Finite Group Databasebeta

← #11867180

Subgroups — #11867180

Order 1152.

1191 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595282C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic, complemented
3C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
4#10594632C211yesmaximal, characteristic, complemented
5#10592469C211yesmaximal, characteristic, complemented
6C3×#4782C211yesmaximal, characteristic, complemented
7C3×#4778C211yesmaximal, characteristic, complemented
8#10591502C211yesmaximal, characteristic, complemented
9#10591498C211yesmaximal, characteristic, complemented
10#10590957C211yesmaximal, characteristic, complemented
11#10590850C211yesmaximal, characteristic, complemented
12#10590826C211yesmaximal, characteristic, complemented
13#10590586C211yesmaximal, characteristic, complemented
14#10590584C211yesmaximal, characteristic, complemented
15#10590577C211yesmaximal, characteristic, complemented
16#80864—31nomaximal
17#80657—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3811—21no—
20C2×C4×D32C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C2×#3743C2211yescharacteristic
23#64101C2211yescharacteristic
24C3×#938C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic, complemented
27C2×C3×#213C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#897C2211yescharacteristic, complemented
31C3×#895C2211yescharacteristic, complemented
32#63974—21no—
33#63971—21no—
34#63971—21no—
35#63937—24no—
36#63922—21no—
37#63909C2211yescharacteristic
38#63909C2211yescharacteristic
39#63908C2211yescharacteristic, complemented
40#63902—21no—
41#63900C2211yescharacteristic
42#63898—21no—
43#63856C2211yescharacteristic, complemented
44#63854—21no—
45C2×#3717C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic, complemented
47C2×#3712C2211yescharacteristic
48C2×#3711C2211yescharacteristic, complemented
49C2×D3×C3⋊C8C2211yescharacteristic, complemented
50D3×ΓL(1,𝔽25)—24no—
51C32×#102C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#808C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59#63575C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#911—31no—
65C2×D3×M16—31no—
66C22×ΓL(1,𝔽25)—31no—
67#5627—31no—
68#5606—31no—
69D3×#121—31no—
70D3×#121—31no—
71C3×#469—31no—
72C3×#465—31no—
73#5174—31no—
74#5157—31no—
75#5134—31no—
76#5115—31no—
77#5048—31no—
78#5042—31no—
79#5039—31no—
80#5038—31no—
81#4865—31no—
82#4864—31no—
83#4861—31no—
84#4861—31no—
85#4812—31no—
86#4803—31no—
87#4782D311yescharacteristic, complemented
88#4778D311yescharacteristic, complemented
89#4775—31no—
90#4771—31no—
91#4770—31no—
92#4770—31no—
93#4770—61no—
94C23×C3⋊D3—21no—
95C22×D32D411yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98D4×C3⋊D3—22no—
99D4×C3⋊D3—22no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×D12—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109#3811—44no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×#624—21no—
115C2×#624D411yescharacteristic
116C2×D3×Dic3—21no—
117C2×D3×Dic3D411yescharacteristic
118C2×D3×Dic3D411yescharacteristic
119C4×D32—22no—
120C4×D32—22no—
121#3796—22no—
122#3796—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125#3752—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127C4×C3⋊Dic3—21no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3743—22no—
130C3×#217—21no—
131C3×#217—21no—
132C3×#214—22no—
133C3×#213—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×ΓL(1,𝔽25)—22no—
142C3×D3×C8—22no—
143#3724—21no—
144#3724—21no—
145#3722—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3717—22no—
150#3714—22no—
151#3712D414yescomplemented
152#3711—22no—
153D3×C3⋊C8—22no—
154#3055—91noSylow
155C2×#239—31no—
156C2×#237—31no—
157C2×D3×D4—31no—
158C2×D3×D4—31no—
159C2×D3×D4—61no—
160C2×D3×D4—61no—
161C2×D3×D4—61no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C2×C3×SD16—31no—
165C2×C3×D8—31no—
166C2×C3×M16—31no—
167C22×C3×C8—31no—
168C3×C22⋊Q8—31no—
169C3×#121—31no—
170C3×#121—31no—
171C3×#121—31no—
172#946—31no—
173C2×#215—31no—
174#939—61no—
175#939—61no—
176#938—31no—
177#938C2×D311yescharacteristic
178#938C2×D311yescharacteristic
179#937—61no—
180D4×Dic3—61no—
181C2×#214C2×D311yescharacteristic, complemented
182C2×#213—31no—
183C2×#213C2×D311yescharacteristic, complemented
184#930—31no—
185#930—31no—
186#930—31no—
187#924—31no—
188C2×#208—31no—
189C22×C3⋊C8—31no—
190#914—64no—
191#911—64no—
192D3×M16—64no—
193C2×D24—31no—
194C2×#204—31no—
195C2×ΓL(1,𝔽25)—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×ΓL(1,𝔽25)—31no—
198C2×ΓL(1,𝔽25)—31no—
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—61no—
201C2×ΓL(1,𝔽25)—64no—
202C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
203C2×D3×C8—31no—
204C2×D3×C8C2×D311yescharacteristic, complemented
205#897C2×D311yescharacteristic, complemented
206#895—31no—
207#895—31no—
208#895C2×D311yescharacteristic, complemented
209#894—61no—
210#893—61no—
211#892—31no—
212#892—31no—
213#892—61no—
214D3×C4⋊C4—31no—
215D3×C4⋊C4—31no—
216#884—61no—
217#884—61no—
218#883—61no—
219#882—61no—
220#67⋊C4—61no—
221#67⋊C4—61no—
222D3×C22⋊C4—61no—
223D3×C22⋊C4—61no—
224C3×#106—31no—
225C3×#106—31no—
226C3×#103—31no—
227C3×#102—21no—
228C3×#102—31no—
229C3×#102C2×D311yescharacteristic, complemented
230C3×#102C2×D311yescharacteristic, complemented
231#835—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—61no—
236#821—31no—
237#821—31no—
238#821—61no—
239#821C2×D311yescharacteristic, complemented
240#818—31no—
241#818—31no—
242#816C2×D311yescharacteristic, complemented
243#810—31no—
244#809—31no—
245#809—31no—
246#809—31no—
247#809—61no—
248#808C2×D311yescharacteristic, complemented
249#808C2×D311yescharacteristic, complemented
250#807—31no—
251#807—31no—
252C23×C32—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—42no—
255C22×C3⋊D3—42no—
256C22×C3⋊D3—42no—
257C22×C3⋊D3C2×D411yescharacteristic
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—22no—
262C2×D32—22no—
263C2×D32—41no—
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⋊D3C2×D412yes—
274C4×C3⋊D3#4112yes—
275C3×#67—42no—
276C3×#67—42no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—42no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—42no—
292#626—42no—
293#626—42no—
294#625—42no—
295#624—22no—
296#624—42no—
297D3×Dic3—22no—
298D3×Dic3—22no—
299D3×Dic3—42no—
300C32×C8—21no—
301C3⋊(C3⋊C8)—21no—
302C3×C3⋊C8C2×D412yescomplemented
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—31no—
315#465—91no—
316#428—91no—
317#418—91no—
318#417—91no—
319C23×D3—31no—
320C23×D3—31no—
321C23×D3—61no—
322C23×D3—61no—
323C23×D3—121no—
324C2×C3×Q8—31no—
325C2×C3×D4—21no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C2×#67—21no—
335C2×#67—21no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—121no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—61no—
347#239—62no—
348#239—62no—
349#237—62no—
350#237—62no—
351D3×D4—62no—
352D3×D4—62no—
353D3×D4—62no—
354D3×D4—62no—
355D3×D4—64no—
356D3×D4—122no—
357D3×D4—124no—
358D3×D4—124no—
359C2×D12—21no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12C22×D311yescharacteristic
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3—31no—
372C2×C4×D3—31no—
373C2×C4×D3—61no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3C22×D311yescharacteristic
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6C22×D311yescharacteristic
384C3×SD16—62no—
385C3×D8—62no—
386C3×M16—62no—
387C2×C3×C8—21no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C2×C3×C8—62no—
391C2×C3×C8C22×D311yescharacteristic
392C2×C3×C8C22×D311yescharacteristic
393C3×C4⋊C4—21no—
394C3×C4⋊C4—31no—
395C3×C4⋊C4—31no—
396C3×C4⋊C4—61no—
397C3×C4⋊C4C22×D311yescharacteristic
398C3×C4⋊C4C22×D311yescharacteristic
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403#217—21no—
404#217—21no—
405#217—61no—
406#217—61no—
407#215—62no—
408#214—22no—
409#213—22no—
410#213—62no—
411(C2×D3)⋊C4—21no—
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—121no—
422C4⋊Dic3—21no—
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3—61no—
426C4⋊Dic3C22×D311yescharacteristic
427C4⋊Dic3C22×D311yescharacteristic
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432C4×Dic3—61no—
433C4×Dic3—61no—
434C4×Dic3—121no—
435#208—62no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—61no—
439C2×C3⋊C8—62no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442D24—62no—
443#204—62no—
444ΓL(1,𝔽25)—22no—
445ΓL(1,𝔽25)—34no—
446ΓL(1,𝔽25)—34no—
447ΓL(1,𝔽25)—62no—
448ΓL(1,𝔽25)—62no—
449ΓL(1,𝔽25)—62no—
450ΓL(1,𝔽25)—122no—
451D3×C8—22no—
452D3×C8—62no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32C22×D411yescharacteristic
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—84no—
463C2×C3⋊D3#12112yes—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3AGL(1,ℤ/8)12yescomplemented
473D32—44no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4C2×#4111yescharacteristic
477C3⋊Dic3—41no—
478C3⋊Dic3#12112yes—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C2×#41—91no—
485C22×D4—91no—
486C22×D4—181no—
487C23×C4—91no—
488AGL(1,ℤ/8)—184no—
489C2×SD16—31no—
490C2×SD16—91no—
491C2×D8—31no—
492C2×D8—91no—
493C2×M16—31no—
494C2×M16—91no—
495C2×M16—91no—
496C2×M16—91no—
497C2×M16—184no—
498C22×C8—31no—
499C22×C8—91no—
500#123—181no—
501C22⋊Q8—31no—
502C22⋊Q8—91no—
503#121—31no—
504#121—31no—
505#121—31no—
506#121—91no—
507#121—91no—
508#121—91no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—181no—
513C4×D4—181no—
514#117—91no—
515C2×C4⋊C4—91no—
516C2×C22⋊C4—181no—
517#107—91no—
518#107—91no—
519#106—31no—
520#106—31no—
521#103—31no—
522#103—91no—
523#102—31no—
524#102—91no—
525#102—91no—
526#102—91no—
527#102—91no—
528#102D3211yescharacteristic, complemented
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—31no—
532C23×C3—31no—
533C23×C3—41no—
534C23×C3—61no—
535C22×D3—21no—
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—61no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—121no—
546C22×D3—121no—
547C22×D3—121no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—124no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—242no—
556C22×D3—242no—
557C22×D3D3×D411yescharacteristic
558C22×D3D3×D411yescharacteristic
559C3×Q8—61no—
560C3×Q8—61no—
561C3×D4—22no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—21no—
566C3×D4—41no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—122no—
570C3×D4—122no—
571C3×D4—122no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—41no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4C23×D311yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587#67—42no—
588#67—42no—
589#67—122no—
590#67—122no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—124no—
595#67—122no—
596#67—122no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—31no—
601C2×Dic3—31no—
602C2×Dic3—61no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—121no—
608C2×Dic3—122no—
609C2×Dic3D3×D411yescharacteristic
610C2×Dic3D3×D411yescharacteristic
611D12—21no—
612D12—21no—
613D12—42no—
614D12—62no—
615D12—61no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—121no—
620D12—122no—
621D12—122no—
622D12—122no—
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—21no—
626C4×D3—21no—
627C4×D3—32no—
628C4×D3—32no—
629C4×D3—32no—
630C4×D3—32no—
631C4×D3—62no—
632C4×D3—62no—
633C4×D3—62no—
634C4×D3—62no—
635C4×D3—62no—
636C4×D3—62no—
637C4×D3—122no—
638C4×D3—122no—
639C4×D3—122no—
640Dic6—21no—
641Dic6—21no—
642C3×C8—21no—
643C3×C8—21no—
644C3×C8—32no—
645C3×C8—32no—
646C3×C8—41no—
647C3⋊C8—61no—
648C3⋊C8—61no—
649C3⋊C8—121no—
650C3⋊C8D3×D412yescomplemented
651C3⋊C8D3×D412yescomplemented
652C2×C32—81no—
653C2×C32C2×#12111yescharacteristic
654C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
655C2×C32#57511yescharacteristic
656C3⋊D3—22no—
657C3⋊D3—81no—
658C3×D3—22no—
659C3×D3—41no—
660C3×D3—81no—
661C24—91no—
662C24—181no—
663#41—182no—
664#41—182no—
665C2×Q8—31no—
666C2×D4—31no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—91no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—181no—
674C2×D4—182no—
675C2×D4—182no—
676C2×D4—181no—
677C2×D4—181no—
678C2×D4—364no—
679C2×D4C2×D3211yescharacteristic
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—91no—
686C22×C4—182no—
687C22×C4—182no—
688C22×C4—181no—
689C22×C4—181no—
690SD16—62no—
691SD16—182no—
692D8—62no—
693D8—182no—
694M16—62no—
695M16—94no—
696M16—182no—
697M16—182no—
698C2×C8—31no—
699C2×C8—31no—
700C2×C8—62no—
701C2×C8—91no—
702C2×C8—182no—
703C2×C8C2×D3211yescharacteristic
704C4⋊C4—31no—
705C4⋊C4—31no—
706C4⋊C4—61no—
707C4⋊C4—91no—
708C4⋊C4—181no—
709C4⋊C4—181no—
710C4⋊C4C2×D3211yescharacteristic
711C22⋊C4—61no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C42—181no—
721C22×C3—21no—
722C22×C3—32no—
723C22×C3—42no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—81no—
736C22×C3—81no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3C2×D3×D411yescharacteristic
741C22×C3C2×D3×D411yescharacteristic
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—32no—
748C2×D3—32no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—62no—
753C2×D3—61no—
754C2×D3—61no—
755C2×D3—61no—
756C2×D3—61no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—124no—
760C2×D3—124no—
761C2×D3—122no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—241no—
769C2×D3—241no—
770C2×D3—244no—
771C2×D3—244no—
772C2×D3—248no—
773C2×D3#91412yescomplemented
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—41no—
777C3×C4—41no—
778C3×C4—61no—
779C3×C4—61no—
780C3×C4—81no—
781C3×C4—121no—
782C3×C4—121no—
783C3×C4—121no—
784C3×C4C2×D3×D411yescharacteristic
785C3×C4C2×D3×D411yescharacteristic
786C3×C4D3×#4111yescharacteristic
787C3×C4D3×#4111yescharacteristic
788Dic3—21no—
789Dic3—21no—
790Dic3—32no—
791Dic3—32no—
792Dic3—41no—
793Dic3—41no—
794Dic3—41no—
795Dic3—62no—
796Dic3—121no—
797Dic3—121no—
798Dic3—241no—
799C32#305511yescharacteristic, complemented, Sylow
800C23—21no—
801C23—31no—
802C23—31no—
803C23—61no—
804C23—91no—
805C23—182no—
806C23—182no—
807C23—181no—
808C23—362no—
809C23—362no—
810C23—362no—
811C23—361no—
812Q8—61no—
813Q8—61no—
814D4—21no—
815D4—21no—
816D4—61no—
817D4—61no—
818D4—122no—
819D4—122no—
820D4—122no—
821D4—181no—
822D4—181no—
823D4—362no—
824D4—362no—
825D4—362no—
826D4—362no—
827D4—362no—
828C2×C4—21no—
829C2×C4—31no—
830C2×C4—31no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—91no—
839C2×C4—92no—
840C2×C4—92no—
841C2×C4—182no—
842C2×C4—182no—
843C2×C4—182no—
844C2×C4—181no—
845C2×C4—362no—
846C2×C4—362no—
847C2×C4C22×D3211yescharacteristic
848C8—21no—
849C8—32no—
850C8—32no—
851C8—181no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—62no—
856C2×C3—82no—
857C2×C3—81no—
858C2×C3—81no—
859C2×C3—121no—
860C2×C3—241no—
861C2×C3D3×#12111yescharacteristic
862C2×C3D3×#12111yescharacteristic
863C2×C3C2×#91411yescharacteristic
864C2×C3#576811yescharacteristic
865C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
866C2×C3#577311yescharacteristic
867D3—22no—
868D3—41no—
869D3—62no—
870D3—62no—
871D3—81no—
872D3—122no—
873D3—242no—
874D3—241no—
875D3—241no—
876C22—32no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—61no—
881C22—61no—
882C22—61no—
883C22—61no—
884C22—61no—
885C22—92no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—181no—
890C22—181no—
891C22—364no—
892C22—361no—
893C22—361no—
894C22—361no—
895C22—724no—
896C22D32×D411yescharacteristic
897C4—41no—
898C4—61no—
899C4—61no—
900C4—92no—
901C4—121no—
902C4—121no—
903C4—121no—
904C4—361no—
905C4#6430611yescharacteristic
906C4D32×D411yescharacteristic
907C3—21no—
908C3#8065711yescharacteristic, complemented
909C3#8086411yescharacteristic, complemented
910C2—62no—
911C2—81no—
912C2—121no—
913C2—182no—
914C2—241no—
915C2—721no—
916C2#1059426511yescharacteristic
917C2#1059472911yescharacteristic
918C2D3×#91411yescharacteristic
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. #10595282C2semidirect
2. C2×#63937C2semidirect
3. C2×D3×ΓL(1,𝔽25)C2semidirect
4. #10594632C2semidirect
5. #10592469C2semidirect
6. C3×#4782C2semidirect
7. C3×#4778C2semidirect
8. #10591502C2semidirect
9. #10591498C2semidirect
10. #10590957C2semidirect
11. #10590850C2semidirect
12. #10590826C2semidirect
13. #10590586C2semidirect
14. #10590584C2semidirect
15. #10590577C2semidirect
26. C2×C3×#214C22semidirect
27. C2×C3×#213C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
29. C2×C3×D3×C8C22semidirect
30. C3×#897C22semidirect
31. C3×#895C22semidirect
39. #63908C22semidirect
43. #63856C22semidirect
45. C2×#3717C22semidirect
46. C2×#3714C22semidirect
48. C2×#3711C22semidirect
49. C2×D3×C3⋊C8C22semidirect
51. C32×#102C22semidirect
52. #63659C22semidirect
53. #63648C22semidirect
54. #63636C22semidirect
55. C3×#821C22semidirect
56. C3×#816C22semidirect
57. C3×#808C22semidirect
58. C3×#808C22semidirect
59. #63575C22semidirect
60. #63575C22semidirect
61. #63565C22semidirect
62. #63562C22semidirect
87. #4782D3semidirect
88. #4778D3semidirect
151. #3712D4semidirect
181. C2×#214C2×D3semidirect
183. C2×#213C2×D3semidirect
202. C2×ΓL(1,𝔽25)C2×D3semidirect
204. C2×D3×C8C2×D3semidirect
205. #897C2×D3semidirect
208. #895C2×D3semidirect
229. C3×#102C2×D3semidirect
230. C3×#102C2×D3semidirect
239. #821C2×D3semidirect
242. #816C2×D3semidirect
248. #808C2×D3semidirect
249. #808C2×D3semidirect
302. C3×C3⋊C8C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
472. C2×C3×D3AGL(1,ℤ/8)semidirect
528. #102D32semidirect
650. C3⋊C8D3×D4semidirect
651. C3⋊C8D3×D4semidirect
773. C2×D3#914semidirect
799. C32#3055semidirect
908. C3#80657semidirect
909. C3#80864semidirect

Maximal subgroups

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

subgroupindex
#105952822
C2×#639372
C2×D3×ΓL(1,𝔽25)2
#105946322
#105924692
C3×#47822
C3×#47782
#105915022
#105914982
#105909572
#105908502
#105908262
#105905862
#105905842
#105905772
#808643
#806573