Finite Group Databasebeta

← #32018238

Subgroups — #32018238

Order 18176.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986116C211yesmaximal, characteristic, complemented
2#22597067C211yesmaximal, characteristic, complemented
3C2×#17986016C211yesmaximal, characteristic, complemented
4#22596789C211yesmaximal, characteristic, complemented
5#22589234C211yesmaximal, characteristic, complemented
6#22589046C211yesmaximal, characteristic, complemented
7#22588990C211yesmaximal, characteristic, complemented
8#22588789C211yesmaximal, characteristic, complemented
9#22588669C211yesmaximal, characteristic, complemented
10#22588669C211yesmaximal, characteristic, complemented
11#22588617C211yesmaximal, characteristic, complemented
12#22588547C211yesmaximal, characteristic, complemented
13#22588187C211yesmaximal, characteristic, complemented
14#22588108C211yesmaximal, characteristic, complemented
15C71×#3002C211yesmaximal, characteristic
16C2×#14556135C2211yescharacteristic
17C2×#14556135C2211yescharacteristic
18C2×#14556135C2211yescharacteristic, complemented
19C22×#11765849C2211yescharacteristic
20C2×#14556087C2211yescharacteristic
21#17986116—24no—
22#17986077—21no—
23#17986071—21no—
24#17986071—21no—
25D4×C71⋊C8—21no—
26C2×#14556064C2211yescharacteristic, complemented
27C2×#14556064C2211yescharacteristic, complemented
28#17986026C2211yescharacteristic, complemented
29#17986016—24no—
30C2×#14556055C2211yescharacteristic
31C2×#14556055C2211yescharacteristic
32C2×#14556055C2211yescharacteristic
33C2×#14556055C2211yescharacteristic
34C2×#14556055C2211yescharacteristic, complemented
35C2×#14556055C2211yescharacteristic, complemented
36#17985966—21no—
37#17985966—21no—
38#17985966C2211yescharacteristic
39#17985966C2211yescharacteristic
40#17985966C2211yescharacteristic, complemented
41#17985963—21no—
42#17985963C2211yescharacteristic
43C2×C22⋊(C71⋊C8)—21no—
44C2×C22⋊(C71⋊C8)C2211yescharacteristic
45#17985955C2211yescharacteristic, complemented
46C2×#14556038C2211yescharacteristic, complemented
47C2×C8×Dic71C2211yescharacteristic, complemented
48#17985764C2211yescharacteristic, complemented
49#17985764C2211yescharacteristic, complemented
50#17985758C2211yescharacteristic, complemented
51#17985758C2211yescharacteristic, complemented
52#17985753C2211yescharacteristic, complemented
53#17985753C2211yescharacteristic, complemented
54C22×#41×C71C2211yescharacteristic
55C2×#135×C71C2211yescharacteristic
56C2×#135×C71C2211yescharacteristic
57#525×C71C2211yescharacteristic
58#452×C71C411yescharacteristic, complemented
59#452×C71C411yescharacteristic, complemented
60#451×C71C411yescharacteristic, complemented
61#450×C71C411yescharacteristic, complemented
62#449×C71C411yescharacteristic, complemented
63#449×C71C411yescharacteristic, complemented
64#448×C71C411yescharacteristic, complemented
65#447×C71C411yescharacteristic, complemented
66#416×C71C2211yescharacteristic
67#416×C71C2211yescharacteristic
68C2×C22⋊C8×C71C2211yescharacteristic
69#14556135—22no—
70#14556135—22no—
71#14556135—22no—
72#14556135—41no—
73#14556135—41no—
74#14556135—41no—
75C2×#11765849—21no—
76C2×#11765849—21no—
77C2×#11765849—21no—
78C2×#11765849—22no—
79C2×#11765849—21no—
80C2×#11765849—41no—
81C2×#11765849C2311yescharacteristic
82C2×#11765849C2311yescharacteristic
83C2×#11765849C2311yescharacteristic
84C2×#11765849C2311yescharacteristic
85C22×C71⋊C8—21no—
86C22×C71⋊C8—21no—
87C22×C71⋊C8—21no—
88C22×C71⋊C8—21no—
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91#14556087—22no—
92#14556087—41no—
93C2×C4⋊Dic71—21no—
94C2×C22⋊Dic71—21no—
95C2×C4×Dic71C2311yescharacteristic
96C2×C4×Dic71C2311yescharacteristic
97#14556064—22no—
98#14556064—41no—
99C4⋊(C71⋊C8)—21no—
100C4⋊(C71⋊C8)—21no—
101#14556055—22no—
102#14556055—22no—
103#14556055—22no—
104#14556055—22no—
105#14556055—41no—
106#14556055D414yescomplemented
107C22⋊(C71⋊C8)—21no—
108C22⋊(C71⋊C8)—21no—
109C22⋊(C71⋊C8)—21no—
110C22⋊(C71⋊C8)—21no—
111C22⋊(C71⋊C8)—21no—
112C22⋊(C71⋊C8)—21no—
113C22⋊(C71⋊C8)—21no—
114C22⋊(C71⋊C8)—21no—
115C22⋊(C71⋊C8)D411yescharacteristic
116C22⋊(C71⋊C8)D411yescharacteristic
117C22⋊(C71⋊C8)D411yescharacteristic
118C22⋊(C71⋊C8)D411yescharacteristic
119#14556039—21no—
120#14556038—41no—
121C4×C71⋊C8—21no—
122C8×Dic71—22no—
123C2×#41×C71—21no—
124C2×#41×C71—21no—
125C2×#41×C71—22no—
126C2×#41×C71—22no—
127C2×#41×C71—41no—
128C2×#41×C71—41no—
129C2×#41×C71C2×C411yescharacteristic
130C2×#41×C71C2×C411yescharacteristic
131C2×#41×C71C2311yescharacteristic
132C2×#41×C71C2311yescharacteristic
133C2×#41×C71C2311yescharacteristic
134C22×Q8×C71C2×C411yescharacteristic
135C22×D4×C71—21no—
136C22×D4×C71C2×C411yescharacteristic
137C23×C4×C71—21no—
138C23×C4×C71C2311yescharacteristic
139#135×C71—22no—
140#135×C71—22no—
141#135×C71—41no—
142#135×C71—41no—
143C2×Q16×C71C2×C411yescharacteristic
144C2×Q16×C71C2×C411yescharacteristic
145C2×SD16×C71C2×C411yescharacteristic
146C2×SD16×C71C2×C411yescharacteristic
147C2×SD16×C71C2×C411yescharacteristic
148C2×SD16×C71C2×C411yescharacteristic
149C2×D8×C71C2×C411yescharacteristic
150C2×D8×C71C2×C411yescharacteristic
151C22×C8×C71C2311yescharacteristic
152C22×C8×C71C2311yescharacteristic
153#123×C71—21no—
154C22⋊Q8×C71C2×C411yescharacteristic
155C22⋊Q8×C71C2×C411yescharacteristic
156#121×C71C2×C411yescharacteristic
157#121×C71C2×C411yescharacteristic
158#120×C71—21no—
159C4×D4×C71—21no—
160C4×D4×C71—21no—
161#117×C71C2311yescharacteristic
162#103×C71C2×C411yescharacteristic
163#103×C71C2×C411yescharacteristic
164#103×C71C2×C411yescharacteristic
165#103×C71C2×C411yescharacteristic
166#102×C71C2×C411yescharacteristic
167#102×C71C2×C411yescharacteristic
168#102×C71C2×C411yescharacteristic
169#102×C71C2×C411yescharacteristic
170C22⋊C8×C71C2×C411yescharacteristic
171C22⋊C8×C71C2×C411yescharacteristic
172C22⋊C8×C71C2×C411yescharacteristic
173C22⋊C8×C71C2×C411yescharacteristic
174C22×Dic71—21no—
175C22×Dic71—21no—
176#11765849—21no—
177#11765849—21no—
178#11765849—21no—
179#11765849—21no—
180#11765849—21no—
181#11765849—21no—
182#11765849—21no—
183#11765849—42no—
184#11765849—42no—
185#11765849—42no—
186#11765849—42no—
187#11765849C2×D412yes—
188C2×C71⋊C8—21no—
189C2×C71⋊C8—21no—
190C2×C71⋊C8—21no—
191C2×C71⋊C8—21no—
192C2×C71⋊C8—21no—
193C2×C71⋊C8—21no—
194C2×C71⋊C8—21no—
195C2×C71⋊C8—21no—
196C2×C71⋊C8—42no—
197C2×C71⋊C8—42no—
198C2×C71⋊C8—42no—
199C2×C71⋊C8—42no—
200C2×C71⋊C8C2×D411yescharacteristic
201C2×C71⋊C8C2×D411yescharacteristic
202C2×C71⋊C8C2×D411yescharacteristic
203C2×C71⋊C8C2×D411yescharacteristic
204C4⋊Dic71—42no—
205C22⋊Dic71—42no—
206C4×Dic71—21no—
207C4×Dic71—21no—
208C4×Dic71—21no—
209C4×Dic71C2×D412yes—
210C24×C71—21no—
211C24×C71#4111yescharacteristic
212#41×C71—21no—
213#41×C71—21no—
214#41×C71—22no—
215#41×C71—22no—
216#41×C71—21no—
217#41×C71—21no—
218#41×C71—21no—
219#41×C71—21no—
220#41×C71—21no—
221#41×C71—21no—
222#41×C71—21no—
223#41×C71—21no—
224#41×C71—42no—
225#41×C71—42no—
226#41×C71—41no—
227#41×C71—41no—
228#41×C71—42no—
229#41×C71—42no—
230#41×C71C2×D412yes—
231#41×C71#4112yes—
232C2×Q8×C71—21no—
233C2×Q8×C71—22no—
234C2×Q8×C71—41no—
235C2×Q8×C71C22×C411yescharacteristic
236C2×Q8×C71C22×C411yescharacteristic
237C2×Q8×C71C22×C411yescharacteristic
238C2×D4×C71—21no—
239C2×D4×C71—22no—
240C2×D4×C71—21no—
241C2×D4×C71—21no—
242C2×D4×C71—21no—
243C2×D4×C71—21no—
244C2×D4×C71—21no—
245C2×D4×C71—21no—
246C2×D4×C71—21no—
247C2×D4×C71—41no—
248C2×D4×C71—42no—
249C2×D4×C71—42no—
250C2×D4×C71C22×C411yescharacteristic
251C2×D4×C71C22×C411yescharacteristic
252C2×D4×C71C22×C411yescharacteristic
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—21no—
259C22×C4×C71—21no—
260C22×C4×C71—21no—
261C22×C4×C71—21no—
262C22×C4×C71—21no—
263C22×C4×C71—42no—
264C22×C4×C71—42no—
265C22×C4×C71C22×C411yescharacteristic
266C22×C4×C71C22×C411yescharacteristic
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2×D411yescharacteristic
269C22×C4×C71#4111yescharacteristic
270C22×C4×C71C2411yescharacteristic
271Q16×C71—22no—
272Q16×C71—41no—
273SD16×C71—22no—
274SD16×C71—22no—
275SD16×C71—41no—
276SD16×C71—41no—
277D8×C71—22no—
278D8×C71—41no—
279C2×C8×C71—21no—
280C2×C8×C71—21no—
281C2×C8×C71—21no—
282C2×C8×C71—21no—
283C2×C8×C71C22×C411yescharacteristic
284C2×C8×C71C22×C411yescharacteristic
285C2×C8×C71C22×C411yescharacteristic
286C2×C8×C71C22×C411yescharacteristic
287C4⋊C4×C71—21no—
288C4⋊C4×C71—21no—
289C4⋊C4×C71C22×C411yescharacteristic
290C4⋊C4×C71C22×C411yescharacteristic
291C22⋊C4×C71—21no—
292C22⋊C4×C71—21no—
293C22⋊C4×C71—21no—
294C22⋊C4×C71—21no—
295C22⋊C4×C71—21no—
296C42×C71—21no—
297C23×C71—21no—
298C23×C71—21no—
299C23×C71—21no—
300C23×C71—21no—
301C23×C71—21no—
302C23×C71—41no—
303C23×C71—41no—
304C23×C71—42no—
305C23×C71—42no—
306C23×C71—81no—
307C23×C71C4×D411yescharacteristic
308C23×C71C4×D411yescharacteristic
309C23×C71C2×#4111yescharacteristic
310Q8×C71—21no—
311Q8×C71—21no—
312Q8×C71—21no—
313Q8×C71—21no—
314Q8×C71—21no—
315Q8×C71—42no—
316Q8×C71C4×D412yes—
317D4×C71—22no—
318D4×C71—22no—
319D4×C71—21no—
320D4×C71—21no—
321D4×C71—21no—
322D4×C71—21no—
323D4×C71—21no—
324D4×C71—42no—
325D4×C71—42no—
326D4×C71—42no—
327D4×C71—42no—
328D4×C71—41no—
329D4×C71—41no—
330D4×C71—41no—
331D4×C71—41no—
332D4×C71—81no—
333D4×C71C4×D412yes—
334C2×C4×C71—21no—
335C2×C4×C71—21no—
336C2×C4×C71—21no—
337C2×C4×C71—21no—
338C2×C4×C71—21no—
339C2×C4×C71—21no—
340C2×C4×C71—21no—
341C2×C4×C71—21no—
342C2×C4×C71—21no—
343C2×C4×C71—22no—
344C2×C4×C71—21no—
345C2×C4×C71—21no—
346C2×C4×C71—22no—
347C2×C4×C71—21no—
348C2×C4×C71—21no—
349C2×C4×C71—21no—
350C2×C4×C71—21no—
351C2×C4×C71—42no—
352C2×C4×C71—42no—
353C2×C4×C71—42no—
354C2×C4×C71—41no—
355C2×C4×C71—41no—
356C2×C4×C71—41no—
357C2×C4×C71—41no—
358C2×C4×C71C4×D411yescharacteristic
359C2×C4×C71C4×D411yescharacteristic
360C2×C4×C71C23×C411yescharacteristic
361C2×C4×C71C22×D411yescharacteristic
362C2×C4×C71C22×D411yescharacteristic
363C2×C4×C71C2×#4111yescharacteristic
364C2×C4×C71H(5,𝔽2)11yescharacteristic
365C2×C4×C71H(5,𝔽2)11yescharacteristic
366C2×Dic71—22no—
367C2×Dic71—41no—
368C2×Dic71—41no—
369C2×Dic71—41no—
370C2×Dic71—41no—
371C2×Dic71—41no—
372C8×C71—21no—
373C8×C71—21no—
374C8×C71—21no—
375C8×C71—21no—
376C71⋊C8—21no—
377C71⋊C8—21no—
378C71⋊C8—22no—
379C71⋊C8—21no—
380C71⋊C8—21no—
381C71⋊C8—41no—
382C71⋊C8—41no—
383C71⋊C8—41no—
384C22×C71—21no—
385C22×C71—21no—
386C22×C71—21no—
387C22×C71—21no—
388C22×C71—22no—
389C22×C71—21no—
390C22×C71—21no—
391C22×C71—21no—
392C22×C71—21no—
393C22×C71—41no—
394C22×C71—41no—
395C22×C71—41no—
396C22×C71—41no—
397C22×C71—41no—
398C22×C71—41no—
399C22×C71—41no—
400C22×C71—41no—
401C22×C71—81no—
402C22×C71—81no—
403C22×C71—84no—
404C22×C71C2×C4×D411yescharacteristic
405C22×C71#54611yescharacteristic
406C22×C71#55111yescharacteristic
407C4×C71—21no—
408C4×C71—21no—
409C4×C71—22no—
410C4×C71—41no—
411C4×C71—41no—
412C4×C71—41no—
413C4×C71—41no—
414C4×C71C2×C4×D411yescharacteristic
415C4×C71#51811yescharacteristic
416C4×C71D4211yescharacteristic
417C4×C71#54611yescharacteristic
418Dic71—42no—
419Dic71—81no—
420#22889—711nomaximal, Sylow
421C2×C71—21no—
422C2×C71—21no—
423C2×C71—41no—
424C2×C71—41no—
425C2×C71—42no—
426C2×C71—81no—
427C2×C71—81no—
428C2×C71#235811yescharacteristic
429C2×C71#295511yescharacteristic
430C2×C71#295711yescharacteristic
431#3002D7111yescharacteristic
432C2×#443—711no—
433#2933—711no—
434C2×#421—711no—
435#2880—711no—
436#1975—711no—
437#1937—711no—
438#1929—711no—
439#1897—711no—
440#1876—711no—
441#1876—711no—
442#1866—711no—
443#1855—711no—
444#1765—711no—
445#1750—711no—
446C71#2288911yescharacteristic, complemented, Sylow
447C22×#41C2×D7111yescharacteristic
448C2×#135C2×D7111yescharacteristic
449C2×#135C2×D7111yescharacteristic
450C2×#131—711no—
451C2×#131—711no—
452C2×#131—711no—
453C22×M16—711no—
454#525C2×D7111yescharacteristic
455C2×#117—711no—
456#452Dic7111yescharacteristic, complemented
457#452Dic7111yescharacteristic, complemented
458#451Dic7111yescharacteristic, complemented
459#450Dic7111yescharacteristic, complemented
460#449Dic7111yescharacteristic, complemented
461#449Dic7111yescharacteristic, complemented
462#448Dic7111yescharacteristic, complemented
463#447Dic7111yescharacteristic, complemented
464#443—1424no—
465#436—1421no—
466#435—1421no—
467#435—1421no—
468C8×D4—1421no—
469C2×#108—711no—
470C2×#108—711no—
471#424—711no—
472#421—1424no—
473C2×#104—711no—
474C2×#104—711no—
475C2×#104—711no—
476C2×#104—711no—
477C2×#104—711no—
478C2×#104—711no—
479#416C2×D7111yescharacteristic
480#416C2×D7111yescharacteristic
481#408—711no—
482#408—711no—
483#408—711no—
484#408—1421no—
485#408—1421no—
486#407—711no—
487#407—1421no—
488C2×C22⋊C8—711no—
489C2×C22⋊C8—1421no—
490C2×C22⋊C8C2×D7111yescharacteristic
491#405—711no—
492C2×#97—711no—
493C2×C4×C8—711no—
494#341—711no—
495#341—711no—
496#339—711no—
497#339—711no—
498#336—711no—
499#336—711no—
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×Dic7111yescharacteristic
507C2×#41C2×Dic7111yescharacteristic
508C2×#41C22×D7111yescharacteristic
509C2×#41C22×D7111yescharacteristic
510C2×#41C22×D7111yescharacteristic
511C22×Q8C2×Dic7111yescharacteristic
512C22×D4—21no—
513C22×D4C2×Dic7111yescharacteristic
514C23×C4—21no—
515C23×C4C22×D7111yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×Dic7111yescharacteristic
521C2×Q16C2×Dic7111yescharacteristic
522C2×SD16C2×Dic7111yescharacteristic
523C2×SD16C2×Dic7111yescharacteristic
524C2×SD16C2×Dic7111yescharacteristic
525C2×SD16C2×Dic7111yescharacteristic
526C2×D8C2×Dic7111yescharacteristic
527C2×D8C2×Dic7111yescharacteristic
528#131—2841no—
529#131—2841no—
530#131—2841no—
531#131—1422no—
532#131—1422no—
533#131—1422no—
534C2×M16—2841no—
535C2×M16—711no—
536C2×M16—711no—
537C2×M16—711no—
538C2×M16—711no—
539C2×M16—1422no—
540C2×M16—1421no—
541C2×M16—1421no—
542C2×M16—1421no—
543C2×M16—1421no—
544C22×C8—711no—
545C22×C8—711no—
546C22×C8—1421no—
547C22×C8—1421no—
548C22×C8—1421no—
549C22×C8—1421no—
550C22×C8C22×D7111yescharacteristic
551C22×C8C22×D7111yescharacteristic
552#123—21no—
553C22⋊Q8C2×Dic7111yescharacteristic
554C22⋊Q8C2×Dic7111yescharacteristic
555#121C2×Dic7111yescharacteristic
556#121C2×Dic7111yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—2841no—
561#117—1422no—
562#117C22×D7111yescharacteristic
563C2×C4⋊C4—1421no—
564C2×C22⋊C4—1421no—
565C2×C42—711no—
566C2×C42—711no—
567#108—2841no—
568#108—1422no—
569C4⋊C8—1421no—
570C4⋊C8—1421no—
571#104—2841no—
572#104—714no—
573#104—1422no—
574#104—1422no—
575#104—1422no—
576#104—1422no—
577#103C2×Dic7111yescharacteristic
578#103C2×Dic7111yescharacteristic
579#103C2×Dic7111yescharacteristic
580#103C2×Dic7111yescharacteristic
581#102C2×Dic7111yescharacteristic
582#102C2×Dic7111yescharacteristic
583#102C2×Dic7111yescharacteristic
584#102C2×Dic7111yescharacteristic
585C22⋊C8—711no—
586C22⋊C8—711no—
587C22⋊C8—711no—
588C22⋊C8—711no—
589C22⋊C8—1421no—
590C22⋊C8—1421no—
591C22⋊C8—1421no—
592C22⋊C8—1421no—
593C22⋊C8—1421no—
594C22⋊C8—1421no—
595C22⋊C8—1421no—
596C22⋊C8—1421no—
597C22⋊C8C2×Dic7111yescharacteristic
598C22⋊C8C2×Dic7111yescharacteristic
599C22⋊C8C2×Dic7111yescharacteristic
600C22⋊C8C2×Dic7111yescharacteristic
601#97—2841no—
602#97—1421no—
603C4×C8—1421no—
604C4×C8—1422no—
605C24—21no—
606C24#1176586411yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41D4×D7112yes—
626#41#1176586412yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×Dic7111yescharacteristic
631C2×Q8C22×Dic7111yescharacteristic
632C2×Q8C22×Dic7111yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×Dic7111yescharacteristic
646C2×D4C22×Dic7111yescharacteristic
647C2×D4C22×Dic7111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—1421no—
661C22×C4—1421no—
662C22×C4C22×Dic7111yescharacteristic
663C22×C4C22×Dic7111yescharacteristic
664C22×C4D4×D7111yescharacteristic
665C22×C4D4×D7111yescharacteristic
666C22×C4#1176586411yescharacteristic
667C22×C4C23×D7111yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—2842no—
677M16—2842no—
678M16—2842no—
679M16—2842no—
680M16—712no—
681M16—1421no—
682M16—1421no—
683M16—1421no—
684M16—1421no—
685M16—1421no—
686M16—1421no—
687M16—1421no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—2842no—
693C2×C8—2842no—
694C2×C8—2842no—
695C2×C8—2842no—
696C2×C8—711no—
697C2×C8—711no—
698C2×C8—711no—
699C2×C8—711no—
700C2×C8—1421no—
701C2×C8—1421no—
702C2×C8—1421no—
703C2×C8—1421no—
704C2×C8—1421no—
705C2×C8—1421no—
706C2×C8—1421no—
707C2×C8—1421no—
708C2×C8C22×Dic7111yescharacteristic
709C2×C8C22×Dic7111yescharacteristic
710C2×C8C22×Dic7111yescharacteristic
711C2×C8C22×Dic7111yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—2842no—
715C4⋊C4C22×Dic7111yescharacteristic
716C4⋊C4C22×Dic7111yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—2842no—
723C42—21no—
724C42—712no—
725C42—1421no—
726C42—1421no—
727C42—1421no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23D4×Dic7111yescharacteristic
739C23D4×Dic7111yescharacteristic
740C23C2×#1176586411yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8D4×Dic7112yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4D4×Dic7112yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—2841no—
790C2×C4—2841no—
791C2×C4—2841no—
792C2×C4—2841no—
793C2×C4—2841no—
794C2×C4—1422no—
795C2×C4D4×Dic7111yescharacteristic
796C2×C4D4×Dic7111yescharacteristic
797C2×C4C23×Dic7111yescharacteristic
798C2×C4C2×D4×D7111yescharacteristic
799C2×C4C2×D4×D7111yescharacteristic
800C2×C4C2×#1176586411yescharacteristic
801C2×C4#1455617311yescharacteristic
802C2×C4#1455617311yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—2841no—
808C8—2841no—
809C8—2841no—
810C8—1421no—
811C8—1422no—
812C8—1421no—
813C8—1421no—
814C8—1421no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×D4×Dic7111yescharacteristic
836C22#1798663611yescharacteristic
837C22#1798668011yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—2842no—
846C4—5681no—
847C4C2×D4×Dic7111yescharacteristic
848C4#1798647411yescharacteristic
849C4#1798663111yescharacteristic
850C4#1798663611yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2#2259132411yescharacteristic
859C2#2259724311yescharacteristic
860C2#2259725711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
Fitting, prime radicalC71×#3002C2
socleC22×C71C2×C4×D4
cosocleC22×C4×C71C24
hypercenter#3002D71
hypocenterC71#22889
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. C2×#17986116C2semidirect
2. #22597067C2semidirect
3. C2×#17986016C2semidirect
4. #22596789C2semidirect
5. #22589234C2semidirect
6. #22589046C2semidirect
7. #22588990C2semidirect
8. #22588789C2semidirect
9. #22588669C2semidirect
10. #22588669C2semidirect
11. #22588617C2semidirect
12. #22588547C2semidirect
13. #22588187C2semidirect
14. #22588108C2semidirect
18. C2×#14556135C22semidirect
26. C2×#14556064C22semidirect
27. C2×#14556064C22semidirect
28. #17986026C22semidirect
34. C2×#14556055C22semidirect
35. C2×#14556055C22semidirect
40. #17985966C22semidirect
45. #17985955C22semidirect
46. C2×#14556038C22semidirect
47. C2×C8×Dic71C22semidirect
48. #17985764C22semidirect
49. #17985764C22semidirect
50. #17985758C22semidirect
51. #17985758C22semidirect
52. #17985753C22semidirect
53. #17985753C22semidirect
58. #452×C71C4semidirect
59. #452×C71C4semidirect
60. #451×C71C4semidirect
61. #450×C71C4semidirect
62. #449×C71C4semidirect
63. #449×C71C4semidirect
64. #448×C71C4semidirect
65. #447×C71C4semidirect
106. #14556055D4semidirect
446. C71#22889semidirect
456. #452Dic71semidirect
457. #452Dic71semidirect
458. #451Dic71semidirect
459. #450Dic71semidirect
460. #449Dic71semidirect
461. #449Dic71semidirect
462. #448Dic71semidirect
463. #447Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179861162
#225970672
C2×#179860162
#225967892
#225892342
#225890462
#225889902
#225887892
#225886692
#225886172
#225885472
#225881872
#225881082
C71×#30022
#2288971