacteristic
210C2×C4⋊Dic67C2311yescharacteristic
211C2×C4⋊Dic67C2311yescharacteristic
212C2×C4⋊Dic67C2311yescharacteristic
213C2×C4⋊Dic67C2311yescharacteristic
214C2×C4⋊Dic67C2311yescharacteristic
215C2×C4⋊Dic67C2311yescharacteristic
216C2×Dic67⋊C4C2311yescharacteristic
217C2×Dic67⋊C4C2311yescharacteristic
218C2×Dic67⋊C4C2311yescharacteristic
219C2×Dic67⋊C4C2311yescharacteristic
220C2×Dic67⋊C4C2311yescharacteristic
221C2×Dic67⋊C4C2311yescharacteristic
222C2×Dic67⋊C4C2311yescharacteristic
223C2×Dic67⋊C4C2311yescharacteristic
224C2×Dic67⋊C4C2311yescharacteristic
225C2×Dic67⋊C4C2311yescharacteristic
226C2×Dic67⋊C4C2311yescharacteristic
227C2×Dic67⋊C4C2311yescharacteristic
228C2×Dic67⋊C4C2311yescharacteristic
229C2×Dic67⋊C4C2311yescharacteristic
230C2×Dic67⋊C4C2311yescharacteristic
231C2×Dic67⋊C4C2311yescharacteristic
232C2×Dic67⋊C4C2311yescharacteristic
233C2×Dic67⋊C4C2311yescharacteristic
234C2×Dic67⋊C4C2311yescharacteristic
235C2×Dic67⋊C4C2311yescharacteristic
236C2×Dic67⋊C4C2311yescharacteristic
237C2×Dic67⋊C4C2311yescharacteristic
238C2×Dic67⋊C4C2311yescharacteristic
239C2×Dic67⋊C4C2311yescharacteristic
240C2×Dic67⋊C4C2311yescharacteristic
241C2×Dic67⋊C4C2311yescharacteristic
242C2×Dic67⋊C4C2311yescharacteristic
243C2×Dic67⋊C4C2311yescharacteristic
244C2×Dic67⋊C4C2311yescharacteristic
245C2×Dic67⋊C4C2311yescharacteristic
246C2×Dic67⋊C4C2311yescharacteristic
247C2×Dic67⋊C4C2311yescharacteristic
248C2×C4×Dic67C2311yescharacteristic
249C2×C4×Dic67C2311yescharacteristic
250C2×C4×Dic67C2311yescharacteristic
251C2×C4×Dic67C2311yescharacteristic
252C2×C4×Dic67C2311yescharacteristic
253C2×C4×Dic67C2311yescharacteristic
254C2×C4×Dic67C2311yescharacteristic
255C2×C4×Dic67C2311yescharacteristic
256C2×C4×Dic67C2311yescharacteristic
257C2×C4×Dic67C2311yescharacteristic
258C2×C4×Dic67C2311yescharacteristic
259C2×C4×Dic67C2311yescharacteristic
260C2×C4×Dic67C2311yescharacteristic
261C2×C4×Dic67C2311yescharacteristic
262C2×C4×Dic67C2311yescharacteristic
263C2×C4×Dic67C2311yescharacteristic
264C2×C4×Dic67C2311yescharacteristic
265C2×C4×Dic67C2311yescharacteristic
266C2×C4×Dic67C2311yescharacteristic
267C2×C4×Dic67C2311yescharacteristic
268C2×C4×Dic67C2311yescharacteristic
269C2×C4×Dic67C2311yescharacteristic
270C2×C4×Dic67C2311yescharacteristic
271C2×C4×Dic67C2311yescharacteristic
272C2×C4×Dic67C2311yescharacteristic
273C2×C4×Dic67C2311yescharacteristic
274C2×C4×Dic67C2311yescharacteristic
275C2×C4×Dic67C2311yescharacteristic
276C67⋊#95C2311yescharacteristic
277C67⋊#95C2311yescharacteristic
278C67⋊#95C2311yescharacteristic
279C67⋊#95C2311yescharacteristic
280C67⋊#95C2311yescharacteristic
281C67⋊#95C2311yescharacteristic
282C67⋊#95C2311yescharacteristic
283C67⋊#95C2311yescharacteristic
284C67⋊#95C2311yescharacteristic
285C67⋊#95C2311yescharacteristic
286C67⋊#95C2311yescharacteristic
287C67⋊#95C2311yescharacteristic
288C67⋊#95C2311yescharacteristic
289C67⋊#95C2311yescharacteristic
290C67⋊#95C2311yescharacteristic
291C67⋊#95C2311yescharacteristic
292C67⋊#95C2311yescharacteristic
293C67⋊#95C2311yescharacteristic
294C67⋊#95C2311yescharacteristic
295C67⋊#95C2311yescharacteristic
296C67⋊#95C2311yescharacteristic
297C67⋊#95C2311yescharacteristic
298C67⋊#95C2311yescharacteristic
299C67⋊#95C2311yescharacteristic
300C67⋊#95C2311yescharacteristic
301C67⋊#95C2311yescharacteristic
302C67⋊#95C2311yescharacteristic
303C67⋊#95C2311yescharacteristic
304C67⋊#95C2311yescharacteristic
305C67⋊#95C2311yescharacteristic
306C67⋊#95C2311yescharacteristic
307C67⋊#95C2311yescharacteristic
308C67⋊#95C2311yescharacteristic
309C67⋊#95C2311yescharacteristic
310C67⋊#95C2311yescharacteristic
311C67⋊#95C2311yescharacteristic
312C67⋊#95C2311yescharacteristic
313C67⋊#95C2311yescharacteristic
314C67⋊#95C2311yescharacteristic
315C67⋊#95C2311yescharacteristic
316C67⋊#95C2311yescharacteristic
317C67⋊#95C2311yescharacteristic
318C67⋊#95C2311yescharacteristic
319C67⋊#95C2311yescharacteristic
320C2×C4⋊C4×C67C2311yescharacteristic
321C2×C4⋊C4×C67C2311yescharacteristic
322C2×C4⋊C4×C67C2311yescharacteristic
323C2×C4⋊C4×C67C2311yescharacteristic
324C2×C4⋊C4×C67C2311yescharacteristic
325C2×C4⋊C4×C67C2311yescharacteristic
326C2×C4⋊C4×C67C2311yescharacteristic
327C2×C4⋊C4×C67C2311yescharacteristic
328C2×C4⋊C4×C67C2311yescharacteristic
329C2×C4⋊C4×C67C2311yescharacteristic
330C2×C4⋊C4×C67C2311yescharacteristic
331C2×C4⋊C4×C67C2311yescharacteristic
332C2×C42×C67C2311yescharacteristic
333C2×C42×C67C2311yescharacteristic
334C2×C42×C67C2311yescharacteristic
335C2×C42×C67C2311yescharacteristic
336C2×C42×C67C2311yescharacteristic
337C2×C42×C67C2311yescharacteristic
338C2×C42×C67C2311yescharacteristic
339#95×C67C2311yescharacteristic
340#95×C67C2311yescharacteristic
341#95×C67C2311yescharacteristic
342#95×C67C2311yescharacteristic
343#95×C67C2311yescharacteristic
344#95×C67C2311yescharacteristic
345#95×C67C2311yescharacteristic
346#95×C67C2311yescharacteristic
347#95×C67C2311yescharacteristic
348#95×C67C2311yescharacteristic
349#95×C67C2311yescharacteristic
350#95×C67C2311yescharacteristic
351#95×C67C2311yescharacteristic
352#95×C67C2311yescharacteristic
353#95×C67C2311yescharacteristic
354#95×C67C2311yescharacteristic
355C2×Dic134—22no—
356C2×Dic134—22no—
357C2×Dic134—22no—
358C2×Dic134—22no—
359C2×Dic134—22no—
360C2×Dic134—22no—
361C2×Dic134—22no—
362C2×Dic134—22no—
363C2×Dic134—22no—
364C2×Dic134—22no—
365C2×Dic134C2×Q814yes—
366C2×Dic134#4114yes—
367C22×Dic67C2411yescharacteristic
368C22×Dic67C2411yescharacteristic
369C22×Dic67C2411yescharacteristic
370C22×Dic67C2411yescharacteristic
371C22×Dic67C2411yescharacteristic
372C22×Dic67C2411yescharacteristic
373C22×Dic67C2411yescharacteristic
374C22×Dic67C2411yescharacteristic
375C22×Dic67C2411yescharacteristic
376C22×Dic67C2411yescharacteristic
377C22×Dic67C2411yescharacteristic
378C22×Dic67C2411yescharacteristic
379C22×Dic67C2411yescharacteristic
380C22×Dic67C2411yescharacteristic
381C22×Dic67C2411yescharacteristic
382C22×Dic67C2411yescharacteristic
383C4⋊Dic67—22no—
384C4⋊Dic67—22no—
385C4⋊Dic67—22no—
386C4⋊Dic67—22no—
387C4⋊Dic67—22no—
388C4⋊Dic67—22no—
389C4⋊Dic67—22no—
390C4⋊Dic67—22no—
391C4⋊Dic67—41no—
392C4⋊Dic67—41no—
393C4⋊Dic67—41no—
394C4⋊Dic67C2×Q814yes—
395Dic67⋊C4—22no—
396Dic67⋊C4—22no—
397Dic67⋊C4—22no—
398Dic67⋊C4—22no—
399Dic67⋊C4—22no—
400Dic67⋊C4—22no—
401Dic67⋊C4—22no—
402Dic67⋊C4—22no—
403Dic67⋊C4—22no—
404Dic67⋊C4—22no—
405Dic67⋊C4—22no—
406Dic67⋊C4—22no—
407Dic67⋊C4—22no—
408Dic67⋊C4—22no—
409Dic67⋊C4—22no—
410Dic67⋊C4—22no—
411Dic67⋊C4—22no—
412Dic67⋊C4—22no—
413Dic67⋊C4—22no—
414Dic67⋊C4—22no—
415Dic67⋊C4—22no—
416Dic67⋊C4—22no—
417Dic67⋊C4—22no—
418Dic67⋊C4—22no—
419Dic67⋊C4—22no—
420Dic67⋊C4—41no—
421Dic67⋊C4—41no—
422Dic67⋊C4—41no—
423Dic67⋊C4—41no—
424Dic67⋊C4C2×Q814yes—
425Dic67⋊C4C2×Q814yes—
426Dic67⋊C4#4114yes—
427C4×Dic67—22no—
428C4×Dic67—22no—
429C4×Dic67—22no—
430C4×Dic67—22no—
431C4×Dic67—22no—
432C4×Dic67—22no—
433C4×Dic67—22no—
434C4×Dic67—22no—
435C4×Dic67—22no—
436C4×Dic67—22no—
437C4×Dic67—22no—
438C4×Dic67—22no—
439C4×Dic67—22no—
440C4×Dic67—22no—
441C4×Dic67—22no—
442C4×Dic67—22no—
443C4×Dic67—22no—
444C4×Dic67—22no—
445C4×Dic67—22no—
446C4×Dic67—41no—
447C4×Dic67—41no—
448C4×Dic67—41no—
449C4×Dic67—41no—
450C4×Dic67—41no—
451C4×Dic67C2×Q814yes—
452C4×Dic67C2×Q814yes—
453C4×Dic67#4114yes—
454C4×Dic67#4114yes—
455C22×C4×C67C2411yescharacteristic
456C22×C4×C67C2411yescharacteristic
457C22×C4×C67C2411yescharacteristic
458C22×C4×C67C2411yescharacteristic
459C22×C4×C67C2411yescharacteristic
460C22×C4×C67C2411yescharacteristic
461C22×C4×C67C2411yescharacteristic
462C22×C4×C67C2411yescharacteristic
463C22×C4×C67C2411yescharacteristic
464C22×C4×C67C2411yescharacteristic
465C22×C4×C67C2411yescharacteristic
466C22×C4×C67C2411yescharacteristic
467C22×C4×C67C2411yescharacteristic
468C22×C4×C67C2411yescharacteristic
469C22×C4×C67C2411yescharacteristic
470C4⋊C4×C67—22no—
471C4⋊C4×C67—22no—
472C4⋊C4×C67—22no—
473C4⋊C4×C67—22no—
474C4⋊C4×C67—22no—
475C4⋊C4×C67—22no—
476C4⋊C4×C67—22no—
477C4⋊C4×C67—22no—
478C4⋊C4×C67—22no—
479C4⋊C4×C67—41no—
480C4⋊C4×C67—41no—
481C4⋊C4×C67—41no—
482C42×C67—22no—
483C42×C67—22no—
484C42×C67—22no—
485C42×C67—22no—
486C42×C67—22no—
487C42×C67—22no—
488C42×C67C2×Q814yes—
489C23×C67C2511yescharacteristic
490C2×C4×C67—21no—
491C2×C4×C67—21no—
492C2×C4×C67—21no—
493C2×C4×C67—21no—
494C2×C4×C67—21no—
495C2×C4×C67—21no—
496C2×C4×C67—21no—
497C2×C4×C67—21no—
498C2×C4×C67—21no—
499C2×C4×C67—21no—
500C2×C4×C67—21no—
501C2×C4×C67—21no—
502C2×C4×C67—21no—
503C2×C4×C67—21no—
504C2×C4×C67—21no—
505C2×C4×C67—21no—
506C2×C4×C67—21no—
507C2×C4×C67—21no—
508C2×C4×C67—21no—
509C2×C4×C67—21no—
510C2×C4×C67—21no—
511C2×C4×C67—21no—
512C2×C4×C67—21no—
513C2×C4×C67—21no—
514C2×C4×C67—21no—
515C2×C4×C67—21no—
516C2×C4×C67—21no—
517C2×C4×C67—21no—
518C2×C4×C67—21no—
519C2×C4×C67—21no—
520C2×C4×C67—21no—
521C2×C4×C67—21no—
522C2×C4×C67—21no—
523C2×C4×C67—21no—
524C2×C4×C67—21no—
525C2×C4×C67—21no—
526C2×C4×C67—21no—
527C2×C4×C67C22×Q812yes—
528C2×C4×C67C22×Q812yes—
529C2×C4×C67C22×Q812yes—
530C2×C4×C67C2×#4112yes—
531C2×C4×C67C2×#4112yes—
532C2×C4×C67C2×#4112yes—
533C2×C4×C67C2×#4112yes—
534C2×C4×C672−1+412yes—
535C2×Dic67—21no—
536C2×Dic67—21no—
537C2×Dic67—21no—
538C2×Dic67—21no—
539C2×Dic67—21no—
540C2×Dic67—21no—
541C2×Dic67—21no—
542C2×Dic67—21no—
543C2×Dic67—21no—
544C2×Dic67—21no—
545C2×Dic67—21no—
546C2×Dic67—21no—
547C2×Dic67—21no—
548C2×Dic67—21no—
549C2×Dic67—21no—
550C2×Dic67—21no—
551C2×Dic67—21no—
552C2×Dic67—21no—
553C2×Dic67—21no—
554C2×Dic67—21no—
555C2×Dic67—21no—
556C2×Dic67—21no—
557C2×Dic67—21no—
558C2×Dic67—21no—
559C2×Dic67—21no—
560C2×Dic67—21no—
561C2×Dic67—21no—
562C2×Dic67—21no—
563C2×Dic67—21no—
564C2×Dic67—21no—
565C2×Dic67—21no—
566C2×Dic67—21no—
567C2×Dic67—21no—
568C2×Dic67—21no—
569C2×Dic67—21no—
570C2×Dic67—21no—
571C2×Dic67C22×Q812yes—
572C2×Dic67C22×Q812yes—
573C2×Dic67C22×Q812yes—
574C2×Dic67C22×Q812yes—
575C2×Dic67C2×#4112yes—
576C2×Dic67C2×#4112yes—
577C2×Dic67C2×#4112yes—
578C2×Dic67C2×#4112yes—
579C2×Dic67C2×#4112yes—
580C2×Dic67C2×#4112yes—
581C2×Dic67C2×#4112yes—
582C2×Dic67C2×#4112yes—
583Dic134—28no—
584Dic134—28no—
585Dic134—44no—
586Dic134—44no—
587C22×C67C23×Q811yescharacteristic
588C22×C67C22×#4111yescharacteristic
589C22×C67C22×#4111yescharacteristic
590C22×C67C22×#4111yescharacteristic
591C22×C67C22×#4111yescharacteristic
592C22×C67C2×2−1+411yescharacteristic
593C22×C67#58511yescharacteristic
594C4×C67—22no—
595C4×C67—22no—
596C4×C67—22no—
597C4×C67—22no—
598C4×C67—22no—
599C4×C67—41no—
600C4×C67—41no—
601C4×C67—41no—
602C4×C67—41no—
603C4×C67—41no—
604C4×C67—41no—
605C4×C67—41no—
606C4×C67—41no—
607C4×C67—41no—
608C4×C67#55714yes—
609Dic67—22no—
610Dic67—22no—
611Dic67—22no—
612Dic67—22no—
613Dic67—22no—
614Dic67—22no—
615Dic67—41no—
616Dic67—41no—
617Dic67—41no—
618Dic67—41no—
619Dic67—41no—
620Dic67—41no—
621Dic67—41no—
622Dic67—41no—
623Dic67#52914yes—
624Dic67#53314yes—
625#34951—671nomaximal, Sylow
626C2×C67C2×#52911yescharacteristic
627C2×C67C2×#53311yescharacteristic
628C2×C67#346111yescharacteristic
629C2×C67C2×#55711yescharacteristic
630C2×C67Q8×#4111yescharacteristic
631C2×C67#348011yescharacteristic
632C2×C67#348211yescharacteristic
633#2585—671no—
634#2585—671no—
635#2585—671no—
636#2585—671no—
637#2582—671no—
638#2568—671no—
639#2552—671no—
640#2546—671no—
641#2511—671no—
642#2511—671no—
643#2509—671no—
644#2509—671no—
645#2453—671no—
646#2453—671no—
647#2446—671no—
648#2446—671no—
649#2402—671no—
650#2402—671no—
651#2402—671no—
652#2402D6711yescharacteristic
653C4×C4⋊Q8—671no—
654C4×C4⋊Q8—671no—
655C4×C4⋊Q8—671no—
656C4×#125—671no—
657C4×#125—671no—
658#2295—671no—
659#2295—671no—
660#2295—671no—
661#2295—671no—
662C42×Q8—671no—
663C42×Q8—671no—
664C67#3495111yescharacteristic, complemented, Sylow
665C2×C4⋊Q8—671no—
666C2×C4⋊Q8—671no—
667C2×C4⋊Q8—671no—
668C2×#125—671no—
669C2×#125—671no—
670C2×C4×Q8—671no—
671C2×C4×Q8—671no—
672C2×C4×Q8—671no—
673C2×C4×Q8—671no—
674C2×C4×Q8—671no—
675C2×C4×Q8—671no—
676C2×C4×Q8—671no—
677C2×C4×Q8—671no—
678#400—671no—
679#400—671no—
680#400—671no—
681#400—671no—
682#400—671no—
683#400—671no—
684#400—671no—
685#400—671no—
686#400—671no—
687#400—671no—
688#400—671no—
689#400—671no—
690#400C2×D6711yescharacteristic
691#400C2×D6711yescharacteristic
692#400C2×D6711yescharacteristic
693#400C2×D6711yescharacteristic
694#398—671no—
695#398—671no—
696#398—671no—
697#398—671no—
698#398—671no—
699#398—671no—
700#398—671no—
701#398—671no—
702#398—671no—
703#398—671no—
704#398—671no—
705#398—671no—
706#398C2×D6711yescharacteristic
707#398C2×D6711yescharacteristic
708#398C2×D6711yescharacteristic
709#398C2×D6711yescharacteristic
710#391—671no—
711#391—671no—
712#391—671no—
713#391—671no—
714#391—671no—
715#391—671no—
716#391—671no—
717#391—671no—
718#391—671no—
719#391—671no—
720#391—671no—
721#391—671no—
722#391—671no—
723#391—671no—
724#389—671no—
725#389—671no—
726#389—671no—
727#389—671no—
728#389—671no—
729#389—671no—
730#389—671no—
731#389—671no—
732#389—671no—
733#389—671no—
734#389—671no—
735#389—671no—
736#389—671no—
737#389—671no—
738#389—671no—
739#389—671no—
740#389—671no—
741#389—671no—
742#389—671no—
743#389—671no—
744#389—671no—
745#389—671no—
746#389—671no—
747#389—671no—
748#387—671no—
749#387—671no—
750#387—671no—
751#387—671no—
752#387—671no—
753#387—671no—
754#387—671no—
755#387—671no—
756#387—671no—
757#387—671no—
758#387—671no—
759#387—671no—
760#387—671no—
761#387—671no—
762#387—671no—
763#387—671no—
764#387—671no—
765#387—671no—
766#387—671no—
767#387—671no—
768#387—671no—
769#387—671no—
770#387—671no—
771#387—671no—
772#384—671no—
773#384—671no—
774#384—671no—
775#382—671no—
776#382—671no—
777C4×C4⋊C4—671no—
778C4×C4⋊C4—671no—
779C4×C4⋊C4—671no—
780C4×C4⋊C4—671no—
781C4×C4⋊C4—671no—
782C4×C4⋊C4—671no—
783C4×C4⋊C4—671no—
784C4×C4⋊C4—671no—
785C4×C4⋊C4—671no—
786C4×C4⋊C4—671no—
787C4×C4⋊C4—671no—
788C4×C4⋊C4—671no—
789C4×C4⋊C4—671no—
790C4×C4⋊C4—671no—
791C4×C4⋊C4—671no—
792C4×C4⋊C4—671no—
793C4×C4⋊C4—671no—
794C4×C4⋊C4—671no—
795C4×C4⋊C4—671no—
796C4×C4⋊C4—671no—
797C4×C4⋊C4—671no—
798C4×C4⋊C4—671no—
799C4×C4⋊C4—671no—
800C4×C4⋊C4—671no—
801C4×C4⋊C4—671no—
802C4×C4⋊C4—671no—
803C4×C4⋊C4—671no—
804C4×C4⋊C4—671no—
805C4×C4⋊C4C2×D6711yescharacteristic
806C4×C4⋊C4C2×D6711yescharacteristic
807C4×C4⋊C4C2×D6711yescharacteristic
808C4×C4⋊C4C2×D6711yescharacteristic
809C4×C4⋊C4C2×D6711yescharacteristic
810C4×C4⋊C4C2×D6711yescharacteristic
811#376—671no—
812#376—671no—
813#376—671no—
814#376C2×D6711yescharacteristic
815C43—671no—
816C43—671no—
817C43—671no—
818C43—671no—
819C43—671no—
820C22×Q8—671no—
821C22×Q8—671no—
822C22×Q8—671no—
823C22×Q8—671no—
824C4⋊Q8—1344no—
825C4⋊Q8—1344no—
826C4⋊Q8—1344no—
827#125—1344no—
828#125—1344no—
829C4×Q8—678no—
830C4×Q8—1344no—
831C4×Q8—1344no—
832C4×Q8—1344no—
833C4×Q8—1344no—
834C4×Q8—1344no—
835C4×Q8—1344no—
836C4×Q8—1344no—
837C2×C4⋊C4—671no—
838C2×C4⋊C4—671no—
839C2×C4⋊C4—671no—
840C2×C4⋊C4—671no—
841C2×C4⋊C4—671no—
842C2×C4⋊C4—671no—
843C2×C4⋊C4—671no—
844C2×C4⋊C4—671no—
845C2×C4⋊C4—671no—
846C2×C4⋊C4—671no—
847C2×C4⋊C4—671no—
848C2×C4⋊C4—671no—
849C2×C4⋊C4—671no—
850C2×C4⋊C4—671no—
851C2×C4⋊C4—671no—
852C2×C4⋊C4—671no—
853C2×C4⋊C4—671no—
854C2×C4⋊C4—671no—
855C2×C4⋊C4—671no—
856C2×C4⋊C4—671no—
857C2×C4⋊C4—671no—
858C2×C4⋊C4—671no—
859C2×C4⋊C4—671no—
860C2×C4⋊C4—671no—
861C2×C4⋊C4—671no—
862C2×C4⋊C4—671no—
863C2×C4⋊C4—671no—
864C2×C4⋊C4—671no—
865C2×C4⋊C4—671no—
866C2×C4⋊C4—671no—
867C2×C4⋊C4—671no—
868C2×C4⋊C4—671no—
869C2×C4⋊C4—671no—
870C2×C4⋊C4—671no—
871C2×C4⋊C4—671no—
872C2×C4⋊C4—671no—
873C2×C4⋊C4—671no—
874C2×C4⋊C4—671no—
875C2×C4⋊C4—671no—
876C2×C4⋊C4—671no—
877C2×C4⋊C4—671no—
878C2×C4⋊C4—671no—
879C2×C4⋊C4—671no—
880C2×C4⋊C4—671no—
881C2×C4⋊C4C22×D6711yescharacteristic
882C2×C4⋊C4C22×D6711yescharacteristic
883C2×C4⋊C4C22×D6711yescharacteristic
884C2×C4⋊C4C22×D6711yescharacteristic
885C2×C4⋊C4C22×D6711yescharacteristic
886C2×C4⋊C4C22×D6711yescharacteristic
887C2×C4⋊C4C22×D6711yescharacteristic
888C2×C4⋊C4C22×D6711yescharacteristic
889C2×C4⋊C4C22×D6711yescharacteristic
890C2×C4⋊C4C22×D6711yescharacteristic
891C2×C4⋊C4C22×D6711yescharacteristic
892C2×C4⋊C4C22×D6711yescharacteristic
893C2×C42—671no—
894C2×C42—671no—
895C2×C42—671no—
896C2×C42—671no—
897C2×C42—671no—
898C2×C42—671no—
899C2×C42—671no—
900C2×C42—671no—
901C2×C42—671no—
902C2×C42—671no—
903C2×C42—671no—
904C2×C42—671no—
905C2×C42—671no—
906C2×C42—671no—
907C2×C42—671no—
908C2×C42—671no—
909C2×C42—671no—
910C2×C42—671no—
911C2×C42—671no—
912C2×C42—671no—
913C2×C42—671no—
914C2×C42—671no—
915C2×C42—671no—
916C2×C42—671no—
917C2×C42—671no—
918C2×C42—671no—
919C2×C42—671no—
920C2×C42—671no—
921C2×C42C22×D6711yescharacteristic
922C2×C42C22×D6711yescharacteristic
923C2×C42C22×D6711yescharacteristic
924C2×C42C22×D6711yescharacteristic
925C2×C42C22×D6711yescharacteristic
926C2×C42C22×D6711yescharacteristic
927C2×C42C22×D6711yescharacteristic
928#95—671no—
929#95—671no—
930#95—671no—
931#95—671no—
932#95—671no—
933#95—671no—
934#95—671no—
935#95—671no—
936#95—671no—
937#95—671no—
938#95—671no—
939#95—671no—
940#95—671no—
941#95—671no—
942#95—671no—
943#95—671no—
944#95—671no—
945#95—671no—
946#95—671no—
947#95—671no—
948#95—671no—
949#95—671no—
950#95—671no—
951#95—671no—
952#95—671no—
953#95—671no—
954#95—671no—
955#95—671no—
956#95—671no—
957#95—671no—
958#95—671no—
959#95—671no—
960#95—671no—
961#95—671no—
962#95—671no—
963#95—671no—
964#95—671no—
965#95—671no—
966#95—671no—
967#95—671no—
968#95—671no—
969#95—671no—
970#95—671no—
971#95—671no—
972#95C22×D6711yescharacteristic
973#95C22×D6711yescharacteristic
974#95C22×D6711yescharacteristic
975#95C22×D6711yescharacteristic
976#95C22×D6711yescharacteristic
977#95C22×D6711yescharacteristic
978#95C22×D6711yescharacteristic
979#95C22×D6711yescharacteristic
980#95C22×D6711yescharacteristic
981#95C22×D6711yescharacteristic
982#95C22×D6711yescharacteristic
983#95C22×D6711yescharacteristic
984#95C22×D6711yescharacteristic
985#95C22×D6711yescharacteristic
986#95C22×D6711yescharacteristic
987#95C22×D6711yescharacteristic
988C2×Q8—674no—
989C2×Q8—674no—
990C2×Q8—1342no—
991C2×Q8—1342no—
992C2×Q8—1342no—
993C2×Q8—1342no—
994C2×Q8—1342no—
995C2×Q8—1342no—
996C2×Q8—1342no—
997C2×Q8—1342no—
998C2×Q8—1342no—
999C2×Q8—1342no—
1000C22×C4—671no—
1001C22×C4—671no—
1002C22×C4—671no—
1003C22×C4—671no—
1004C22×C4—671no—
1005C22×C4—671no—
1006C22×C4—671no—
1007C22×C4—671no—
1008C22×C4—671no—
1009C22×C4—671no—
1010C22×C4—671no—
1011C22×C4—671no—
1012C22×C4—671no—
1013C22×C4—671no—
1014C22×C4—671no—
1015C22×C4—671no—
1016C22×C4C23×D6711yescharacteristic
1017C22×C4C23×D6711yescharacteristic
1018C22×C4C23×D6711yescharacteristic
1019C22×C4C23×D6711yescharacteristic
1020C22×C4C23×D6711yescharacteristic
1021C22×C4C23×D6711yescharacteristic
1022C22×C4C23×D6711yescharacteristic
1023C22×C4C23×D6711yescharacteristic
1024C22×C4C23×D6711yescharacteristic
1025C22×C4C23×D6711yescharacteristic
1026C22×C4C23×D6711yescharacteristic
1027C22×C4C23×D6711yescharacteristic
1028C22×C4C23×D6711yescharacteristic
1029C22×C4C23×D6711yescharacteristic
1030C22×C4C23×D6711yescharacteristic
1031C4⋊C4—22no—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—22no—
1037C4⋊C4—22no—
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—2681no—
1044C4⋊C4—2681no—
1045C4⋊C4—2681no—
1046C4⋊C4—2681no—
1047C4⋊C4—2681no—
1048C4⋊C4—2681no—
1049C4⋊C4—2681no—
1050C4⋊C4—674no—
1051C4⋊C4—674no—
1052C4⋊C4—674no—
1053C4⋊C4—674no—
1054C4⋊C4—1342no—
1055C4⋊C4—1342no—
1056C4⋊C4—1342no—
1057C4⋊C4—1342no—
1058C4⋊C4—1342no—
1059C4⋊C4—1342no—
1060C4⋊C4—1342no—
1061C4⋊C4—1342no—
1062C4⋊C4—1342no—
1063C4⋊C4—1342no—
1064C4⋊C4—1342no—
1065C4⋊C4—1342no—
1066C4⋊C4—1342no—
1067C4⋊C4—1342no—
1068C4⋊C4—1342no—
1069C4⋊C4—1342no—
1070C4⋊C4—1342no—
1071C4⋊C4—1342no—
1072C4⋊C4—1342no—
1073C4⋊C4—1342no—
1074C4⋊C4—1342no—
1075C4⋊C4—1342no—
1076C4⋊C4—1342no—
1077C4⋊C4—1342no—
1078C4⋊C4—1342no—
1079C4⋊C4—1342no—
1080C4⋊C4—1342no—
1081C4⋊C4—1342no—
1082C4⋊C4—1342no—
1083C4⋊C4—1342no—
1084C4⋊C4—1342no—
1085C4⋊C4—1342no—
1086C4⋊C4—1342no—
1087C42—22no—
1088C42—22no—
1089C42—22no—
1090C42—22no—
1091C42—22no—
1092C42—22no—
1093C42—2681no—
1094C42—2681no—
1095C42—2681no—
1096C42—2681no—
1097C42—2681no—
1098C42—674no—
1099C42—674no—
1100C42—674no—
1101C42—674no—
1102C42—1342no—
1103C42—1342no—
1104C42—1342no—
1105C42—1342no—
1106C42—1342no—
1107C42—1342no—
1108C42—1342no—
1109C42—1342no—
1110C42—1342no—
1111C42—1342no—
1112C42—1342no—
1113C42—1342no—
1114C42—1342no—
1115C42—1342no—
1116C42—1342no—
1117C42—1342no—
1118C42—1342no—
1119C42—1342no—
1120C42—1342no—
1121C42Q8×D6714yes—
1122C23C24×D6711yescharacteristic
1123Q8—2684no—
1124Q8—2684no—
1125Q8—1348no—
1126Q8—1348no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—672no—
1165C2×C4—672no—
1166C2×C4—672no—
1167C2×C4—672no—
1168C2×C4—672no—
1169C2×C4—672no—
1170C2×C4—672no—
1171C2×C4—672no—
1172C2×C4—672no—
1173C2×C4—672no—
1174C2×C4—672no—
1175C2×C4—672no—
1176C2×C4—1341no—
1177C2×C4—1341no—
1178C2×C4—1341no—
1179C2×C4—1341no—
1180C2×C4—1341no—
1181C2×C4—1341no—
1182C2×C4—1341no—
1183C2×C4—1341no—
1184C2×C4—1341no—
1185C2×C4—1341no—
1186C2×C4—1341no—
1187C2×C4—1341no—
1188C2×C4—1341no—
1189C2×C4—1341no—
1190C2×C4—1341no—
1191C2×C4—1341no—
1192C2×C4—1341no—
1193C2×C4—1341no—
1194C2×C4—1341no—
1195C2×C4—1341no—
1196C2×C4—1341no—
1197C2×C4—1341no—
1198C2×C4—1341no—
1199C2×C4—1341no—
1200C2×C4—1341no—
1201C2×C4—1341no—
1202C2×C4—1341no—
1203C2×C4—1341no—
1204C2×C4—1341no—
1205C2×C4—1341no—
1206C2×C4—1341no—
1207C2×C4—1341no—
1208C2×C4—1341no—
1209C2×C4—1341no—
1210C2×C4—1341no—
1211C2×C4—1341no—
1212C2×C4C2×Q8×D6712yes—
1213C2×C4C2×Q8×D6712yes—
1214C2×C4C2×Q8×D6712yes—
1215C2×C4#41×D6712yes—
1216C2×C4#41×D6712yes—
1217C2×C4#41×D6712yes—
1218C2×C4#41×D6712yes—
1219C2×C4#1452409012yes—
1220C22C22×Q8×D6711yescharacteristic
1221C22C2×#41×D6711yescharacteristic
1222C22C2×#41×D6711yescharacteristic
1223C22C2×#41×D6711yescharacteristic
1224C22C2×#41×D6711yescharacteristic
1225C22C2×#1452409011yescharacteristic
1226C22#1686423211yescharacteristic
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—22no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—2681no—
1242C4—2681no—
1243C4—2681no—
1244C4—2681no—
1245C4—2681no—
1246C4—2681no—
1247C4—2681no—
1248C4—2681no—
1249C4—674no—
1250C4—674no—
1251C4—1342no—
1252C4—1342no—
1253C4—1342no—
1254C4—1342no—
1255C4—1342no—
1256C4—1342no—
1257C4#1686412314yes—
1258C2#529×D6711yescharacteristic
1259C2#533×D6711yescharacteristic
1260C2#2257363811yescharacteristic
1261C2C2×#1686412311yescharacteristic
1262C2#2257378711yescharacteristic
1263C2#2257380011yescharacteristic
1264C2#2257382211yescharacteristic
subgroupG/H
centerC22×C4C23×D67
commutator, socle, prime radical, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC67×#2402C2
hypercenter#2402D67
hypocenterC67#34951
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ #2402

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
199. C4×Dic134Q8semidirect
664. C67#34951semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225656092
#225656072
#225656012
#225655992
#225655782
#225654202
#225652392
#225651932
#225647792
#225647772
#225647532
#225647512
#225640652
#225640632
#225639802
#225639782
#225635172
#225635162
C4×#145240422
C4×#145240332
#225626852
#225626812
C4×#145240082
C67×#24022
#3495167