Finite Group Databasebeta

← #35568403

Subgroups — #35568403

Order 21248.

2758 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128268C211yesmaximal, characteristic
2#24910615C212yesmaximal, complemented
3#24910602C212yesmaximal, complemented
4#24910536C211yesmaximal, characteristic, complemented
5#24910536C211yesmaximal, characteristic, complemented
6#24910524C211yesmaximal, characteristic, complemented
7#24910524C211yesmaximal, characteristic, complemented
8#24910512C212yesmaximal, complemented
9#24910442C212yesmaximal, complemented
10#24910300C211yesmaximal, characteristic, complemented
11#24910294C211yesmaximal, characteristic, complemented
12D4×C22⋊Dic83C211yesmaximal, characteristic, complemented
13#24910224C212yesmaximal, complemented
14#24910185C211yesmaximal, characteristic, complemented
15#24910173C211yesmaximal, characteristic, complemented
16#24910165C212yesmaximal, complemented
17#24910121C212yesmaximal, complemented
18#24910118C212yesmaximal, complemented
19#24910070C211yesmaximal, characteristic, complemented
20C4×#14581788C211yesmaximal, characteristic, complemented
21#24910010C211yesmaximal, characteristic, complemented
22#24909959C211yesmaximal, characteristic, complemented
23D4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
24C22×#13050590C2211yescharacteristic
25#19128268C4116yescomplemented
26C2×#14581788C2211yescharacteristic
27C2×#14581788C2211yescharacteristic
28C2×#14581779C2211yescharacteristic
29C2×#14581779C2211yescharacteristic
30C2×#14581763C2212yes—
31C2×#14581763C2212yes—
32C2×#14581761C2212yes—
33C2×#14581761C2212yes—
34C2×#14581757C2211yescharacteristic, complemented
35C2×#14581757C2211yescharacteristic, complemented
36C2×C4×D332C2211yescharacteristic, complemented
37C2×C4×D332C2211yescharacteristic, complemented
38C2×D4×Dic83C2211yescharacteristic
39C2×D4×Dic83C2211yescharacteristic
40C2×C4×C22⋊D83C2212yescomplemented
41C2×C4×C22⋊D83C2212yescomplemented
42C2×(C22⋊D83)⋊C4C2212yescomplemented
43C2×(C22⋊D83)⋊C4C2212yescomplemented
44C2×#14581751C2211yescharacteristic
45C22×C22⋊Dic83C2212yes—
46#19127607C2211yescharacteristic, complemented
47#19127607C2211yescharacteristic, complemented
48#19127604C2211yescharacteristic
49#19127604C2211yescharacteristic
50#19127602C2211yescharacteristic, complemented
51#19127602C2211yescharacteristic, complemented
52#19127601C2212yes—
53#19127601C2212yes—
54#19127601C2212yescomplemented
55#19127601C2212yescomplemented
56#19127601C2212yescomplemented
57#19127601C2212yescomplemented
58#19127595C2211yescharacteristic
59#19127595C2212yes—
60#19127595C2211yescharacteristic
61#19127595C2212yescomplemented
62#19127595C2212yescomplemented
63#19127595C2212yescomplemented
64#19127595C2212yescomplemented
65#19127589C2212yes—
66#19127589C2211yescharacteristic
67#19127589C2211yescharacteristic
68#19127589C2212yescomplemented
69#19127589C2212yescomplemented
70#19127589C2212yescomplemented
71#19127589C2212yescomplemented
72#19127586C2212yescomplemented
73#19127586C2211yescharacteristic, complemented
74#19127586C2211yescharacteristic, complemented
75#19127584C2211yescharacteristic, complemented
76#19127584C2212yescomplemented
77#19127584C2211yescharacteristic, complemented
78#19127581C2212yes—
79#19127581C2212yes—
80#19127580C2212yescomplemented
81#19127580C2212yescomplemented
82#19127578C2212yescomplemented
83#19127578C2212yescomplemented
84#19127577C2212yes—
85#19127577C2212yes—
86#19127577C2212yescomplemented
87#19127577C2212yescomplemented
88#19127577C2212yescomplemented
89#19127577C2212yescomplemented
90#19127574C2212yescomplemented
91#19127574C2212yescomplemented
92#19127573C2212yescomplemented
93#19127573C2212yescomplemented
94#19127570C2211yescharacteristic, complemented
95#19127566C2211yescharacteristic, complemented
96#19127563C2212yescomplemented
97#19127561C2211yescharacteristic
98#19127560C2212yescomplemented
99#19127557C2212yes—
100C4⋊C4×Dic83C2211yescharacteristic, complemented
101C4⋊C4×Dic83C2211yescharacteristic, complemented
102C4×Dic83⋊C4C2211yescharacteristic, complemented
103C4×Dic83⋊C4C2211yescharacteristic, complemented
104C22⋊C4×Dic83C2212yescomplemented
105C22⋊C4×Dic83C2212yescomplemented
106C4×C22⋊Dic83C2211yescharacteristic
107C4×C22⋊Dic83C2212yescomplemented
108C4×C22⋊Dic83C2212yescomplemented
109#19127548C2212yescomplemented
110#19127547C2211yescharacteristic, complemented
111#95×D83C2212yescomplemented
112C42×Dic83C2211yescharacteristic, complemented
113C23×D4×C83C2211yescharacteristic
114C2×C4×D4×C83C2211yescharacteristic
115C2×C4×D4×C83C2211yescharacteristic
116C22×C22⋊C4×C83C2212yes—
117#390×C83C2211yescharacteristic
118#390×C83C2211yescharacteristic
119#386×C83C2212yes—
120#386×C83C2212yes—
121#380×C83C2211yescharacteristic
122#379×C83C2212yes—
123C4×C22⋊C4×C83C2211yescharacteristic
124C2×#13050590—42no—
125C2×#13050590—42no—
126C2×#13050590C2×C418yescomplemented
127C22×Dic166C2311yescharacteristic
128C22×D332C2311yescharacteristic
129C22×C22⋊D83C2312yes—
130C22×C22⋊D83C2312yes—
131C22×C22⋊D83C2312yes—
132C22×C22⋊D83C2312yes—
133C22×C22⋊D83C2312yes—
134C23×Dic83C2312yes—
135C23×Dic83C2312yes—
136C22×C4×D83C2312yes—
137C22×C4×D83C2312yes—
138C22×C4×D83C2312yes—
139#14581788C2×C418yescomplemented
140#14581788C2×C418yescomplemented
141#14581779C2×C418yescomplemented
142#14581779C2×C418yescomplemented
143#14581763C2×C4116yescomplemented
144#14581763C2×C4116yescomplemented
145#14581761C2×C4116yescomplemented
146#14581761C2×C4116yescomplemented
147#14581757—42no—
148#14581757—42no—
149C4×D332—42no—
150C4×D332—42no—
151D4×Dic83—42no—
152D4×Dic83—42no—
153C4×C22⋊D83—44no—
154C4×C22⋊D83—44no—
155(C22⋊D83)⋊C4—44no—
156(C22⋊D83)⋊C4—44no—
157#14581751C2×C418yescomplemented
158C2×C4⋊Dic83C2311yescharacteristic
159C2×C4⋊Dic83C2311yescharacteristic
160C2×C4⋊Dic83C2311yescharacteristic
161C2×C4⋊Dic83C2311yescharacteristic
162C2×Dic83⋊C4C2311yescharacteristic
163C2×Dic83⋊C4C2311yescharacteristic
164C2×Dic83⋊C4C2311yescharacteristic
165C2×Dic83⋊C4C2311yescharacteristic
166C2×Dic83⋊C4C2312yes—
167C2×Dic83⋊C4C2312yes—
168C2×Dic83⋊C4C2312yes—
169C2×Dic83⋊C4C2312yes—
170C2×C22⋊Dic83—44no—
171C2×C22⋊Dic83C2312yes—
172C2×C22⋊Dic83C2311yescharacteristic
173C2×C22⋊Dic83C2311yescharacteristic
174C2×C22⋊Dic83C2312yes—
175C2×C22⋊Dic83C2312yes—
176C2×C22⋊Dic83C2312yes—
177C2×C22⋊Dic83C2312yes—
178C2×C22⋊Dic83C2312yes—
179C2×C22⋊Dic83C2312yes—
180C2×C22⋊Dic83C2312yes—
181C2×C22⋊Dic83C2312yes—
182C2×C22⋊Dic83C2312yes—
183C2×C22⋊Dic83C2312yes—
184C2×C22⋊Dic83C2311yescharacteristic
185C2×C22⋊Dic83C2311yescharacteristic
186C2×(C2×D83)⋊C4C2312yes—
187C2×(C2×D83)⋊C4C2312yes—
188C2×(C2×D83)⋊C4C2312yes—
189C2×(C2×D83)⋊C4C2312yes—
190C2×(C2×D83)⋊C4C2312yes—
191C2×(C2×D83)⋊C4C2312yes—
192C2×C4×Dic83C2311yescharacteristic
193C2×C4×Dic83C2311yescharacteristic
194C2×C4×Dic83C2311yescharacteristic
195C2×C4×Dic83C2311yescharacteristic
196C2×C4×Dic83C2312yes—
197C2×C4×Dic83C2312yes—
198C2×C4×Dic83C2311yescharacteristic
199C2×C4×Dic83C2311yescharacteristic
200C2×C4×Dic83C2312yes—
201C2×C4×Dic83C2312yes—
202C2×C4×Dic83C2311yescharacteristic
203C2×C4×Dic83C2311yescharacteristic
204C83⋊#95C2311yescharacteristic
205C83⋊#95C2311yescharacteristic
206C83⋊#95C2311yescharacteristic
207C83⋊#95C2311yescharacteristic
208C83⋊#95C2312yes—
209C83⋊#95C2312yes—
210C83⋊#95C2311yescharacteristic
211C83⋊#95C2312yes—
212C83⋊#95C2312yes—
213C83⋊#95C2312yes—
214C83⋊#95C2312yes—
215C83⋊#95C2312yes—
216C83⋊#95C2311yescharacteristic
217C83⋊#95C2311yescharacteristic
218C83⋊#95C2312yes—
219C83⋊#95C2312yes—
220C83⋊#95C2311yescharacteristic
221C83⋊#95C2311yescharacteristic
222C83⋊#95C2311yescharacteristic
223C25×C83C2312yes—
224C22×D4×C83—42no—
225C22×D4×C83—42no—
226C22×D4×C83C2×C418yescomplemented
227C22×D4×C83C2311yescharacteristic
228C22×D4×C83C2311yescharacteristic
229C22×D4×C83C2312yes—
230C23×C4×C83C2311yescharacteristic
231C23×C4×C83C2312yes—
232C23×C4×C83C2312yes—
233C4×D4×C83—42no—
234C4×D4×C83—42no—
235C2×C4⋊C4×C83C2311yescharacteristic
236C2×C4⋊C4×C83C2311yescharacteristic
237C2×C22⋊C4×C83—44no—
238C2×C22⋊C4×C83C2311yescharacteristic
239C2×C22⋊C4×C83C2312yes—
240C2×C22⋊C4×C83C2312yes—
241C2×C22⋊C4×C83C2312yes—
242C2×C22⋊C4×C83C2311yescharacteristic
243C2×C22⋊C4×C83C2312yes—
244C2×C22⋊C4×C83C2312yes—
245C2×C22⋊C4×C83C2312yes—
246C2×C22⋊C4×C83C2312yes—
247C2×C42×C83C2311yescharacteristic
248C2×C42×C83C2311yescharacteristic
249#95×C83C2312yes—
250#95×C83C2311yescharacteristic
251#95×C83C2311yescharacteristic
252C23×D83C2412yes—
253#13050590—416no—
254C2×Dic166—22no—
255C2×Dic166—22no—
256C2×Dic166C22×C414yes—
257C2×D332—22no—
258C2×D332—22no—
259C2×D332C22×C414yes—
260C2×C22⋊D83—42no—
261C2×C22⋊D83—42no—
262C2×C22⋊D83—42no—
263C2×C22⋊D83—42no—
264C2×C22⋊D83—42no—
265C2×C22⋊D83—42no—
266C2×C22⋊D83—42no—
267C2×C22⋊D83—42no—
268C2×C22⋊D83—42no—
269C2×C22⋊D83—42no—
270C2×C22⋊D83C22×C418yes—
271C2×C22⋊D83C22×C418yes—
272C2×C22⋊D83C22×C418yes—
273C2×C22⋊D83C22×C418yes—
274C2×C22⋊D83C22×C418yes—
275C22×Dic83—24no—
276C22×Dic83—42no—
277C22×Dic83—42no—
278C22×Dic83—42no—
279C22×Dic83—42no—
280C22×Dic83—42no—
281C22×Dic83C2412yes—
282C22×Dic83C2412yes—
283C22×Dic83C2411yescharacteristic
284C22×Dic83C2411yescharacteristic
285C22×Dic83C2411yescharacteristic
286C22×Dic83C2412yes—
287C22×Dic83C2411yescharacteristic
288C22×Dic83C2411yescharacteristic
289C22×Dic83C2411yescharacteristic
290C22×Dic83C2411yescharacteristic
291C22×Dic83C2411yescharacteristic
292C2×C4×D83—24no—
293C2×C4×D83—42no—
294C2×C4×D83—42no—
295C2×C4×D83—42no—
296C2×C4×D83—42no—
297C2×C4×D83—42no—
298C2×C4×D83—42no—
299C2×C4×D83—42no—
300C2×C4×D83C22×C418yes—
301C4⋊Dic83—22no—
302C4⋊Dic83—22no—
303C4⋊Dic83C22×C414yes—
304C4⋊Dic83C22×C414yes—
305Dic83⋊C4—22no—
306Dic83⋊C4—22no—
307Dic83⋊C4—41no—
308Dic83⋊C4—41no—
309Dic83⋊C4—42no—
310Dic83⋊C4—42no—
311Dic83⋊C4—42no—
312Dic83⋊C4—42no—
313C22⋊Dic83—22no—
314C22⋊Dic83—24no—
315C22⋊Dic83—42no—
316C22⋊Dic83—42no—
317C22⋊Dic83—41no—
318C22⋊Dic83—42no—
319C22⋊Dic83—42no—
320C22⋊Dic83—42no—
321C22⋊Dic83—42no—
322C22⋊Dic83C22×C414yes—
323C22⋊Dic83C22×C414yes—
324C22⋊Dic83C22×C418yes—
325C22⋊Dic83C22×C418yes—
326C22⋊Dic83C22×C418yes—
327C22⋊Dic83C22×C418yes—
328(C2×D83)⋊C4—24no—
329(C2×D83)⋊C4—42no—
330(C2×D83)⋊C4—42no—
331(C2×D83)⋊C4—42no—
332(C2×D83)⋊C4—42no—
333(C2×D83)⋊C4—42no—
334C4×Dic83—22no—
335C4×Dic83—22no—
336C4×Dic83—22no—
337C4×Dic83—22no—
338C4×Dic83—41no—
339C4×Dic83—41no—
340C4×Dic83—42no—
341C4×Dic83—42no—
342C4×Dic83—42no—
343C4×Dic83—42no—
344C4×Dic83C22×C414yes—
345C4×Dic83C22×C414yes—
346C24×C83—42no—
347C24×C83—42no—
348C24×C83—42no—
349C24×C83—42no—
350C24×C83—42no—
351C24×C83—42no—
352C24×C83C22×C418yes—
353C24×C83C2412yes—
354C24×C83C2411yescharacteristic
355C24×C83C2412yes—
356C2×D4×C83—22no—
357C2×D4×C83—22no—
358C2×D4×C83—22no—
359C2×D4×C83—22no—
360C2×D4×C83—416no—
361C2×D4×C83—42no—
362C2×D4×C83—42no—
363C2×D4×C83C22×C414yes—
364C2×D4×C83C22×C414yes—
365C2×D4×C83C22×C418yes—
366C22×C4×C83—22no—
367C22×C4×C83—22no—
368C22×C4×C83—24no—
369C22×C4×C83—42no—
370C22×C4×C83—42no—
371C22×C4×C83—42no—
372C22×C4×C83—42no—
373C22×C4×C83—42no—
374C22×C4×C83C22×C414yes—
375C22×C4×C83C2411yescharacteristic
376C22×C4×C83C2411yescharacteristic
377C22×C4×C83C2411yescharacteristic
378C22×C4×C83C2412yes—
379C22×C4×C83C2412yes—
380C22×C4×C83C2411yescharacteristic
381C22×C4×C83C2411yescharacteristic
382C22×C4×C83C2411yescharacteristic
383C4⋊C4×C83—22no—
384C4⋊C4×C83—22no—
385C22⋊C4×C83—22no—
386C22⋊C4×C83—24no—
387C22⋊C4×C83—42no—
388C22⋊C4×C83—42no—
389C22⋊C4×C83—42no—
390C22⋊C4×C83—41no—
391C22⋊C4×C83—42no—
392C22⋊C4×C83—42no—
393C22⋊C4×C83—42no—
394C42×C83—22no—
395C42×C83—22no—
396C23×C83—21no—
397C23×C83—22no—
398C23×C83—22no—
399C23×C83—22no—
400C23×C83—22no—
401C23×C83—22no—
402C23×C83—21no—
403C23×C83—21no—
404C23×C83—22no—
405C23×C83—22no—
406C23×C83—22no—
407C23×C83—21no—
408C23×C83—21no—
409C23×C83—22no—
410C23×C83—22no—
411C23×C83—21no—
412C23×C83—22no—
413C23×C83—22no—
414C23×C83—48no—
415C23×C83—48no—
416C23×C83—48no—
417C23×C83—84no—
418C23×C83—84no—
419C23×C83—84no—
420C23×C83—84no—
421C23×C83C23×C412yes—
422C23×C83C23×C414yes—
423C23×C83C23×C414yes—
424C23×C83C2511yescharacteristic
425C22×D83—22no—
426C22×D83—22no—
427C22×D83—22no—
428C22×D83—22no—
429C22×D83—22no—
430C22×D83—22no—
431C22×D83C23×C414yes—
432D4×C83—28no—
433D4×C83—28no—
434D4×C83—48no—
435C2×C4×C83—21no—
436C2×C4×C83—21no—
437C2×C4×C83—21no—
438C2×C4×C83—21no—
439C2×C4×C83—28no—
440C2×C4×C83—21no—
441C2×C4×C83—21no—
442C2×C4×C83—21no—
443C2×C4×C83—21no—
444C2×C4×C83—22no—
445C2×C4×C83—22no—
446C2×C4×C83—21no—
447C2×C4×C83—22no—
448C2×C4×C83—22no—
449C2×C4×C83—22no—
450C2×C4×C83—21no—
451C2×C4×C83—22no—
452C2×C4×C83—21no—
453C2×C4×C83—21no—
454C2×C4×C83—21no—
455C2×C4×C83—84no—
456C2×C4×C83—84no—
457C2×C4×C83C23×C412yes—
458C2×C4×C83C23×C412yes—
459C2×C4×C83H(5,𝔽2)12yes—
460C2×C4×C83H(5,𝔽2)12yes—
461C2×C4×C83H(5,𝔽2)12yes—
462C22⋊D83—48no—
463C22⋊D83—48no—
464C22⋊D83—48no—
465C22⋊D83—48no—
466C22⋊D83—48no—
467C2×Dic83—21no—
468C2×Dic83—21no—
469C2×Dic83—21no—
470C2×Dic83—21no—
471C2×Dic83—21no—
472C2×Dic83—22no—
473C2×Dic83—22no—
474C2×Dic83—21no—
475C2×Dic83—21no—
476C2×Dic83—21no—
477C2×Dic83—21no—
478C2×Dic83—21no—
479C2×Dic83—21no—
480C2×Dic83—21no—
481C2×Dic83—21no—
482C2×Dic83—21no—
483C2×Dic83—22no—
484C2×Dic83—22no—
485C2×Dic83—21no—
486C2×Dic83—22no—
487C2×Dic83—22no—
488C2×Dic83—21no—
489C2×Dic83—22no—
490C2×Dic83—21no—
491C2×Dic83—21no—
492C2×Dic83—21no—
493C2×Dic83—22no—
494C2×Dic83—84no—
495C2×Dic83—84no—
496C2×Dic83C23×C412yes—
497C2×Dic83C23×C412yes—
498C2×Dic83C23×C412yes—
499C2×Dic83C23×C412yes—
500C2×Dic83C23×C414yes—
501C2×Dic83H(5,𝔽2)12yes—
502D332—28no—
503C4×D83—48no—
504C4×D83—84no—
505C4×D83—84no—
506Dic166—28no—
507C22×C83—22no—
508C22×C83—24no—
509C22×C83—24no—
510C22×C83—24no—
511C22×C83—24no—
512C22×C83—24no—
513C22×C83—24no—
514C22×C83—22no—
515C22×C83—22no—
516C22×C83—42no—
517C22×C83—42no—
518C22×C83—41no—
519C22×C83—42no—
520C22×C83—42no—
521C22×C83—41no—
522C22×C83—42no—
523C22×C83—42no—
524C22×C83—41no—
525C22×C83—42no—
526C22×C83—42no—
527C22×C83—41no—
528C22×C83—816no—
529C22×C83C24×C411yescharacteristic
530C22×C83C2×H(5,𝔽2)11yescharacteristic
531C22×C83C2×H(5,𝔽2)11yescharacteristic
532C22×C83C2×H(5,𝔽2)11yescharacteristic
533C22×C83C2×H(5,𝔽2)11yescharacteristic
534C22×C83#58511yescharacteristic
535C22×C83#58511yescharacteristic
536C2×D83—24no—
537C2×D83—24no—
538C2×D83—24no—
539C2×D83—42no—
540C2×D83—42no—
541C2×D83—42no—
542C2×D83—42no—
543C4×C83—22no—
544C4×C83—22no—
545C4×C83—42no—
546C4×C83—42no—
547C4×C83—41no—
548C4×C83—41no—
549C4×C83—41no—
550C4×C83#51814yes—
551Dic83—24no—
552Dic83—22no—
553Dic83—22no—
554Dic83—22no—
555Dic83—22no—
556Dic83—22no—
557Dic83—42no—
558Dic83—41no—
559Dic83—41no—
560Dic83—42no—
561Dic83—41no—
562#34438—831nomaximal, Sylow
563C2×C83—44no—
564C2×C83—44no—
565C2×C83—42no—
566C2×C83C2×#51811yescharacteristic
567C2×C83C4×H(5,𝔽2)11yescharacteristic
568C2×C83C4×H(5,𝔽2)11yescharacteristic
569C2×C83#354311yescharacteristic
570C2×C83#354611yescharacteristic
571C2×C83#355811yescharacteristic
572C2×C83#356211yescharacteristic
573D83—44no—
574C2×#535—831no—
575#2377—832no—
576#2375—832no—
577#2367—831no—
578#2367—831no—
579#2366—831no—
580#2366—831no—
581#2364—832no—
582#2358—832no—
583#2341—831no—
584#2339—831no—
585D4×C22⋊C4—831no—
586D4×C22⋊C4D8311yescharacteristic, complemented
587#2333—832no—
588#2328—831no—
589#2326—831no—
590#2325—832no—
591#2321—832no—
592#2321—832no—
593#2314—831no—
594C4×#127—831no—
595C4×#124—831no—
596#2298—831no—
597C83#3443811yescharacteristic, complemented, Sylow
598C22×#41—831no—
599C23×D4C2×D8311yescharacteristic
600#535—8316no—
601C2×#127—831no—
602C2×#127—831no—
603C2×#124—831no—
604C2×#124—831no—
605C2×#121—832no—
606C2×#121—832no—
607C2×#120—832no—
608C2×#120—832no—
609C2×C4×Q8—831no—
610C2×C4×Q8—831no—
611C2×C4×D4—831no—
612C2×C4×D4—831no—
613C2×C4×D4—832no—
614C2×C4×D4—832no—
615C2×C4×D4—832no—
616C2×C4×D4—832no—
617C2×C4×D4—831no—
618C2×C4×D4—831no—
619C2×C4×D4C2×D8311yescharacteristic
620C2×C4×D4C2×D8311yescharacteristic
621C2×#117—831no—
622C22×C22⋊C4—832no—
623C22×C22⋊C4C2×D8312yes—
624#391—831no—
625#391—831no—
626#390—831no—
627#390—831no—
628#390—831no—
629#390—831no—
630#390—832no—
631#390—832no—
632#390—832no—
633#390—832no—
634#390—832no—
635#390—832no—
636#390C2×D8311yescharacteristic
637#390C2×D8311yescharacteristic
638#388—832no—
639#388—832no—
640#388—831no—
641#388—831no—
642#388—832no—
643#388—832no—
644#388—832no—
645#388—832no—
646#388—832no—
647#388—832no—
648#388—832no—
649#388—832no—
650#388—831no—
651#388—831no—
652#387—832no—
653#387—832no—
654#387—831no—
655#387—831no—
656#387—831no—
657#387—831no—
658#386—832no—
659#386—832no—
660#386—832no—
661#386—832no—
662#386—832no—
663#386—832no—
664#386—832no—
665#386—832no—
666#386—832no—
667#386—832no—
668#386—832no—
669#386—832no—
670#386C2×D8312yes—
671#386C2×D8312yes—
672#385—832no—
673#385—832no—
674#385—832no—
675#385—832no—
676#384—831no—
677#382—831no—
678#381—832no—
679#380—831no—
680#380—832no—
681#380C2×D8311yescharacteristic
682#379—832no—
683#379C2×D8312yes—
684C4×C4⋊C4—831no—
685C4×C4⋊C4—831no—
686C4×C4⋊C4—831no—
687C4×C4⋊C4—831no—
688C4×C22⋊C4—832no—
689C4×C22⋊C4—832no—
690C4×C22⋊C4—831no—
691C4×C22⋊C4—832no—
692C4×C22⋊C4—832no—
693C4×C22⋊C4—832no—
694C4×C22⋊C4C2×D8311yescharacteristic
695#376—831no—
696C2×#95—832no—
697C43—831no—
698C25C22×D8312yes—
699C2×#41—3322no—
700C2×#41—3322no—
701C2×#41—838no—
702C22×Q8—831no—
703C22×D4—42no—
704C22×D4—42no—
705C22×D4—832no—
706C22×D4—832no—
707C22×D4—832no—
708C22×D4—832no—
709C22×D4—832no—
710C22×D4—831no—
711C22×D4C4×D8318yescomplemented
712C22×D4C22×D8311yescharacteristic
713C22×D4C22×D8311yescharacteristic
714C22×D4C22×D8312yes—
715C23×C4—832no—
716C23×C4—832no—
717C23×C4—832no—
718C23×C4—832no—
719C23×C4—832no—
720C23×C4C22×D8311yescharacteristic
721C23×C4C22×D8312yes—
722C23×C4C22×D8312yes—
723#127—838no—
724#127—838no—
725#124—838no—
726#124—838no—
727#121—8316no—
728#121—8316no—
729#120—8316no—
730#120—8316no—
731C4×Q8—3322no—
732C4×Q8—3322no—
733C4×D4—42no—
734C4×D4—42no—
735C4×D4—3322no—
736C4×D4—3322no—
737C4×D4—3324no—
738C4×D4—3324no—
739C4×D4—3324no—
740C4×D4—3322no—
741C4×D4—3322no—
742C4×D4—3324no—
743#117—838no—
744C2×C4⋊C4—832no—
745C2×C4⋊C4—832no—
746C2×C4⋊C4—832no—
747C2×C4⋊C4—832no—
748C2×C4⋊C4—831no—
749C2×C4⋊C4—831no—
750C2×C4⋊C4—831no—
751C2×C4⋊C4—831no—
752C2×C4⋊C4—831no—
753C2×C4⋊C4—831no—
754C2×C4⋊C4—831no—
755C2×C4⋊C4—831no—
756C2×C4⋊C4C22×D8311yescharacteristic
757C2×C4⋊C4C22×D8311yescharacteristic
758C2×C22⋊C4—44no—
759C2×C22⋊C4—3324no—
760C2×C22⋊C4—832no—
761C2×C22⋊C4—832no—
762C2×C22⋊C4—832no—
763C2×C22⋊C4—832no—
764C2×C22⋊C4—832no—
765C2×C22⋊C4—831no—
766C2×C22⋊C4—832no—
767C2×C22⋊C4—832no—
768C2×C22⋊C4—832no—
769C2×C22⋊C4—832no—
770C2×C22⋊C4—832no—
771C2×C22⋊C4—832no—
772C2×C22⋊C4—831no—
773C2×C22⋊C4—831no—
774C2×C22⋊C4—832no—
775C2×C22⋊C4—832no—
776C2×C22⋊C4—832no—
777C2×C22⋊C4—832no—
778C2×C22⋊C4—831no—
779C2×C22⋊C4—832no—
780C2×C22⋊C4—832no—
781C2×C22⋊C4C22×D8311yescharacteristic
782C2×C22⋊C4C22×D8312yes—
783C2×C22⋊C4C22×D8312yes—
784C2×C22⋊C4C22×D8312yes—
785C2×C22⋊C4C22×D8312yes—
786C2×C22⋊C4C22×D8312yes—
787C2×C22⋊C4C22×D8312yes—
788C2×C22⋊C4C22×D8312yes—
789C2×C22⋊C4C22×D8311yescharacteristic
790C2×C42—832no—
791C2×C42—832no—
792C2×C42—832no—
793C2×C42—832no—
794C2×C42—831no—
795C2×C42—831no—
796C2×C42—831no—
797C2×C42—831no—
798C2×C42—831no—
799C2×C42—831no—
800C2×C42—831no—
801C2×C42—831no—
802C2×C42C22×D8311yescharacteristic
803C2×C42C22×D8311yescharacteristic
804#95—832no—
805#95—832no—
806#95—832no—
807#95—831no—
808#95—831no—
809#95—831no—
810#95—831no—
811#95—831no—
812#95—831no—
813#95—831no—
814#95—831no—
815#95—832no—
816#95—832no—
817#95—832no—
818#95—832no—
819#95—832no—
820#95—832no—
821#95—831no—
822#95—831no—
823#95C22×D8311yescharacteristic
824#95C22×D8312yes—
825#95C22×D8311yescharacteristic
826C24—42no—
827C24—42no—
828C24—42no—
829C24—42no—
830C24—42no—
831C24—42no—
832C24—832no—
833C24C2×C4×D8318yes—
834C24C23×D8311yescharacteristic
835C24C23×D8312yes—
836C24C23×D8312yes—
837#41—33216no—
838C2×Q8—834no—
839C2×Q8—1662no—
840C2×Q8—1662no—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—416no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—3322no—
849C2×D4—3322no—
850C2×D4—3322no—
851C2×D4—3322no—
852C2×D4—3322no—
853C2×D4—3322no—
854C2×D4—3322no—
855C2×D4—3322no—
856C2×D4—3322no—
857C2×D4—3322no—
858C2×D4—838no—
859C2×D4—838no—
860C2×D4—838no—
861C2×D4—838no—
862C2×D4—838no—
863C2×D4—834no—
864C2×D4—1662no—
865C2×D4—1662no—
866C2×D4C2×C4×D8314yes—
867C2×D4C2×C4×D8314yes—
868C2×D4C2×C4×D8318yes—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—24no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—3322no—
878C22×C4—3322no—
879C22×C4—3322no—
880C22×C4—3322no—
881C22×C4—3322no—
882C22×C4—3322no—
883C22×C4—3322no—
884C22×C4—3322no—
885C22×C4—3322no—
886C22×C4—3322no—
887C22×C4—3322no—
888C22×C4—3322no—
889C22×C4—838no—
890C22×C4—831no—
891C22×C4—831no—
892C22×C4—831no—
893C22×C4—831no—
894C22×C4—832no—
895C22×C4—831no—
896C22×C4—832no—
897C22×C4—831no—
898C22×C4—831no—
899C22×C4—832no—
900C22×C4—831no—
901C22×C4—1664no—
902C22×C4—1664no—
903C22×C4C2×C4×D8314yes—
904C22×C4C23×D8311yescharacteristic
905C22×C4C23×D8311yescharacteristic
906C22×C4C23×D8311yescharacteristic
907C22×C4C23×D8312yes—
908C22×C4C23×D8312yes—
909C22×C4C23×D8311yescharacteristic
910C22×C4C23×D8311yescharacteristic
911C22×C4C23×D8311yescharacteristic
912C4⋊C4—22no—
913C4⋊C4—22no—
914C4⋊C4—3322no—
915C4⋊C4—3322no—
916C4⋊C4—3322no—
917C4⋊C4—3322no—
918C4⋊C4—3321no—
919C4⋊C4—3321no—
920C4⋊C4—834no—
921C4⋊C4—834no—
922C4⋊C4—1662no—
923C4⋊C4—1662no—
924C4⋊C4—1662no—
925C4⋊C4—1662no—
926C22⋊C4—22no—
927C22⋊C4—24no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—41no—
935C22⋊C4—3322no—
936C22⋊C4—3322no—
937C22⋊C4—3322no—
938C22⋊C4—3322no—
939C22⋊C4—3322no—
940C22⋊C4—3322no—
941C22⋊C4—3322no—
942C22⋊C4—3322no—
943C22⋊C4—3322no—
944C22⋊C4—3322no—
945C22⋊C4—3321no—
946C22⋊C4—3322no—
947C22⋊C4—834no—
948C22⋊C4—834no—
949C22⋊C4—838no—
950C22⋊C4—838no—
951C22⋊C4—838no—
952C22⋊C4—838no—
953C22⋊C4—1664no—
954C22⋊C4—1662no—
955C22⋊C4—1664no—
956C42—22no—
957C42—22no—
958C42—3322no—
959C42—3322no—
960C42—3322no—
961C42—3322no—
962C42—3321no—
963C42—3321no—
964C42—834no—
965C42—834no—
966C42—1662no—
967C42—1662no—
968C42—1662no—
969C42—1662no—
970C23—22no—
971C23—21no—
972C23—22no—
973C23—21no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—21no—
981C23—21no—
982C23—22no—
983C23—21no—
984C23—22no—
985C23—21no—
986C23—22no—
987C23—22no—
988C23—48no—
989C23—48no—
990C23—48no—
991C23—84no—
992C23—84no—
993C23—84no—
994C23—84no—
995C23—834no—
996C23—1662no—
997C23—1662no—
998C23—1662no—
999C23—1662no—
1000C23—1662no—
1001C23—1662no—
1002C23C22×C4×D8312yes—
1003C23C22×C4×D8314yes—
1004C23C22×C4×D8314yes—
1005C23C24×D8311yescharacteristic
1006Q8—1668no—
1007D4—28no—
1008D4—28no—
1009D4—48no—
1010D4—3328no—
1011D4—3328no—
1012D4—3328no—
1013D4—3328no—
1014D4—3328no—
1015D4—1668no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—28no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—84no—
1037C2×C4—84no—
1038C2×C4—3328no—
1039C2×C4—832no—
1040C2×C4—832no—
1041C2×C4—832no—
1042C2×C4—832no—
1043C2×C4—834no—
1044C2×C4—832no—
1045C2×C4—6644no—
1046C2×C4—6644no—
1047C2×C4—6644no—
1048C2×C4—6644no—
1049C2×C4—1662no—
1050C2×C4—1661no—
1051C2×C4—1662no—
1052C2×C4—1661no—
1053C2×C4—1662no—
1054C2×C4—1661no—
1055C2×C4—1661no—
1056C2×C4—1661no—
1057C2×C4—1662no—
1058C2×C4—1662no—
1059C2×C4—1661no—
1060C2×C4—1661no—
1061C2×C4—1661no—
1062C2×C4—1661no—
1063C2×C4—1662no—
1064C2×C4—1661no—
1065C2×C4—1661no—
1066C2×C4—1661no—
1067C2×C4—1661no—
1068C2×C4—1662no—
1069C2×C4—1662no—
1070C2×C4—1661no—
1071C2×C4—1661no—
1072C2×C4—1661no—
1073C2×C4—1661no—
1074C2×C4—1661no—
1075C2×C4—1661no—
1076C2×C4C22×C4×D8312yes—
1077C2×C4C22×C4×D8312yes—
1078C2×C4#1458183712yes—
1079C2×C4#1458183712yes—
1080C2×C4#1458183712yes—
1081C22—22no—
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—24no—
1086C22—22no—
1087C22—24no—
1088C22—24no—
1089C22—22no—
1090C22—42no—
1091C22—41no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—41no—
1096C22—41no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—41no—
1101C22—42no—
1102C22—816no—
1103C22—3322no—
1104C22—3322no—
1105C22—3322no—
1106C22—3322no—
1107C22—1664no—
1108C22—1664no—
1109C22—1664no—
1110C22C23×C4×D8311yescharacteristic
1111C22H(5,𝔽2)×D8311yescharacteristic
1112C22C2×#1458183711yescharacteristic
1113C22C2×#1458183711yescharacteristic
1114C22C2×#1458183711yescharacteristic
1115C22#1912853611yescharacteristic
1116C22#1912853711yescharacteristic
1117C4—22no—
1118C4—22no—
1119C4—41no—
1120C4—42no—
1121C4—41no—
1122C4—41no—
1123C4—42no—
1124C4—3322no—
1125C4—3322no—
1126C4—3321no—
1127C4—3321no—
1128C4—3321no—
1129C4—1664no—
1130C4—1662no—
1131C4—1662no—
1132C4—1662no—
1133C4—1662no—
1134C4—1662no—
1135C4#1912817414yes—
1136C2—42no—
1137C2—44no—
1138C2—44no—
1139C2—3324no—
1140C2C2×#1912817411yescharacteristic
1141C2#2492066711yescharacteristic
1142C2C4×#1458183711yescharacteristic
1143C2#2492178811yescharacteristic
1144C2#2492183111yescharacteristic
1145C2#2492197211yescharacteristic
1146C2#2492204511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingD4×C22⋊C4×C83C2
socle, cosocleC23×C83C25
prime radicalC2×#19128268C2
hypercenterD4×C22⋊C4D83
hypocenterC83#34438
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #24910615C2semidirect
3. #24910602C2semidirect
4. #24910536C2semidirect
5. #24910536C2semidirect
6. #24910524C2semidirect
7. #24910524C2semidirect
8. #24910512C2semidirect
9. #24910442C2semidirect
10. #24910300C2semidirect
11. #24910294C2semidirect
12. D4×C22⋊Dic83C2semidirect
13. #24910224C2semidirect
14. #24910185C2semidirect
15. #24910173C2semidirect
16. #24910165C2semidirect
17. #24910121C2semidirect
18. #24910118C2semidirect
19. #24910070C2semidirect
20. C4×#14581788C2semidirect
21. #24910010C2semidirect
22. #24909959C2semidirect
23. D4×C22⋊C4×C83C2semidirect
25. #19128268C4semidirect
34. C2×#14581757C22semidirect
35. C2×#14581757C22semidirect
36. C2×C4×D332C22semidirect
37. C2×C4×D332C22semidirect
40. C2×C4×C22⋊D83C22semidirect
41. C2×C4×C22⋊D83C22semidirect
42. C2×(C22⋊D83)⋊C4C22semidirect
43. C2×(C22⋊D83)⋊C4C22semidirect
46. #19127607C22semidirect
47. #19127607C22semidirect
50. #19127602C22semidirect
51. #19127602C22semidirect
54. #19127601C22semidirect
55. #19127601C22semidirect
56. #19127601C22semidirect
57. #19127601C22semidirect
61. #19127595C22semidirect
62. #19127595C22semidirect
63. #19127595C22semidirect
64. #19127595C22semidirect
68. #19127589C22semidirect
69. #19127589C22semidirect
70. #19127589C22semidirect
71. #19127589C22semidirect
72. #19127586C22semidirect
73. #19127586C22semidirect
74. #19127586C22semidirect
75. #19127584C22semidirect
76. #19127584C22semidirect
77. #19127584C22semidirect
80. #19127580C22semidirect
81. #19127580C22semidirect
82. #19127578C22semidirect
83. #19127578C22semidirect
86. #19127577C22semidirect
87. #19127577C22semidirect
88. #19127577C22semidirect
89. #19127577C22semidirect
90. #19127574C22semidirect
91. #19127574C22semidirect
92. #19127573C22semidirect
93. #19127573C22semidirect
94. #19127570C22semidirect
95. #19127566C22semidirect
96. #19127563C22semidirect
98. #19127560C22semidirect
100. C4⋊C4×Dic83C22semidirect
101. C4⋊C4×Dic83C22semidirect
102. C4×Dic83⋊C4C22semidirect
103. C4×Dic83⋊C4C22semidirect
104. C22⋊C4×Dic83C22semidirect
105. C22⋊C4×Dic83C22semidirect
107. C4×C22⋊Dic83C22semidirect
108. C4×C22⋊Dic83C22semidirect
109. #19127548C22semidirect
110. #19127547C22semidirect
111. #95×D83C22semidirect
112. C42×Dic83C22semidirect
126. C2×#13050590C2×C4semidirect
139. #14581788C2×C4semidirect
140. #14581788C2×C4semidirect
141. #14581779C2×C4semidirect
142. #14581779C2×C4semidirect
143. #14581763C2×C4semidirect
144. #14581763C2×C4semidirect
145. #14581761C2×C4semidirect
146. #14581761C2×C4semidirect
157. #14581751C2×C4semidirect
226. C22×D4×C83C2×C4semidirect
586. D4×C22⋊C4D83semidirect
597. C83#34438semidirect
711. C22×D4C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191282682
#249106152
#249106022
#249105362
#249105242
#249105122
#249104422
#249103002
#249102942
D4×C22⋊Dic832
#249102242
#249101852
#249101732
#249101652
#249101212
#249101182
#249100702
C4×#145817882
#249100102
#249099592
D4×C22⋊C4×C832
#3443883