Finite Group Databasebeta

← #11867188

Subgroups — #11867188

Order 1152.

1163 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595301C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3C2×#63791C211yesmaximal, characteristic, complemented
4D3×#895C211yesmaximal, characteristic, complemented
5#10592474C211yesmaximal, characteristic, complemented
6C3×#4782C211yesmaximal, characteristic, complemented
7C3×#4771C211yesmaximal, characteristic, complemented
8#10591455C211yesmaximal, characteristic, complemented
9#10591453C211yesmaximal, characteristic, complemented
10#10590939C211yesmaximal, characteristic, complemented
11#10590850C211yesmaximal, characteristic, complemented
12#10590841C211yesmaximal, characteristic, complemented
13#10590581C211yesmaximal, characteristic, complemented
14#10590523C211yesmaximal, characteristic, complemented
15#10590515C211yesmaximal, characteristic, complemented
16#80864—31nomaximal
17#78888—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21C2×C4×D32C2211yescharacteristic
22#64147C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic, complemented
24C2×C8×C3⋊D3C2211yescharacteristic, complemented
25#64104C2211yescharacteristic
26C3×#938C2211yescharacteristic, complemented
27C2×C3×#213C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×D3×C4⋊C4C2211yescharacteristic
32#63983—21no—
33Dic3×#67—21no—
34#63969—21no—
35#63952—21no—
36#63925—24no—
37D3×(C2×D3)⋊C4—21no—
38#63916C2211yescharacteristic
39#63910—21no—
40#63909C2211yescharacteristic
41#63886—21no—
42#63871C2211yescharacteristic, complemented
43#63856C2211yescharacteristic, complemented
44#63841C2211yescharacteristic
45C2×#3717C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C2×#3711C2211yescharacteristic
48C2×#3711C2211yescharacteristic, complemented
49C2×#3710C2211yescharacteristic, complemented
50#63791—24no—
51C32×#102C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63634C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59#63575C2211yescharacteristic, complemented
60#63574C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#5828—31no—
64C2×#949—31no—
65C2×#911—31no—
66C2×D3×M16—31no—
67C2×D3×M16—31no—
68#5606—31no—
69D3×#121—31no—
70C2×#895—31no—
71C3×#469—31no—
72C3×#417—31no—
73#5157—31no—
74#5134—31no—
75#5131—31no—
76#5042—31no—
77#5039—31no—
78#4964—31no—
79#4864—31no—
80#4861—31no—
81#4812—31no—
82#4812—31no—
83#4807—31no—
84#4807—31no—
85#4782—31no—
86#4782D311yescharacteristic, complemented
87#4778—31no—
88#4775—31no—
89#4775—31no—
90#4775—31no—
91#4775—61no—
92#4771D311yescharacteristic, complemented
93#4770—31no—
94C22×D32—21no—
95C22×D32D411yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C3×#237—22no—
105C3×#237—22no—
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#624D411yescharacteristic
116C2×D3×Dic3D411yescharacteristic
117C2×D3×Dic3D411yescharacteristic
118D3×D12—22no—
119D3×D12—22no—
120D3×D12—44no—
121C4×D32—22no—
122C4×D32—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125#3757—21no—
126#3753—22no—
127#3752—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C8×C3⋊D3—22no—
131C3×#217—21no—
132C3×#213—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×ΓL(1,𝔽25)—22no—
140C3×ΓL(1,𝔽25)—22no—
141#3724—21no—
142Dic3⋊Dic3—21no—
143#3722—21no—
144#3722—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3717—22no—
150#3715—22no—
151#3711—22no—
152#3711D414yescomplemented
153#3710—22no—
154#3055—91noSylow
155C2×C3×#41—31no—
156C2×#237C2×D311yescharacteristic
157C2×D3×D4—31no—
158C2×D3×D4—61no—
159C22×D12—31no—
160C22×D12—61no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C2×C3×D8—31no—
164C2×C3×M16—31no—
165C2×C3×M16—31no—
166C3×#121—31no—
167C3×#121—31no—
168C2×C3×C4⋊C4—31no—
169#949—64no—
170#946—31no—
171#946—31no—
172C2×#215—31no—
173C2×#215—31no—
174#939—61no—
175#938—31no—
176#938—31no—
177#938—31no—
178#938—61no—
179#938C2×D311yescharacteristic, complemented
180#937—61no—
181#937—61no—
182#935—61no—
183D4×Dic3—61no—
184C2×#214—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—61no—
188C2×#213C2×D311yescharacteristic, complemented
189#930—31no—
190C4×#67—61no—
191C4×#67—61no—
192C2×(C2×D3)⋊C4—61no—
193#926—31no—
194#924—31no—
195C2×#208—31no—
196C2×#208—31no—
197#911—64no—
198D3×M16—64no—
199D3×M16—64no—
200C2×#204—31no—
201C2×ΓL(1,𝔽25)—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)C2×D311yescharacteristic
204C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
205C2×D3×C8—31no—
206C2×D3×C8—31no—
207C2×D3×C8—31no—
208C2×D3×C8—31no—
209C2×D3×C8—61no—
210#897—31no—
211#895—31no—
212#895—31no—
213#895—31no—
214#895—31no—
215#895—61no—
216#895—61no—
217#895—61no—
218#895C2×D311yescharacteristic
219#892—31no—
220D3×C4⋊C4C2×D311yescharacteristic
221#884—61no—
222#883—61no—
223#67⋊C4—61no—
224D3×C22⋊C4—61no—
225C3×#106—31no—
226C3×#103—31no—
227C3×#103—31no—
228C3×#102—21no—
229C3×#102—31no—
230C3×#102—31no—
231C3×#102C2×D311yescharacteristic, complemented
232C3×#102C2×D311yescharacteristic, complemented
233#832—31no—
234#832C2×D311yescharacteristic, complemented
235#821—31no—
236#821—31no—
237#821—31no—
238#821—31no—
239#821—61no—
240#821C2×D311yescharacteristic, complemented
241#818—31no—
242#816C2×D311yescharacteristic, complemented
243#810C2×D311yescharacteristic, complemented
244#809—31no—
245#808—31no—
246#808—31no—
247#808C2×D311yescharacteristic, complemented
248#807—31no—
249#807—31no—
250#807—31no—
251#807—61no—
252C23×C32—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—22no—
259C2×D32—22no—
260C2×D32—41no—
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C32×D4—21no—
265C32×D4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268#638—42no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—42no—
274C4×C3⋊D3—21no—
275C4×C3⋊D3—21no—
276C3×#67—42no—
277C3×#67—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—42no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×C4×D3C2×D412yes—
291C3×C4×D3#4112yes—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#626—42no—
295#626—42no—
296#626—42no—
297#624—22no—
298D3×Dic3—22no—
299D3×Dic3—22no—
300C32×C8—21no—
301C3⋊(C3⋊C8)C2×D412yescomplemented
302C3×C3⋊C8—21no—
303C3×C3⋊C8C2×D412yescomplemented
304C2×AGL(1,ℤ/8)—91no—
305C22×M16—91no—
306#525—91no—
307C2×#121—91no—
308#469—31no—
309#469—91no—
310#468—91no—
311#468—91no—
312#466—91no—
313#466—91no—
314#465—91no—
315#465—91no—
316#428—91no—
317#418—91no—
318#417—31no—
319C23×D3—31no—
320C23×D3—31no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—62no—
325C2×C3×Q8—31no—
326C2×C3×D4—21no—
327C2×C3×D4—31no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C2×#67—21no—
338C2×#67—21no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—121no—
345C22×Dic3—21no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348#237—22no—
349#237—22no—
350D3×D4—62no—
351D3×D4—62no—
352D3×D4—124no—
353C2×D12—21no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—61no—
357C2×D12—62no—
358C2×D12—62no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—121no—
365C2×D12—124no—
366C2×D12C22×D311yescharacteristic
367C2×C4×D3—21no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3—31no—
372C2×C4×D3—31no—
373C2×C4×D3—31no—
374C2×C4×D3—61no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3C22×D311yescharacteristic
380C2×C4×D3C22×D311yescharacteristic
381C2×Dic6C22×D311yescharacteristic
382C3×D8—62no—
383C3×M16—62no—
384C3×M16—62no—
385C2×C3×C8—21no—
386C2×C3×C8—31no—
387C2×C3×C8—31no—
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390C3×C4⋊C4—21no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398#217—21no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—121no—
405#215—62no—
406#215—62no—
407#214—62no—
408#213—22no—
409#213—62no—
410#213—62no—
411#213—122no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—121no—
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3C22×D311yescharacteristic
428C4⋊Dic3C22×D311yescharacteristic
429Dic3⋊C4—21no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433C4×Dic3—61no—
434C4×Dic3—61no—
435#208—34no—
436#208—62no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—61no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442#204—62no—
443ΓL(1,𝔽25)—22no—
444ΓL(1,𝔽25)—22no—
445ΓL(1,𝔽25)—34no—
446ΓL(1,𝔽25)—62no—
447D3×C8—62no—
448D3×C8—62no—
449D3×C8—62no—
450D3×C8—62no—
451D3×C8—122no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3#12112yes—
471D32—44no—
472D32—84no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4C2×#4111yescharacteristic
476C3⋊Dic3—21no—
477C3⋊Dic3—41no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3#12112yes—
483C2×#41—31no—
484C22×D4—91no—
485C22×D4—181no—
486C23×C4—91no—
487AGL(1,ℤ/8)—184no—
488C2×SD16—91no—
489C2×SD16—91no—
490C2×D8—31no—
491C2×D8—91no—
492C2×M16—31no—
493C2×M16—31no—
494C2×M16—91no—
495C2×M16—91no—
496C2×M16—184no—
497C22×C8—91no—
498C22×C8—91no—
499#123—181no—
500C22⋊Q8—91no—
501C22⋊Q8—91no—
502#121—31no—
503#121—31no—
504#121—91no—
505#121—91no—
506#121—91no—
507#121—91no—
508#121—181no—
509#121—181no—
510#120—181no—
511C4×D4—181no—
512C4×D4—181no—
513#117—91no—
514C2×C4⋊C4—31no—
515C2×C22⋊C4—181no—
516#107—91no—
517#107—91no—
518#106—31no—
519#106—91no—
520#103—31no—
521#103—31no—
522#102—31no—
523#102—31no—
524#102—91no—
525#102—91no—
526#102—91no—
527#102D3211yescharacteristic, complemented
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—31no—
532C23×C3—41no—
533C23×C3—61no—
534C22×D3—21no—
535C22×D3—31no—
536C22×D3—31no—
537C22×D3—61no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—62no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—121no—
545C22×D3—121no—
546C22×D3—121no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3D3×D411yescharacteristic
554C22×D3D3×D411yescharacteristic
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—41no—
562C3×D4—41no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—122no—
566C3×D4—122no—
567C3×D4—122no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—31no—
575C2×C3×C4—41no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—122no—
582C2×C3×C4—122no—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585#67—42no—
586#67—42no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—122no—
592#67—242no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—42no—
599C2×Dic3—61no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—121no—
605C2×Dic3D3×D411yescharacteristic
606C2×Dic3D3×D411yescharacteristic
607D12—21no—
608D12—21no—
609D12—42no—
610D12—61no—
611D12—61no—
612D12—61no—
613D12—61no—
614D12—121no—
615D12—121no—
616D12—122no—
617D12—122no—
618D12—122no—
619D12—122no—
620D12—122no—
621D12—242no—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—42no—
625C4×D3—62no—
626C4×D3—62no—
627C4×D3—62no—
628C4×D3—61no—
629C4×D3—61no—
630C4×D3—61no—
631C4×D3—61no—
632C4×D3—62no—
633C4×D3—121no—
634C4×D3—121no—
635C4×D3#23512yes—
636C4×D3D3×D412yes—
637Dic6—21no—
638Dic6—21no—
639C3×C8—21no—
640C3×C8—21no—
641C3×C8—32no—
642C3×C8—41no—
643C3×C8—61no—
644C3⋊C8—21no—
645C3⋊C8—32no—
646C3⋊C8—32no—
647C3⋊C8—62no—
648C3⋊C8D3×D412yescomplemented
649C2×C32—81no—
650C2×C32C2×#12111yescharacteristic
651C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
652C2×C32#57511yescharacteristic
653C3⋊D3—22no—
654C3⋊D3—81no—
655C3×D3—22no—
656C3×D3—41no—
657C3×D3—81no—
658C24—91no—
659C24—181no—
660#41—62no—
661#41—62no—
662C2×Q8—31no—
663C2×D4—31no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—91no—
668C2×D4—181no—
669C2×D4—182no—
670C2×D4—182no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—181no—
674C2×D4—181no—
675C2×D4—364no—
676C2×D4C2×D3211yescharacteristic
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—182no—
686C22×C4—182no—
687SD16—182no—
688SD16—182no—
689D8—62no—
690D8—182no—
691M16—62no—
692M16—62no—
693M16—94no—
694M16—182no—
695C2×C8—31no—
696C2×C8—31no—
697C2×C8—91no—
698C2×C8—182no—
699C2×C8—182no—
700C2×C8C2×D3211yescharacteristic
701C4⋊C4—31no—
702C4⋊C4—31no—
703C4⋊C4—61no—
704C4⋊C4—91no—
705C4⋊C4—181no—
706C4⋊C4—181no—
707C4⋊C4C2×D3211yescharacteristic
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—181no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C42—181no—
718C22×C3—21no—
719C22×C3—32no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—81no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3C2×D3×D411yescharacteristic
738C22×C3C2×D3×D411yescharacteristic
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—32no—
745C2×D3—32no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—62no—
750C2×D3—61no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—61no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—124no—
757C2×D3—124no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—241no—
765C2×D3—241no—
766C2×D3—241no—
767C2×D3—244no—
768C2×D3—244no—
769C2×D3#88412yes—
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—32no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—61no—
776C3×C4—81no—
777C3×C4—121no—
778C3×C4—121no—
779C3×C4—121no—
780C3×C4C2×#23511yescharacteristic
781C3×C4C2×D3×D411yescharacteristic
782C3×C4C2×D3×D411yescharacteristic
783C3×C4D3×#4111yescharacteristic
784Dic3—21no—
785Dic3—41no—
786Dic3—41no—
787Dic3—41no—
788Dic3—61no—
789Dic3—61no—
790Dic3—121no—
791Dic3—121no—
792Dic3—121no—
793Dic3—241no—
794Dic3#88412yes—
795C32#305511yescharacteristic, complemented, Sylow
796C23—21no—
797C23—31no—
798C23—31no—
799C23—61no—
800C23—91no—
801C23—182no—
802C23—182no—
803C23—181no—
804C23—362no—
805C23—361no—
806C23—362no—
807C23—362no—
808Q8—61no—
809Q8—61no—
810D4—21no—
811D4—21no—
812D4—61no—
813D4—61no—
814D4—122no—
815D4—122no—
816D4—122no—
817D4—181no—
818D4—181no—
819D4—362no—
820D4—362no—
821D4—362no—
822D4—362no—
823D4—362no—
824C2×C4—21no—
825C2×C4—31no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—31no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—91no—
835C2×C4—122no—
836C2×C4—122no—
837C2×C4—182no—
838C2×C4—182no—
839C2×C4—182no—
840C2×C4—181no—
841C2×C4—181no—
842C2×C4—181no—
843C2×C4C22×D3211yescharacteristic
844C8—21no—
845C8—32no—
846C8—61no—
847C8—92no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—62no—
852C2×C3—81no—
853C2×C3—81no—
854C2×C3—121no—
855C2×C3—161no—
856C2×C3—241no—
857C2×C3C2×#88411yescharacteristic
858C2×C3D3×#12111yescharacteristic
859C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
860C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
861C2×C3#577311yescharacteristic
862C2×C3#577711yescharacteristic
863D3—22no—
864D3—41no—
865D3—62no—
866D3—62no—
867D3—81no—
868D3—122no—
869D3—241no—
870D3—241no—
871D3—481no—
872C22—32no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—61no—
877C22—61no—
878C22—61no—
879C22—61no—
880C22—61no—
881C22—92no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—181no—
886C22—181no—
887C22—364no—
888C22—361no—
889C22—361no—
890C22—361no—
891C22—724no—
892C22D32×D411yescharacteristic
893C4—32no—
894C4—41no—
895C4—61no—
896C4—121no—
897C4—121no—
898C4—121no—
899C4—181no—
900C4—361no—
901C4D3×#23511yescharacteristic
902C4D32×D411yescharacteristic
903C3—21no—
904C3#7888811yescharacteristic, complemented
905C3#8086411yescharacteristic, complemented
906C2—62no—
907C2—81no—
908C2—121no—
909C2—182no—
910C2—241no—
911C2—721no—
912C2D3×#88411yescharacteristic
913C2#1059472611yescharacteristic
914C2#1059474411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595301C2semidirect
2. C2×#63925C2semidirect
3. C2×#63791C2semidirect
4. D3×#895C2semidirect
5. #10592474C2semidirect
6. C3×#4782C2semidirect
7. C3×#4771C2semidirect
8. #10591455C2semidirect
9. #10591453C2semidirect
10. #10590939C2semidirect
11. #10590850C2semidirect
12. #10590841C2semidirect
13. #10590581C2semidirect
14. #10590523C2semidirect
15. #10590515C2semidirect
22. #64147C22semidirect
23. C2×#3753C22semidirect
24. C2×C8×C3⋊D3C22semidirect
26. C3×#938C22semidirect
27. C2×C3×#213C22semidirect
29. C2×C3×ΓL(1,𝔽25)C22semidirect
42. #63871C22semidirect
43. #63856C22semidirect
45. C2×#3717C22semidirect
46. C2×#3715C22semidirect
48. C2×#3711C22semidirect
49. C2×#3710C22semidirect
51. C32×#102C22semidirect
52. #63648C22semidirect
53. #63634C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
56. C3×#816C22semidirect
57. C3×#810C22semidirect
58. C3×#808C22semidirect
59. #63575C22semidirect
60. #63574C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
86. #4782D3semidirect
92. #4771D3semidirect
152. #3711D4semidirect
179. #938C2×D3semidirect
188. C2×#213C2×D3semidirect
204. C2×ΓL(1,𝔽25)C2×D3semidirect
231. C3×#102C2×D3semidirect
232. C3×#102C2×D3semidirect
234. #832C2×D3semidirect
240. #821C2×D3semidirect
242. #816C2×D3semidirect
243. #810C2×D3semidirect
247. #808C2×D3semidirect
301. C3⋊(C3⋊C8)C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
461. C2×C3⋊D3AGL(1,ℤ/8)semidirect
527. #102D32semidirect
648. C3⋊C8D3×D4semidirect
795. C32#3055semidirect
904. C3#78888semidirect
905. C3#80864semidirect

Maximal subgroups

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

subgroupindex
#105953012
C2×#639252
C2×#637912
D3×#8952
#105924742
C3×#47822
C3×#47712
#105914552
#105914532
#105909392
#105908502
#105908412
#105905812
#105905232
#105905152
#808643
#788883