Finite Group Databasebeta

← #32882362

Subgroups — #32882362

Order 18176.

2254 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986645C211yesmaximal, characteristic, complemented
2#22600490C214yesmaximal, complemented
3#22600370C214yesmaximal, complemented
4#22599881C214yesmaximal, complemented
5#22599866C214yesmaximal, complemented
6#22599339C211yesmaximal, characteristic, complemented
7#22599323C211yesmaximal, characteristic, complemented
8#22599166C212yesmaximal, complemented
9#22599101C212yesmaximal, complemented
10#22598435C211yesmaximal, characteristic, complemented
11#22598427C211yesmaximal, characteristic, complemented
12#22597566C212yesmaximal, complemented
13#22597556C212yesmaximal, complemented
14#22597369C211yesmaximal, characteristic, complemented
15C71×#3506C211yesmaximal, characteristic, complemented
16C22×#11765865C2211yescharacteristic
17C23×D284C2211yescharacteristic
18C2×#14556153C2214yescomplemented
19C2×#14556148C2214yescomplemented
20#17986645—22no—
21#17986645—22no—
22#17986645C2214yes—
23#17986645C2214yes—
24C2×#14556116C2211yescharacteristic
25C2×#14556113—21no—
26C2×#14556107C2211yescharacteristic
27C2×#14556102C2211yescharacteristic
28C2×#14556101—21no—
29C2×#14556096—21no—
30C2×C4×D284C2211yescharacteristic
31C2×C22⋊C4×D71—21no—
32#17986391C2212yescomplemented
33#17986386C2212yescomplemented
34#17986361C2212yescomplemented
35#17986361C2212yescomplemented
36#17986340C2214yescomplemented
37#17986332C2212yescomplemented
38#17986323C2214yescomplemented
39#17986315C2212yescomplemented
40#17986286C2212yescomplemented
41#17986276C2212yescomplemented
42#17986255C2214yescomplemented
43#17986243C2214yescomplemented
44#17986233C2214yescomplemented
45#17986230C2214yescomplemented
46#17986221C2214yescomplemented
47#17986214C2214yescomplemented
48#17986201C2212yescomplemented
49#17986191C2212yescomplemented
50#17986161C2214yescomplemented
51#17986159C2214yescomplemented
52#17986154C2212yescomplemented
53#17986149C2212yes—
54#17986149C2212yes—
55#17986149C2214yescomplemented
56#17986144C2214yescomplemented
57#17986142C2214yescomplemented
58#17986137C2212yescomplemented
59#17986132C2212yes—
60#17986132C2212yes—
61#17986132C2214yescomplemented
62#17986109C2214yescomplemented
63#17986097C2214yescomplemented
64#17986071C2214yescomplemented
65#17986071C2214yescomplemented
66#17986056C2211yescharacteristic, complemented
67#17986056C2211yescharacteristic, complemented
68#17986003C2214yescomplemented
69#17985993C2214yescomplemented
70#17985963C2212yes—
71C2×C22⋊(C71⋊C8)C2212yescomplemented
72#559×C71—22no—
73#556×C71C2212yescomplemented
74#555×C71C2212yescomplemented
75#553×C71—22no—
76#550×C71C2212yescomplemented
77#547×C71C2212yescomplemented
78#538×C71—21no—
79#538×C71—21no—
80#535×C71—21no—
81#533×C71C2211yescharacteristic, complemented
82#532×C71C2211yescharacteristic, complemented
83#525×C71C2212yes—
84#525×C71C2212yescomplemented
85#520×C71—21no—
86C2×C4×D4×C71C2211yescharacteristic
87C24×D71—21no—
88C2×#11765865—22no—
89C2×#11765865—44no—
90C2×#11765865C2314yes—
91C22×Dic142C2311yescharacteristic
92C22×D284—22no—
93C22×D284—21no—
94C22×D284—44no—
95C22×D284C2311yescharacteristic
96C22×D284C2314yes—
97C22×D284C2311yescharacteristic
98C22×C22⋊D71—21no—
99C22×C22⋊D71—21no—
100C22×C4×D71—21no—
101C22×C4×D71—21no—
102#14556153—48no—
103#14556148—48no—
104C2×#11765855C2314yescomplemented
105C2×#11765853C2314yescomplemented
106C2×#11765852C2314yes—
107C2×#11765852C2314yes—
108C2×#11765850C2314yes—
109C2×#11765850C2314yes—
110C2×#11765849C2314yes—
111C22×C71⋊C8C2314yescomplemented
112#14556116—21no—
113#14556116—21no—
114#14556116C2312yes—
115#14556116C2312yes—
116#14556113—24no—
117#14556113—24no—
118#14556107—22no—
119#14556107C2314yes—
120#14556102—22no—
121#14556102C2314yes—
122#14556101—24no—
123#14556101—24no—
124#14556096—24no—
125#14556096—24no—
126C4×D284—21no—
127C4×D284—21no—
128C4×D284C2312yes—
129C4×D284C2312yes—
130C2×C4⋊Dic71C2311yescharacteristic
131C2×Dic71⋊C4—21no—
132C2×C22⋊Dic71—21no—
133C2×(C2×D71)⋊C4—21no—
134C2×(C2×D71)⋊C4—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C22⋊C4×D71—24no—
138C22⋊C4×D71—24no—
139#14556061C2314yescomplemented
140#14556059C2314yescomplemented
141C4⋊(C71⋊C8)C2312yescomplemented
142C4⋊(C71⋊C8)C2312yescomplemented
143#14556052C2314yescomplemented
144#14556051C2314yescomplemented
145#14556051C2314yescomplemented
146#14556049C2314yescomplemented
147#14556048C2314yes—
148#14556048C2314yes—
149#14556048C2314yes—
150#14556048C2314yes—
151C22⋊(C71⋊C8)C2312yes—
152C22⋊(C71⋊C8)C2312yes—
153C22⋊(C71⋊C8)C2314yes—
154C22⋊(C71⋊C8)C2314yescomplemented
155#14556039C2312yescomplemented
156#14556039C2312yescomplemented
157C2×#41×C71—21no—
158C2×#41×C71C2312yes—
159C2×#41×C71C2312yescomplemented
160C22×D4×C71D411yescharacteristic
161C23×C4×C71C2311yescharacteristic
162C23×C4×C71C2311yescharacteristic
163C4⋊Q8×C71C2311yescharacteristic, complemented
164C4⋊Q8×C71C2311yescharacteristic, complemented
165C4⋊Q8×C71C2311yescharacteristic, complemented
166#127×C71—22no—
167#127×C71C2311yescharacteristic, complemented
168#126×C71—22no—
169#126×C71—22no—
170#125×C71—21no—
171#124×C71—22no—
172#124×C71—22no—
173#124×C71—22no—
174#124×C71—21no—
175#123×C71—22no—
176#123×C71—22no—
177#123×C71—22no—
178#123×C71—22no—
179C22⋊Q8×C71—21no—
180C22⋊Q8×C71C2312yes—
181C22⋊Q8×C71C2312yes—
182C22⋊Q8×C71C2312yescomplemented
183#121×C71—22no—
184#121×C71—22no—
185#121×C71—21no—
186#121×C71—22no—
187#121×C71—22no—
188#121×C71C2312yes—
189#121×C71C2312yes—
190#121×C71C2312yescomplemented
191#120×C71—22no—
192#120×C71—22no—
193C4×Q8×C71—22no—
194C4×Q8×C71—21no—
195C4×Q8×C71C2312yescomplemented
196C4×D4×C71—22no—
197C4×D4×C71—22no—
198C4×D4×C71—22no—
199C4×D4×C71—22no—
200C4×D4×C71—22no—
201C4×D4×C71—21no—
202C4×D4×C71D412yes—
203C4×D4×C71D412yes—
204C4×D4×C71C2312yes—
205C4×D4×C71C2312yes—
206C4×D4×C71C2312yescomplemented
207#117×C71—21no—
208#117×C71—22no—
209#117×C71C2312yes—
210#117×C71C2312yescomplemented
211C2×C4⋊C4×C71—22no—
212C2×C4⋊C4×C71D411yescharacteristic
213C2×C22⋊C4×C71D411yescharacteristic
214C2×C22⋊C4×C71D411yescharacteristic
215C2×C42×C71C2311yescharacteristic
216C23×D71—21no—
217C23×D71—21no—
218C23×D71—24no—
219C23×D71—44no—
220C23×D71—44no—
221C23×D71—82no—
222#11765865—28no—
223#11765865—44no—
224#11765865—48no—
225C2×Dic142—21no—
226C2×Dic142—42no—
227C2×Dic142C2412yes—
228C2×D284—21no—
229C2×D284—24no—
230C2×D284—28no—
231C2×D284—24no—
232C2×D284—21no—
233C2×D284—44no—
234C2×D284—42no—
235C2×D284—48no—
236C2×D284—44no—
237C2×D284C2412yes—
238C2×D284C2412yes—
239C2×C22⋊D71—24no—
240C2×C22⋊D71—24no—
241C2×C22⋊D71—44no—
242C2×C22⋊D71—82no—
243C22×Dic71—21no—
244C22×Dic71—21no—
245C2×C4×D71—24no—
246C2×C4×D71—22no—
247C2×C4×D71—22no—
248C2×C4×D71—44no—
249C2×C4×D71—82no—
250#11765855—44no—
251#11765853—44no—
252#11765852—28no—
253#11765852—44no—
254#11765850—28no—
255#11765850—44no—
256#11765849—44no—
257C2×C71⋊C8—44no—
258C2×C71⋊C8C2414yes—
259C2×C71⋊C8C2414yes—
260C4⋊Dic71—21no—
261C4⋊Dic71C2412yes—
262Dic71⋊C4—24no—
263C22⋊Dic71—24no—
264(C2×D71)⋊C4—22no—
265(C2×D71)⋊C4—22no—
266(C2×D71)⋊C4—24no—
267(C2×D71)⋊C4—22no—
268(C2×D71)⋊C4—22no—
269(C2×D71)⋊C4—22no—
270(C2×D71)⋊C4—22no—
271C24×C71C2×D411yescharacteristic
272C24×C71C2×D411yescharacteristic
273#41×C71—44no—
274#41×C71—44no—
275#41×C71—44no—
276C2×Q8×C71—21no—
277C2×Q8×C71—21no—
278C2×Q8×C71C2412yes—
279C2×D4×C71—22no—
280C2×D4×C71—22no—
281C2×D4×C71—22no—
282C2×D4×C71—22no—
283C2×D4×C71—22no—
284C2×D4×C71—21no—
285C2×D4×C71—21no—
286C2×D4×C71—42no—
287C2×D4×C71C2×D412yes—
288C2×D4×C71C2×D412yes—
289C2×D4×C71C2412yes—
290C22×C4×C71—22no—
291C22×C4×C71—22no—
292C22×C4×C71—22no—
293C22×C4×C71—42no—
294C22×C4×C71—42no—
295C22×C4×C71C2×D411yescharacteristic
296C22×C4×C71C2×D411yescharacteristic
297C22×C4×C71C2×D411yescharacteristic
298C22×C4×C71C2×D411yescharacteristic
299C22×C4×C71C2×D412yes—
300C22×C4×C71C2×D412yes—
301C22×C4×C71C2411yescharacteristic
302C22×C4×C71C2412yes—
303C22×C4×C71C2412yes—
304C4⋊C4×C71—21no—
305C4⋊C4×C71—22no—
306C4⋊C4×C71—22no—
307C4⋊C4×C71—21no—
308C4⋊C4×C71—22no—
309C4⋊C4×C71—21no—
310C4⋊C4×C71—21no—
311C4⋊C4×C71—22no—
312C4⋊C4×C71C2×D412yes—
313C4⋊C4×C71C2×D412yes—
314C4⋊C4×C71C2412yes—
315C4⋊C4×C71C2412yes—
316C22⋊C4×C71—22no—
317C22⋊C4×C71—22no—
318C22⋊C4×C71—22no—
319C22⋊C4×C71—22no—
320C22⋊C4×C71—22no—
321C22⋊C4×C71—22no—
322C22⋊C4×C71—22no—
323C22⋊C4×C71—22no—
324C22⋊C4×C71—22no—
325C22⋊C4×C71C2×D412yes—
326C22⋊C4×C71C2×D412yes—
327C22⋊C4×C71C2×D412yes—
328C22⋊C4×C71C2×D412yes—
329C42×C71—22no—
330C42×C71—22no—
331C42×C71—22no—
332C42×C71C2×D411yescharacteristic
333C42×C71C2×D411yescharacteristic
334C42×C71C2411yescharacteristic
335C42×C71C2411yescharacteristic
336C23×C71—22no—
337C23×C71—22no—
338C23×C71—22no—
339C23×C71—41no—
340C23×C71—41no—
341C23×C71—41no—
342C23×C71—41no—
343C23×C71C22×D412yes—
344C23×C71C22×D412yes—
345C23×C71C22×D411yescharacteristic
346C22×D71—24no—
347C22×D71—22no—
348C22×D71—22no—
349C22×D71—48no—
350C22×D71—42no—
351C22×D71—42no—
352C22×D71—42no—
353C22×D71—42no—
354C22×D71—48no—
355C22×D71—42no—
356C22×D71—84no—
357C22×D71—816no—
358Q8×C71—24no—
359Q8×C71—42no—
360Q8×C71—81no—
361D4×C71—24no—
362D4×C71—42no—
363D4×C71—42no—
364D4×C71—42no—
365D4×C71—44no—
366D4×C71—81no—
367D4×C71—82no—
368D4×C71—82no—
369D4×C71—82no—
370D4×C71—82no—
371C2×C4×C71—22no—
372C2×C4×C71—22no—
373C2×C4×C71—24no—
374C2×C4×C71—24no—
375C2×C4×C71—22no—
376C2×C4×C71—22no—
377C2×C4×C71—22no—
378C2×C4×C71—41no—
379C2×C4×C71—42no—
380C2×C4×C71—41no—
381C2×C4×C71—42no—
382C2×C4×C71—41no—
383C2×C4×C71—44no—
384C2×C4×C71—82no—
385C2×C4×C71—82no—
386C2×C4×C71C22×D411yescharacteristic
387C2×C4×C71C22×D412yes—
388C2×C4×C71C22×D412yes—
389C2×C4×C71C22×D411yescharacteristic
390C2×C4×C71C22×D411yescharacteristic
391C2×C4×C71C22×D411yescharacteristic
392C2×C4×C71C22×D411yescharacteristic
393C2×C4×C71C2511yescharacteristic
394C22⋊D71—48no—
395C22⋊D71—84no—
396C2×Dic71—22no—
397C2×Dic71—22no—
398C2×Dic71—42no—
399C2×Dic71—42no—
400D284—24no—
401D284—22no—
402D284—24no—
403D284—48no—
404D284—42no—
405D284H(5,𝔽2)14yes—
406C4×D71—48no—
407C4×D71—82no—
408C4×D71—82no—
409Dic142—24no—
410Dic142—42no—
411C71⋊C8—24no—
412C71⋊C8—24no—
413C22×C71—21no—
414C22×C71—21no—
415C22×C71—22no—
416C22×C71—22no—
417C22×C71—22no—
418C22×C71—22no—
419C22×C71—22no—
420C22×C71—22no—
421C22×C71—44no—
422C22×C71—42no—
423C22×C71—42no—
424C22×C71—42no—
425C22×C71—82no—
426C22×C71#57512yes—
427C22×C71C23×D411yescharacteristic
428C2×D71—24no—
429C2×D71—48no—
430C2×D71—42no—
431C2×D71—42no—
432C2×D71—42no—
433C2×D71—42no—
434C2×D71—42no—
435C2×D71—816no—
436C2×D71—84no—
437C4×C71—21no—
438C4×C71—21no—
439C4×C71—21no—
440C4×C71—22no—
441C4×C71—22no—
442C4×C71—21no—
443C4×C71—21no—
444C4×C71—42no—
445C4×C71—42no—
446C4×C71—42no—
447C4×C71C2×H(5,𝔽2)12yes—
448Dic71—42no—
449Dic71—42no—
450#61576—711nomaximal, Sylow
451C2×C71—22no—
452C2×C71—42no—
453C2×C71—42no—
454C2×C71—82no—
455C2×C71#348411yescharacteristic
456C2×C71C2×#57511yescharacteristic
457C2×C71#358511yescharacteristic
458D71—44no—
459D71—82no—
460#3506D7111yescharacteristic, complemented
461C2×#546—711no—
462#3319—714no—
463#3311—714no—
464#3268—714no—
465#3267—714no—
466#3215—711no—
467#3213—711no—
468#3196—712no—
469#3188—712no—
470#3110—711no—
471#3109—711no—
472#3003—712no—
473#3002—712no—
474#2973—711no—
475C71#6157611yescharacteristic, complemented, Sylow
476C22×#41—711no—
477C23×D4—711no—
478C2×AGL(1,ℤ/8)—714no—
479C2×#135—714no—
480#559—22no—
481#556C2×D7112yescomplemented
482#555C2×D7112yescomplemented
483#553—22no—
484#550C2×D7112yescomplemented
485#547C2×D7112yescomplemented
486#546—714no—
487#546—714no—
488#546—1422no—
489#546—1422no—
490#538—21no—
491#538—21no—
492#535—21no—
493#533C2×D7111yescharacteristic, complemented
494#532C2×D7111yescharacteristic, complemented
495C2×#124—711no—
496#525C2×D7112yes—
497#525C2×D7112yescomplemented
498C2×#123—1421no—
499C2×C22⋊Q8—711no—
500C2×#121—711no—
501C2×#121—1421no—
502C2×#120—1421no—
503#520—21no—
504C2×C4×D4—711no—
505C2×C4×D4C2×D7111yescharacteristic
506C22×C22⋊C4—1421no—
507#497—712no—
508#496—712no—
509#489—712no—
510#489—712no—
511#485—714no—
512#484—712no—
513#482—714no—
514#481—712no—
515#476—712no—
516#474—712no—
517#470—714no—
518#468—714no—
519#466—714no—
520#465—714no—
521#464—714no—
522#463—714no—
523#461—712no—
524#459—712no—
525#452—714no—
526#452—714no—
527#451—712no—
528#450—712no—
529#450—712no—
530#450—714no—
531#449—714no—
532#449—714no—
533#448—712no—
534#447—712no—
535#447—712no—
536#447—714no—
537#442—714no—
538#440—714no—
539#435—714no—
540#435—714no—
541#432—711no—
542#432—711no—
543#418—714no—
544#416—714no—
545#407—712no—
546C2×C22⋊C8—712no—
547C25—1421no—
548C2×#41—21no—
549C2×#41—2844no—
550C2×#41—714no—
551C2×#41—1422no—
552C2×#41C22×D7112yes—
553C2×#41C22×D7112yescomplemented
554C22×Q8—711no—
555C22×D4—2844no—
556C22×D4—711no—
557C22×D4—714no—
558C22×D4—711no—
559C22×D4—1421no—
560C22×D4—1421no—
561C22×D4—1421no—
562C22×D4—1422no—
563C22×D4C22⋊D7111yescharacteristic
564C23×C4—1421no—
565C23×C4—1421no—
566C23×C4C22×D7111yescharacteristic
567C23×C4C22×D7111yescharacteristic
568AGL(1,ℤ/8)—2848no—
569#135—2848no—
570C2×Q16—714no—
571C2×SD16—714no—
572C2×SD16—714no—
573C2×SD16—714no—
574C2×D8—714no—
575C2×D8—714no—
576C2×M16—714no—
577C22×C8—714no—
578C4⋊Q8C22×D7111yescharacteristic, complemented
579C4⋊Q8C22×D7111yescharacteristic, complemented
580C4⋊Q8C22×D7111yescharacteristic, complemented
581#127—22no—
582#127C22×D7111yescharacteristic, complemented
583#126—22no—
584#126—22no—
585#125—21no—
586#124—22no—
587#124—22no—
588#124—22no—
589#124—21no—
590#124—712no—
591#124—712no—
592#124—1421no—
593#124—1421no—
594#123—22no—
595#123—22no—
596#123—22no—
597#123—22no—
598#123—1424no—
599#123—1424no—
600C22⋊Q8—21no—
601C22⋊Q8—714no—
602C22⋊Q8—1422no—
603C22⋊Q8C22×D7112yes—
604C22⋊Q8C22×D7112yes—
605C22⋊Q8C22×D7112yescomplemented
606#121—22no—
607#121—22no—
608#121—21no—
609#121—22no—
610#121—22no—
611#121—714no—
612#121—1422no—
613#121—1424no—
614#121—1424no—
615#121C22×D7112yes—
616#121C22×D7112yes—
617#121C22×D7112yescomplemented
618#120—22no—
619#120—22no—
620#120—1424no—
621#120—1424no—
622C4×Q8—22no—
623C4×Q8—21no—
624C4×Q8C22×D7112yescomplemented
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—21no—
631C4×D4—712no—
632C4×D4—712no—
633C4×D4—1421no—
634C4×D4—1421no—
635C4×D4C22⋊D7112yes—
636C4×D4C22⋊D7112yes—
637C4×D4C22×D7112yes—
638C4×D4C22×D7112yes—
639C4×D4C22×D7112yescomplemented
640#117—21no—
641#117—22no—
642#117C22×D7112yes—
643#117C22×D7112yescomplemented
644C2×C4⋊C4—22no—
645C2×C4⋊C4—711no—
646C2×C4⋊C4—1421no—
647C2×C4⋊C4C22⋊D7111yescharacteristic
648C2×C22⋊C4—1421no—
649C2×C22⋊C4—1421no—
650C2×C22⋊C4—1421no—
651C2×C22⋊C4—1421no—
652C2×C22⋊C4—1421no—
653C2×C22⋊C4—1424no—
654C2×C22⋊C4—1424no—
655C2×C22⋊C4C22⋊D7111yescharacteristic
656C2×C22⋊C4C22⋊D7111yescharacteristic
657C2×C42C22×D7111yescharacteristic
658#107—714no—
659#106—714no—
660C4⋊C8—712no—
661C4⋊C8—712no—
662#103—714no—
663#103—714no—
664#103—714no—
665#102—714no—
666#102—714no—
667#102—714no—
668#102—714no—
669#102—714no—
670C22⋊C8—712no—
671C22⋊C8—712no—
672C22⋊C8—714no—
673C22⋊C8—714no—
674#97—712no—
675#97—712no—
676C24—2844no—
677C24—2844no—
678C24—5682no—
679C24—1421no—
680C24—1424no—
681C24—1421no—
682C24C2×C22⋊D7111yescharacteristic
683C24C2×C22⋊D7111yescharacteristic
684#41—44no—
685#41—44no—
686#41—44no—
687#41—2844no—
688#41—2848no—
689#41—1428no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—2842no—
693C2×Q8—712no—
694C2×Q8—1421no—
695C2×Q8C23×D7112yes—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—22no—
700C2×D4—22no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—42no—
704C2×D4—2844no—
705C2×D4—2842no—
706C2×D4—2844no—
707C2×D4—2848no—
708C2×D4—2844no—
709C2×D4—5682no—
710C2×D4—712no—
711C2×D4—712no—
712C2×D4—1428no—
713C2×D4—1424no—
714C2×D4—1424no—
715C2×D4—1424no—
716C2×D4—1424no—
717C2×D4—1421no—
718C2×D4—1421no—
719C2×D4C2×C22⋊D7112yes—
720C2×D4C2×C22⋊D7112yes—
721C2×D4C23×D7112yes—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—2844no—
728C22×C4—5682no—
729C22×C4—1421no—
730C22×C4—1421no—
731C22×C4—1424no—
732C22×C4—1422no—
733C22×C4—1422no—
734C22×C4C2×C22⋊D7111yescharacteristic
735C22×C4C2×C22⋊D7111yescharacteristic
736C22×C4C2×C22⋊D7111yescharacteristic
737C22×C4C2×C22⋊D7111yescharacteristic
738C22×C4C2×C22⋊D7112yes—
739C22×C4C2×C22⋊D7112yes—
740C22×C4C23×D7111yescharacteristic
741C22×C4C23×D7112yes—
742C22×C4C23×D7112yes—
743Q16—2844no—
744SD16—2844no—
745SD16—2844no—
746SD16—1428no—
747D8—2844no—
748D8—1428no—
749M16—2844no—
750C2×C8—2844no—
751C2×C8—714no—
752C2×C8—714no—
753C4⋊C4—21no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—22no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—22no—
761C4⋊C4—712no—
762C4⋊C4—1424no—
763C4⋊C4—1421no—
764C4⋊C4C2×C22⋊D7112yes—
765C4⋊C4C2×C22⋊D7112yes—
766C4⋊C4C23×D7112yes—
767C4⋊C4C23×D7112yes—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—22no—
775C22⋊C4—22no—
776C22⋊C4—22no—
777C22⋊C4—1424no—
778C22⋊C4—1424no—
779C22⋊C4—1422no—
780C22⋊C4—1422no—
781C22⋊C4—1422no—
782C22⋊C4—1422no—
783C22⋊C4—1422no—
784C22⋊C4—1422no—
785C22⋊C4C2×C22⋊D7112yes—
786C22⋊C4C2×C22⋊D7112yes—
787C22⋊C4C2×C22⋊D7112yes—
788C22⋊C4C2×C22⋊D7112yes—
789C42—22no—
790C42—22no—
791C42—22no—
792C42C2×C22⋊D7111yescharacteristic
793C42C2×C22⋊D7111yescharacteristic
794C42C23×D7111yescharacteristic
795C42C23×D7111yescharacteristic
796C23—22no—
797C23—22no—
798C23—22no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—2842no—
804C23—2842no—
805C23—2842no—
806C23—2848no—
807C23—2848no—
808C23—2842no—
809C23—2842no—
810C23—5684no—
811C23—56816no—
812C23—1424no—
813C23—1422no—
814C23—1422no—
815C23C22×C22⋊D7112yes—
816C23C22×C22⋊D7112yes—
817C23C22×C22⋊D7111yescharacteristic
818Q8—24no—
819Q8—42no—
820Q8—81no—
821Q8—2842no—
822Q8—1424no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—44no—
828D4—81no—
829D4—82no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—2842no—
834D4—2848no—
835D4—2848no—
836D4—5684no—
837D4—714no—
838D4—1424no—
839D4—1424no—
840D4—1422no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—44no—
854C2×C4—82no—
855C2×C4—82no—
856C2×C4—2848no—
857C2×C4—2842no—
858C2×C4—2842no—
859C2×C4—5682no—
860C2×C4—5682no—
861C2×C4—1422no—
862C2×C4—1422no—
863C2×C4C22×C22⋊D7111yescharacteristic
864C2×C4C22×C22⋊D7112yes—
865C2×C4C22×C22⋊D7112yes—
866C2×C4C22×C22⋊D7111yescharacteristic
867C2×C4C22×C22⋊D7111yescharacteristic
868C2×C4C22×C22⋊D7111yescharacteristic
869C2×C4C22×C22⋊D7111yescharacteristic
870C2×C4C24×D7111yescharacteristic
871C8—1424no—
872C8—1424no—
873C22—21no—
874C22—21no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—44no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—82no—
886C22—2848no—
887C22—2842no—
888C22—2842no—
889C22—2842no—
890C22—2842no—
891C22—2842no—
892C22—5684no—
893C22—56816no—
894C22—1424no—
895C22#1798679712yes—
896C22C23×C22⋊D7111yescharacteristic
897C4—21no—
898C4—21no—
899C4—21no—
900C4—21no—
901C4—21no—
902C4—22no—
903C4—22no—
904C4—42no—
905C4—42no—
906C4—42no—
907C4—2842no—
908C4—2842no—
909C4H(5,𝔽2)×D7112yes—
910C2—22no—
911C2—42no—
912C2—42no—
913C2—82no—
914C2—2844no—
915C2—5682no—
916C2#2260197111yescharacteristic
917C2C2×#1798679711yescharacteristic
918C2#2260311911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC71×#3506C2
socleC22×C71C23×D4
hypercenter#3506D71
hypocenterC71#61576
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. C2×#17986645C2semidirect
2. #22600490C2semidirect
3. #22600370C2semidirect
4. #22599881C2semidirect
5. #22599866C2semidirect
6. #22599339C2semidirect
7. #22599323C2semidirect
8. #22599166C2semidirect
9. #22599101C2semidirect
10. #22598435C2semidirect
11. #22598427C2semidirect
12. #22597566C2semidirect
13. #22597556C2semidirect
14. #22597369C2semidirect
15. C71×#3506C2semidirect
18. C2×#14556153C22semidirect
19. C2×#14556148C22semidirect
32. #17986391C22semidirect
33. #17986386C22semidirect
34. #17986361C22semidirect
35. #17986361C22semidirect
36. #17986340C22semidirect
37. #17986332C22semidirect
38. #17986323C22semidirect
39. #17986315C22semidirect
40. #17986286C22semidirect
41. #17986276C22semidirect
42. #17986255C22semidirect
43. #17986243C22semidirect
44. #17986233C22semidirect
45. #17986230C22semidirect
46. #17986221C22semidirect
47. #17986214C22semidirect
48. #17986201C22semidirect
49. #17986191C22semidirect
50. #17986161C22semidirect
51. #17986159C22semidirect
52. #17986154C22semidirect
55. #17986149C22semidirect
56. #17986144C22semidirect
57. #17986142C22semidirect
58. #17986137C22semidirect
61. #17986132C22semidirect
62. #17986109C22semidirect
63. #17986097C22semidirect
64. #17986071C22semidirect
65. #17986071C22semidirect
66. #17986056C22semidirect
67. #17986056C22semidirect
68. #17986003C22semidirect
69. #17985993C22semidirect
71. C2×C22⋊(C71⋊C8)C22semidirect
73. #556×C71C22semidirect
74. #555×C71C22semidirect
76. #550×C71C22semidirect
77. #547×C71C22semidirect
81. #533×C71C22semidirect
82. #532×C71C22semidirect
84. #525×C71C22semidirect
104. C2×#11765855C23semidirect
105. C2×#11765853C23semidirect
111. C22×C71⋊C8C23semidirect
139. #14556061C23semidirect
140. #14556059C23semidirect
141. C4⋊(C71⋊C8)C23semidirect
142. C4⋊(C71⋊C8)C23semidirect
143. #14556052C23semidirect
144. #14556051C23semidirect
145. #14556051C23semidirect
146. #14556049C23semidirect
154. C22⋊(C71⋊C8)C23semidirect
155. #14556039C23semidirect
156. #14556039C23semidirect
159. C2×#41×C71C23semidirect
163. C4⋊Q8×C71C23semidirect
164. C4⋊Q8×C71C23semidirect
165. C4⋊Q8×C71C23semidirect
167. #127×C71C23semidirect
182. C22⋊Q8×C71C23semidirect
190. #121×C71C23semidirect
195. C4×Q8×C71C23semidirect
206. C4×D4×C71C23semidirect
210. #117×C71C23semidirect
460. #3506D71semidirect
475. C71#61576semidirect
481. #556C2×D71semidirect
482. #555C2×D71semidirect
484. #550C2×D71semidirect
485. #547C2×D71semidirect
493. #533C2×D71semidirect
494. #532C2×D71semidirect
497. #525C2×D71semidirect
553. C2×#41C22×D71semidirect
578. C4⋊Q8C22×D71semidirect
579. C4⋊Q8C22×D71semidirect
580. C4⋊Q8C22×D71semidirect
582. #127C22×D71semidirect
605. C22⋊Q8C22×D71semidirect
617. #121C22×D71semidirect
624. C4×Q8C22×D71semidirect
639. C4×D4C22×D71semidirect
643. #117C22×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179866452
#226004902
#226003702
#225998812
#225998662
#225993392
#225993232
#225991662
#225991012
#225984352
#225984272
#225975662
#225975562
#225973692
C71×#35062
#6157671