Finite Group Databasebeta

← #32014338

Subgroups — #32014338

Order 18176.

1118 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986130C211yesmaximal, characteristic, complemented
2#22591297C211yesmaximal, characteristic, complemented
3#22589273C211yesmaximal, characteristic, complemented
4#22589273C211yesmaximal, characteristic, complemented
5#22589268C211yesmaximal, characteristic
6#22589165C211yesmaximal, characteristic
7#22589157C211yesmaximal, characteristic, complemented
8#22589152C211yesmaximal, characteristic, complemented
9#22588355C211yesmaximal, characteristic, complemented
10#22588350C211yesmaximal, characteristic, complemented
11#22588340C211yesmaximal, characteristic, complemented
12#22588170C211yesmaximal, characteristic, complemented
13#22588165C211yesmaximal, characteristic, complemented
14C4×#14556049C211yesmaximal, characteristic, complemented
15C2×#559×C71C211yesmaximal, characteristic
16#17986130—24no—
17C2×C4⋊(C71⋊C8)C2211yescharacteristic
18C2×C4⋊(C71⋊C8)C2211yescharacteristic
19C2×C4⋊(C71⋊C8)C2211yescharacteristic
20C2×#14556052C2211yescharacteristic
21C2×#14556052C2211yescharacteristic
22C2×#14556052C2211yescharacteristic
23C2×#14556052C2211yescharacteristic
24C2×#14556049C2211yescharacteristic
25C2×#14556049C2211yescharacteristic
26C2×#14556049C2211yescharacteristic
27C2×#14556049C2211yescharacteristic
28C2×#14556049C2211yescharacteristic
29C2×#14556049C2211yescharacteristic
30C2×#14556049C2211yescharacteristic
31C2×#14556049C2211yescharacteristic
32C2×#14556039C2211yescharacteristic
33C2×#14556039C2211yescharacteristic
34C2×C4×C71⋊C8C2211yescharacteristic
35#17985906—21no—
36#17985885—21no—
37#17985885—21no—
38#17985869C2211yescharacteristic
39#17985865C2211yescharacteristic
40#17985865C2211yescharacteristic
41C4⋊C4×Dic71—21no—
42C4×C4⋊Dic71C2211yescharacteristic
43C4×C4⋊Dic71C2211yescharacteristic
44C4×C4⋊Dic71C2211yescharacteristic
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49#559×C71—24no—
50#559×C71C418yescomplemented
51C2×#127×C71C2211yescharacteristic
52C2×#124×C71—21no—
53C2×#124×C71C2211yescharacteristic
54C2×#124×C71C2211yescharacteristic
55C2×#123×C71—21no—
56C2×#123×C71—21no—
57C2×C4×Q8×C71C2211yescharacteristic
58C2×C4×Q8×C71C2211yescharacteristic
59C2×C4×D4×C71—21no—
60C2×C4×D4×C71C2211yescharacteristic
61C2×C4×D4×C71C2211yescharacteristic
62C22×C71⋊C8C2311yescharacteristic
63C22×C71⋊C8C2311yescharacteristic
64C22×C71⋊C8C2311yescharacteristic
65C22×C71⋊C8C2311yescharacteristic
66C2×C4⋊Dic71—21no—
67C2×C4⋊Dic71—21no—
68C2×C4⋊Dic71C2311yescharacteristic
69C2×C4⋊Dic71C2311yescharacteristic
70C2×C4⋊Dic71C2311yescharacteristic
71C2×C4⋊Dic71C2311yescharacteristic
72C2×C4×Dic71—21no—
73C2×C4×Dic71—21no—
74C2×C4×Dic71—21no—
75C4⋊(C71⋊C8)—22no—
76C4⋊(C71⋊C8)—22no—
77C4⋊(C71⋊C8)—22no—
78#14556052—22no—
79#14556052—22no—
80#14556052—41no—
81#14556052—41no—
82#14556049—22no—
83#14556049—22no—
84#14556049—22no—
85#14556049—22no—
86#14556049—41no—
87#14556049—41no—
88#14556049—41no—
89#14556049—41no—
90#14556039—22no—
91#14556039—22no—
92C4×C71⋊C8—22no—
93C71⋊#95—21no—
94C71⋊#95—21no—
95C71⋊#95—21no—
96C71⋊#95—21no—
97C71⋊#95—21no—
98C71⋊#95—21no—
99C71⋊#95—21no—
100C22×Q8×C71D411yescharacteristic
101C22×Q8×C71C2311yescharacteristic
102C22×D4×C71—21no—
103C22×D4×C71—21no—
104C22×D4×C71C2311yescharacteristic
105C22×D4×C71C2311yescharacteristic
106C23×C4×C71—21no—
107C23×C4×C71—21no—
108#127×C71—22no—
109#127×C71C2×C414yes—
110#124×C71—28no—
111#124×C71—22no—
112#124×C71—22no—
113#124×C71C2×C414yes—
114#124×C71C2×C414yes—
115#123×C71—28no—
116#123×C71—28no—
117C4×Q8×C71—22no—
118C4×Q8×C71C2×C414yes—
119C4×Q8×C71C2×C414yes—
120C4×Q8×C71D414yes—
121C4×D4×C71—28no—
122C4×D4×C71—22no—
123C4×D4×C71—22no—
124C4×D4×C71C2×C414yes—
125C4×D4×C71C2×C414yes—
126C2×C4⋊C4×C71—21no—
127C2×C4⋊C4×C71D411yescharacteristic
128C2×C4⋊C4×C71D411yescharacteristic
129C2×C4⋊C4×C71D411yescharacteristic
130C2×C4⋊C4×C71C2311yescharacteristic
131C2×C22⋊C4×C71—21no—
132C2×C22⋊C4×C71—21no—
133C2×C22⋊C4×C71—21no—
134C2×C22⋊C4×C71—21no—
135C2×C22⋊C4×C71—21no—
136C2×C22⋊C4×C71—21no—
137C2×C42×C71—21no—
138C2×C42×C71C2311yescharacteristic
139C2×C42×C71C2311yescharacteristic
140C2×C42×C71C2311yescharacteristic
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—21no—
145C2×C71⋊C8—21no—
146C2×C71⋊C8—21no—
147C2×C71⋊C8—21no—
148C2×C71⋊C8—21no—
149C2×C71⋊C8—21no—
150C2×C71⋊C8—21no—
151C2×C71⋊C8—21no—
152C2×C71⋊C8—21no—
153C2×C71⋊C8—21no—
154C2×C71⋊C8—21no—
155C2×C71⋊C8—21no—
156C2×C71⋊C8#4112yes—
157C4⋊Dic71—21no—
158C4⋊Dic71—21no—
159C4⋊Dic71—21no—
160C4⋊Dic71—21no—
161C4⋊Dic71—21no—
162C4⋊Dic71—21no—
163C4⋊Dic71—21no—
164C4⋊Dic71—42no—
165C4⋊Dic71—81no—
166C4⋊Dic71#4112yes—
167C4×Dic71—42no—
168C4×Dic71—81no—
169C4×Dic71—81no—
170C24×C71—21no—
171C24×C71—21no—
172C2×Q8×C71—21no—
173C2×Q8×C71—21no—
174C2×Q8×C71—21no—
175C2×Q8×C71—21no—
176C2×Q8×C71—21no—
177C2×Q8×C71—41no—
178C2×Q8×C71—41no—
179C2×Q8×C71C22⋊C414yes—
180C2×Q8×C71C22×C412yes—
181C2×D4×C71—24no—
182C2×D4×C71—24no—
183C2×D4×C71—21no—
184C2×D4×C71—21no—
185C2×D4×C71—21no—
186C2×D4×C71—21no—
187C2×D4×C71—21no—
188C2×D4×C71—21no—
189C2×D4×C71—21no—
190C2×D4×C71—21no—
191C2×D4×C71—21no—
192C2×D4×C71—21no—
193C2×D4×C71—42no—
194C2×D4×C71—42no—
195C2×D4×C71—81no—
196C2×D4×C71—81no—
197C2×D4×C71C22×C412yes—
198C2×D4×C71C22×C412yes—
199C22×C4×C71—21no—
200C22×C4×C71—21no—
201C22×C4×C71—24no—
202C22×C4×C71—24no—
203C22×C4×C71—81no—
204C22×C4×C71—81no—
205C22×C4×C71—81no—
206C22×C4×C71—81no—
207C22×C4×C71C2×D411yescharacteristic
208C22×C4×C71C2×D411yescharacteristic
209C22×C4×C71C2×D411yescharacteristic
210C22×C4×C71C2×D411yescharacteristic
211C22×C4×C71C2×D411yescharacteristic
212C22×C4×C71C2×D411yescharacteristic
213C22×C4×C71C2411yescharacteristic
214C4⋊C4×C71—24no—
215C4⋊C4×C71—21no—
216C4⋊C4×C71C22⋊C414yes—
217C4⋊C4×C71C22⋊C414yes—
218C4⋊C4×C71C22⋊C414yes—
219C4⋊C4×C71C22×C412yes—
220C22⋊C4×C71—24no—
221C22⋊C4×C71—24no—
222C22⋊C4×C71—24no—
223C22⋊C4×C71—24no—
224C22⋊C4×C71—24no—
225C22⋊C4×C71—24no—
226C42×C71—24no—
227C42×C71C22×C412yes—
228C42×C71C22×C412yes—
229C42×C71C22×C412yes—
230C42×C71C2×D412yes—
231C42×C71C2×D412yes—
232C42×C71C2×D412yes—
233C23×C71—22no—
234C23×C71—22no—
235C23×C71—41no—
236C23×C71—41no—
237C23×C71—41no—
238C23×C71—41no—
239C23×C71—41no—
240C23×C71—41no—
241C23×C71—41no—
242C23×C71—41no—
243C23×C71—41no—
244C23×C71—41no—
245C23×C71—41no—
246C23×C71—41no—
247C23×C71C22×D411yescharacteristic
248Q8×C71—22no—
249Q8×C71—22no—
250Q8×C71—44no—
251Q8×C71—41no—
252Q8×C71—41no—
253D4×C71—22no—
254D4×C71—22no—
255D4×C71—22no—
256D4×C71—22no—
257D4×C71—48no—
258D4×C71—41no—
259D4×C71—41no—
260D4×C71—41no—
261D4×C71—41no—
262D4×C71—84no—
263C2×C4×C71—21no—
264C2×C4×C71—21no—
265C2×C4×C71—21no—
266C2×C4×C71—21no—
267C2×C4×C71—21no—
268C2×C4×C71—21no—
269C2×C4×C71—21no—
270C2×C4×C71—21no—
271C2×C4×C71—21no—
272C2×C4×C71—21no—
273C2×C4×C71—21no—
274C2×C4×C71—21no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—41no—
278C2×C4×C71—41no—
279C2×C4×C71—41no—
280C2×C4×C71—41no—
281C2×C4×C71—84no—
282C2×C4×C71—84no—
283C2×C4×C71C2×C22⋊C412yes—
284C2×C4×C71C2×C22⋊C412yes—
285C2×C4×C71C2×C22⋊C412yes—
286C2×C4×C71C2×C22⋊C412yes—
287C2×C4×C71C2×C22⋊C412yes—
288C2×C4×C71C2×C22⋊C412yes—
289C2×C4×C71C23×C411yescharacteristic
290C2×C4×C71C22×D411yescharacteristic
291C2×C4×C71C2×#4111yescharacteristic
292C2×C4×C71C2×#4111yescharacteristic
293C2×C4×C71H(5,𝔽2)11yescharacteristic
294C2×C4×C712−1+411yescharacteristic
295C2×Dic71—22no—
296C2×Dic71—41no—
297C2×Dic71—41no—
298C2×Dic71—41no—
299C2×Dic71—41no—
300C2×Dic71—41no—
301C2×Dic71—41no—
302C2×Dic71—41no—
303C2×Dic71—41no—
304C2×Dic71—41no—
305C2×Dic71—41no—
306C2×Dic71—41no—
307C71⋊C8—22no—
308C71⋊C8—41no—
309C71⋊C8—41no—
310C71⋊C8—41no—
311C22×C71—42no—
312C22×C71—42no—
313C22×C71—42no—
314C22×C71—42no—
315C22×C71—42no—
316C22×C71—42no—
317C22×C71—81no—
318C22×C71—81no—
319C22×C71—81no—
320C22×C71—81no—
321C22×C71—81no—
322C22×C71—81no—
323C22×C71—81no—
324C22×C71—81no—
325C22×C71C22×C22⋊C411yescharacteristic
326C22×C71#54811yescharacteristic
327C22×C71#55011yescharacteristic
328C22×C71#57511yescharacteristic
329C22×C71#57511yescharacteristic
330C22×C71#57611yescharacteristic
331C22×C71#57711yescharacteristic
332C4×C71—22no—
333C4×C71—22no—
334C4×C71—22no—
335C4×C71—22no—
336C4×C71—22no—
337C4×C71—22no—
338C4×C71—42no—
339C4×C71—42no—
340C4×C71C4×#4111yescharacteristic
341C4×C71#52011yescharacteristic
342C4×C71#54811yescharacteristic
343C4×C71#55011yescharacteristic
344Dic71—42no—
345Dic71—81no—
346Dic71—81no—
347Dic71—81no—
348#22549—711nomaximal, Sylow
349C2×C71—82no—
350C2×C71—82no—
351C2×C71#234111yescharacteristic
352C2×C71#289611yescharacteristic
353C2×C71#289711yescharacteristic
354C2×C71#337011yescharacteristic
355C2×C71#337111yescharacteristic
356C2×C71#340111yescharacteristic
357C2×C71#340311yescharacteristic
358C2×#559D7111yescharacteristic
359C2×#446—711no—
360#2355—711no—
361#1983—711no—
362#1983—711no—
363#1982—711no—
364#1961—711no—
365#1959—711no—
366#1958—711no—
367#1805—711no—
368#1804—711no—
369#1802—711no—
370#1763—711no—
371#1762—711no—
372C4×#102—711no—
373C71#2254911yescharacteristic, complemented, Sylow
374#559—24no—
375#559Dic7118yescomplemented
376C2×#127C2×D7111yescharacteristic
377C2×#124—21no—
378C2×#124C2×D7111yescharacteristic
379C2×#124C2×D7111yescharacteristic
380C2×#123—21no—
381C2×#123—21no—
382C2×C4×Q8C2×D7111yescharacteristic
383C2×C4×Q8C2×D7111yescharacteristic
384C2×C4×D4—21no—
385C2×C4×D4C2×D7111yescharacteristic
386C2×C4×D4C2×D7111yescharacteristic
387#446—1424no—
388C2×C4⋊C8—711no—
389C2×C4⋊C8—711no—
390C2×C4⋊C8—711no—
391C2×#103—711no—
392C2×#103—711no—
393C2×#103—711no—
394C2×#103—711no—
395C2×#102—711no—
396C2×#102—711no—
397C2×#102—711no—
398C2×#102—711no—
399C2×#102—711no—
400C2×#102—711no—
401C2×#102—711no—
402C2×#102—711no—
403C2×#97—711no—
404C2×#97—711no—
405C2×C4×C8—711no—
406#391—1421no—
407#387—1421no—
408#387—1421no—
409#384—711no—
410#382—711no—
411#382—711no—
412C4×C4⋊C4—711no—
413C4×C4⋊C4—711no—
414C4×C4⋊C4—711no—
415C4×C4⋊C4—1421no—
416#340—711no—
417#340—711no—
418#340—711no—
419#340—711no—
420C22×Q8C22⋊D7111yescharacteristic
421C22×Q8C22×D7111yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4C22×D7111yescharacteristic
425C22×D4C22×D7111yescharacteristic
426C23×C4—21no—
427C23×C4—21no—
428C22×C8—711no—
429C22×C8—711no—
430C22×C8—711no—
431C22×C8—711no—
432#127—22no—
433#127C2×Dic7114yes—
434#124—28no—
435#124—22no—
436#124—22no—
437#124C2×Dic7114yes—
438#124C2×Dic7114yes—
439#123—28no—
440#123—28no—
441C4×Q8—22no—
442C4×Q8C2×Dic7114yes—
443C4×Q8C2×Dic7114yes—
444C4×Q8C22⋊D7114yes—
445C4×D4—28no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4C2×Dic7114yes—
449C4×D4C2×Dic7114yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—711no—
452C2×C4⋊C4—711no—
453C2×C4⋊C4—711no—
454C2×C4⋊C4—711no—
455C2×C4⋊C4—1421no—
456C2×C4⋊C4—1421no—
457C2×C4⋊C4C22⋊D7111yescharacteristic
458C2×C4⋊C4C22⋊D7111yescharacteristic
459C2×C4⋊C4C22⋊D7111yescharacteristic
460C2×C4⋊C4C22×D7111yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C42—21no—
468C2×C42—1421no—
469C2×C42—1421no—
470C2×C42—1421no—
471C2×C42C22×D7111yescharacteristic
472C2×C42C22×D7111yescharacteristic
473C2×C42C22×D7111yescharacteristic
474C4⋊C8—1422no—
475C4⋊C8—1422no—
476C4⋊C8—1422no—
477#103—2841no—
478#103—2841no—
479#103—1422no—
480#103—1422no—
481#102—2841no—
482#102—2841no—
483#102—2841no—
484#102—2841no—
485#102—1422no—
486#102—1422no—
487#102—1422no—
488#102—1422no—
489#97—1422no—
490#97—1422no—
491C4×C8—1422no—
492#95—1421no—
493#95—1421no—
494#95—1421no—
495#95—1421no—
496#95—1421no—
497#95—1421no—
498#95—1421no—
499C24—21no—
500C24—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8C22⋊Dic7114yes—
509C2×Q8C22×Dic7112yes—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4C22×Dic7112yes—
527C2×D4C22×Dic7112yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4—1421no—
537C22×C4—1421no—
538C22×C4—1421no—
539C22×C4—1421no—
540C22×C4C2×C22⋊D7111yescharacteristic
541C22×C4C2×C22⋊D7111yescharacteristic
542C22×C4C2×C22⋊D7111yescharacteristic
543C22×C4C2×C22⋊D7111yescharacteristic
544C22×C4C2×C22⋊D7111yescharacteristic
545C22×C4C2×C22⋊D7111yescharacteristic
546C22×C4C23×D7111yescharacteristic
547C2×C8—712no—
548C2×C8—1421no—
549C2×C8—1421no—
550C2×C8—1421no—
551C2×C8—1421no—
552C2×C8—1421no—
553C2×C8—1421no—
554C2×C8—1421no—
555C2×C8—1421no—
556C2×C8—1421no—
557C2×C8—1421no—
558C2×C8—1421no—
559C4⋊C4—21no—
560C4⋊C4—24no—
561C4⋊C4—2842no—
562C4⋊C4—5681no—
563C4⋊C4—712no—
564C4⋊C4—1421no—
565C4⋊C4—1421no—
566C4⋊C4—1421no—
567C4⋊C4—1421no—
568C4⋊C4—1421no—
569C4⋊C4—1421no—
570C4⋊C4—1421no—
571C4⋊C4C22⋊Dic7114yes—
572C4⋊C4C22⋊Dic7114yes—
573C4⋊C4C22⋊Dic7114yes—
574C4⋊C4C22×Dic7112yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C42—24no—
582C42—2842no—
583C42—5681no—
584C42—5681no—
585C42C22×Dic7112yes—
586C42C22×Dic7112yes—
587C42C22×Dic7112yes—
588C42C2×C22⋊D7112yes—
589C42C2×C22⋊D7112yes—
590C42C2×C22⋊D7112yes—
591C23—22no—
592C23—22no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C22×C22⋊D7111yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—44no—
609Q8—41no—
610Q8—41no—
611D4—22no—
612D4—22no—
613D4—22no—
614D4—22no—
615D4—48no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—84no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—84no—
640C2×C4—84no—
641C2×C4—2841no—
642C2×C4—2841no—
643C2×C4—2841no—
644C2×C4—2841no—
645C2×C4—2841no—
646C2×C4—2841no—
647C2×C4—2841no—
648C2×C4—2841no—
649C2×C4—2841no—
650C2×C4—2841no—
651C2×C4—2841no—
652C2×C4—1422no—
653C2×C4C2×C22⋊Dic7112yes—
654C2×C4C2×C22⋊Dic7112yes—
655C2×C4C2×C22⋊Dic7112yes—
656C2×C4C2×C22⋊Dic7112yes—
657C2×C4C2×C22⋊Dic7112yes—
658C2×C4C2×C22⋊Dic7112yes—
659C2×C4C23×Dic7111yescharacteristic
660C2×C4C22×C22⋊D7111yescharacteristic
661C2×C4#41×D7111yescharacteristic
662C2×C4#41×D7111yescharacteristic
663C2×C4#1455617411yescharacteristic
664C2×C4#1455617511yescharacteristic
665C8—2841no—
666C8—2841no—
667C8—2841no—
668C8—1422no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C22⋊Dic7111yescharacteristic
684C22#1798665611yescharacteristic
685C22#1798666811yescharacteristic
686C22#1798679711yescharacteristic
687C22#1798679711yescharacteristic
688C22#1798680211yescharacteristic
689C22#1798681011yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—22no—
696C4—42no—
697C4—42no—
698C4—2842no—
699C4—5681no—
700C4—5681no—
701C4—5681no—
702C4#41×Dic7111yescharacteristic
703C4#1798648211yescharacteristic
704C4#1798665611yescharacteristic
705C4#1798666811yescharacteristic
706C2—82no—
707C2—82no—
708C2#2259118111yescharacteristic
709C2#2259685911yescharacteristic
710C2#2259686611yescharacteristic
711C2#2260108711yescharacteristic
712C2#2260110211yescharacteristic
713C2#2260140011yescharacteristic
714C2#2260142411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC2×#559×C71C2
socleC23×C71C22×D4
prime radicalC2×#127×C71C22
cosocleC22×C4×C71C24
hypercenterC2×#559D71
hypocenterC71#22549
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#17986130C2semidirect
2. #22591297C2semidirect
3. #22589273C2semidirect
4. #22589273C2semidirect
7. #22589157C2semidirect
8. #22589152C2semidirect
9. #22588355C2semidirect
10. #22588350C2semidirect
11. #22588340C2semidirect
12. #22588170C2semidirect
13. #22588165C2semidirect
14. C4×#14556049C2semidirect
50. #559×C71C4semidirect
373. C71#22549semidirect
375. #559Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179861302
#225912972
#225892732
#225892682
#225891652
#225891572
#225891522
#225883552
#225883502
#225883402
#225881702
#225881652
C4×#145560492
C2×#559×C712
#2254971