Finite Group Databasebeta

← #32170002

Subgroups — #32170002

Order 18176.

4046 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986624C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D71C211yesmaximal, characteristic
3#22596628C211yesmaximal, characteristic, complemented
4#22596626C212yesmaximal, complemented
5#22596624C211yesmaximal, characteristic, complemented
6#22594149C212yesmaximal, complemented
7#22594145C211yesmaximal, characteristic, complemented
8#22592007C214yesmaximal, complemented
9#22592002C214yesmaximal, complemented
10#22592002C214yesmaximal, complemented
11#22592000C214yesmaximal, complemented
12#22590953C211yesmaximal, characteristic, complemented
13#22590951C212yesmaximal, complemented
14#379×D71C212yesmaximal
15C71×#2626C211yesmaximal, characteristic, complemented
16C25×D71C2211yescharacteristic
17C23×C4×D71C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19#17986624—28no—
20C2×#14556108C2212yescomplemented
21C2×#14556108C2212yescomplemented
22C2×#14556107C2211yescharacteristic, complemented
23C2×#14556106C2212yescomplemented
24C2×#14556106C2212yescomplemented
25C2×#14556106C2214yescomplemented
26C2×#14556105C2212yescomplemented
27C2×#14556104C2212yescomplemented
28C2×#14556104C2212yescomplemented
29C22×C22⋊Dic71C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C2×C22⋊C4×D71—28no—
33C2×C22⋊C4×D71C2214yes—
34C2×C22⋊C4×D71C2214yes—
35C2×C22⋊C4×D71C2212yes—
36C2×C22⋊C4×D71C2212yes—
37C2×C22⋊C4×D71C2214yes—
38C2×C22⋊C4×D71C2214yes—
39#17985935C2214yescomplemented
40#17985935C2212yescomplemented
41#17985922C2214yescomplemented
42#17985922C2214yescomplemented
43#17985922C2214yescomplemented
44#17985911C2212yescomplemented
45#17985911C2214yescomplemented
46#17985874C2212yescomplemented
47#17985873C2214yescomplemented
48#17985873C2214yescomplemented
49#17985873C2214yescomplemented
50#17985873C2214yescomplemented
51#17985872C2212yescomplemented
52#17985871C2212yescomplemented
53#17985870C2214yescomplemented
54#17985870C2214yescomplemented
55#17985870C2214yescomplemented
56#17985870C2214yescomplemented
57#17985859C2211yescharacteristic, complemented
58#17985858C2214yescomplemented
59#17985858C2214yescomplemented
60#17985857C2212yescomplemented
61#17985856C2212yescomplemented
62#17985856C2214yescomplemented
63#17985856C2212yescomplemented
64#17985855C2212yes—
65#17985854C2214yes—
66#17985854C2214yes—
67#17985854C2212yes—
68#17985854C2212yes—
69C2×C22⋊Q8×C71C2211yescharacteristic, complemented
70C22×C22⋊C4×C71C2211yescharacteristic
71#399×C71C2212yescomplemented
72#396×C71C2214yescomplemented
73#393×C71C2212yescomplemented
74#385×C71C2212yescomplemented
75#380×C71C2211yescharacteristic, complemented
76#379×C71C2212yes—
77C24×D71—24no—
78C24×D71—24no—
79C24×D71—44no—
80C24×D71—44no—
81C24×D71Q818yescomplemented
82C24×D71C2311yescharacteristic
83C24×D71C2314yes—
84C24×D71C2311yescharacteristic
85C22×Dic142C2312yescomplemented
86C22×Dic142C2311yescharacteristic, complemented
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C22×C4×D71—24no—
90C22×C4×D71—24no—
91C22×C4×D71—44no—
92C22×C4×D71—44no—
93C22×C4×D71C2312yes—
94C22×C4×D71C2312yes—
95C22×C4×D71C2314yes—
96C22×C4×D71C2314yes—
97C22×C4×D71C2312yes—
98C22×C4×D71C2312yes—
99#14556108—28no—
100#14556108—44no—
101#14556107—24no—
102#14556106—28no—
103#14556106—28no—
104#14556106—48no—
105#14556105—28no—
106#14556104—28no—
107#14556104—44no—
108C2×C4⋊Dic71C2311yescharacteristic, complemented
109C2×C4⋊Dic71C2312yescomplemented
110C2×C4⋊Dic71C2312yescomplemented
111C2×C4⋊Dic71C2314yescomplemented
112C2×Dic71⋊C4C2312yescomplemented
113C2×Dic71⋊C4C2312yescomplemented
114C2×Dic71⋊C4C2312yescomplemented
115C2×Dic71⋊C4C2314yescomplemented
116C2×Dic71⋊C4C2314yescomplemented
117C2×Dic71⋊C4C2314yescomplemented
118C2×C22⋊Dic71—24no—
119C2×C22⋊Dic71C2312yes—
120C2×C22⋊Dic71C2312yes—
121C2×C22⋊Dic71C2314yes—
122C2×C22⋊Dic71C2314yes—
123C2×C22⋊Dic71C2314yes—
124C2×(C2×D71)⋊C4—24no—
125C2×(C2×D71)⋊C4D418yes—
126C2×(C2×D71)⋊C4C2312yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×(C2×D71)⋊C4C2314yes—
129C2×(C2×D71)⋊C4C2312yes—
130C2×(C2×D71)⋊C4C2314yes—
131C2×(C2×D71)⋊C4C2314yes—
132C2×(C2×D71)⋊C4C2314yes—
133C2×(C2×D71)⋊C4C2314yes—
134C2×(C2×D71)⋊C4C2312yes—
135C2×(C2×D71)⋊C4C2312yes—
136C22⋊C4×D71—28no—
137C22⋊C4×D71—28no—
138C22⋊C4×D71—216no—
139C22⋊C4×D71—216no—
140C22⋊C4×D71—48no—
141C22⋊C4×D71—48no—
142C71⋊#95C2314yescomplemented
143C71⋊#95C2314yescomplemented
144C71⋊#95C2314yescomplemented
145C71⋊#95C2314yescomplemented
146C71⋊#95C2312yescomplemented
147C25×C71C2311yescharacteristic
148C22×Q8×C71C2311yescharacteristic, complemented
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2311yescharacteristic
151C22⋊Q8×C71—24no—
152C2×C4⋊C4×C71C2311yescharacteristic, complemented
153C2×C4⋊C4×C71C2312yescomplemented
154C2×C4⋊C4×C71C2314yescomplemented
155C2×C4⋊C4×C71C2312yescomplemented
156C2×C22⋊C4×C71—24no—
157C2×C22⋊C4×C71C2312yes—
158C2×C22⋊C4×C71C2312yes—
159C2×C22⋊C4×C71C2312yes—
160C2×C22⋊C4×C71C2312yes—
161C2×C22⋊C4×C71C2314yes—
162C2×C22⋊C4×C71C2314yes—
163#95×C71C2314yescomplemented
164#95×C71C2312yescomplemented
165C23×D71—22no—
166C23×D71—22no—
167C23×D71—24no—
168C23×D71—24no—
169C23×D71—232no—
170C23×D71—28no—
171C23×D71—28no—
172C23×D71—28no—
173C23×D71—28no—
174C23×D71—432no—
175C23×D71—42no—
176C23×D71—42no—
177C23×D71—44no—
178C23×D71—44no—
179C23×D71—416no—
180C23×D71—416no—
181C23×D71—432no—
182C23×D71C2×D414yes—
183C23×D71C2×Q814yes—
184C23×D71C2×Q8116yes—
185C23×D71C2×Q814yes—
186C23×D71#4114yes—
187C23×D71C2412yes—
188C23×D71C2412yes—
189C2×Dic142—22no—
190C2×Dic142—24no—
191C2×Dic142—44no—
192C2×Dic142—42no—
193C22×Dic71—22no—
194C22×Dic71—42no—
195C22×Dic71—42no—
196C22×Dic71C2×D414yes—
197C22×Dic71C2412yes—
198C22×Dic71C2412yes—
199C22×Dic71C2412yes—
200C22×Dic71C2414yes—
201C22×Dic71C2412yes—
202C2×C4×D71—24no—
203C2×C4×D71—28no—
204C2×C4×D71—24no—
205C2×C4×D71—24no—
206C2×C4×D71—24no—
207C2×C4×D71—28no—
208C2×C4×D71—24no—
209C2×C4×D71—24no—
210C2×C4×D71—28no—
211C2×C4×D71—44no—
212C2×C4×D71—42no—
213C2×C4×D71—42no—
214C2×C4×D71—416no—
215C2×C4×D71—416no—
216C2×C4×D71—44no—
217C2×C4×D71—44no—
218C2×C4×D71—44no—
219C2×C4×D71—44no—
220C4⋊Dic71—22no—
221C4⋊Dic71—24no—
222C4⋊Dic71—42no—
223C4⋊Dic71—44no—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226Dic71⋊C4—24no—
227Dic71⋊C4—44no—
228Dic71⋊C4—44no—
229Dic71⋊C4—44no—
230C22⋊Dic71—24no—
231C22⋊Dic71—24no—
232C22⋊Dic71—28no—
233C22⋊Dic71—44no—
234C22⋊Dic71—44no—
235(C2×D71)⋊C4—28no—
236(C2×D71)⋊C4—24no—
237(C2×D71)⋊C4—24no—
238(C2×D71)⋊C4—28no—
239(C2×D71)⋊C4—28no—
240(C2×D71)⋊C4—28no—
241(C2×D71)⋊C4—28no—
242(C2×D71)⋊C4—28no—
243(C2×D71)⋊C4C2×D418yes—
244(C2×D71)⋊C4C2×D418yes—
245C24×C71—22no—
246C24×C71—22no—
247C24×C71—42no—
248C24×C71—42no—
249C24×C71C2×Q814yes—
250C24×C71C2412yes—
251C24×C71C2411yescharacteristic
252C2×Q8×C71—22no—
253C2×Q8×C71—42no—
254C22×C4×C71—22no—
255C22×C4×C71—42no—
256C22×C4×C71—42no—
257C22×C4×C71C2×D414yes—
258C22×C4×C71C2412yes—
259C22×C4×C71C2412yes—
260C22×C4×C71C2414yes—
261C22×C4×C71C2412yes—
262C22×C4×C71C2411yescharacteristic
263C22×C4×C71C2411yescharacteristic
264C4⋊C4×C71—22no—
265C4⋊C4×C71—24no—
266C4⋊C4×C71—44no—
267C4⋊C4×C71—42no—
268C22⋊C4×C71—24no—
269C22⋊C4×C71—24no—
270C22⋊C4×C71—24no—
271C22⋊C4×C71—24no—
272C22⋊C4×C71—44no—
273C22⋊C4×C71—44no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—28no—
277C23×C71—22no—
278C23×C71—22no—
279C23×C71—24no—
280C23×C71—24no—
281C23×C71—48no—
282C23×C71—44no—
283C23×C71—44no—
284C23×C71—48no—
285C23×C71C22×D412yes—
286C23×C71C22×Q814yes—
287C23×C71C22×Q812yes—
288C23×C71C2×#4112yes—
289C23×C71C2511yescharacteristic
290C22×D71—28no—
291C22×D71—28no—
292C22×D71—216no—
293C22×D71—28no—
294C22×D71—22no—
295C22×D71—22no—
296C22×D71—22no—
297C22×D71—22no—
298C22×D71—24no—
299C22×D71—24no—
300C22×D71—216no—
301C22×D71—232no—
302C22×D71—232no—
303C22×D71—44no—
304C22×D71—44no—
305C22×D71—48no—
306C22×D71—416no—
307C22×D71—48no—
308C22×D71—416no—
309C22×D71—416no—
310C22×D71—416no—
311C22×D71—416no—
312C22×D71—4128no—
313C22×D71C22⋊Q8116yescomplemented
314C22×D71C22×D414yes—
315C22×D71C22×Q814yes—
316C22×D71C22×Q814yes—
317C22×D71C2×#4114yes—
318C22×D71H(5,𝔽2)14yes—
319C22×D71H(5,𝔽2)14yes—
320Q8×C71—82no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—24no—
327C2×C4×C71—24no—
328C2×C4×C71—24no—
329C2×C4×C71—24no—
330C2×C4×C71—24no—
331C2×C4×C71—24no—
332C2×C4×C71—44no—
333C2×C4×C71—44no—
334C2×C4×C71C22×D412yes—
335C2×C4×C71C22×D412yes—
336C2×Dic71—24no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—24no—
341C2×Dic71—24no—
342C2×Dic71—24no—
343C2×Dic71—24no—
344C2×Dic71—24no—
345C2×Dic71—22no—
346C2×Dic71—22no—
347C2×Dic71—44no—
348C2×Dic71—44no—
349C2×Dic71C22×D414yes—
350C4×D71—416no—
351C4×D71—48no—
352C4×D71—48no—
353C4×D71—84no—
354C4×D71—84no—
355C4×D71—88no—
356Dic142—84no—
357Dic142—82no—
358C22×C71—24no—
359C22×C71—22no—
360C22×C71—22no—
361C22×C71—24no—
362C22×C71—24no—
363C22×C71—28no—
364C22×C71—416no—
365C22×C71—42no—
366C22×C71—42no—
367C22×C71—44no—
368C22×C71C2×C22⋊Q814yes—
369C22×C71C23×D411yescharacteristic
370C22×C71C23×Q811yescharacteristic
371C22×C71C22×#4111yescharacteristic
372C22×C71C2×H(5,𝔽2)12yes—
373C22×C71C2×H(5,𝔽2)12yes—
374C2×D71—232no—
375C2×D71—24no—
376C2×D71—24no—
377C2×D71—28no—
378C2×D71—24no—
379C2×D71—24no—
380C2×D71—24no—
381C2×D71—24no—
382C2×D71—28no—
383C2×D71—24no—
384C2×D71—24no—
385C2×D71—416no—
386C2×D71—464no—
387C2×D71C2×C22⋊Q818yes—
388C2×D71#54318yescomplemented
389C4×C71—22no—
390C4×C71—22no—
391C4×C71—42no—
392C4×C71—42no—
393C4×C71—42no—
394C4×C71—44no—
395Dic71—24no—
396Dic71—42no—
397Dic71—42no—
398Dic71—42no—
399Dic71—44no—
400#34982—711nomaximal, Sylow
401C2×C71—24no—
402C2×C71—44no—
403C2×C71C22×C22⋊Q811yescharacteristic
404C2×C71C2×#54312yes—
405C2×C71#348411yescharacteristic
406C2×C71#348411yescharacteristic
407C2×C71#349012yes—
408D71—28no—
409D71—28no—
410C2×#543—711no—
411C23×C22⋊C4—711no—
412#2848—712no—
413#2848—711no—
414#2848—711no—
415#2626—712no—
416#2626—711no—
417#2626D7111yescharacteristic, complemented
418#2437—714no—
419#2437—714no—
420#2437—714no—
421#2437—714no—
422#2315—712no—
423#2315—711no—
424C2×#379—712no—
425C71#3498211yescharacteristic, complemented, Sylow
426C26—711no—
427C24×C4—711no—
428C24×C4—711no—
429#543—1428no—
430C2×C22⋊Q8—712no—
431C2×C22⋊Q8—712no—
432C2×C22⋊Q8—711no—
433C2×C22⋊Q8—714no—
434C2×C22⋊Q8—712no—
435C2×C22⋊Q8—712no—
436C2×C22⋊Q8—712no—
437C2×C22⋊Q8—712no—
438C2×C22⋊Q8—712no—
439C2×C22⋊Q8C2×D7111yescharacteristic, complemented
440C22×C22⋊C4—714no—
441C22×C22⋊C4—714no—
442C22×C22⋊C4—711no—
443C22×C22⋊C4—711no—
444C22×C22⋊C4—711no—
445C22×C22⋊C4—712no—
446C22×C22⋊C4—712no—
447C22×C22⋊C4—714no—
448C22×C22⋊C4—714no—
449C22×C22⋊C4—1428no—
450C22×C22⋊C4C2×D7111yescharacteristic
451#399—712no—
452#399—714no—
453#399C2×D7112yescomplemented
454#396—714no—
455#396—714no—
456#396—714no—
457#396C2×D7114yescomplemented
458#393—712no—
459#393—714no—
460#393C2×D7112yescomplemented
461#385—712no—
462#385—714no—
463#385—714no—
464#385—714no—
465#385—714no—
466#385—712no—
467#385—712no—
468#385—714no—
469#385—714no—
470#385—714no—
471#385—714no—
472#385C2×D7112yescomplemented
473#380—711no—
474#380—714no—
475#380—712no—
476#380—712no—
477#380—712no—
478#380—714no—
479#380—714no—
480#380C2×D7111yescharacteristic, complemented
481#379—712no—
482#379—712no—
483#379—712no—
484#379—714no—
485#379—714no—
486#379C2×D7112yes—
487C25—2844no—
488C25—2844no—
489C25—711no—
490C25—718no—
491C25—714no—
492C25—711no—
493C25—1424no—
494C25—1424no—
495C25C22×D7111yescharacteristic
496C22×Q8—712no—
497C22×Q8—711no—
498C22×Q8C22×D7111yescharacteristic, complemented
499C23×C4—2844no—
500C23×C4—2844no—
501C23×C4—711no—
502C23×C4—711no—
503C23×C4—712no—
504C23×C4—712no—
505C23×C4—714no—
506C23×C4—714no—
507C23×C4—712no—
508C23×C4—712no—
509C23×C4—1424no—
510C23×C4—1424no—
511C23×C4C22×D7111yescharacteristic
512C23×C4C22×D7111yescharacteristic
513C22⋊Q8—24no—
514C22⋊Q8—2848no—
515C22⋊Q8—2844no—
516C22⋊Q8—2844no—
517C22⋊Q8—1428no—
518C22⋊Q8—1428no—
519C22⋊Q8—1428no—
520C22⋊Q8—1428no—
521C22⋊Q8—1428no—
522C22⋊Q8—1424no—
523C2×C4⋊C4—714no—
524C2×C4⋊C4—712no—
525C2×C4⋊C4—714no—
526C2×C4⋊C4—714no—
527C2×C4⋊C4—714no—
528C2×C4⋊C4—712no—
529C2×C4⋊C4—711no—
530C2×C4⋊C4—712no—
531C2×C4⋊C4—712no—
532C2×C4⋊C4—712no—
533C2×C4⋊C4C22×D7111yescharacteristic, complemented
534C2×C4⋊C4C22×D7112yescomplemented
535C2×C4⋊C4C22×D7112yescomplemented
536C2×C4⋊C4C22×D7114yescomplemented
537C2×C22⋊C4—24no—
538C2×C22⋊C4—2848no—
539C2×C22⋊C4—2848no—
540C2×C22⋊C4—714no—
541C2×C22⋊C4—714no—
542C2×C22⋊C4—718no—
543C2×C22⋊C4—712no—
544C2×C22⋊C4—712no—
545C2×C22⋊C4—714no—
546C2×C22⋊C4—712no—
547C2×C22⋊C4—712no—
548C2×C22⋊C4—714no—
549C2×C22⋊C4—712no—
550C2×C22⋊C4—712no—
551C2×C22⋊C4—714no—
552C2×C22⋊C4—714no—
553C2×C22⋊C4—714no—
554C2×C22⋊C4—714no—
555C2×C22⋊C4—714no—
556C2×C22⋊C4—14216no—
557C2×C22⋊C4—14216no—
558C2×C22⋊C4—1428no—
559C2×C22⋊C4—1428no—
560C2×C22⋊C4—1424no—
561C2×C22⋊C4—1424no—
562C2×C22⋊C4C22×D7112yes—
563C2×C22⋊C4C22×D7112yes—
564C2×C22⋊C4C22×D7112yes—
565C2×C22⋊C4C22×D7112yes—
566C2×C22⋊C4C22×D7114yes—
567C2×C22⋊C4C22×D7114yes—
568#95—714no—
569#95—714no—
570#95—714no—
571#95—714no—
572#95—712no—
573#95C22×D7114yescomplemented
574#95C22×D7112yescomplemented
575C24—22no—
576C24—22no—
577C24—42no—
578C24—42no—
579C24—2842no—
580C24—2842no—
581C24—2844no—
582C24—2844no—
583C24—28416no—
584C24—28416no—
585C24—28432no—
586C24—28432no—
587C24—714no—
588C24—714no—
589C24—714no—
590C24—7116no—
591C24—712no—
592C24—712no—
593C24—714no—
594C24—1428no—
595C24—1428no—
596C24—1428no—
597C24—1428no—
598C24—14232no—
599C24—1424no—
600C24—1424no—
601C24—1422no—
602C24—1422no—
603C24Q8×D7114yes—
604C24C23×D7112yes—
605C24C23×D7111yescharacteristic
606C2×Q8—22no—
607C2×Q8—42no—
608C2×Q8—2842no—
609C2×Q8—2844no—
610C2×Q8—1424no—
611C2×Q8—1422no—
612C22×C4—22no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—2842no—
616C22×C4—2842no—
617C22×C4—2844no—
618C22×C4—2844no—
619C22×C4—2844no—
620C22×C4—2844no—
621C22×C4—2844no—
622C22×C4—28416no—
623C22×C4—28416no—
624C22×C4—2842no—
625C22×C4—2842no—
626C22×C4—714no—
627C22×C4—712no—
628C22×C4—714no—
629C22×C4—712no—
630C22×C4—712no—
631C22×C4—712no—
632C22×C4—1428no—
633C22×C4—1424no—
634C22×C4—1424no—
635C22×C4—1428no—
636C22×C4—1424no—
637C22×C4—1424no—
638C22×C4—1428no—
639C22×C4—1422no—
640C22×C4—1424no—
641C22×C4—1424no—
642C22×C4D4×D7114yes—
643C22×C4C23×D7114yes—
644C22×C4C23×D7112yes—
645C22×C4C23×D7112yes—
646C22×C4C23×D7112yes—
647C22×C4C23×D7111yescharacteristic
648C22×C4C23×D7111yescharacteristic
649C4⋊C4—22no—
650C4⋊C4—24no—
651C4⋊C4—42no—
652C4⋊C4—44no—
653C4⋊C4—2844no—
654C4⋊C4—2844no—
655C4⋊C4—2844no—
656C4⋊C4—2842no—
657C4⋊C4—2844no—
658C4⋊C4—1424no—
659C4⋊C4—1424no—
660C4⋊C4—1424no—
661C4⋊C4—1424no—
662C4⋊C4—1422no—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—2844no—
670C22⋊C4—2844no—
671C22⋊C4—718no—
672C22⋊C4—718no—
673C22⋊C4—1428no—
674C22⋊C4—1428no—
675C22⋊C4—1428no—
676C22⋊C4—1428no—
677C22⋊C4—1428no—
678C22⋊C4—1428no—
679C22⋊C4—1424no—
680C22⋊C4—1424no—
681C22⋊C4—1428no—
682C22⋊C4—1424no—
683C22⋊C4—1424no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—24no—
689C23—24no—
690C23—28no—
691C23—48no—
692C23—48no—
693C23—44no—
694C23—44no—
695C23—2848no—
696C23—2848no—
697C23—2844no—
698C23—2844no—
699C23—28416no—
700C23—284128no—
701C23—28416no—
702C23—28416no—
703C23—28416no—
704C23—28416no—
705C23—7116no—
706C23—714no—
707C23—714no—
708C23—714no—
709C23—714no—
710C23—714no—
711C23—714no—
712C23—14232no—
713C23—14232no—
714C23—14216no—
715C23—1428no—
716C23—1428no—
717C23—14216no—
718C23—1422no—
719C23—1422no—
720C23—1424no—
721C23—1424no—
722C23—1422no—
723C23—1422no—
724C23—1428no—
725C23C2×D4×D7112yes—
726C23C2×Q8×D7114yes—
727C23C2×Q8×D7112yes—
728C23#41×D7112yes—
729C23C24×D7111yescharacteristic
730Q8—82no—
731Q8—5682no—
732Q8—5684no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—2848no—
747C2×C4—2848no—
748C2×C4—28416no—
749C2×C4—2844no—
750C2×C4—2844no—
751C2×C4—5688no—
752C2×C4—5684no—
753C2×C4—5684no—
754C2×C4—714no—
755C2×C4—1422no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4—1424no—
759C2×C4—1424no—
760C2×C4—1424no—
761C2×C4—1424no—
762C2×C4—1424no—
763C2×C4—1422no—
764C2×C4—1422no—
765C2×C4—1424no—
766C2×C4C2×D4×D7112yes—
767C2×C4C2×D4×D7112yes—
768C22—24no—
769C22—24no—
770C22—22no—
771C22—22no—
772C22—28no—
773C22—24no—
774C22—416no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—28416no—
779C22—28464no—
780C22—718no—
781C22—718no—
782C22—14232no—
783C22—1428no—
784C22—1424no—
785C22—1428no—
786C22—1424no—
787C22—1424no—
788C22—1424no—
789C22—1424no—
790C22—1424no—
791C22—1424no—
792C22—1424no—
793C22C22⋊Q8×D7114yes—
794C22C22×D4×D7111yescharacteristic
795C22C22×Q8×D7111yescharacteristic
796C22C2×#41×D7111yescharacteristic
797C22H(5,𝔽2)×D7112yes—
798C22H(5,𝔽2)×D7112yes—
799C4—22no—
800C4—22no—
801C4—44no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—2844no—
806C4—2842no—
807C4—2842no—
808C4—2842no—
809C4—1424no—
810C2—24no—
811C2—44no—
812C2—1428no—
813C2—1428no—
814C2C2×C22⋊Q8×D7111yescharacteristic
815C2#543×D7112yes—
816C2#2260197211yescharacteristic
817C2#2260197411yescharacteristic
818C2#2260202612yes—
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2626C2
prime radicalC25×D71C22
hypercenter#2626D71
hypocenterC71#34982
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2626

Complements

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

NH ≅ G/Ntype
1. C2×#17986624C2semidirect
3. #22596628C2semidirect
4. #22596626C2semidirect
5. #22596624C2semidirect
6. #22594149C2semidirect
7. #22594145C2semidirect
8. #22592007C2semidirect
9. #22592002C2semidirect
10. #22592002C2semidirect
11. #22592000C2semidirect
12. #22590953C2semidirect
13. #22590951C2semidirect
15. C71×#2626C2semidirect
20. C2×#14556108C22semidirect
21. C2×#14556108C22semidirect
22. C2×#14556107C22semidirect
23. C2×#14556106C22semidirect
24. C2×#14556106C22semidirect
25. C2×#14556106C22semidirect
26. C2×#14556105C22semidirect
27. C2×#14556104C22semidirect
28. C2×#14556104C22semidirect
39. #17985935C22semidirect
40. #17985935C22semidirect
41. #17985922C22semidirect
42. #17985922C22semidirect
43. #17985922C22semidirect
44. #17985911C22semidirect
45. #17985911C22semidirect
46. #17985874C22semidirect
47. #17985873C22semidirect
48. #17985873C22semidirect
49. #17985873C22semidirect
50. #17985873C22semidirect
51. #17985872C22semidirect
52. #17985871C22semidirect
53. #17985870C22semidirect
54. #17985870C22semidirect
55. #17985870C22semidirect
56. #17985870C22semidirect
57. #17985859C22semidirect
58. #17985858C22semidirect
59. #17985858C22semidirect
60. #17985857C22semidirect
61. #17985856C22semidirect
62. #17985856C22semidirect
63. #17985856C22semidirect
69. C2×C22⋊Q8×C71C22semidirect
71. #399×C71C22semidirect
72. #396×C71C22semidirect
73. #393×C71C22semidirect
74. #385×C71C22semidirect
75. #380×C71C22semidirect
81. C24×D71Q8semidirect
85. C22×Dic142C23semidirect
86. C22×Dic142C23semidirect
108. C2×C4⋊Dic71C23semidirect
109. C2×C4⋊Dic71C23semidirect
110. C2×C4⋊Dic71C23semidirect
111. C2×C4⋊Dic71C23semidirect
112. C2×Dic71⋊C4C23semidirect
113. C2×Dic71⋊C4C23semidirect
114. C2×Dic71⋊C4C23semidirect
115. C2×Dic71⋊C4C23semidirect
116. C2×Dic71⋊C4C23semidirect
117. C2×Dic71⋊C4C23semidirect
142. C71⋊#95C23semidirect
143. C71⋊#95C23semidirect
144. C71⋊#95C23semidirect
145. C71⋊#95C23semidirect
146. C71⋊#95C23semidirect
148. C22×Q8×C71C23semidirect
152. C2×C4⋊C4×C71C23semidirect
153. C2×C4⋊C4×C71C23semidirect
154. C2×C4⋊C4×C71C23semidirect
155. C2×C4⋊C4×C71C23semidirect
163. #95×C71C23semidirect
164. #95×C71C23semidirect
313. C22×D71C22⋊Q8semidirect
388. C2×D71#543semidirect
417. #2626D71semidirect
425. C71#34982semidirect
439. C2×C22⋊Q8C2×D71semidirect
453. #399C2×D71semidirect
457. #396C2×D71semidirect
460. #393C2×D71semidirect
472. #385C2×D71semidirect
480. #380C2×D71semidirect
498. C22×Q8C22×D71semidirect
533. C2×C4⋊C4C22×D71semidirect
534. C2×C4⋊C4C22×D71semidirect
535. C2×C4⋊C4C22×D71semidirect
536. C2×C4⋊C4C22×D71semidirect
573. #95C22×D71semidirect
574. #95C22×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179866242
C22×C22⋊C4×D712
#225966282
#225966262
#225966242
#225941492
#225941452
#225920072
#225920022
#225920002
#225909532
#225909512
#379×D712
C71×#26262
#3498271