Finite Group Databasebeta

← #30865472

Subgroups — #30865472

Order 17152.

1128 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863457C211yesmaximal, characteristic, complemented
2C2×#16863423C211yesmaximal, characteristic, complemented
3#22561150C211yesmaximal, characteristic, complemented
4#22561146C211yesmaximal, characteristic, complemented
5#22561008C211yesmaximal, characteristic, complemented
6#22561004C211yesmaximal, characteristic, complemented
7#22560507C211yesmaximal, characteristic, complemented
8#22560507C211yesmaximal, characteristic, complemented
9#22560502C211yesmaximal, characteristic, complemented
10#22560502C211yesmaximal, characteristic, complemented
11#22560193C211yesmaximal, characteristic, complemented
12#22560193C211yesmaximal, characteristic, complemented
13#22560189C211yesmaximal, characteristic, complemented
14#22560189C211yesmaximal, characteristic, complemented
15C2×#529×C67C211yesmaximal, characteristic
16C22×#11761612C2211yescharacteristic
17C23×C67⋊C8C2211yescharacteristic
18#16863457—24no—
19#16863423—24no—
20C2×C4⋊(C67⋊C8)C2211yescharacteristic
21C2×C4⋊(C67⋊C8)C2211yescharacteristic
22C2×C4⋊(C67⋊C8)C2211yescharacteristic
23C2×C4⋊(C67⋊C8)C2211yescharacteristic
24C2×C4⋊(C67⋊C8)C2211yescharacteristic
25C2×C4⋊(C67⋊C8)C2211yescharacteristic
26C2×C22⋊(C67⋊C8)C2211yescharacteristic
27C2×C22⋊(C67⋊C8)C2211yescharacteristic
28C2×C22⋊(C67⋊C8)C2211yescharacteristic
29C2×C22⋊(C67⋊C8)C2211yescharacteristic
30C2×C22⋊(C67⋊C8)C2211yescharacteristic
31C2×C22⋊(C67⋊C8)C2211yescharacteristic
32C2×C22⋊(C67⋊C8)C2211yescharacteristic
33C2×C22⋊(C67⋊C8)C2211yescharacteristic
34C2×C22⋊(C67⋊C8)C2211yescharacteristic
35C2×C22⋊(C67⋊C8)C2211yescharacteristic
36C2×#14523954C2211yescharacteristic
37C2×C4×C67⋊C8C2211yescharacteristic
38#16863151C2211yescharacteristic
39#16863151C2211yescharacteristic
40#16863151C2211yescharacteristic
41#16863151C2211yescharacteristic
42#16863151C2211yescharacteristic
43#16863151C2211yescharacteristic
44#16863151C2211yescharacteristic
45#16863151C2211yescharacteristic
46#529×C67—24no—
47#529×C67—24no—
48C2×#126×C67C411yescharacteristic
49C2×#126×C67C411yescharacteristic
50C2×#125×C67C411yescharacteristic
51C2×#124×C67C411yescharacteristic
52C2×#123×C67C411yescharacteristic
53C2×#123×C67C411yescharacteristic
54C2×C22⋊Q8×C67C411yescharacteristic
55C2×#121×C67C411yescharacteristic
56C2×C4×Q8×C67C2211yescharacteristic
57C2×C4×D4×C67C2211yescharacteristic
58C2×C4×D4×C67C2211yescharacteristic
59C2×C4×D4×C67C2211yescharacteristic
60C2×#117×C67C2211yescharacteristic
61C2×#117×C67C2211yescharacteristic
62C22×C42×C67C2211yescharacteristic
63C2×#11761612—22no—
64C2×#11761612—41no—
65C2×#11761612—41no—
66C22×C67⋊C8—22no—
67C22×C67⋊C8—41no—
68C22×C67⋊C8—41no—
69C22×C67⋊C8C2311yescharacteristic
70C22×C67⋊C8C2311yescharacteristic
71C22×C67⋊C8C2311yescharacteristic
72C22×C67⋊C8C2311yescharacteristic
73C22×C67⋊C8C2311yescharacteristic
74C22×C67⋊C8C2311yescharacteristic
75C22×C67⋊C8C2311yescharacteristic
76C22×C67⋊C8C2311yescharacteristic
77C4⋊(C67⋊C8)—22no—
78C4⋊(C67⋊C8)—22no—
79C4⋊(C67⋊C8)—22no—
80C4⋊(C67⋊C8)—22no—
81C4⋊(C67⋊C8)—22no—
82C4⋊(C67⋊C8)—22no—
83C22⋊(C67⋊C8)—22no—
84C22⋊(C67⋊C8)—22no—
85C22⋊(C67⋊C8)—41no—
86C22⋊(C67⋊C8)—41no—
87C22⋊(C67⋊C8)—41no—
88C22⋊(C67⋊C8)—41no—
89C22⋊(C67⋊C8)—41no—
90C22⋊(C67⋊C8)—41no—
91C22⋊(C67⋊C8)—41no—
92C22⋊(C67⋊C8)—41no—
93#14523954—22no—
94C4×C67⋊C8—22no—
95C22×Q8×C67C2×C411yescharacteristic
96C22×D4×C67C2×C411yescharacteristic
97C22×D4×C67C2×C411yescharacteristic
98C22×D4×C67C2×C411yescharacteristic
99C23×C4×C67C2×C411yescharacteristic
100C23×C4×C67C2×C411yescharacteristic
101C23×C4×C67C2311yescharacteristic
102C23×C4×C67C2311yescharacteristic
103C23×C4×C67C2311yescharacteristic
104#126×C67—24no—
105#126×C67—24no—
106#125×C67—24no—
107#124×C67—24no—
108#123×C67—24no—
109#123×C67—24no—
110C22⋊Q8×C67—24no—
111#121×C67—24no—
112C4×Q8×C67—22no—
113C4×Q8×C67—22no—
114C4×D4×C67—22no—
115C4×D4×C67—22no—
116C4×D4×C67—22no—
117C4×D4×C67—22no—
118C4×D4×C67—22no—
119C4×D4×C67—22no—
120#117×C67—22no—
121#117×C67—22no—
122#117×C67D414yes—
123#117×C67D414yes—
124C2×C4⋊C4×C67C2×C411yescharacteristic
125C2×C4⋊C4×C67C2×C411yescharacteristic
126C2×C4⋊C4×C67C2×C411yescharacteristic
127C2×C4⋊C4×C67C2×C411yescharacteristic
128C2×C4⋊C4×C67C2×C411yescharacteristic
129C2×C4⋊C4×C67C2×C411yescharacteristic
130C2×C4⋊C4×C67C2×C411yescharacteristic
131C2×C4⋊C4×C67C2×C411yescharacteristic
132C2×C4⋊C4×C67C2×C411yescharacteristic
133C2×C4⋊C4×C67C2×C411yescharacteristic
134C2×C22⋊C4×C67C2×C411yescharacteristic
135C2×C22⋊C4×C67C2×C411yescharacteristic
136C2×C22⋊C4×C67C2×C411yescharacteristic
137C2×C22⋊C4×C67C2×C411yescharacteristic
138C2×C22⋊C4×C67C2×C411yescharacteristic
139C2×C22⋊C4×C67C2×C411yescharacteristic
140C2×C22⋊C4×C67C2×C411yescharacteristic
141C2×C22⋊C4×C67C2×C411yescharacteristic
142C2×C22⋊C4×C67C2×C411yescharacteristic
143C2×C22⋊C4×C67C2×C411yescharacteristic
144C2×C42×C67—22no—
145C2×C42×C67—22no—
146C2×C42×C67C2×C411yescharacteristic
147C2×C42×C67C2×C411yescharacteristic
148C2×C42×C67C2311yescharacteristic
149C2×C42×C67C2311yescharacteristic
150C2×C42×C67C2311yescharacteristic
151C2×C42×C67C2311yescharacteristic
152#11761612—44no—
153C2×C67⋊C8—21no—
154C2×C67⋊C8—21no—
155C2×C67⋊C8—21no—
156C2×C67⋊C8—21no—
157C2×C67⋊C8—21no—
158C2×C67⋊C8—21no—
159C2×C67⋊C8—21no—
160C2×C67⋊C8—21no—
161C2×C67⋊C8—21no—
162C2×C67⋊C8—21no—
163C2×C67⋊C8—21no—
164C2×C67⋊C8—21no—
165C2×C67⋊C8—21no—
166C2×C67⋊C8—21no—
167C2×C67⋊C8—21no—
168C2×C67⋊C8—21no—
169C2×C67⋊C8—21no—
170C2×C67⋊C8—21no—
171C2×C67⋊C8—21no—
172C2×C67⋊C8—21no—
173C2×C67⋊C8—21no—
174C2×C67⋊C8—21no—
175C2×C67⋊C8—21no—
176C2×C67⋊C8—21no—
177C2×C67⋊C8—44no—
178C24×C67C22×C411yescharacteristic
179C24×C67C22×C411yescharacteristic
180C24×C67C22×C411yescharacteristic
181C2×Q8×C67—22no—
182C2×Q8×C67—22no—
183C2×Q8×C67—41no—
184C2×D4×C67—22no—
185C2×D4×C67—22no—
186C2×D4×C67—22no—
187C2×D4×C67—22no—
188C2×D4×C67—22no—
189C2×D4×C67—22no—
190C2×D4×C67—41no—
191C2×D4×C67—41no—
192C2×D4×C67—41no—
193C22×C4×C67—21no—
194C22×C4×C67—21no—
195C22×C4×C67—21no—
196C22×C4×C67—21no—
197C22×C4×C67—22no—
198C22×C4×C67—22no—
199C22×C4×C67—22no—
200C22×C4×C67—22no—
201C22×C4×C67—21no—
202C22×C4×C67—21no—
203C22×C4×C67—21no—
204C22×C4×C67—21no—
205C22×C4×C67—21no—
206C22×C4×C67—21no—
207C22×C4×C67—21no—
208C22×C4×C67—21no—
209C22×C4×C67—21no—
210C22×C4×C67—21no—
211C22×C4×C67—21no—
212C22×C4×C67—21no—
213C22×C4×C67—41no—
214C22×C4×C67—41no—
215C22×C4×C67C22×C411yescharacteristic
216C22×C4×C67C22×C411yescharacteristic
217C22×C4×C67C22×C411yescharacteristic
218C22×C4×C67C22×C411yescharacteristic
219C22×C4×C67C22×C411yescharacteristic
220C22×C4×C67C22×C411yescharacteristic
221C22×C4×C67C22×C411yescharacteristic
222C22×C4×C67C22×C411yescharacteristic
223C22×C4×C67C22×C411yescharacteristic
224C22×C4×C67C22×C411yescharacteristic
225C22×C4×C67C22×C411yescharacteristic
226C22×C4×C67C2×D412yes—
227C22×C4×C67C2×D412yes—
228C22×C4×C67C2411yescharacteristic
229C4⋊C4×C67—22no—
230C4⋊C4×C67—22no—
231C4⋊C4×C67—22no—
232C4⋊C4×C67—22no—
233C4⋊C4×C67—22no—
234C4⋊C4×C67—22no—
235C4⋊C4×C67—22no—
236C4⋊C4×C67—22no—
237C4⋊C4×C67C22⋊C414yes—
238C4⋊C4×C67C22⋊C414yes—
239C22⋊C4×C67—22no—
240C22⋊C4×C67—22no—
241C22⋊C4×C67—22no—
242C22⋊C4×C67—22no—
243C22⋊C4×C67—22no—
244C22⋊C4×C67—22no—
245C22⋊C4×C67—22no—
246C22⋊C4×C67—22no—
247C22⋊C4×C67C22⋊C414yes—
248C22⋊C4×C67C22⋊C414yes—
249C42×C67—22no—
250C42×C67—22no—
251C42×C67—21no—
252C42×C67—21no—
253C42×C67—21no—
254C42×C67—21no—
255C42×C67C2×D412yes—
256C42×C67C2×D412yes—
257C42×C67C2×D412yes—
258C42×C67C2×D412yes—
259C23×C67—21no—
260C23×C67—21no—
261C23×C67—21no—
262C23×C67—21no—
263C23×C67—21no—
264C23×C67—21no—
265C23×C67—21no—
266C23×C67—21no—
267C23×C67—21no—
268C23×C67—21no—
269C23×C67—21no—
270C23×C67—21no—
271C23×C67—21no—
272C23×C67—21no—
273C23×C67—21no—
274C23×C67—21no—
275C23×C67—21no—
276C23×C67—21no—
277C23×C67—21no—
278C23×C67C2×C22⋊C412yes—
279C23×C67#13112yes—
280C23×C67C23×C411yescharacteristic
281Q8×C67—44no—
282D4×C67—44no—
283D4×C67—44no—
284D4×C67—44no—
285C2×C4×C67—21no—
286C2×C4×C67—21no—
287C2×C4×C67—21no—
288C2×C4×C67—21no—
289C2×C4×C67—21no—
290C2×C4×C67—21no—
291C2×C4×C67—21no—
292C2×C4×C67—21no—
293C2×C4×C67—21no—
294C2×C4×C67—21no—
295C2×C4×C67—21no—
296C2×C4×C67—21no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—21no—
302C2×C4×C67—21no—
303C2×C4×C67—21no—
304C2×C4×C67—21no—
305C2×C4×C67—21no—
306C2×C4×C67—21no—
307C2×C4×C67—21no—
308C2×C4×C67—21no—
309C2×C4×C67—21no—
310C2×C4×C67—21no—
311C2×C4×C67—21no—
312C2×C4×C67—21no—
313C2×C4×C67—21no—
314C2×C4×C67—21no—
315C2×C4×C67—21no—
316C2×C4×C67—44no—
317C2×C4×C67—44no—
318C2×C4×C67—41no—
319C2×C4×C67—41no—
320C2×C4×C67—41no—
321C2×C4×C67—41no—
322C2×C4×C67—41no—
323C2×C4×C67—41no—
324C2×C4×C67—41no—
325C2×C4×C67—41no—
326C2×C4×C67C2×C22⋊C412yes—
327C2×C4×C67C2×C22⋊C412yes—
328C2×C4×C67C2×C22⋊C412yes—
329C2×C4×C67C2×C22⋊C412yes—
330C2×C4×C67C2×C22⋊C412yes—
331C2×C4×C67#13112yes—
332C2×C4×C67C22×D411yescharacteristic
333C2×C4×C67C22×D411yescharacteristic
334C2×C4×C67H(5,𝔽2)11yescharacteristic
335C2×C4×C67H(5,𝔽2)11yescharacteristic
336C2×C4×C672−1+411yescharacteristic
337C2×C4×C672−1+411yescharacteristic
338C67⋊C8—41no—
339C67⋊C8—41no—
340C67⋊C8—41no—
341C67⋊C8—41no—
342C67⋊C8—41no—
343C67⋊C8—41no—
344C67⋊C8—41no—
345C67⋊C8—41no—
346C22×C67—22no—
347C22×C67—22no—
348C22×C67—22no—
349C22×C67—22no—
350C22×C67—22no—
351C22×C67—22no—
352C22×C67—41no—
353C22×C67—41no—
354C22×C67—41no—
355C22×C67—41no—
356C22×C67—41no—
357C22×C67—41no—
358C22×C67—41no—
359C22×C67—41no—
360C22×C67—41no—
361C22×C67—41no—
362C22×C67—41no—
363C22×C67—41no—
364C22×C67—41no—
365C22×C67—41no—
366C22×C67—41no—
367C22×C67C22×C22⋊C411yescharacteristic
368C22×C67#52011yescharacteristic
369C22×C67#52011yescharacteristic
370C22×C67C2×#13111yescharacteristic
371C22×C67C2×#13111yescharacteristic
372C22×C67#56811yescharacteristic
373C22×C67#56811yescharacteristic
374C4×C67—22no—
375C4×C67—22no—
376C4×C67—22no—
377C4×C67—22no—
378C4×C67—22no—
379C4×C67—22no—
380C4×C67—41no—
381C4×C67—41no—
382C4×C67—41no—
383C4×C67—41no—
384C4×C67—41no—
385C4×C67#53511yescharacteristic
386C4×C67#53611yescharacteristic
387C4×C67#53711yescharacteristic
388C4×C67#53711yescharacteristic
389#21855—671nomaximal, Sylow
390C2×C67—42no—
391C2×C67—42no—
392C2×C67—81no—
393C2×C67#231111yescharacteristic
394C2×C67#288011yescharacteristic
395C2×C67#288011yescharacteristic
396C2×C67#299211yescharacteristic
397C2×C67#299311yescharacteristic
398C2×C67#299411yescharacteristic
399C2×C67#299511yescharacteristic
400C2×#529D6711yescharacteristic
401C2×#433—671no—
402C2×#424—671no—
403#1985—671no—
404#1984—671no—
405#1955—671no—
406#1954—671no—
407#1870—671no—
408#1870—671no—
409#1869—671no—
410#1869—671no—
411#1798—671no—
412#1798—671no—
413#1797—671no—
414#1797—671no—
415C67#2185511yescharacteristic, complemented, Sylow
416C22×M16—671no—
417C23×C8—671no—
418#529—24no—
419#529—24no—
420C2×#126Dic6711yescharacteristic
421C2×#126Dic6711yescharacteristic
422C2×#125Dic6711yescharacteristic
423C2×#124Dic6711yescharacteristic
424C2×#123Dic6711yescharacteristic
425C2×#123Dic6711yescharacteristic
426C2×C22⋊Q8Dic6711yescharacteristic
427C2×#121Dic6711yescharacteristic
428C2×C4×Q8C2×D6711yescharacteristic
429C2×C4×D4C2×D6711yescharacteristic
430C2×C4×D4C2×D6711yescharacteristic
431C2×C4×D4C2×D6711yescharacteristic
432C2×#117C2×D6711yescharacteristic
433C2×#117C2×D6711yescharacteristic
434C22×C42C2×D6711yescharacteristic
435#433—1344no—
436#424—1344no—
437C2×C4⋊C8—671no—
438C2×C4⋊C8—671no—
439C2×C4⋊C8—671no—
440C2×C4⋊C8—671no—
441C2×C4⋊C8—671no—
442C2×C4⋊C8—671no—
443C2×C22⋊C8—671no—
444C2×C22⋊C8—671no—
445C2×C22⋊C8—671no—
446C2×C22⋊C8—671no—
447C2×C22⋊C8—671no—
448C2×C22⋊C8—671no—
449C2×C22⋊C8—671no—
450C2×C22⋊C8—671no—
451C2×C22⋊C8—671no—
452C2×C22⋊C8—671no—
453C2×#97—671no—
454C2×C4×C8—671no—
455#336—671no—
456#336—671no—
457#336—671no—
458#336—671no—
459#336—671no—
460#336—671no—
461#336—671no—
462#336—671no—
463C22×Q8C2×Dic6711yescharacteristic
464C22×D4C2×Dic6711yescharacteristic
465C22×D4C2×Dic6711yescharacteristic
466C22×D4C2×Dic6711yescharacteristic
467C23×C4C2×Dic6711yescharacteristic
468C23×C4C2×Dic6711yescharacteristic
469C23×C4C22×D6711yescharacteristic
470C23×C4C22×D6711yescharacteristic
471C23×C4C22×D6711yescharacteristic
472C2×M16—2681no—
473C2×M16—2681no—
474C2×M16—1342no—
475C22×C8—2681no—
476C22×C8—2681no—
477C22×C8—671no—
478C22×C8—671no—
479C22×C8—671no—
480C22×C8—671no—
481C22×C8—671no—
482C22×C8—671no—
483C22×C8—671no—
484C22×C8—671no—
485C22×C8—1342no—
486#126—24no—
487#126—24no—
488#125—24no—
489#124—24no—
490#123—24no—
491#123—24no—
492C22⋊Q8—24no—
493#121—24no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—22no—
503#117—22no—
504#117C22⋊D6714yes—
505#117C22⋊D6714yes—
506C2×C4⋊C4C2×Dic6711yescharacteristic
507C2×C4⋊C4C2×Dic6711yescharacteristic
508C2×C4⋊C4C2×Dic6711yescharacteristic
509C2×C4⋊C4C2×Dic6711yescharacteristic
510C2×C4⋊C4C2×Dic6711yescharacteristic
511C2×C4⋊C4C2×Dic6711yescharacteristic
512C2×C4⋊C4C2×Dic6711yescharacteristic
513C2×C4⋊C4C2×Dic6711yescharacteristic
514C2×C4⋊C4C2×Dic6711yescharacteristic
515C2×C4⋊C4C2×Dic6711yescharacteristic
516C2×C22⋊C4C2×Dic6711yescharacteristic
517C2×C22⋊C4C2×Dic6711yescharacteristic
518C2×C22⋊C4C2×Dic6711yescharacteristic
519C2×C22⋊C4C2×Dic6711yescharacteristic
520C2×C22⋊C4C2×Dic6711yescharacteristic
521C2×C22⋊C4C2×Dic6711yescharacteristic
522C2×C22⋊C4C2×Dic6711yescharacteristic
523C2×C22⋊C4C2×Dic6711yescharacteristic
524C2×C22⋊C4C2×Dic6711yescharacteristic
525C2×C22⋊C4C2×Dic6711yescharacteristic
526C2×C42—22no—
527C2×C42—22no—
528C2×C42C2×Dic6711yescharacteristic
529C2×C42C2×Dic6711yescharacteristic
530C2×C42C22×D6711yescharacteristic
531C2×C42C22×D6711yescharacteristic
532C2×C42C22×D6711yescharacteristic
533C2×C42C22×D6711yescharacteristic
534C4⋊C8—1342no—
535C4⋊C8—1342no—
536C4⋊C8—1342no—
537C4⋊C8—1342no—
538C4⋊C8—1342no—
539C4⋊C8—1342no—
540C22⋊C8—2681no—
541C22⋊C8—2681no—
542C22⋊C8—2681no—
543C22⋊C8—2681no—
544C22⋊C8—2681no—
545C22⋊C8—2681no—
546C22⋊C8—2681no—
547C22⋊C8—2681no—
548C22⋊C8—1342no—
549C22⋊C8—1342no—
550#97—1342no—
551C4×C8—1342no—
552C24C22×Dic6711yescharacteristic
553C24C22×Dic6711yescharacteristic
554C24C22×Dic6711yescharacteristic
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—41no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4C22×Dic6711yescharacteristic
590C22×C4C22×Dic6711yescharacteristic
591C22×C4C22×Dic6711yescharacteristic
592C22×C4C22×Dic6711yescharacteristic
593C22×C4C22×Dic6711yescharacteristic
594C22×C4C22×Dic6711yescharacteristic
595C22×C4C22×Dic6711yescharacteristic
596C22×C4C22×Dic6711yescharacteristic
597C22×C4C22×Dic6711yescharacteristic
598C22×C4C22×Dic6711yescharacteristic
599C22×C4C22×Dic6711yescharacteristic
600C22×C4C2×C22⋊D6712yes—
601C22×C4C2×C22⋊D6712yes—
602C22×C4C23×D6711yescharacteristic
603M16—2684no—
604C2×C8—2684no—
605C2×C8—1341no—
606C2×C8—1341no—
607C2×C8—1341no—
608C2×C8—1341no—
609C2×C8—1341no—
610C2×C8—1341no—
611C2×C8—1341no—
612C2×C8—1341no—
613C2×C8—1341no—
614C2×C8—1341no—
615C2×C8—1341no—
616C2×C8—1341no—
617C2×C8—1341no—
618C2×C8—1341no—
619C2×C8—1341no—
620C2×C8—1341no—
621C2×C8—1341no—
622C2×C8—1341no—
623C2×C8—1341no—
624C2×C8—1341no—
625C2×C8—1341no—
626C2×C8—1341no—
627C2×C8—1341no—
628C2×C8—1341no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4C22⋊Dic6714yes—
638C4⋊C4C22⋊Dic6714yes—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4C22⋊Dic6714yes—
648C22⋊C4C22⋊Dic6714yes—
649C42—22no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42C2×C22⋊D6712yes—
656C42C2×C22⋊D6712yes—
657C42C2×C22⋊D6712yes—
658C42C2×C22⋊D6712yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23C2×C22⋊Dic6712yes—
679C23#1452405012yes—
680C23C23×Dic6711yescharacteristic
681Q8—44no—
682D4—44no—
683D4—44no—
684D4—44no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4C2×C22⋊Dic6712yes—
727C2×C4C2×C22⋊Dic6712yes—
728C2×C4C2×C22⋊Dic6712yes—
729C2×C4C2×C22⋊Dic6712yes—
730C2×C4C2×C22⋊Dic6712yes—
731C2×C4#1452405012yes—
732C2×C4C22×C22⋊D6711yescharacteristic
733C2×C4C22×C22⋊D6711yescharacteristic
734C2×C4#1452408911yescharacteristic
735C2×C4#1452408911yescharacteristic
736C2×C4#1452409011yescharacteristic
737C2×C4#1452409011yescharacteristic
738C8—2681no—
739C8—2681no—
740C8—2681no—
741C8—2681no—
742C8—2681no—
743C8—2681no—
744C8—2681no—
745C8—2681no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22C22×C22⋊Dic6711yescharacteristic
768C22#1686387911yescharacteristic
769C22#1686387911yescharacteristic
770C22C2×#1452405011yescharacteristic
771C22C2×#1452405011yescharacteristic
772C22#1686416311yescharacteristic
773C22#1686416311yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4#1686396011yescharacteristic
786C4#1686396711yescharacteristic
787C4#1686397411yescharacteristic
788C4#1686397411yescharacteristic
789C2—42no—
790C2—42no—
791C2—81no—
792C2#2256280111yescharacteristic
793C2#2256865811yescharacteristic
794C2#2256865811yescharacteristic
795C2#2256934811yescharacteristic
796C2#2256935811yescharacteristic
797C2#2256936911yescharacteristic
798C2#2256937911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D67
commutator, socleC23×C67C23×C4
FittingC2×#529×C67C2
prime radicalC2×#121×C67C4
cosocleC22×C4×C67C24
hypercenterC2×#529D67
hypocenterC67#21855
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#16863457C2semidirect
2. C2×#16863423C2semidirect
3. #22561150C2semidirect
4. #22561146C2semidirect
5. #22561008C2semidirect
6. #22561004C2semidirect
7. #22560507C2semidirect
8. #22560507C2semidirect
9. #22560502C2semidirect
10. #22560502C2semidirect
11. #22560193C2semidirect
12. #22560193C2semidirect
13. #22560189C2semidirect
14. #22560189C2semidirect
415. C67#21855semidirect

Maximal subgroups

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

subgroupindex
C2×#168634572
C2×#168634232
#225611502
#225611462
#225610082
#225610042
#225605072
#225605022
#225601932
#225601892
C2×#529×C672
#2185567