Finite Group Databasebeta

← #25259432

Subgroups — #25259432

Order 11008.

2510 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583446C211yesmaximal, characteristic
2#19137748C214yesmaximal, complemented
3#19137638C212yesmaximal, complemented
4#19137635C212yesmaximal, complemented
5#19137542C211yesmaximal, characteristic, complemented
6#19137526C212yesmaximal, complemented
7#19137525C212yesmaximal, complemented
8D4×C4⋊Dic43C211yesmaximal, characteristic, complemented
9#19137495C211yesmaximal, characteristic, complemented
10#19137402C214yesmaximal, complemented
11#19137339C212yesmaximal, complemented
12#19137319C212yesmaximal, complemented
13#19137184C212yesmaximal, complemented
14#19137183C212yesmaximal, complemented
15#19137000C211yesmaximal, characteristic, complemented
16#19136991C211yesmaximal, characteristic, complemented
17C43×#2354C211yesmaximal, characteristic, complemented
18C22×#10621898C2212yes—
19#14583446C4116yescomplemented
20C2×#13063324C2211yescharacteristic
21C2×#13063321C2211yescharacteristic
22C2×#13063311C2212yes—
23C2×#13063300C2211yescharacteristic
24C2×#13063298C2212yes—
25C2×#13063296C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27C2×D4×Dic43C2212yes—
28C2×#13063287C2212yes—
29C2×C4×C22⋊D43C2212yes—
30C2×#13063283C2212yes—
31C2×#13063283C2212yes—
32C22×C4⋊Dic43C2212yes—
33C2×C4⋊C4×D43C2212yes—
34C2×C42×D43C2211yescharacteristic
35#14582805C2214yes—
36#14582803C2214yes—
37#14582801C2212yes—
38#14582801C2214yes—
39#14582799C2214yes—
40#14582798C2212yes—
41#14582795C2212yes—
42#14582793C2214yes—
43#14582791C2214yes—
44#14582791C2214yes—
45#14582786C2214yes—
46#14582783C2214yes—
47#14582777C2214yes—
48#14582776C2214yes—
49#14582776C2214yes—
50#14582776C2214yes—
51#14582775C2214yes—
52#14582775C2214yes—
53#14582774C2214yes—
54#14582770C2214yes—
55#14582769C2211yescharacteristic
56#14582766C2212yes—
57#14582764C2212yes—
58#14582764C2211yescharacteristic
59#14582764C2211yescharacteristic
60#14582761C2212yes—
61#14582759C2212yes—
62#14582756C2212yes—
63#14582756C2211yescharacteristic
64#14582756C2212yes—
65#14582756C2212yes—
66#14582756C2211yescharacteristic
67#14582756C2212yes—
68C4⋊C4×Dic43C2212yes—
69C4⋊C4×Dic43C2212yes—
70C4×C4⋊Dic43C2212yes—
71C4×C4⋊Dic43C2211yescharacteristic
72C22⋊C4×Dic43C2214yes—
73C4×(C2×D43)⋊C4C2212yes—
74C4×(C2×D43)⋊C4C2214yes—
75#14582745C2212yes—
76C2×C4×D4×C43C2211yescharacteristic
77C2×#117×C43C2212yes—
78C43×#390C2212yes—
79C43×#388C2214yes—
80C43×#384C2211yescharacteristic
81C43×#380C2212yes—
82C4×C4⋊C4×C43C2211yescharacteristic
83C4×C4⋊C4×C43C2212yes—
84C2×#10621898—44no—
85C2×#10621898—44no—
86C2×#10621898C2×C4116yescomplemented
87C22×Dic86C2312yes—
88C22×D172C2311yescharacteristic
89C22×D172C2312yes—
90C22×C22⋊D43C2312yes—
91C22×C22⋊D43C2312yes—
92C22×C22⋊D43C2312yes—
93C23×Dic43C2314yes—
94C22×C4×D43C2311yescharacteristic
95C22×C4×D43C2311yescharacteristic
96C22×C4×D43C2312yes—
97C22×C4×D43C2314yes—
98C22×C4×D43C2311yescharacteristic
99#13063324C2×C418yescomplemented
100#13063321C2×C418yes—
101#13063311C2×C4116yescomplemented
102#13063300C2×C418yescomplemented
103#13063298C2×C4116yescomplemented
104#13063296C2×C418yescomplemented
105C4×D172C2×C418yescomplemented
106D4×Dic43—44no—
107#13063287—44no—
108C4×C22⋊D43C2×C4116yescomplemented
109#13063283—44no—
110#13063283—44no—
111C2×C4⋊Dic43—44no—
112C2×C4⋊Dic43C2312yes—
113C2×C4⋊Dic43C2311yescharacteristic
114C2×C4⋊Dic43C2311yescharacteristic
115C2×C4⋊Dic43C2312yes—
116C2×C4⋊Dic43C2314yes—
117C2×C4⋊Dic43C2312yes—
118C2×C4⋊Dic43C2311yescharacteristic
119C2×Dic43⋊C4C2314yes—
120C2×Dic43⋊C4C2312yes—
121C4⋊C4×D43—44no—
122C2×C22⋊Dic43C2314yes—
123C2×C22⋊Dic43C2312yes—
124C2×(C2×D43)⋊C4C2314yes—
125C2×(C2×D43)⋊C4C2314yes—
126C2×(C2×D43)⋊C4C2314yes—
127C2×(C2×D43)⋊C4C2312yes—
128C2×(C2×D43)⋊C4C2314yes—
129C2×(C2×D43)⋊C4C2312yes—
130C2×(C2×D43)⋊C4C2312yes—
131C2×(C2×D43)⋊C4C2312yes—
132C2×C4×Dic43C2312yes—
133C2×C4×Dic43C2314yes—
134C2×C4×Dic43C2314yes—
135C2×C4×Dic43C2311yescharacteristic
136C2×C4×Dic43C2311yescharacteristic
137C2×C4×Dic43C2311yescharacteristic
138C42×D43C2×C418yescomplemented
139C43⋊#95C2312yes—
140C43⋊#95C2314yes—
141C43⋊#95C2314yes—
142C43⋊#95C2312yes—
143C43⋊#95C2314yes—
144C43⋊#95C2312yes—
145C43⋊#95C2314yes—
146C43⋊#95C2312yes—
147C43⋊#95C2314yes—
148C43⋊#95C2312yes—
149C43⋊#95C2312yes—
150C43⋊#95C2312yes—
151C22×D4×C43C2311yescharacteristic
152C23×C4×C43C2312yes—
153C4×D4×C43C2×C418yescomplemented
154#117×C43—44no—
155C2×C4⋊C4×C43C2312yes—
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C4⋊C4×C43C2312yes—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2312yes—
160C2×C4⋊C4×C43C2311yescharacteristic
161C2×C22⋊C4×C43C2314yes—
162C2×C22⋊C4×C43C2314yes—
163C2×C22⋊C4×C43C2312yes—
164C2×C42×C43C2312yes—
165C2×C42×C43C2314yes—
166C2×C42×C43C2311yescharacteristic
167#95×C43C2314yes—
168#95×C43C2312yes—
169C24×C43C2412yes—
170C23×D43C2411yescharacteristic
171C23×D43C2412yes—
172C2×D4×C43—22no—
173C2×D4×C43—22no—
174C2×D4×C43C22×C414yes—
175C22×C4×C43—24no—
176C22×C4×C43—24no—
177C22×C4×C43C22×C418yes—
178C22×C4×C43C2412yes—
179C22×C4×C43C2412yes—
180C22×C4×C43C2414yes—
181C22×C4×C43C2412yes—
182C22×C4×C43C2411yescharacteristic
183C22×C4×C43C2411yescharacteristic
184C22×C4×C43C2411yescharacteristic
185C2×C22⋊D43—42no—
186C2×C22⋊D43—42no—
187C2×C22⋊D43—42no—
188C2×C22⋊D43—42no—
189C2×C22⋊D43—42no—
190C2×C22⋊D43—42no—
191C2×C22⋊D43C22×C418yes—
192C2×C22⋊D43C22×C418yes—
193C2×C22⋊D43C22×C418yes—
194C22×Dic43—44no—
195C22×Dic43—44no—
196C22×Dic43—44no—
197C22×Dic43C2412yes—
198C22×Dic43C2412yes—
199C22×Dic43C2414yes—
200C22×Dic43C2411yescharacteristic
201C22×Dic43C2411yescharacteristic
202C22×Dic43C2411yescharacteristic
203C22×Dic43C2412yes—
204#10621898—432no—
205C2×D172—22no—
206C2×D172—22no—
207C2×D172—42no—
208C2×D172—42no—
209C2×D172C22×C414yes—
210C2×D172C22×C418yes—
211C2×C4×D43—24no—
212C2×C4×D43—22no—
213C2×C4×D43—24no—
214C2×C4×D43—22no—
215C2×C4×D43—22no—
216C2×C4×D43—22no—
217C2×C4×D43—41no—
218C2×C4×D43—41no—
219C2×C4×D43—44no—
220C2×C4×D43—44no—
221C2×C4×D43—44no—
222C2×C4×D43C22×C414yes—
223C2×C4×D43C22×C414yes—
224C2×C4×D43C22×C418yes—
225C2×C4×D43C22×C414yes—
226C2×Dic86—42no—
227C2×Dic86—42no—
228C2×Dic86C22×C418yes—
229C4⋊C4×C43—22no—
230C4⋊C4×C43—24no—
231C4⋊C4×C43—22no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—42no—
234C4⋊C4×C43C22×C414yes—
235C22⋊C4×C43—44no—
236C22⋊C4×C43—44no—
237C22⋊C4×C43C22×C418yes—
238C42×C43—24no—
239C42×C43—44no—
240C42×C43C22×C414yes—
241C22⋊Dic43—44no—
242C22⋊Dic43C22×C418yes—
243(C2×D43)⋊C4—42no—
244(C2×D43)⋊C4—42no—
245(C2×D43)⋊C4—44no—
246(C2×D43)⋊C4—44no—
247(C2×D43)⋊C4—44no—
248(C2×D43)⋊C4—44no—
249(C2×D43)⋊C4C22×C418yes—
250(C2×D43)⋊C4C22×C418yes—
251C4⋊Dic43—22no—
252C4⋊Dic43—22no—
253C4⋊Dic43—24no—
254C4⋊Dic43—24no—
255C4⋊Dic43—44no—
256C4⋊Dic43—42no—
257C4⋊Dic43C22×C414yes—
258Dic43⋊C4—44no—
259Dic43⋊C4C22×C418yes—
260C4×Dic43—24no—
261C4×Dic43—44no—
262C4×Dic43—44no—
263C4×Dic43C22×C414yes—
264C4×Dic43C22×C414yes—
265C4×Dic43C22×C414yes—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43C23×C414yes—
273C23×C43C2511yescharacteristic
274C22×D43—21no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—22no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43C23×C414yes—
287C22×D43C23×C412yes—
288D4×C43—28no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—216no—
294C2×C4×C43—22no—
295C2×C4×C43—24no—
296C2×C4×C43—24no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—24no—
303C2×C4×C43C23×C412yes—
304C2×C4×C43C23×C414yes—
305C2×C4×C43C23×C412yes—
306C2×C4×C43C23×C412yes—
307C2×C4×C43H(5,𝔽2)12yes—
308C2×C4×C43H(5,𝔽2)12yes—
309C2×C4×C43H(5,𝔽2)12yes—
310C2×C4×C432−1+412yes—
311C22⋊D43—48no—
312C22⋊D43—48no—
313C22⋊D43—48no—
314C2×Dic43—21no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—24no—
325C2×Dic43—24no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—24no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—88no—
332C2×Dic43C23×C412yes—
333C2×Dic43C23×C412yes—
334C2×Dic43C23×C412yes—
335C2×Dic43C23×C414yes—
336D172—28no—
337D172—48no—
338C4×D43—216no—
339C4×D43—28no—
340C4×D43—28no—
341C4×D43—44no—
342C4×D43—88no—
343Dic86—48no—
344#34367—431nomaximal, Sylow
345C22×C43—24no—
346C22×C43—24no—
347C22×C43—24no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43C24×C411yescharacteristic
353C22×C43C2×H(5,𝔽2)11yescharacteristic
354C22×C43C2×H(5,𝔽2)11yescharacteristic
355C22×C43C2×H(5,𝔽2)11yescharacteristic
356C22×C43C2×2−1+411yescharacteristic
357C22×C43#58511yescharacteristic
358C22×C43#58511yescharacteristic
359C2×D43—22no—
360C2×D43—24no—
361C2×D43—22no—
362C2×D43—24no—
363C2×D43—22no—
364C2×D43—24no—
365C2×D43—41no—
366C2×D43—41no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—41no—
371C2×D43—42no—
372C2×D43—41no—
373C4×C43—24no—
374C4×C43—22no—
375C4×C43—44no—
376C4×C43—42no—
377C4×C43—42no—
378C4×C43#51814yes—
379C4×C43#52014yes—
380Dic43—22no—
381Dic43—24no—
382Dic43—22no—
383Dic43—22no—
384Dic43—42no—
385Dic43—44no—
386Dic43—42no—
387C2×#532—431no—
388#2377—434no—
389#2363—432no—
390#2363—432no—
391#2354—431no—
392#2354D4311yescharacteristic, complemented
393#2352—432no—
394#2352—432no—
395D4×C4⋊C4—431no—
396D4×C4⋊C4—431no—
397#2337—434no—
398#2331—432no—
399#2328—432no—
400#2311—432no—
401#2311—432no—
402#2285—431no—
403#2283—431no—
404C2×C43—44no—
405C2×C43C2×#51811yescharacteristic
406C2×C43C2×#52011yescharacteristic
407C2×C43#342811yescharacteristic
408C2×C43#354611yescharacteristic
409C2×C43#354611yescharacteristic
410C2×C43#354711yescharacteristic
411C2×C43#354711yescharacteristic
412D43—42no—
413D43—44no—
414C22×#41—432no—
415#532—4316no—
416C2×C4⋊Q8—431no—
417C2×#127—431no—
418C2×#124—432no—
419C2×#121—431no—
420C2×#121—431no—
421C2×#121—432no—
422C2×C4×D4—432no—
423C2×C4×D4—432no—
424C2×C4×D4—432no—
425C2×C4×D4—431no—
426C2×C4×D4C2×D4311yescharacteristic
427C2×#117—432no—
428C2×#117—432no—
429C2×#117C2×D4312yes—
430C22×C4⋊C4—432no—
431C22×C4⋊C4—432no—
432C22×C42—431no—
433#391—434no—
434#391—434no—
435#390—434no—
436#390—434no—
437#390—432no—
438#390C2×D4312yes—
439#389—432no—
440#389—432no—
441#388—434no—
442#388—434no—
443#388—434no—
444#388C2×D4314yes—
445#387—434no—
446#387—434no—
447#386—434no—
448#386—434no—
449#386—434no—
450#386—434no—
451#386—434no—
452#386—434no—
453#385—434no—
454#385—434no—
455#384—431no—
456#384C2×D4311yescharacteristic
457#383—432no—
458#382—432no—
459#382—431no—
460#382—431no—
461#381—432no—
462#380—432no—
463#380—431no—
464#380—431no—
465#380—432no—
466#380—432no—
467#380—432no—
468#380—432no—
469#380C2×D4312yes—
470C4×C4⋊C4—432no—
471C4×C4⋊C4—432no—
472C4×C4⋊C4—432no—
473C4×C4⋊C4—431no—
474C4×C4⋊C4C2×D4312yes—
475C4×C4⋊C4C2×D4311yescharacteristic
476C4×C22⋊C4—434no—
477C4×C22⋊C4—434no—
478C4×C22⋊C4—432no—
479#376—432no—
480C43#3436711yescharacteristic, complemented, Sylow
481C2×#41—4316no—
482C2×#41—1724no—
483C2×#41—1724no—
484C22×Q8—432no—
485C22×D4—432no—
486C22×D4—432no—
487C22×D4—432no—
488C22×D4—431no—
489C22×D4—432no—
490C22×D4C22×D4311yescharacteristic
491C23×C4—432no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—434no—
496C23×C4—434no—
497C23×C4C22×D4312yes—
498C4⋊Q8—438no—
499#127—438no—
500#124—4316no—
501#121—438no—
502#121—438no—
503#121—4316no—
504C4×D4—4316no—
505C4×D4—438no—
506C4×D4—1724no—
507C4×D4—1724no—
508C4×D4C4×D4318yescomplemented
509#117—44no—
510#117—1724no—
511#117—1724no—
512C2×C4⋊C4—432no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—432no—
517C2×C4⋊C4—432no—
518C2×C4⋊C4—434no—
519C2×C4⋊C4—434no—
520C2×C4⋊C4—432no—
521C2×C4⋊C4—1724no—
522C2×C4⋊C4—1724no—
523C2×C4⋊C4C22×D4312yes—
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C4⋊C4C22×D4312yes—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4312yes—
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C22⋊C4—432no—
530C2×C22⋊C4—432no—
531C2×C22⋊C4—432no—
532C2×C22⋊C4—434no—
533C2×C22⋊C4—434no—
534C2×C22⋊C4—434no—
535C2×C22⋊C4—434no—
536C2×C22⋊C4—432no—
537C2×C22⋊C4—432no—
538C2×C22⋊C4—434no—
539C2×C22⋊C4C22×D4314yes—
540C2×C22⋊C4C22×D4314yes—
541C2×C22⋊C4C22×D4312yes—
542C2×C42—431no—
543C2×C42—431no—
544C2×C42—431no—
545C2×C42—438no—
546C2×C42—432no—
547C2×C42—434no—
548C2×C42—434no—
549C2×C42C22×D4312yes—
550C2×C42C22×D4314yes—
551C2×C42C22×D4311yescharacteristic
552#95—432no—
553#95—432no—
554#95—432no—
555#95—432no—
556#95—432no—
557#95—432no—
558#95—434no—
559#95—434no—
560#95—434no—
561#95—434no—
562#95—434no—
563#95—432no—
564#95C22×D4314yes—
565#95C22×D4312yes—
566C24—432no—
567C24—431no—
568C24C23×D4312yes—
569#41—17232no—
570C2×Q8—438no—
571C2×Q8—1722no—
572C2×Q8—1722no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—438no—
576C2×D4—438no—
577C2×D4—438no—
578C2×D4—434no—
579C2×D4—438no—
580C2×D4—862no—
581C2×D4—862no—
582C2×D4—1722no—
583C2×D4—1722no—
584C2×D4—1722no—
585C2×D4—1722no—
586C2×D4—1722no—
587C2×D4—1722no—
588C2×D4—1722no—
589C2×D4—1722no—
590C2×D4C2×C4×D4314yes—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—431no—
594C22×C4—431no—
595C22×C4—431no—
596C22×C4—432no—
597C22×C4—434no—
598C22×C4—434no—
599C22×C4—438no—
600C22×C4—434no—
601C22×C4—432no—
602C22×C4—432no—
603C22×C4—434no—
604C22×C4—864no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—864no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—1724no—
611C22×C4—1724no—
612C22×C4—1724no—
613C22×C4—1721no—
614C22×C4—1721no—
615C22×C4—1724no—
616C22×C4—1724no—
617C22×C4—1724no—
618C22×C4C2×C4×D4318yes—
619C22×C4C23×D4312yes—
620C22×C4C23×D4312yes—
621C22×C4C23×D4314yes—
622C22×C4C23×D4311yescharacteristic
623C22×C4C23×D4312yes—
624C22×C4C23×D4311yescharacteristic
625C22×C4C23×D4311yescharacteristic
626C4⋊C4—24no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—24no—
630C4⋊C4—42no—
631C4⋊C4—438no—
632C4⋊C4—434no—
633C4⋊C4—862no—
634C4⋊C4—862no—
635C4⋊C4—864no—
636C4⋊C4—864no—
637C4⋊C4—1724no—
638C4⋊C4—1724no—
639C4⋊C4—1722no—
640C4⋊C4C2×C4×D4314yes—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—438no—
644C22⋊C4—438no—
645C22⋊C4—438no—
646C22⋊C4—1724no—
647C22⋊C4—1724no—
648C22⋊C4—1724no—
649C22⋊C4—1722no—
650C22⋊C4—1724no—
651C22⋊C4—1722no—
652C22⋊C4—1724no—
653C22⋊C4C2×C4×D4318yes—
654C42—24no—
655C42—44no—
656C42—434no—
657C42—434no—
658C42—434no—
659C42—864no—
660C42—1724no—
661C42—1724no—
662C42C2×C4×D4314yes—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—434no—
670C23—432no—
671C23—862no—
672C23—861no—
673C23—861no—
674C23—862no—
675C23—862no—
676C23—861no—
677C23—861no—
678C23—862no—
679C23—861no—
680C23—862no—
681C23—861no—
682C23—862no—
683C23C22×C4×D4314yes—
684C23C24×D4311yescharacteristic
685Q8—1728no—
686D4—28no—
687D4—868no—
688D4—1728no—
689D4—1728no—
690D4—1728no—
691D4—1728no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—216no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—432no—
707C2×C4—432no—
708C2×C4—432no—
709C2×C4—434no—
710C2×C4—862no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—862no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—868no—
719C2×C4—8616no—
720C2×C4—868no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—864no—
725C2×C4—864no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—864no—
729C2×C4—862no—
730C2×C4—3448no—
731C2×C4—3448no—
732C2×C4—1724no—
733C2×C4C22×C4×D4312yes—
734C2×C4C22×C4×D4314yes—
735C2×C4C22×C4×D4312yes—
736C2×C4C22×C4×D4312yes—
737C2×C4#1306337012yes—
738C2×C4#1306337112yes—
739C2×C4#1306337112yes—
740C2×C4#1306337212yes—
741C22—24no—
742C22—24no—
743C22—24no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—862no—
749C22—864no—
750C22—862no—
751C22—864no—
752C22—862no—
753C22—864no—
754C22—1722no—
755C22—1721no—
756C22—1721no—
757C22—1722no—
758C22—1722no—
759C22—1721no—
760C22—1722no—
761C22—1721no—
762C22C23×C4×D4311yescharacteristic
763C22C2×#1306337011yescharacteristic
764C22C2×#1306337111yescharacteristic
765C22C2×#1306337111yescharacteristic
766C22C2×#1306337211yescharacteristic
767C22#1458373411yescharacteristic
768C22#1458373611yescharacteristic
769C4—24no—
770C4—22no—
771C4—44no—
772C4—42no—
773C4—42no—
774C4—862no—
775C4—864no—
776C4—862no—
777C4—862no—
778C4—1722no—
779C4—1722no—
780C4—1724no—
781C4#1458337114yes—
782C4#1458337914yes—
783C2—44no—
784C2—1722no—
785C2—1724no—
786C2C2×#1458337111yescharacteristic
787C2C2×#1458337911yescharacteristic
788C2#1914779511yescharacteristic
789C2#1914895511yescharacteristic
790C2#1914897011yescharacteristic
791C2#1914897211yescharacteristic
792C2#1914898711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2354C2
socle, cosocleC23×C43C25
prime radicalC2×#14583446C2
hypercenter#2354D43
hypocenterC43#34367
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #19137748C2semidirect
3. #19137638C2semidirect
4. #19137635C2semidirect
5. #19137542C2semidirect
6. #19137526C2semidirect
7. #19137525C2semidirect
8. D4×C4⋊Dic43C2semidirect
9. #19137495C2semidirect
10. #19137402C2semidirect
11. #19137339C2semidirect
12. #19137319C2semidirect
13. #19137184C2semidirect
14. #19137183C2semidirect
15. #19137000C2semidirect
16. #19136991C2semidirect
17. C43×#2354C2semidirect
19. #14583446C4semidirect
86. C2×#10621898C2×C4semidirect
99. #13063324C2×C4semidirect
101. #13063311C2×C4semidirect
102. #13063300C2×C4semidirect
103. #13063298C2×C4semidirect
104. #13063296C2×C4semidirect
105. C4×D172C2×C4semidirect
108. C4×C22⋊D43C2×C4semidirect
138. C42×D43C2×C4semidirect
153. C4×D4×C43C2×C4semidirect
392. #2354D43semidirect
480. C43#34367semidirect
508. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834462
#191377482
#191376382
#191376352
#191375422
#191375262
#191375252
D4×C4⋊Dic432
#191374952
#191374022
#191373392
#191373192
#191371842
#191371832
#191370002
#191369912
C43×#23542
#3436743