Finite Group Databasebeta

← #31966346

Subgroups — #31966346

Order 18176.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22597465C211yesmaximal, characteristic, complemented
2#22597465C211yesmaximal, characteristic, complemented
3#22587070C211yesmaximal, characteristic, complemented
4#22587062C211yesmaximal, characteristic, complemented
5#22587057C211yesmaximal, characteristic, complemented
6#22587050C211yesmaximal, characteristic, complemented
7#22587045C211yesmaximal, characteristic, complemented
8#22587035C211yesmaximal, characteristic, complemented
9#22587035C211yesmaximal, characteristic, complemented
10#22587030C211yesmaximal, characteristic, complemented
11#22587017C211yesmaximal, characteristic, complemented
12#22586997C211yesmaximal, characteristic, complemented
13#22586989C211yesmaximal, characteristic, complemented
14C2×#17985745C211yesmaximal, characteristic, complemented
15C71×#3511C211yesmaximal, characteristic
16#17986130—21no—
17#17986130—21no—
18#17986071—21no—
19#17986071—21no—
20#17986071—21no—
21#17986071—21no—
22D4×C71⋊C8—21no—
23D4×C71⋊C8—21no—
24#17986056C2211yescharacteristic
25#17986056C2211yescharacteristic
26#17986056C2211yescharacteristic
27#17986056C2211yescharacteristic
28#17986052C2211yescharacteristic
29#17986052C2211yescharacteristic
30#17986023C2211yescharacteristic
31#17986023C2211yescharacteristic
32C2×C4⋊(C71⋊C8)C2211yescharacteristic
33C2×C4⋊(C71⋊C8)C2211yescharacteristic
34C2×C4⋊(C71⋊C8)C2211yescharacteristic
35C2×C4⋊(C71⋊C8)C2211yescharacteristic
36#17985748C2211yescharacteristic
37#17985748C2211yescharacteristic
38#17985748C2211yescharacteristic
39#17985748C2211yescharacteristic
40#17985745C2211yescharacteristic
41#17985745C2211yescharacteristic
42#17985745C2211yescharacteristic
43#17985745C2211yescharacteristic
44#17985745C2211yescharacteristic
45#17985745C2211yescharacteristic
46#17985745C2211yescharacteristic
47#17985745C2211yescharacteristic
48#17985743C2211yescharacteristic
49#17985743C2211yescharacteristic
50#17985743C2211yescharacteristic
51#17985743C2211yescharacteristic
52#556×C71—21no—
53#555×C71—21no—
54#554×C71—21no—
55#553×C71—21no—
56#553×C71—21no—
57#548×C71—21no—
58#548×C71—21no—
59#547×C71—21no—
60#542×C71C412yes—
61#542×C71C412yes—
62#537×C71C412yes—
63#533×C71C2211yescharacteristic
64#533×C71C2211yescharacteristic
65#532×C71C2211yescharacteristic
66#532×C71C2211yescharacteristic
67#532×C71C2211yescharacteristic
68C2×C4⋊Q8×C71C2211yescharacteristic
69#520×C71C412yes—
70C4×#41×C71C2211yescharacteristic
71C2×#11765849—21no—
72C2×#11765849—21no—
73C22×C71⋊C8—21no—
74C22×C71⋊C8—21no—
75C22×C71⋊C8—21no—
76C22×C71⋊C8—21no—
77C4⋊(C71⋊C8)—21no—
78C4⋊(C71⋊C8)—21no—
79C4⋊(C71⋊C8)—21no—
80C4⋊(C71⋊C8)—21no—
81C4⋊(C71⋊C8)—21no—
82C4⋊(C71⋊C8)—21no—
83C4⋊(C71⋊C8)C2311yescharacteristic
84C4⋊(C71⋊C8)C2311yescharacteristic
85C4⋊(C71⋊C8)C2311yescharacteristic
86C4⋊(C71⋊C8)C2311yescharacteristic
87C4⋊(C71⋊C8)C2311yescharacteristic
88C4⋊(C71⋊C8)C2311yescharacteristic
89C4⋊(C71⋊C8)C2311yescharacteristic
90C4⋊(C71⋊C8)C2311yescharacteristic
91C22⋊(C71⋊C8)—21no—
92C22⋊(C71⋊C8)—21no—
93C22⋊(C71⋊C8)—21no—
94C22⋊(C71⋊C8)—21no—
95C22⋊(C71⋊C8)—21no—
96C22⋊(C71⋊C8)—21no—
97#14556039—21no—
98#14556039—21no—
99#14556039—21no—
100#14556039—21no—
101C4×C71⋊C8—21no—
102C4×C71⋊C8—21no—
103C2×#41×C71—21no—
104C2×#41×C71—21no—
105C2×#41×C71C2×C412yes—
106C2×#41×C71C2×C411yescharacteristic
107C22×Q8×C71—21no—
108C4⋊Q8×C71—21no—
109C4⋊Q8×C71—21no—
110C4⋊Q8×C71C2×C412yes—
111C4⋊Q8×C71C2311yescharacteristic
112C4⋊Q8×C71C2311yescharacteristic
113C4⋊Q8×C71C2311yescharacteristic
114#127×C71C2311yescharacteristic
115#126×C71—22no—
116#126×C71—22no—
117#125×C71—21no—
118#125×C71—21no—
119#124×C71—22no—
120#124×C71—22no—
121#124×C71—21no—
122#124×C71—21no—
123#124×C71C2×C412yes—
124#123×C71—22no—
125#123×C71—22no—
126C22⋊Q8×C71—22no—
127C22⋊Q8×C71—21no—
128C22⋊Q8×C71—21no—
129C22⋊Q8×C71—22no—
130C22⋊Q8×C71—22no—
131C22⋊Q8×C71C2×C412yes—
132C22⋊Q8×C71C2×C412yes—
133#121×C71—22no—
134#121×C71—22no—
135#121×C71—22no—
136#121×C71—21no—
137#121×C71—21no—
138#121×C71—21no—
139#121×C71—21no—
140#121×C71C2×C412yes—
141#121×C71C2×C412yes—
142C4×Q8×C71—21no—
143C4×Q8×C71—21no—
144C4×Q8×C71C2×C412yes—
145C4×Q8×C71C2×C412yes—
146C4×Q8×C71D411yescharacteristic
147C4×Q8×C71D411yescharacteristic
148C4×D4×C71—22no—
149C4×D4×C71—22no—
150C4×D4×C71—21no—
151C4×D4×C71—21no—
152C4×D4×C71—21no—
153C4×D4×C71—21no—
154C4×D4×C71C2×C412yes—
155C4×D4×C71C2×C412yes—
156C4×D4×C71D411yescharacteristic
157C4×D4×C71D411yescharacteristic
158C4×D4×C71D411yescharacteristic
159C4×D4×C71D411yescharacteristic
160C4×D4×C71D411yescharacteristic
161C4×D4×C71D411yescharacteristic
162#117×C71—21no—
163#117×C71—21no—
164#117×C71—22no—
165#117×C71C2×C411yescharacteristic
166#117×C71C2×C411yescharacteristic
167#117×C71C2×C411yescharacteristic
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71—22no—
170C2×C4⋊C4×C71C2×C412yes—
171C2×C42×C71C2311yescharacteristic
172C2×C42×C71C2311yescharacteristic
173C2×C42×C71C2311yescharacteristic
174#11765849—81no—
175#11765849—81no—
176C2×C71⋊C8—21no—
177C2×C71⋊C8—21no—
178C2×C71⋊C8—21no—
179C2×C71⋊C8—21no—
180C2×C71⋊C8—21no—
181C2×C71⋊C8—21no—
182C2×C71⋊C8—21no—
183C2×C71⋊C8—21no—
184C2×C71⋊C8—81no—
185C2×C71⋊C8—81no—
186C2×C71⋊C8—81no—
187C2×C71⋊C8—81no—
188#41×C71—42no—
189#41×C71—44no—
190#41×C71—81no—
191#41×C71—81no—
192#41×C71—81no—
193#41×C71—81no—
194C2×Q8×C71—22no—
195C2×Q8×C71—21no—
196C2×Q8×C71—21no—
197C2×Q8×C71—81no—
198C2×Q8×C71—81no—
199C2×Q8×C71C22⋊C411yescharacteristic
200C2×Q8×C71C22×C412yes—
201C2×D4×C71—22no—
202C2×D4×C71—22no—
203C2×D4×C71—22no—
204C2×D4×C71—21no—
205C2×D4×C71—21no—
206C2×D4×C71C22⋊C411yescharacteristic
207C2×D4×C71C22⋊C411yescharacteristic
208C2×D4×C71C22⋊C411yescharacteristic
209C2×D4×C71C22×C412yes—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—22no—
213C22×C4×C71—22no—
214C22×C4×C71C22×C411yescharacteristic
215C22×C4×C71C22×C411yescharacteristic
216C22×C4×C71C22×C411yescharacteristic
217C22×C4×C71C2×D411yescharacteristic
218C22×C4×C71C2×D411yescharacteristic
219C22×C4×C71C2×D411yescharacteristic
220C22×C4×C71C2×D411yescharacteristic
221C22×C4×C71C2×D411yescharacteristic
222C22×C4×C71C2×D411yescharacteristic
223C4⋊C4×C71—22no—
224C4⋊C4×C71—22no—
225C4⋊C4×C71—22no—
226C4⋊C4×C71—22no—
227C4⋊C4×C71—22no—
228C4⋊C4×C71—22no—
229C4⋊C4×C71—21no—
230C4⋊C4×C71—21no—
231C4⋊C4×C71—21no—
232C4⋊C4×C71—21no—
233C4⋊C4×C71C22⋊C411yescharacteristic
234C4⋊C4×C71C22⋊C411yescharacteristic
235C4⋊C4×C71C22⋊C411yescharacteristic
236C4⋊C4×C71C22⋊C411yescharacteristic
237C4⋊C4×C71C22⋊C411yescharacteristic
238C4⋊C4×C71C22⋊C411yescharacteristic
239C4⋊C4×C71C22×C412yes—
240C4⋊C4×C71C22×C412yes—
241C22⋊C4×C71—22no—
242C22⋊C4×C71—22no—
243C22⋊C4×C71—22no—
244C22⋊C4×C71—22no—
245C22⋊C4×C71—22no—
246C22⋊C4×C71—22no—
247C22⋊C4×C71—22no—
248C22⋊C4×C71—22no—
249C22⋊C4×C71C22⋊C411yescharacteristic
250C22⋊C4×C71C22⋊C411yescharacteristic
251C22⋊C4×C71C22⋊C411yescharacteristic
252C22⋊C4×C71C22⋊C411yescharacteristic
253C22⋊C4×C71C22⋊C411yescharacteristic
254C22⋊C4×C71C22⋊C411yescharacteristic
255C42×C71—22no—
256C42×C71—22no—
257C42×C71C22×C411yescharacteristic
258C42×C71C22×C411yescharacteristic
259C42×C71C22×C411yescharacteristic
260C42×C71C2×D411yescharacteristic
261C42×C71C2×D411yescharacteristic
262C42×C71C2×D411yescharacteristic
263C42×C71C2×D411yescharacteristic
264C42×C71C2×D411yescharacteristic
265C42×C71C2×D411yescharacteristic
266C42×C71C2411yescharacteristic
267C23×C71—22no—
268C23×C71C2×C22⋊C411yescharacteristic
269C23×C71C2×C22⋊C411yescharacteristic
270C23×C71C2×C22⋊C411yescharacteristic
271Q8×C71—41no—
272Q8×C71—42no—
273Q8×C71—41no—
274Q8×C71—41no—
275Q8×C71—41no—
276Q8×C71—41no—
277Q8×C71—82no—
278D4×C71—22no—
279D4×C71—22no—
280D4×C71—41no—
281D4×C71—42no—
282D4×C71—44no—
283D4×C71—41no—
284D4×C71—41no—
285D4×C71—41no—
286D4×C71—41no—
287D4×C71—82no—
288D4×C71—82no—
289C2×C4×C71—22no—
290C2×C4×C71—21no—
291C2×C4×C71—21no—
292C2×C4×C71—21no—
293C2×C4×C71—21no—
294C2×C4×C71—21no—
295C2×C4×C71—21no—
296C2×C4×C71—21no—
297C2×C4×C71—21no—
298C2×C4×C71—21no—
299C2×C4×C71—21no—
300C2×C4×C71—21no—
301C2×C4×C71—21no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—41no—
306C2×C4×C71—41no—
307C2×C4×C71—44no—
308C2×C4×C71—82no—
309C2×C4×C71—82no—
310C2×C4×C71—82no—
311C2×C4×C71C2×C22⋊C411yescharacteristic
312C2×C4×C71C2×C22⋊C411yescharacteristic
313C2×C4×C71C2×C22⋊C411yescharacteristic
314C2×C4×C71C2×C22⋊C411yescharacteristic
315C2×C4×C71C2×C22⋊C411yescharacteristic
316C2×C4×C71C2×C22⋊C411yescharacteristic
317C2×C4×C71C2×C22⋊C411yescharacteristic
318C2×C4×C71C2×C22⋊C411yescharacteristic
319C2×C4×C71C2×C22⋊C411yescharacteristic
320C2×C4×C71C23×C411yescharacteristic
321C2×C4×C71C22×D411yescharacteristic
322C2×C4×C71C22×D411yescharacteristic
323C71⋊C8—41no—
324C71⋊C8—41no—
325C71⋊C8—41no—
326C71⋊C8—41no—
327C71⋊C8—41no—
328C71⋊C8—41no—
329C71⋊C8—41no—
330C71⋊C8—41no—
331C22×C71—21no—
332C22×C71—21no—
333C22×C71—21no—
334C22×C71—21no—
335C22×C71—21no—
336C22×C71—21no—
337C22×C71—21no—
338C22×C71—21no—
339C22×C71—42no—
340C22×C71—42no—
341C22×C71—42no—
342C22×C71#41312yes—
343C22×C71C22×C22⋊C411yescharacteristic
344C4×C71—21no—
345C4×C71—21no—
346C4×C71—21no—
347C4×C71—21no—
348C4×C71—21no—
349C4×C71—21no—
350C4×C71—21no—
351C4×C71—21no—
352C4×C71—21no—
353C4×C71—21no—
354C4×C71—42no—
355C4×C71—42no—
356C4×C71—42no—
357C4×C71#57611yescharacteristic
358C4×C71#57711yescharacteristic
359C4×C71#57711yescharacteristic
360C4×C71#57811yescharacteristic
361#17775—711nomaximal, Sylow
362C2×C71—22no—
363C2×C71—41no—
364C2×C71—41no—
365C2×C71—82no—
366C2×C71C2×#41311yescharacteristic
367C2×C71#289711yescharacteristic
368C2×C71#289811yescharacteristic
369#3511D7111yescharacteristic
370#2990—711no—
371#2990—711no—
372#1559—711no—
373#1557—711no—
374#1556—711no—
375#1554—711no—
376#1553—711no—
377#1551—711no—
378#1551—711no—
379#1550—711no—
380#1547—711no—
381#1542—711no—
382#1540—711no—
383C2×#332—711no—
384C71#1777511yescharacteristic, complemented, Sylow
385#556—21no—
386#555—21no—
387#554—21no—
388#553—21no—
389#553—21no—
390#548—21no—
391#548—21no—
392#547—21no—
393#542Dic7112yes—
394#542Dic7112yes—
395#537Dic7112yes—
396#533C2×D7111yescharacteristic
397#533C2×D7111yescharacteristic
398#532C2×D7111yescharacteristic
399#532C2×D7111yescharacteristic
400#532C2×D7111yescharacteristic
401C2×C4⋊Q8C2×D7111yescharacteristic
402#520Dic7112yes—
403C4×#41C2×D7111yescharacteristic
404#446—1421no—
405#446—1421no—
406#435—1421no—
407#435—1421no—
408#435—1421no—
409#435—1421no—
410C8×D4—1421no—
411C8×D4—1421no—
412#432—711no—
413#432—711no—
414#432—711no—
415#432—711no—
416#431—711no—
417#431—711no—
418#423—711no—
419#423—711no—
420C2×C4⋊C8—711no—
421C2×C4⋊C8—711no—
422C2×C4⋊C8—711no—
423C2×C4⋊C8—711no—
424#333—711no—
425#333—711no—
426#333—711no—
427#333—711no—
428#332—711no—
429#332—711no—
430#332—711no—
431#332—711no—
432#332—711no—
433#332—711no—
434#332—711no—
435#332—711no—
436#331—711no—
437#331—711no—
438#331—711no—
439#331—711no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41C2×Dic7112yes—
443C2×#41C2×Dic7111yescharacteristic
444C22×Q8—21no—
445C2×M16—1421no—
446C2×M16—1421no—
447C22×C8—1421no—
448C22×C8—1421no—
449C22×C8—1421no—
450C22×C8—1421no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8C2×Dic7112yes—
454C4⋊Q8C22×D7111yescharacteristic
455C4⋊Q8C22×D7111yescharacteristic
456C4⋊Q8C22×D7111yescharacteristic
457#127C22×D7111yescharacteristic
458#126—22no—
459#126—22no—
460#125—21no—
461#125—21no—
462#124—22no—
463#124—22no—
464#124—21no—
465#124—21no—
466#124C2×Dic7112yes—
467#123—22no—
468#123—22no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8C2×Dic7112yes—
475C22⋊Q8C2×Dic7112yes—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121C2×Dic7112yes—
484#121C2×Dic7112yes—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8C2×Dic7112yes—
488C4×Q8C2×Dic7112yes—
489C4×Q8C22⋊D7111yescharacteristic
490C4×Q8C22⋊D7111yescharacteristic
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4C2×Dic7112yes—
498C4×D4C2×Dic7112yes—
499C4×D4C22⋊D7111yescharacteristic
500C4×D4C22⋊D7111yescharacteristic
501C4×D4C22⋊D7111yescharacteristic
502C4×D4C22⋊D7111yescharacteristic
503C4×D4C22⋊D7111yescharacteristic
504C4×D4C22⋊D7111yescharacteristic
505#117—21no—
506#117—21no—
507#117—22no—
508#117C2×Dic7111yescharacteristic
509#117C2×Dic7111yescharacteristic
510#117C2×Dic7111yescharacteristic
511C2×C4⋊C4—21no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4C2×Dic7112yes—
514C2×C42C22×D7111yescharacteristic
515C2×C42C22×D7111yescharacteristic
516C2×C42C22×D7111yescharacteristic
517C4⋊C8—711no—
518C4⋊C8—711no—
519C4⋊C8—711no—
520C4⋊C8—711no—
521C4⋊C8—711no—
522C4⋊C8—711no—
523C4⋊C8—711no—
524C4⋊C8—711no—
525C4⋊C8—1421no—
526C4⋊C8—1421no—
527C4⋊C8—1421no—
528C4⋊C8—1421no—
529C4⋊C8—1421no—
530C4⋊C8—1421no—
531C22⋊C8—1421no—
532C22⋊C8—1421no—
533C22⋊C8—1421no—
534C22⋊C8—1421no—
535C22⋊C8—1421no—
536C22⋊C8—1421no—
537#97—1421no—
538#97—1421no—
539#97—1421no—
540#97—1421no—
541C4×C8—1421no—
542C4×C8—1421no—
543#41—42no—
544#41—44no—
545#41—81no—
546#41—81no—
547#41—81no—
548#41—81no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—81no—
553C2×Q8—81no—
554C2×Q8C22⋊Dic7111yescharacteristic
555C2×Q8C22×Dic7112yes—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4C22⋊Dic7111yescharacteristic
562C2×D4C22⋊Dic7111yescharacteristic
563C2×D4C22⋊Dic7111yescharacteristic
564C2×D4C22×Dic7112yes—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4C22×Dic7111yescharacteristic
570C22×C4C22×Dic7111yescharacteristic
571C22×C4C22×Dic7111yescharacteristic
572C22×C4C2×C22⋊D7111yescharacteristic
573C22×C4C2×C22⋊D7111yescharacteristic
574C22×C4C2×C22⋊D7111yescharacteristic
575C22×C4C2×C22⋊D7111yescharacteristic
576C22×C4C2×C22⋊D7111yescharacteristic
577C22×C4C2×C22⋊D7111yescharacteristic
578M16—5681no—
579M16—5681no—
580C2×C8—5681no—
581C2×C8—5681no—
582C2×C8—5681no—
583C2×C8—5681no—
584C2×C8—1421no—
585C2×C8—1421no—
586C2×C8—1421no—
587C2×C8—1421no—
588C2×C8—1421no—
589C2×C8—1421no—
590C2×C8—1421no—
591C2×C8—1421no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4C22⋊Dic7111yescharacteristic
603C4⋊C4C22⋊Dic7111yescharacteristic
604C4⋊C4C22⋊Dic7111yescharacteristic
605C4⋊C4C22⋊Dic7111yescharacteristic
606C4⋊C4C22⋊Dic7111yescharacteristic
607C4⋊C4C22⋊Dic7111yescharacteristic
608C4⋊C4C22×Dic7112yes—
609C4⋊C4C22×Dic7112yes—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4C22⋊Dic7111yescharacteristic
619C22⋊C4C22⋊Dic7111yescharacteristic
620C22⋊C4C22⋊Dic7111yescharacteristic
621C22⋊C4C22⋊Dic7111yescharacteristic
622C22⋊C4C22⋊Dic7111yescharacteristic
623C22⋊C4C22⋊Dic7111yescharacteristic
624C42—22no—
625C42—22no—
626C42C22×Dic7111yescharacteristic
627C42C22×Dic7111yescharacteristic
628C42C22×Dic7111yescharacteristic
629C42C2×C22⋊D7111yescharacteristic
630C42C2×C22⋊D7111yescharacteristic
631C42C2×C22⋊D7111yescharacteristic
632C42C2×C22⋊D7111yescharacteristic
633C42C2×C22⋊D7111yescharacteristic
634C42C2×C22⋊D7111yescharacteristic
635C42C23×D7111yescharacteristic
636C23—22no—
637C23C2×C22⋊Dic7111yescharacteristic
638C23C2×C22⋊Dic7111yescharacteristic
639C23C2×C22⋊Dic7111yescharacteristic
640Q8—41no—
641Q8—42no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—82no—
647D4—22no—
648D4—22no—
649D4—41no—
650D4—42no—
651D4—44no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—82no—
657D4—82no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—44no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4C2×C22⋊Dic7111yescharacteristic
681C2×C4C2×C22⋊Dic7111yescharacteristic
682C2×C4C2×C22⋊Dic7111yescharacteristic
683C2×C4C2×C22⋊Dic7111yescharacteristic
684C2×C4C2×C22⋊Dic7111yescharacteristic
685C2×C4C2×C22⋊Dic7111yescharacteristic
686C2×C4C2×C22⋊Dic7111yescharacteristic
687C2×C4C2×C22⋊Dic7111yescharacteristic
688C2×C4C2×C22⋊Dic7111yescharacteristic
689C2×C4C23×Dic7111yescharacteristic
690C2×C4C22×C22⋊D7111yescharacteristic
691C2×C4C22×C22⋊D7111yescharacteristic
692C8—2841no—
693C8—2841no—
694C8—2841no—
695C8—2841no—
696C8—2841no—
697C8—2841no—
698C8—2841no—
699C8—2841no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22#1798598312yes—
712C22C22×C22⋊Dic7111yescharacteristic
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4#1798680211yescharacteristic
727C4#1798680711yescharacteristic
728C4#1798681011yescharacteristic
729C4#1798681411yescharacteristic
730C2—22no—
731C2—41no—
732C2—41no—
733C2—82no—
734C2C2×#1798598311yescharacteristic
735C2#2259686611yescharacteristic
736C2#2259687311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic71
commutatorC2×C4×C71C23×C4
FrattiniC42C23×D71
Fitting, prime radicalC71×#3511C2
socleC22×C71C22×C22⋊C4
cosocleC42×C71C24
hypercenter#3511D71
hypocenterC71#17775
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #22597465C2semidirect
2. #22597465C2semidirect
3. #22587070C2semidirect
4. #22587062C2semidirect
5. #22587057C2semidirect
6. #22587050C2semidirect
7. #22587045C2semidirect
8. #22587035C2semidirect
9. #22587035C2semidirect
10. #22587030C2semidirect
11. #22587017C2semidirect
12. #22586997C2semidirect
13. #22586989C2semidirect
14. C2×#17985745C2semidirect
384. C71#17775semidirect

Maximal subgroups

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

subgroupindex
#225974652
#225870702
#225870622
#225870572
#225870502
#225870452
#225870352
#225870302
#225870172
#225869972
#225869892
C2×#179857452
C71×#35112
#1777571