Finite Group Databasebeta

← #32868189

Subgroups — #32868189

Order 18176.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556102C211yesmaximal, characteristic, complemented
2#22599150C214yesmaximal, complemented
3#22599142C212yesmaximal, complemented
4#22599137C212yesmaximal, complemented
5#22599101C214yesmaximal, complemented
6#22599093C212yesmaximal, complemented
7#22599088C212yesmaximal, complemented
8#22598280C212yesmaximal, complemented
9#22598260C212yesmaximal, complemented
10#22597961C214yesmaximal, complemented
11#22597592C212yesmaximal, complemented
12#22597566C212yesmaximal, complemented
13C2×#17985963C211yesmaximal, characteristic, complemented
14C2×#525×C71C211yesmaximal, characteristic, complemented
15C23×D284C2211yescharacteristic, complemented
16C23×C22⋊D71—21no—
17C2×#14556153C2214yescomplemented
18C22×#11765849C2212yescomplemented
19C2×#14556102—21no—
20C2×#14556102—21no—
21C2×#14556102—21no—
22C2×#14556102—21no—
23C2×#14556102—21no—
24C2×#14556102—21no—
25C2×#14556102C2212yes—
26C2×#14556102C2212yes—
27C2×#14556102C2212yes—
28C2×#14556102C2212yescomplemented
29C2×#14556102C2212yescomplemented
30C2×#14556102C2212yescomplemented
31C22×C4⋊Dic71C2211yescharacteristic, complemented
32C22×(C2×D71)⋊C4—21no—
33#17986332C2214yescomplemented
34#17986327C2214yescomplemented
35#17986323C2218yescomplemented
36#17986317C2214yescomplemented
37#17986315C2214yescomplemented
38#17986312C2214yescomplemented
39#17986310C2214yescomplemented
40#17986250C2218yescomplemented
41#17986247C2218yescomplemented
42#17986233C2218yescomplemented
43#17986230C2218yescomplemented
44#17986149C2214yescomplemented
45#17986149C2214yescomplemented
46#17986144C2218yescomplemented
47#17986138C2214yescomplemented
48#17986133C2214yescomplemented
49#17986132C2214yescomplemented
50#17986132C2214yescomplemented
51#17986042C2214yescomplemented
52#17986003C2214yescomplemented
53#17986000C2214yescomplemented
54#17985963C2212yescomplemented
55#17985963C2212yescomplemented
56#17985963C2212yescomplemented
57#17985963C2212yescomplemented
58C2×C22⋊(C71⋊C8)C2212yescomplemented
59C2×C22⋊(C71⋊C8)C2212yescomplemented
60C22×#41×C71C2211yescharacteristic, complemented
61C24×C4×C71C2211yescharacteristic
62#525×C71—21no—
63#525×C71—21no—
64#525×C71—21no—
65#525×C71—21no—
66#525×C71C2212yes—
67#525×C71C2212yescomplemented
68#525×C71C2212yescomplemented
69#525×C71C2212yescomplemented
70C2×#123×C71—21no—
71C2×C22⋊Q8×C71C2211yescharacteristic, complemented
72C2×C22⋊Q8×C71C2211yescharacteristic, complemented
73C2×#121×C71C2211yescharacteristic, complemented
74C2×#121×C71C2211yescharacteristic, complemented
75C2×#120×C71—21no—
76C2×C4×D4×C71—21no—
77C2×C4×D4×C71—21no—
78C2×#117×C71C2211yescharacteristic, complemented
79C24×D71—21no—
80C22×D284—21no—
81C22×D284—21no—
82C22×D284—21no—
83C22×D284—44no—
84C22×D284C2312yes—
85C22×D284C2312yes—
86C22×D284C2312yes—
87C22×C22⋊D71—22no—
88C22×C22⋊D71—22no—
89C22×C22⋊D71—22no—
90C22×C22⋊D71—22no—
91C22×C22⋊D71—22no—
92C22×C22⋊D71—22no—
93C22×C22⋊D71—48no—
94C23×Dic71—21no—
95#14556153—48no—
96C2×#11765852C2318yescomplemented
97C2×#11765850C2318yescomplemented
98C2×#11765849—44no—
99C2×#11765849C2314yes—
100C2×#11765849C2314yescomplemented
101C22×C71⋊C8C2314yescomplemented
102#14556102—22no—
103#14556102—22no—
104#14556102—22no—
105#14556102—22no—
106#14556102—22no—
107#14556102—22no—
108#14556102—22no—
109#14556102—22no—
110#14556102—22no—
111#14556102—22no—
112#14556102—22no—
113#14556102—22no—
114#14556102C2314yes—
115#14556102C2314yes—
116#14556102C2314yes—
117#14556102C2314yes—
118C2×C4⋊Dic71—21no—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71C2312yes—
122C2×C4⋊Dic71C2312yes—
123C2×C4⋊Dic71C2312yes—
124C2×(C2×D71)⋊C4—22no—
125C2×(C2×D71)⋊C4—22no—
126C2×(C2×D71)⋊C4—22no—
127C2×(C2×D71)⋊C4—22no—
128C2×(C2×D71)⋊C4—22no—
129C2×(C2×D71)⋊C4—22no—
130#14556061C2318yescomplemented
131#14556059C2318yescomplemented
132#14556052C2318yescomplemented
133#14556049C2318yescomplemented
134#14556048C2318yescomplemented
135#14556048C2318yescomplemented
136C22⋊(C71⋊C8)C2314yes—
137C22⋊(C71⋊C8)C2314yes—
138C22⋊(C71⋊C8)C2314yescomplemented
139C22⋊(C71⋊C8)C2314yescomplemented
140C25×C71D411yescharacteristic
141C2×#41×C71—21no—
142C2×#41×C71—21no—
143C2×#41×C71—44no—
144C2×#41×C71C2312yes—
145C2×#41×C71C2312yescomplemented
146C22×Q8×C71C2311yescharacteristic, complemented
147C22×D4×C71—21no—
148C22×D4×C71—21no—
149C22×D4×C71—21no—
150C22×D4×C71C2311yescharacteristic, complemented
151C23×C4×C71—21no—
152C23×C4×C71—44no—
153C23×C4×C71D411yescharacteristic
154C23×C4×C71D411yescharacteristic
155C23×C4×C71D411yescharacteristic
156C23×C4×C71D411yescharacteristic
157C23×C4×C71D411yescharacteristic
158C23×C4×C71D411yescharacteristic
159C23×C4×C71D411yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C23×C4×C71C2311yescharacteristic
162C23×C4×C71C2311yescharacteristic
163C23×C4×C71C2311yescharacteristic
164C23×C4×C71C2311yescharacteristic
165C23×C4×C71C2311yescharacteristic
166C23×C4×C71C2311yescharacteristic
167#123×C71—22no—
168#123×C71—22no—
169#123×C71—22no—
170#123×C71—22no—
171C22⋊Q8×C71—21no—
172C22⋊Q8×C71—21no—
173C22⋊Q8×C71—21no—
174C22⋊Q8×C71—21no—
175C22⋊Q8×C71C2312yes—
176C22⋊Q8×C71C2312yes—
177C22⋊Q8×C71C2312yescomplemented
178C22⋊Q8×C71C2312yescomplemented
179#121×C71—21no—
180#121×C71—21no—
181#121×C71—21no—
182#121×C71—21no—
183#121×C71C2312yes—
184#121×C71C2312yes—
185#121×C71C2312yescomplemented
186#121×C71C2312yescomplemented
187#120×C71—22no—
188#120×C71—22no—
189#120×C71—22no—
190#120×C71—22no—
191C4×D4×C71—22no—
192C4×D4×C71—22no—
193C4×D4×C71—22no—
194C4×D4×C71—22no—
195C4×D4×C71—22no—
196C4×D4×C71—22no—
197C4×D4×C71—22no—
198C4×D4×C71—22no—
199#117×C71—21no—
200#117×C71—21no—
201#117×C71C2312yes—
202#117×C71C2312yescomplemented
203C2×C4⋊C4×C71—21no—
204C2×C4⋊C4×C71—21no—
205C2×C4⋊C4×C71C2311yescharacteristic, complemented
206C2×C4⋊C4×C71C2311yescharacteristic, complemented
207C2×C22⋊C4×C71—21no—
208C2×C22⋊C4×C71—21no—
209C2×C22⋊C4×C71—21no—
210C2×C22⋊C4×C71—21no—
211C2×C22⋊C4×C71—21no—
212C2×C42×C71—21no—
213C23×D71—22no—
214C23×D71—22no—
215C23×D71—22no—
216C23×D71—44no—
217C23×D71—44no—
218C23×D71—44no—
219C2×D284—28no—
220C2×D284—22no—
221C2×D284—22no—
222C2×D284—22no—
223C2×D284—44no—
224C2×D284—44no—
225C2×D284—44no—
226C2×D284—44no—
227C2×D284—44no—
228C2×D284C2414yes—
229C2×C22⋊D71—24no—
230C2×C22⋊D71—24no—
231C2×C22⋊D71—24no—
232C2×C22⋊D71—24no—
233C2×C22⋊D71—48no—
234C2×C22⋊D71—48no—
235C2×C22⋊D71—48no—
236C2×C22⋊D71—48no—
237C2×C22⋊D71—48no—
238C2×C22⋊D71—48no—
239C22×Dic71—22no—
240C22×Dic71—22no—
241C22×Dic71—22no—
242C22×Dic71—44no—
243#11765852—48no—
244#11765850—48no—
245#11765849—28no—
246#11765849—44no—
247C2×C71⋊C8—44no—
248C2×C71⋊C8C2418yes—
249C4⋊Dic71—22no—
250C4⋊Dic71—22no—
251C4⋊Dic71—22no—
252C4⋊Dic71C2414yes—
253(C2×D71)⋊C4—24no—
254(C2×D71)⋊C4—24no—
255(C2×D71)⋊C4—24no—
256(C2×D71)⋊C4—24no—
257C24×C71—24no—
258C24×C71—21no—
259C24×C71—42no—
260C24×C71—42no—
261C24×C71C2×D411yescharacteristic
262C24×C71C2×D411yescharacteristic
263C24×C71C2×D411yescharacteristic
264C24×C71C2×D411yescharacteristic
265C24×C71C2×D411yescharacteristic
266C24×C71C2×D411yescharacteristic
267C24×C71C2×D411yescharacteristic
268#41×C71—28no—
269#41×C71—44no—
270#41×C71—44no—
271#41×C71—44no—
272C2×Q8×C71—21no—
273C2×Q8×C71—42no—
274C2×Q8×C71C2412yes—
275C2×D4×C71—22no—
276C2×D4×C71—22no—
277C2×D4×C71—22no—
278C2×D4×C71—22no—
279C2×D4×C71—22no—
280C2×D4×C71—22no—
281C2×D4×C71—21no—
282C2×D4×C71—42no—
283C2×D4×C71—44no—
284C2×D4×C71—44no—
285C2×D4×C71—44no—
286C2×D4×C71C2412yes—
287C22×C4×C71—24no—
288C22×C4×C71—24no—
289C22×C4×C71—24no—
290C22×C4×C71—21no—
291C22×C4×C71—21no—
292C22×C4×C71—21no—
293C22×C4×C71—22no—
294C22×C4×C71—22no—
295C22×C4×C71—42no—
296C22×C4×C71—42no—
297C22×C4×C71—42no—
298C22×C4×C71—42no—
299C22×C4×C71—42no—
300C22×C4×C71—42no—
301C22×C4×C71—42no—
302C22×C4×C71—42no—
303C22×C4×C71—42no—
304C22×C4×C71—42no—
305C22×C4×C71—42no—
306C22×C4×C71—44no—
307C22×C4×C71C2×D411yescharacteristic
308C22×C4×C71C2×D411yescharacteristic
309C22×C4×C71C2×D411yescharacteristic
310C22×C4×C71C2×D411yescharacteristic
311C22×C4×C71C2×D411yescharacteristic
312C22×C4×C71C2×D411yescharacteristic
313C22×C4×C71C2×D411yescharacteristic
314C22×C4×C71C2×D411yescharacteristic
315C22×C4×C71C2×D411yescharacteristic
316C22×C4×C71C2×D411yescharacteristic
317C22×C4×C71C2×D411yescharacteristic
318C22×C4×C71C2×D411yescharacteristic
319C22×C4×C71C2×D411yescharacteristic
320C22×C4×C71C2×D411yescharacteristic
321C22×C4×C71C2×D411yescharacteristic
322C22×C4×C71C2×D411yescharacteristic
323C22×C4×C71C2×D411yescharacteristic
324C22×C4×C71C2×D411yescharacteristic
325C22×C4×C71C2×D411yescharacteristic
326C22×C4×C71C2×D411yescharacteristic
327C22×C4×C71C2×D411yescharacteristic
328C22×C4×C71C2411yescharacteristic
329C22×C4×C71C2411yescharacteristic
330C22×C4×C71C2411yescharacteristic
331C22×C4×C71C2411yescharacteristic
332C22×C4×C71C2411yescharacteristic
333C22×C4×C71C2411yescharacteristic
334C22×C4×C71C2411yescharacteristic
335C4⋊C4×C71—22no—
336C4⋊C4×C71—22no—
337C4⋊C4×C71—22no—
338C4⋊C4×C71—22no—
339C4⋊C4×C71—21no—
340C4⋊C4×C71—21no—
341C4⋊C4×C71C2412yes—
342C4⋊C4×C71C2412yes—
343C22⋊C4×C71—22no—
344C22⋊C4×C71—22no—
345C22⋊C4×C71—22no—
346C22⋊C4×C71—22no—
347C22⋊C4×C71—22no—
348C22⋊C4×C71—22no—
349C22⋊C4×C71—22no—
350C22⋊C4×C71—22no—
351C22⋊C4×C71—22no—
352C22⋊C4×C71—22no—
353C42×C71—22no—
354C42×C71—22no—
355C23×C71—22no—
356C23×C71—22no—
357C23×C71—22no—
358C23×C71—22no—
359C23×C71—22no—
360C23×C71—22no—
361C23×C71—22no—
362C23×C71—22no—
363C23×C71—22no—
364C23×C71—22no—
365C23×C71—22no—
366C23×C71—22no—
367C23×C71—22no—
368C23×C71—41no—
369C23×C71—41no—
370C23×C71—41no—
371C23×C71—41no—
372C23×C71—41no—
373C23×C71—41no—
374C23×C71—41no—
375C23×C71—41no—
376C23×C71—416no—
377C23×C71—42no—
378C23×C71—42no—
379C23×C71—42no—
380C23×C71AGL(1,ℤ/8)14yescomplemented
381C23×C71C22×D411yescharacteristic
382C23×C71C22×D411yescharacteristic
383C23×C71C22×D411yescharacteristic
384C23×C71C22×D411yescharacteristic
385C23×C71C22×D411yescharacteristic
386C23×C71C22×D411yescharacteristic
387C23×C71C22×D411yescharacteristic
388C22×D71—24no—
389C22×D71—44no—
390C22×D71—44no—
391C22×D71—44no—
392C22×D71—44no—
393C22×D71—44no—
394C22×D71—44no—
395C22×D71—44no—
396C22×D71—44no—
397C22×D71—44no—
398C22×D71—816no—
399Q8×C71—24no—
400Q8×C71—42no—
401D4×C71—24no—
402D4×C71—42no—
403D4×C71—44no—
404D4×C71—44no—
405D4×C71—44no—
406D4×C71—44no—
407D4×C71—44no—
408D4×C71—44no—
409C2×C4×C71—22no—
410C2×C4×C71—22no—
411C2×C4×C71—22no—
412C2×C4×C71—22no—
413C2×C4×C71—22no—
414C2×C4×C71—22no—
415C2×C4×C71—22no—
416C2×C4×C71—22no—
417C2×C4×C71—22no—
418C2×C4×C71—22no—
419C2×C4×C71—22no—
420C2×C4×C71—22no—
421C2×C4×C71—22no—
422C2×C4×C71—22no—
423C2×C4×C71—22no—
424C2×C4×C71—22no—
425C2×C4×C71—22no—
426C2×C4×C71—22no—
427C2×C4×C71—41no—
428C2×C4×C71—41no—
429C2×C4×C71—41no—
430C2×C4×C71—41no—
431C2×C4×C71—41no—
432C2×C4×C71—41no—
433C2×C4×C71—41no—
434C2×C4×C71—41no—
435C2×C4×C71—41no—
436C2×C4×C71—41no—
437C2×C4×C71—41no—
438C2×C4×C71—41no—
439C2×C4×C71—44no—
440C2×C4×C71—42no—
441C2×C4×C71—42no—
442C2×C4×C71—42no—
443C2×C4×C71—44no—
444C2×C4×C71C22×D411yescharacteristic
445C2×C4×C71C22×D411yescharacteristic
446C2×C4×C71C22×D411yescharacteristic
447C2×C4×C71C22×D411yescharacteristic
448C2×C4×C71C22×D411yescharacteristic
449C2×C4×C71C22×D411yescharacteristic
450C2×C4×C71C22×D411yescharacteristic
451C2×C4×C71H(5,𝔽2)14yes—
452C2×C4×C71C2511yescharacteristic
453C22⋊D71—48no—
454C22⋊D71—48no—
455C22⋊D71—48no—
456C22⋊D71—48no—
457C2×Dic71—24no—
458C2×Dic71—44no—
459C2×Dic71—44no—
460C2×Dic71—44no—
461D284—28no—
462D284—44no—
463D284—44no—
464D284—44no—
465C71⋊C8—28no—
466C22×C71—28no—
467C22×C71—21no—
468C22×C71—21no—
469C22×C71—21no—
470C22×C71—21no—
471C22×C71—21no—
472C22×C71—21no—
473C22×C71—21no—
474C22×C71—21no—
475C22×C71—21no—
476C22×C71—21no—
477C22×C71—21no—
478C22×C71—21no—
479C22×C71—21no—
480C22×C71—21no—
481C22×C71—21no—
482C22×C71—21no—
483C22×C71—44no—
484C22×C71—44no—
485C22×C71—44no—
486C22×C71—44no—
487C22×C71—44no—
488C22×C71—44no—
489C22×C71—42no—
490C22×C71—42no—
491C22×C71—42no—
492C22×C71—84no—
493C22×C71#53412yes—
494C22×C71C2×AGL(1,ℤ/8)12yes—
495C22×C71C2×AGL(1,ℤ/8)12yes—
496C22×C71C2×AGL(1,ℤ/8)12yes—
497C22×C71#57512yes—
498C22×C71C23×D411yescharacteristic
499C2×D71—44no—
500C2×D71—44no—
501C2×D71—44no—
502C2×D71—88no—
503C2×D71—88no—
504C2×D71—88no—
505C4×C71—21no—
506C4×C71—21no—
507C4×C71—21no—
508C4×C71—21no—
509C4×C71—21no—
510C4×C71—21no—
511C4×C71—42no—
512C4×C71—42no—
513C4×C71—42no—
514C4×C71#53412yes—
515C4×C71C2×H(5,𝔽2)12yes—
516Dic71—44no—
517#60750—711nomaximal, Sylow
518C2×C71—22no—
519C2×C71—22no—
520C2×C71—22no—
521C2×C71—22no—
522C2×C71—22no—
523C2×C71—41no—
524C2×C71—41no—
525C2×C71—82no—
526C2×C71C2×#53411yescharacteristic
527C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
528C2×C71C2×#57511yescharacteristic
529D71—84no—
530C2×#525D7111yescharacteristic, complemented
531C22×#121—711no—
532#3194—714no—
533#3193—712no—
534#3192—712no—
535#3188—714no—
536#3187—712no—
537#3186—712no—
538#3094—712no—
539#3092—712no—
540#3055—714no—
541#3006—712no—
542#3003—712no—
543C2×#407—711no—
544C71#6075011yescharacteristic, complemented, Sylow
545C22×#41C2×D7111yescharacteristic, complemented
546C23×D4—711no—
547C23×D4—1421no—
548C24×C4C2×D7111yescharacteristic
549C2×AGL(1,ℤ/8)—714no—
550C22×M16—712no—
551#525—21no—
552#525—21no—
553#525—21no—
554#525—21no—
555#525C2×D7112yes—
556#525C2×D7112yescomplemented
557#525C2×D7112yescomplemented
558#525C2×D7112yescomplemented
559C2×#123—21no—
560C2×C22⋊Q8C2×D7111yescharacteristic, complemented
561C2×C22⋊Q8C2×D7111yescharacteristic, complemented
562C2×#121—712no—
563C2×#121—712no—
564C2×#121—712no—
565C2×#121—712no—
566C2×#121—712no—
567C2×#121—712no—
568C2×#121—1421no—
569C2×#121—1421no—
570C2×#121—1421no—
571C2×#121—1421no—
572C2×#121—1421no—
573C2×#121—1421no—
574C2×#121C2×D7111yescharacteristic, complemented
575C2×#121C2×D7111yescharacteristic, complemented
576C2×#120—21no—
577C2×C4×D4—21no—
578C2×C4×D4—21no—
579C2×#117C2×D7111yescharacteristic, complemented
580C22×C4⋊C4—711no—
581C22×C22⋊C4—1421no—
582#484—714no—
583#483—714no—
584#482—718no—
585#481—714no—
586#481—714no—
587#480—714no—
588#480—714no—
589#469—718no—
590#468—718no—
591#466—718no—
592#465—718no—
593#450—714no—
594#450—714no—
595#449—718no—
596#448—714no—
597#447—714no—
598#447—714no—
599#447—714no—
600#428—714no—
601#418—714no—
602#417—714no—
603#407—712no—
604#407—712no—
605#407—712no—
606#407—712no—
607C2×C22⋊C8—712no—
608C2×C22⋊C8—712no—
609C25—1421no—
610C25C22⋊D7111yescharacteristic
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—44no—
614C2×#41C22×D7112yes—
615C2×#41C22×D7112yescomplemented
616C22×Q8C22×D7111yescharacteristic, complemented
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4—2844no—
621C22×D4—2848no—
622C22×D4—712no—
623C22×D4—712no—
624C22×D4—712no—
625C22×D4—1422no—
626C22×D4—1422no—
627C22×D4—1422no—
628C22×D4—1422no—
629C22×D4—1422no—
630C22×D4—1422no—
631C22×D4—1421no—
632C22×D4—1421no—
633C22×D4—1421no—
634C22×D4C22×D7111yescharacteristic, complemented
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—1421no—
638C23×C4C22⋊D7111yescharacteristic
639C23×C4C22⋊D7111yescharacteristic
640C23×C4C22⋊D7111yescharacteristic
641C23×C4C22⋊D7111yescharacteristic
642C23×C4C22⋊D7111yescharacteristic
643C23×C4C22⋊D7111yescharacteristic
644C23×C4C22⋊D7111yescharacteristic
645C23×C4C22×D7111yescharacteristic
646C23×C4C22×D7111yescharacteristic
647C23×C4C22×D7111yescharacteristic
648C23×C4C22×D7111yescharacteristic
649C23×C4C22×D7111yescharacteristic
650C23×C4C22×D7111yescharacteristic
651C23×C4C22×D7111yescharacteristic
652AGL(1,ℤ/8)—2848no—
653C2×SD16—718no—
654C2×D8—718no—
655C2×M16—2844no—
656C2×M16—714no—
657C2×M16—714no—
658C22×C8—714no—
659#123—22no—
660#123—22no—
661#123—22no—
662#123—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8C22×D7112yes—
668C22⋊Q8C22×D7112yes—
669C22⋊Q8C22×D7112yescomplemented
670C22⋊Q8C22×D7112yescomplemented
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—714no—
676#121—714no—
677#121—714no—
678#121—714no—
679#121—1422no—
680#121—1422no—
681#121—1422no—
682#121—1422no—
683#121—1422no—
684#121—1422no—
685#121—1422no—
686#121—1422no—
687#121—1422no—
688#121—1422no—
689#121—1422no—
690#121—1422no—
691#121C22×D7112yes—
692#121C22×D7112yes—
693#121C22×D7112yescomplemented
694#121C22×D7112yescomplemented
695#120—22no—
696#120—22no—
697#120—22no—
698#120—22no—
699C4×D4—22no—
700C4×D4—22no—
701C4×D4—22no—
702C4×D4—22no—
703C4×D4—22no—
704C4×D4—22no—
705C4×D4—22no—
706C4×D4—22no—
707#117—21no—
708#117—21no—
709#117C22×D7112yes—
710#117C22×D7112yescomplemented
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—712no—
714C2×C4⋊C4—712no—
715C2×C4⋊C4—712no—
716C2×C4⋊C4—1421no—
717C2×C4⋊C4—1421no—
718C2×C4⋊C4—1421no—
719C2×C4⋊C4C22×D7111yescharacteristic, complemented
720C2×C4⋊C4C22×D7111yescharacteristic, complemented
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—1422no—
727C2×C22⋊C4—1422no—
728C2×C22⋊C4—1422no—
729C2×C22⋊C4—1422no—
730C2×C22⋊C4—1422no—
731C2×C22⋊C4—1422no—
732C2×C42—21no—
733#107—718no—
734#106—718no—
735#103—718no—
736#102—718no—
737#102—718no—
738#102—718no—
739C22⋊C8—714no—
740C22⋊C8—714no—
741C22⋊C8—714no—
742C22⋊C8—714no—
743C24—24no—
744C24—21no—
745C24—42no—
746C24—42no—
747C24—2844no—
748C24—2844no—
749C24—2844no—
750C24—1422no—
751C24—1422no—
752C24—1422no—
753C24C2×C22⋊D7111yescharacteristic
754C24C2×C22⋊D7111yescharacteristic
755C24C2×C22⋊D7111yescharacteristic
756C24C2×C22⋊D7111yescharacteristic
757C24C2×C22⋊D7111yescharacteristic
758C24C2×C22⋊D7111yescharacteristic
759C24C2×C22⋊D7111yescharacteristic
760#41—28no—
761#41—44no—
762#41—44no—
763#41—44no—
764C2×Q8—21no—
765C2×Q8—42no—
766C2×Q8C23×D7112yes—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—21no—
774C2×D4—42no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—2844no—
779C2×D4—2844no—
780C2×D4—2844no—
781C2×D4—2844no—
782C2×D4—2844no—
783C2×D4—2848no—
784C2×D4—2848no—
785C2×D4—2848no—
786C2×D4—2848no—
787C2×D4—2848no—
788C2×D4—2848no—
789C2×D4—714no—
790C2×D4—1424no—
791C2×D4—1424no—
792C2×D4—1424no—
793C2×D4—1424no—
794C2×D4—1422no—
795C2×D4—1422no—
796C2×D4—1422no—
797C2×D4—1428no—
798C2×D4C23×D7112yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—44no—
819C22×C4—2844no—
820C22×C4—1422no—
821C22×C4—1422no—
822C22×C4—1422no—
823C22×C4C2×C22⋊D7111yescharacteristic
824C22×C4C2×C22⋊D7111yescharacteristic
825C22×C4C2×C22⋊D7111yescharacteristic
826C22×C4C2×C22⋊D7111yescharacteristic
827C22×C4C2×C22⋊D7111yescharacteristic
828C22×C4C2×C22⋊D7111yescharacteristic
829C22×C4C2×C22⋊D7111yescharacteristic
830C22×C4C2×C22⋊D7111yescharacteristic
831C22×C4C2×C22⋊D7111yescharacteristic
832C22×C4C2×C22⋊D7111yescharacteristic
833C22×C4C2×C22⋊D7111yescharacteristic
834C22×C4C2×C22⋊D7111yescharacteristic
835C22×C4C2×C22⋊D7111yescharacteristic
836C22×C4C2×C22⋊D7111yescharacteristic
837C22×C4C2×C22⋊D7111yescharacteristic
838C22×C4C2×C22⋊D7111yescharacteristic
839C22×C4C2×C22⋊D7111yescharacteristic
840C22×C4C2×C22⋊D7111yescharacteristic
841C22×C4C2×C22⋊D7111yescharacteristic
842C22×C4C2×C22⋊D7111yescharacteristic
843C22×C4C2×C22⋊D7111yescharacteristic
844C22×C4C23×D7111yescharacteristic
845C22×C4C23×D7111yescharacteristic
846C22×C4C23×D7111yescharacteristic
847C22×C4C23×D7111yescharacteristic
848C22×C4C23×D7111yescharacteristic
849C22×C4C23×D7111yescharacteristic
850C22×C4C23×D7111yescharacteristic
851SD16—2848no—
852D8—2848no—
853M16—2844no—
854M16—1428no—
855C2×C8—2844no—
856C2×C8—718no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—714no—
864C4⋊C4—1422no—
865C4⋊C4—1422no—
866C4⋊C4—1422no—
867C4⋊C4C23×D7112yes—
868C4⋊C4C23×D7112yes—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—1424no—
880C22⋊C4—1424no—
881C22⋊C4—1424no—
882C22⋊C4—1424no—
883C42—22no—
884C42—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—2844no—
911C23—2844no—
912C23—2844no—
913C23—2844no—
914C23—2844no—
915C23—2844no—
916C23—2844no—
917C23—2844no—
918C23—2844no—
919C23—56816no—
920C23—1424no—
921C23#1455615314yescomplemented
922C23C22×C22⋊D7111yescharacteristic
923C23C22×C22⋊D7111yescharacteristic
924C23C22×C22⋊D7111yescharacteristic
925C23C22×C22⋊D7111yescharacteristic
926C23C22×C22⋊D7111yescharacteristic
927C23C22×C22⋊D7111yescharacteristic
928C23C22×C22⋊D7111yescharacteristic
929Q8—24no—
930Q8—42no—
931D4—24no—
932D4—42no—
933D4—44no—
934D4—44no—
935D4—44no—
936D4—44no—
937D4—44no—
938D4—44no—
939D4—2844no—
940D4—2844no—
941D4—2848no—
942D4—2848no—
943D4—2848no—
944D4—2848no—
945D4—2844no—
946D4—1428no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—44no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—44no—
982C2×C4—2844no—
983C2×C4—2844no—
984C2×C4—2844no—
985C2×C4—1424no—
986C2×C4C22×C22⋊D7111yescharacteristic
987C2×C4C22×C22⋊D7111yescharacteristic
988C2×C4C22×C22⋊D7111yescharacteristic
989C2×C4C22×C22⋊D7111yescharacteristic
990C2×C4C22×C22⋊D7111yescharacteristic
991C2×C4C22×C22⋊D7111yescharacteristic
992C2×C4C22×C22⋊D7111yescharacteristic
993C2×C4#1455617314yes—
994C2×C4C24×D7111yescharacteristic
995C8—1428no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—84no—
1023C22—2844no—
1024C22—2844no—
1025C22—2844no—
1026C22—5688no—
1027C22—5688no—
1028C22—5688no—
1029C22#1798655812yes—
1030C22C2×#1455615312yes—
1031C22C2×#1455615312yes—
1032C22C2×#1455615312yes—
1033C22#1798679712yes—
1034C22C23×C22⋊D7111yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—2844no—
1045C4#1798655812yes—
1046C4C2×#1455617312yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—82no—
1055C2—5684no—
1056C2C2×#1798655811yescharacteristic
1057C2C22×#1455615311yescharacteristic
1058C2C2×#1798679711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#525×C71C2
socleC22×C71C23×D4
hypercenterC2×#525D71
hypocenterC71#60750
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C22×#14556102C2semidirect
2. #22599150C2semidirect
3. #22599142C2semidirect
4. #22599137C2semidirect
5. #22599101C2semidirect
6. #22599093C2semidirect
7. #22599088C2semidirect
8. #22598280C2semidirect
9. #22598260C2semidirect
10. #22597961C2semidirect
11. #22597592C2semidirect
12. #22597566C2semidirect
13. C2×#17985963C2semidirect
14. C2×#525×C71C2semidirect
15. C23×D284C22semidirect
17. C2×#14556153C22semidirect
18. C22×#11765849C22semidirect
28. C2×#14556102C22semidirect
29. C2×#14556102C22semidirect
30. C2×#14556102C22semidirect
31. C22×C4⋊Dic71C22semidirect
33. #17986332C22semidirect
34. #17986327C22semidirect
35. #17986323C22semidirect
36. #17986317C22semidirect
37. #17986315C22semidirect
38. #17986312C22semidirect
39. #17986310C22semidirect
40. #17986250C22semidirect
41. #17986247C22semidirect
42. #17986233C22semidirect
43. #17986230C22semidirect
44. #17986149C22semidirect
45. #17986149C22semidirect
46. #17986144C22semidirect
47. #17986138C22semidirect
48. #17986133C22semidirect
49. #17986132C22semidirect
50. #17986132C22semidirect
51. #17986042C22semidirect
52. #17986003C22semidirect
53. #17986000C22semidirect
54. #17985963C22semidirect
55. #17985963C22semidirect
56. #17985963C22semidirect
57. #17985963C22semidirect
58. C2×C22⋊(C71⋊C8)C22semidirect
59. C2×C22⋊(C71⋊C8)C22semidirect
60. C22×#41×C71C22semidirect
67. #525×C71C22semidirect
68. #525×C71C22semidirect
69. #525×C71C22semidirect
71. C2×C22⋊Q8×C71C22semidirect
72. C2×C22⋊Q8×C71C22semidirect
73. C2×#121×C71C22semidirect
74. C2×#121×C71C22semidirect
78. C2×#117×C71C22semidirect
96. C2×#11765852C23semidirect
97. C2×#11765850C23semidirect
100. C2×#11765849C23semidirect
101. C22×C71⋊C8C23semidirect
130. #14556061C23semidirect
131. #14556059C23semidirect
132. #14556052C23semidirect
133. #14556049C23semidirect
134. #14556048C23semidirect
135. #14556048C23semidirect
138. C22⋊(C71⋊C8)C23semidirect
139. C22⋊(C71⋊C8)C23semidirect
145. C2×#41×C71C23semidirect
146. C22×Q8×C71C23semidirect
150. C22×D4×C71C23semidirect
177. C22⋊Q8×C71C23semidirect
178. C22⋊Q8×C71C23semidirect
185. #121×C71C23semidirect
186. #121×C71C23semidirect
202. #117×C71C23semidirect
205. C2×C4⋊C4×C71C23semidirect
206. C2×C4⋊C4×C71C23semidirect
380. C23×C71AGL(1,ℤ/8)semidirect
530. C2×#525D71semidirect
544. C71#60750semidirect
545. C22×#41C2×D71semidirect
556. #525C2×D71semidirect
557. #525C2×D71semidirect
558. #525C2×D71semidirect
560. C2×C22⋊Q8C2×D71semidirect
561. C2×C22⋊Q8C2×D71semidirect
574. C2×#121C2×D71semidirect
575. C2×#121C2×D71semidirect
579. C2×#117C2×D71semidirect
615. C2×#41C22×D71semidirect
616. C22×Q8C22×D71semidirect
634. C22×D4C22×D71semidirect
669. C22⋊Q8C22×D71semidirect
670. C22⋊Q8C22×D71semidirect
693. #121C22×D71semidirect
694. #121C22×D71semidirect
710. #117C22×D71semidirect
719. C2×C4⋊C4C22×D71semidirect
720. C2×C4⋊C4C22×D71semidirect
921. C23#14556153semidirect

Maximal subgroups

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

subgroupindex
C22×#145561022
#225991502
#225991422
#225991372
#225991012
#225990932
#225990882
#225982802
#225982602
#225979612
#225975922
#225975662
C2×#179859632
C2×#525×C712
#6075071