Finite Group Databasebeta

← #31999963

Subgroups — #31999963

Order 18176.

1050 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986046C211yesmaximal, characteristic, complemented
2C2×#104×D71C211yesmaximal, characteristic
3#22596855C211yesmaximal, characteristic
4#22596782C211yesmaximal, characteristic
5#22596756C211yesmaximal, characteristic, complemented
6#22588991C211yesmaximal, characteristic, complemented
7#22588990C211yesmaximal, characteristic, complemented
8#22588989C211yesmaximal, characteristic, complemented
9#22588988C211yesmaximal, characteristic, complemented
10#22588987C211yesmaximal, characteristic, complemented
11#22588986C211yesmaximal, characteristic, complemented
12#22588985C211yesmaximal, characteristic, complemented
13#339×D71C211yesmaximal, characteristic, complemented
14#22588032C211yesmaximal, characteristic, complemented
15C71×#1929C211yesmaximal, characteristic, complemented
16C2×#41×D71C2211yescharacteristic
17C22×#11765848C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19C2×M16×D71C2211yescharacteristic
20C2×M16×D71C2211yescharacteristic
21#117×D71C2211yescharacteristic
22C2×C42×D71C2211yescharacteristic
23#17986046—24no—
24C2×#14556064C2211yescharacteristic, complemented
25C2×#14556063C2211yescharacteristic, complemented
26C2×#14556063C2211yescharacteristic, complemented
27C2×#14556056C2211yescharacteristic
28C2×#14556055C2211yescharacteristic
29C2×#14556054C2211yescharacteristic
30#104×D71—24no—
31#17986006C411yescharacteristic, complemented
32#17986006C411yescharacteristic, complemented
33#17986002C411yescharacteristic, complemented
34#17986002C411yescharacteristic, complemented
35#17985999C411yescharacteristic, complemented
36#17985999C411yescharacteristic, complemented
37#17985997C411yescharacteristic, complemented
38#17985997C411yescharacteristic, complemented
39#17985996C2211yescharacteristic
40#17985995C2211yescharacteristic
41#17985993C2211yescharacteristic
42#17985967C2211yescharacteristic
43#17985966C2211yescharacteristic
44#17985965C2211yescharacteristic
45#17985964—21no—
46#17985964—21no—
47#17985961—21no—
48#17985961—21no—
49#17985957C2211yescharacteristic, complemented
50#17985956—21no—
51#17985955C2211yescharacteristic, complemented
52#17985954C2211yescharacteristic, complemented
53#17985953—21no—
54#17985951—21no—
55C4×#11765848—21no—
56#17985760C2211yescharacteristic, complemented
57#17985759C2211yescharacteristic, complemented
58#17985758C2211yescharacteristic, complemented
59#17985754C2211yescharacteristic, complemented
60#17985753C2211yescharacteristic, complemented
61#17985753C2211yescharacteristic, complemented
62C2×#108×C71C2211yescharacteristic, complemented
63C2×#104×C71C2211yescharacteristic
64#416×C71C2211yescharacteristic
65#408×C71C2211yescharacteristic
66#405×C71C2211yescharacteristic, complemented
67#339×C71C2211yescharacteristic, complemented
68#336×C71C2211yescharacteristic, complemented
69C2×#11765866C2×C411yescharacteristic
70C2×#11765865—21no—
71C2×#11765865C2311yescharacteristic
72C2×#11765864—21no—
73C2×#11765864C2×C411yescharacteristic
74#41×D71—22no—
75#41×D71—22no—
76#41×D71—22no—
77#41×D71—22no—
78C2×Q8×D71C2×C411yescharacteristic
79C2×D4×D71—21no—
80C2×D4×D71C2×C411yescharacteristic
81C22×C4×D71—21no—
82C22×C4×D71—21no—
83C22×C4×D71C2311yescharacteristic
84C2×#11765849C2311yescharacteristic
85C2×#11765849C2311yescharacteristic
86C2×#11765848—21no—
87C2×#11765848—22no—
88C2×#11765848—22no—
89C2×#11765848—22no—
90C2×#11765848—22no—
91C2×#11765848—21no—
92C2×#11765848C2×C411yescharacteristic
93C2×#11765848C2×C411yescharacteristic
94C2×#11765848C2×C411yescharacteristic
95C2×#11765848C2×C411yescharacteristic
96C2×#11765848D411yescharacteristic
97C2×#11765848D411yescharacteristic
98C2×#11765848D411yescharacteristic
99C2×#11765848D411yescharacteristic
100M16×D71—22no—
101M16×D71—22no—
102M16×D71—22no—
103M16×D71D414yes—
104C22×C71⋊C8C2311yescharacteristic
105C22×C71⋊C8C2311yescharacteristic
106C2×C8×D71—21no—
107C2×C8×D71—21no—
108#14556087C2311yescharacteristic
109#14556086C2×C411yescharacteristic
110#14556086C2×C411yescharacteristic
111#14556085—21no—
112#14556084—21no—
113C4⋊C4×D71C2×C411yescharacteristic
114C4⋊C4×D71C2×C411yescharacteristic
115C22⋊C4×D71—21no—
116C2×C4×Dic71—21no—
117C2×C4×Dic71C2311yescharacteristic
118C42×D71—21no—
119C42×D71—22no—
120C42×D71—22no—
121#14556064—22no—
122#14556063—22no—
123#14556063—22no—
124#14556056—22no—
125#14556055—22no—
126#14556054—22no—
127#14556053C2×C411yescharacteristic, complemented
128#14556053C2×C411yescharacteristic, complemented
129#14556052C2×C411yescharacteristic, complemented
130#14556052C2×C411yescharacteristic, complemented
131#14556051C2×C411yescharacteristic, complemented
132#14556051C2×C411yescharacteristic, complemented
133#14556050C2×C411yescharacteristic, complemented
134#14556050C2×C411yescharacteristic, complemented
135#14556049C2×C411yescharacteristic, complemented
136#14556049C2×C411yescharacteristic, complemented
137#14556048C2×C411yescharacteristic, complemented
138#14556048C2×C411yescharacteristic, complemented
139C22⋊(C71⋊C8)—21no—
140C22⋊(C71⋊C8)—21no—
141(C2×D71)⋊C8—21no—
142(C2×D71)⋊C8—21no—
143(C2×D71)⋊C8—21no—
144(C2×D71)⋊C8—21no—
145#14556039—21no—
146#14556038—21no—
147#14556038—21no—
148C4×C71⋊C8—21no—
149C8×Dic71—21no—
150C8×Dic71—21no—
151C2×#41×C71C2311yescharacteristic
152C2×M16×C71C2311yescharacteristic
153C2×M16×C71C2311yescharacteristic
154C22×C8×C71C2311yescharacteristic
155C22×C8×C71C2311yescharacteristic
156#117×C71C2311yescharacteristic
157C2×C42×C71C2311yescharacteristic
158#108×C71—22no—
159#104×C71—22no—
160#103×C71C2×C411yescharacteristic, complemented
161#103×C71C2×C411yescharacteristic, complemented
162#102×C71C2×C411yescharacteristic, complemented
163#102×C71C2×C411yescharacteristic, complemented
164C22⋊C8×C71—21no—
165C22⋊C8×C71—21no—
166#97×C71—21no—
167C4×C8×C71—21no—
168C23×D71—21no—
169C23×D71#4111yescharacteristic
170#11765866—22no—
171#11765866—22no—
172#11765865—21no—
173#11765865—21no—
174#11765865—21no—
175#11765865—21no—
176#11765865—42no—
177#11765865—42no—
178#11765864—22no—
179#11765864—22no—
180#11765864—42no—
181#11765864—42no—
182C2×Dic142—21no—
183C2×Dic142C22×C411yescharacteristic
184Q8×D71—22no—
185Q8×D71—22no—
186C2×D284—21no—
187C2×D284C22×C411yescharacteristic
188C2×C22⋊D71—21no—
189C2×C22⋊D71—21no—
190C2×C22⋊D71—21no—
191D4×D71—22no—
192D4×D71—22no—
193D4×D71—42no—
194D4×D71—42no—
195C22×Dic71—21no—
196C22×Dic71—21no—
197C22×Dic71#4111yescharacteristic
198C2×C4×D71—21no—
199C2×C4×D71—21no—
200C2×C4×D71—21no—
201C2×C4×D71—21no—
202C2×C4×D71—21no—
203C2×C4×D71—42no—
204C2×C4×D71—42no—
205C2×C4×D71—42no—
206C2×C4×D71—42no—
207C2×C4×D71—42no—
208C2×C4×D71C22×C411yescharacteristic
209C2×C4×D71C22×C411yescharacteristic
210C2×C4×D71C2×D412yes—
211C2×C4×D71C2×D411yescharacteristic
212C2×C4×D71C2×D411yescharacteristic
213C2×C4×D71#4112yes—
214C2×C4×D71#4112yes—
215C2×C4×D71#4112yes—
216#11765849—21no—
217#11765849—21no—
218#11765849—21no—
219#11765849C2×D412yes—
220#11765848—22no—
221#11765848—22no—
222#11765848—22no—
223#11765848—22no—
224#11765848—24no—
225#11765848—22no—
226#11765848—22no—
227#11765848—22no—
228#11765848—22no—
229#11765848—42no—
230C2×C71⋊C8—21no—
231C2×C71⋊C8—21no—
232C2×C71⋊C8—21no—
233C2×C71⋊C8—21no—
234C2×C71⋊C8—21no—
235C2×C71⋊C8—21no—
236C2×C71⋊C8C22×C411yescharacteristic
237C2×C71⋊C8C22×C411yescharacteristic
238C2×C71⋊C8C2×D411yescharacteristic
239C2×C71⋊C8C2×D411yescharacteristic
240C8×D71—24no—
241C8×D71—42no—
242C4⋊Dic71C22×C411yescharacteristic
243C4⋊Dic71C22×C411yescharacteristic
244Dic71⋊C4—21no—
245Dic71⋊C4—21no—
246C22⋊Dic71—21no—
247(C2×D71)⋊C4—21no—
248(C2×D71)⋊C4—21no—
249C4×Dic71—21no—
250C4×Dic71—21no—
251C4×Dic71—21no—
252C4×Dic71—21no—
253C4×Dic71—21no—
254C4×Dic71—42no—
255#41×C71—21no—
256#41×C71—21no—
257#41×C71—21no—
258#41×C71—21no—
259C2×Q8×C71C22×C411yescharacteristic
260C2×D4×C71—21no—
261C2×D4×C71C22×C411yescharacteristic
262C22×C4×C71—21no—
263C22×C4×C71—21no—
264C22×C4×C71C2411yescharacteristic
265M16×C71—21no—
266M16×C71—21no—
267M16×C71—21no—
268M16×C71C2×D412yes—
269C2×C8×C71—21no—
270C2×C8×C71—21no—
271C2×C8×C71—21no—
272C2×C8×C71—21no—
273C2×C8×C71—21no—
274C2×C8×C71—21no—
275C2×C8×C71C22×C411yescharacteristic
276C2×C8×C71C22×C411yescharacteristic
277C2×C8×C71C2×D411yescharacteristic
278C2×C8×C71C2×D411yescharacteristic
279C4⋊C4×C71C22×C411yescharacteristic
280C4⋊C4×C71C22×C411yescharacteristic
281C22⋊C4×C71—21no—
282C42×C71—21no—
283C42×C71—21no—
284C42×C71—21no—
285C23×C71—21no—
286C23×C71C2×#4111yescharacteristic
287C22×D71—21no—
288C22×D71—41no—
289C22×D71—41no—
290C22×D71—42no—
291C22×D71—81no—
292C22×D71—81no—
293C22×D71C4×D411yescharacteristic
294C22×D71C4×D411yescharacteristic
295C22×D71#12412yes—
296C22×D71#12612yes—
297Q8×C71—21no—
298Q8×C71—21no—
299D4×C71—21no—
300D4×C71—21no—
301D4×C71—41no—
302D4×C71—41no—
303C2×C4×C71—22no—
304C2×C4×C71—21no—
305C2×C4×C71—21no—
306C2×C4×C71—21no—
307C2×C4×C71—41no—
308C2×C4×C71—41no—
309C2×C4×C71—41no—
310C2×C4×C71—41no—
311C2×C4×C71C23×C411yescharacteristic
312C2×C4×C71C22×D411yescharacteristic
313C2×C4×C71C22×D411yescharacteristic
314C2×C4×C71C2×#4111yescharacteristic
315C2×C4×C71C2×#4111yescharacteristic
316C2×C4×C71C2×#4111yescharacteristic
317C22⋊D71—41no—
318C22⋊D71—41no—
319C22⋊D71—42no—
320C22⋊D71—42no—
321C2×Dic71—22no—
322C2×Dic71—21no—
323C2×Dic71—21no—
324C2×Dic71—21no—
325C2×Dic71—41no—
326C2×Dic71—41no—
327C2×Dic71—42no—
328C2×Dic71C4×D411yescharacteristic
329C2×Dic71C4×D411yescharacteristic
330C2×Dic71#12412yes—
331C2×Dic71#12612yes—
332D284—21no—
333D284—21no—
334D284—42no—
335C4×D71—48no—
336C4×D71—42no—
337C4×D71—41no—
338C4×D71—41no—
339C4×D71—42no—
340C4×D71—81no—
341C4×D71—81no—
342C4×D71#11712yes—
343C4×D71#11712yes—
344C4×D71C4×D412yes—
345C4×D71C4×D412yes—
346C4×D71#12112yes—
347C4×D71#12112yes—
348C4×D71#12312yes—
349C4×D71#12312yes—
350Dic142—21no—
351Dic142—21no—
352Dic142—42no—
353C8×C71—21no—
354C8×C71—21no—
355C8×C71—22no—
356C8×C71—21no—
357C8×C71—21no—
358C8×C71—41no—
359C71⋊C8—21no—
360C71⋊C8—21no—
361C71⋊C8—22no—
362C71⋊C8—21no—
363C71⋊C8—21no—
364C71⋊C8—41no—
365C22×C71—21no—
366C22×C71—21no—
367C22×C71—41no—
368C22×C71—41no—
369C22×C71—41no—
370C22×C71C2×C4×D411yescharacteristic
371C22×C71C2×#12411yescharacteristic
372C22×C71C2×#12611yescharacteristic
373C2×D71—21no—
374C2×D71—21no—
375C2×D71—21no—
376C2×D71—21no—
377C2×D71—42no—
378C2×D71—42no—
379C2×D71—41no—
380C2×D71—41no—
381C2×D71—41no—
382C2×D71—84no—
383C2×D71#38812yes—
384C2×D71#38812yes—
385C4×C71—42no—
386C4×C71—41no—
387C4×C71—41no—
388C4×C71—41no—
389C4×C71C2×#11711yescharacteristic
390C4×C71C2×C4×D411yescharacteristic
391C4×C71C2×#12111yescharacteristic
392C4×C71C2×#12311yescharacteristic
393Dic71—42no—
394Dic71—41no—
395Dic71—41no—
396Dic71—41no—
397Dic71#38812yes—
398Dic71#38812yes—
399#21071—711nomaximal, Sylow
400C2×C71—21no—
401C2×C71—21no—
402C2×C71—81no—
403C2×C71C2×#38811yescharacteristic
404C2×C71#295611yescharacteristic
405C2×C71#295611yescharacteristic
406D71—22no—
407D71—22no—
408D71—81no—
409C2×#430—711no—
410C22×#104—711no—
411#2896—711no—
412#2879—711no—
413#2873—711no—
414#1929—711no—
415#1929—711no—
416#1929—711no—
417#1929—711no—
418#1929—711no—
419#1929—711no—
420#1929—711no—
421#1929D7111yescharacteristic, complemented
422C2×#339—711no—
423#1728—711no—
424C71#2107111yescharacteristic, complemented, Sylow
425C22×#41—711no—
426C22×M16—711no—
427C22×M16—711no—
428C22×M16—711no—
429C22×M16—711no—
430C2×#117—711no—
431C22×C42—711no—
432#430—1424no—
433C2×#108—711no—
434C2×#108—711no—
435C2×#108—711no—
436C2×#108C2×D7111yescharacteristic, complemented
437C2×#104—711no—
438C2×#104—711no—
439C2×#104—711no—
440C2×#104—1424no—
441C2×#104C2×D7111yescharacteristic
442#419—711no—
443#419—711no—
444#418—711no—
445#418—711no—
446#417—711no—
447#417—711no—
448#417—711no—
449#417—711no—
450#416—711no—
451#416—711no—
452#416—711no—
453#416C2×D7111yescharacteristic
454#408—711no—
455#408—711no—
456#408—711no—
457#408—1421no—
458#408—1421no—
459#408C2×D7111yescharacteristic
460#407—1421no—
461#407—1421no—
462#405—711no—
463#405—711no—
464#405—711no—
465#405—1421no—
466#405—1421no—
467#405C2×D7111yescharacteristic, complemented
468C4×M16—1421no—
469C4×M16—1421no—
470#339—711no—
471#339—711no—
472#339—711no—
473#339C2×D7111yescharacteristic, complemented
474#336—711no—
475#336—711no—
476#336—711no—
477#336C2×D7111yescharacteristic, complemented
478C2×#41—711no—
479C2×#41—711no—
480C2×#41—711no—
481C2×#41—1421no—
482C2×#41—1422no—
483C2×#41—1422no—
484C2×#41—1422no—
485C2×#41—1422no—
486C2×#41—1421no—
487C2×#41C22×D7111yescharacteristic
488C22×Q8—711no—
489C22×D4—711no—
490C22×D4—1421no—
491C23×C4—711no—
492C23×C4—1421no—
493C23×C4—1421no—
494C2×M16—711no—
495C2×M16—711no—
496C2×M16—711no—
497C2×M16—711no—
498C2×M16—711no—
499C2×M16—711no—
500C2×M16—711no—
501C2×M16—711no—
502C2×M16—711no—
503C2×M16—714no—
504C2×M16—711no—
505C2×M16—1421no—
506C2×M16—1421no—
507C2×M16—1422no—
508C2×M16—1422no—
509C2×M16—1422no—
510C2×M16—1422no—
511C2×M16—1422no—
512C2×M16—1422no—
513C2×M16—1422no—
514C2×M16C22×D7111yescharacteristic
515C2×M16C22×D7111yescharacteristic
516C22×C8—711no—
517C22×C8—711no—
518C22×C8—1421no—
519C22×C8—1421no—
520C22×C8C22×D7111yescharacteristic
521C22×C8C22×D7111yescharacteristic
522#117—711no—
523#117—711no—
524#117—711no—
525#117—1421no—
526#117—1421no—
527#117C22×D7111yescharacteristic
528C2×C4⋊C4—711no—
529C2×C4⋊C4—711no—
530C2×C22⋊C4—1421no—
531C2×C42—711no—
532C2×C42—1422no—
533C2×C42—1422no—
534C2×C42—1421no—
535C2×C42—1421no—
536C2×C42C22×D7111yescharacteristic
537#108—22no—
538#108—1422no—
539#108—1422no—
540#108—1422no—
541#104—22no—
542#104—1422no—
543#104—1422no—
544#104—1422no—
545#103—711no—
546#103—711no—
547#103—711no—
548#103—711no—
549#103—711no—
550#103—711no—
551#103C4×D7111yescharacteristic, complemented
552#103C4×D7111yescharacteristic, complemented
553#102—711no—
554#102—711no—
555#102—711no—
556#102—711no—
557#102—711no—
558#102—711no—
559#102C4×D7111yescharacteristic, complemented
560#102C4×D7111yescharacteristic, complemented
561C22⋊C8—21no—
562C22⋊C8—21no—
563C22⋊C8—1421no—
564C22⋊C8—1421no—
565C22⋊C8—1421no—
566C22⋊C8—1421no—
567C22⋊C8—1421no—
568C22⋊C8—1421no—
569#97—21no—
570#97—1421no—
571#97—1421no—
572#97—1421no—
573C4×C8—21no—
574C4×C8—1421no—
575C4×C8—1421no—
576C4×C8—1421no—
577C24—711no—
578C24—1421no—
579#41—21no—
580#41—21no—
581#41—21no—
582#41—21no—
583#41—2842no—
584#41—2842no—
585#41—2842no—
586#41—2842no—
587#41—1422no—
588#41—1422no—
589#41—1422no—
590#41—1422no—
591#41—1421no—
592#41—1421no—
593#41—1421no—
594#41—1421no—
595C2×Q8—711no—
596C2×Q8—1421no—
597C2×Q8—1422no—
598C2×Q8—1422no—
599C2×Q8C2×C4×D7111yescharacteristic
600C2×D4—21no—
601C2×D4—2842no—
602C2×D4—2842no—
603C2×D4—711no—
604C2×D4—1421no—
605C2×D4—1422no—
606C2×D4—1422no—
607C2×D4—1421no—
608C2×D4—1421no—
609C2×D4—1421no—
610C2×D4C2×C4×D7111yescharacteristic
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—2842no—
614C22×C4—2842no—
615C22×C4—2842no—
616C22×C4—2842no—
617C22×C4—2842no—
618C22×C4—711no—
619C22×C4—711no—
620C22×C4—711no—
621C22×C4—712no—
622C22×C4—711no—
623C22×C4—711no—
624C22×C4—712no—
625C22×C4—712no—
626C22×C4—712no—
627C22×C4—1421no—
628C22×C4—1421no—
629C22×C4—1421no—
630C22×C4—1421no—
631C22×C4—1421no—
632C22×C4—1421no—
633C22×C4—1421no—
634C22×C4C23×D7111yescharacteristic
635M16—21no—
636M16—21no—
637M16—21no—
638M16—2842no—
639M16—712no—
640M16—1422no—
641M16—1422no—
642M16—1422no—
643M16—1422no—
644M16—1424no—
645M16—1422no—
646M16—1422no—
647M16—1422no—
648M16—1422no—
649M16—1421no—
650M16—1421no—
651M16—1421no—
652M16D4×D7112yes—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—2842no—
660C2×C8—711no—
661C2×C8—711no—
662C2×C8—711no—
663C2×C8—711no—
664C2×C8—1424no—
665C2×C8—1421no—
666C2×C8—1421no—
667C2×C8—1421no—
668C2×C8—1421no—
669C2×C8—1421no—
670C2×C8—1421no—
671C2×C8C2×C4×D7111yescharacteristic
672C2×C8C2×C4×D7111yescharacteristic
673C2×C8D4×D7111yescharacteristic
674C2×C8D4×D7111yescharacteristic
675C4⋊C4—711no—
676C4⋊C4—711no—
677C4⋊C4—1421no—
678C4⋊C4—1421no—
679C4⋊C4C2×C4×D7111yescharacteristic
680C4⋊C4C2×C4×D7111yescharacteristic
681C22⋊C4—21no—
682C22⋊C4—1421no—
683C22⋊C4—1421no—
684C22⋊C4—1421no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—2842no—
689C42—1421no—
690C42—1421no—
691C42—1421no—
692C42—1421no—
693C42—1421no—
694C23—21no—
695C23—2841no—
696C23—2841no—
697C23—2842no—
698C23—5681no—
699C23—5681no—
700C23—712no—
701C23—712no—
702C23—711no—
703C23—711no—
704C23—1421no—
705C23#41×D7111yescharacteristic
706Q8—21no—
707Q8—21no—
708Q8—2842no—
709Q8—1421no—
710Q8—1421no—
711D4—21no—
712D4—21no—
713D4—41no—
714D4—41no—
715D4—2842no—
716D4—2842no—
717D4—2841no—
718D4—2841no—
719D4—2842no—
720D4—1421no—
721D4—1421no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—2848no—
731C2×C4—2842no—
732C2×C4—2842no—
733C2×C4—2841no—
734C2×C4—2841no—
735C2×C4—2842no—
736C2×C4—2841no—
737C2×C4—2841no—
738C2×C4—5681no—
739C2×C4—5681no—
740C2×C4—711no—
741C2×C4—711no—
742C2×C4—712no—
743C2×C4—712no—
744C2×C4—712no—
745C2×C4—712no—
746C2×C4—712no—
747C2×C4—712no—
748C2×C4—712no—
749C2×C4—712no—
750C2×C4—712no—
751C2×C4—712no—
752C2×C4—1422no—
753C2×C4—1421no—
754C2×C4—1421no—
755C2×C4—1421no—
756C2×C4C22×C4×D7111yescharacteristic
757C2×C4C2×D4×D7111yescharacteristic
758C2×C4C2×D4×D7111yescharacteristic
759C2×C4#41×D7111yescharacteristic
760C2×C4#41×D7111yescharacteristic
761C2×C4#41×D7111yescharacteristic
762C8—21no—
763C8—21no—
764C8—22no—
765C8—21no—
766C8—21no—
767C8—41no—
768C8—2841no—
769C8—1421no—
770C8—1421no—
771C8—1422no—
772C8—1421no—
773C8—1421no—
774C22—21no—
775C22—21no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—2842no—
780C22—2842no—
781C22—2841no—
782C22—2841no—
783C22—2841no—
784C22—5684no—
785C22—712no—
786C22—712no—
787C22—1421no—
788C22—1421no—
789C22—1421no—
790C22—1421no—
791C22C4×D4×D7111yescharacteristic
792C22#124×D7111yescharacteristic
793C22#126×D7111yescharacteristic
794C4—42no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—2842no—
799C4—2841no—
800C4—2841no—
801C4—2841no—
802C4—712no—
803C4—712no—
804C4#117×D7111yescharacteristic
805C4C4×D4×D7111yescharacteristic
806C4#121×D7111yescharacteristic
807C4#123×D7111yescharacteristic
808C2—21no—
809C2—21no—
810C2—81no—
811C2—5681no—
812C2—1422no—
813C2—1422no—
814C2#388×D7111yescharacteristic
815C2#2259724511yescharacteristic
816C2#2259724811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#1929C2
socleC22×C71C2×C4×D4
prime radicalC2×#41×D71C22
cosocleC22×C4×C71C24
hypercenter#1929D71
hypocenterC71#21071
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
1. C2×#17986046C2semidirect
5. #22596756C2semidirect
6. #22588991C2semidirect
7. #22588990C2semidirect
8. #22588989C2semidirect
9. #22588988C2semidirect
10. #22588987C2semidirect
11. #22588986C2semidirect
12. #22588985C2semidirect
13. #339×D71C2semidirect
14. #22588032C2semidirect
15. C71×#1929C2semidirect
24. C2×#14556064C22semidirect
25. C2×#14556063C22semidirect
26. C2×#14556063C22semidirect
31. #17986006C4semidirect
32. #17986006C4semidirect
33. #17986002C4semidirect
34. #17986002C4semidirect
35. #17985999C4semidirect
36. #17985999C4semidirect
37. #17985997C4semidirect
38. #17985997C4semidirect
49. #17985957C22semidirect
51. #17985955C22semidirect
52. #17985954C22semidirect
56. #17985760C22semidirect
57. #17985759C22semidirect
58. #17985758C22semidirect
59. #17985754C22semidirect
60. #17985753C22semidirect
61. #17985753C22semidirect
62. C2×#108×C71C22semidirect
66. #405×C71C22semidirect
67. #339×C71C22semidirect
68. #336×C71C22semidirect
127. #14556053C2×C4semidirect
128. #14556053C2×C4semidirect
129. #14556052C2×C4semidirect
130. #14556052C2×C4semidirect
131. #14556051C2×C4semidirect
132. #14556051C2×C4semidirect
133. #14556050C2×C4semidirect
134. #14556050C2×C4semidirect
135. #14556049C2×C4semidirect
136. #14556049C2×C4semidirect
137. #14556048C2×C4semidirect
138. #14556048C2×C4semidirect
160. #103×C71C2×C4semidirect
161. #103×C71C2×C4semidirect
162. #102×C71C2×C4semidirect
163. #102×C71C2×C4semidirect
421. #1929D71semidirect
424. C71#21071semidirect
436. C2×#108C2×D71semidirect
467. #405C2×D71semidirect
473. #339C2×D71semidirect
477. #336C2×D71semidirect
551. #103C4×D71semidirect
552. #103C4×D71semidirect
559. #102C4×D71semidirect
560. #102C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860462
C2×#104×D712
#225968552
#225967822
#225967562
#225889912
#225889902
#225889892
#225889882
#225889872
#225889862
#225889852
#339×D712
#225880322
C71×#19292
#2107171