Finite Group Databasebeta

← #11878657

Subgroups — #11878657

Order 1152.

1163 conjugacy classes of subgroups.

The subgroup lattice has 947 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595300C211yesmaximal, characteristic, complemented
2#10595139C211yesmaximal, characteristic, complemented
3#10592855C211yesmaximal, characteristic, complemented
4C3×#5151C211yesmaximal, characteristic, complemented
5C3×#5150C211yesmaximal, characteristic, complemented
6#10591516C211yesmaximal, characteristic, complemented
7#10591487C211yesmaximal, characteristic, complemented
8#10591482C211yesmaximal, characteristic, complemented
9#10591481C211yesmaximal, characteristic, complemented
10#10591456C211yesmaximal, characteristic, complemented
11#10591428C211yesmaximal, characteristic, complemented
12#10590945C211yesmaximal, characteristic, complemented
13#10590878C211yesmaximal, characteristic, complemented
14#10590753C211yesmaximal, characteristic, complemented
15#10590643C211yesmaximal, characteristic, complemented
16#81785—31nomaximal
17#80336—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3811—21no—
20C2×#3811—21no—
21C2×#3804—21no—
22C2×#3802C2211yescharacteristic
23C2×C32×D8C2211yescharacteristic, complemented
24#64147C2211yescharacteristic
25C2×#3753C2211yescharacteristic, complemented
26C3×#940C2211yescharacteristic
27C3×#940C2211yescharacteristic
28C3×#940C2211yescharacteristic, complemented
29C3×D4×Dic3C2211yescharacteristic, complemented
30C2×C3×#213C2211yescharacteristic, complemented
31C2×C3×#213C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic, complemented
33C2×C3×D24C2211yescharacteristic, complemented
34#63979—21no—
35#63979—21no—
36Dic3×#67—21no—
37#63959—21no—
38#63958—21no—
39#63918C2211yescharacteristic, complemented
40#63916C2211yescharacteristic
41#63911C2211yescharacteristic
42#63911C2211yescharacteristic
43Dic3×D12C2211yescharacteristic, complemented
44C4×#624C2211yescharacteristic
45C2×#3714C2211yescharacteristic, complemented
46C2×#3713C2211yescharacteristic, complemented
47#63659C2211yescharacteristic, complemented
48#63648C2211yescharacteristic, complemented
49#63647C2211yescharacteristic
50C3×#832C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5716—31no—
62D3×#127—31no—
63D3×#127—31no—
64#5548—31no—
65C3×#493—31no—
66C3×#459—31no—
67#5156—31no—
68#5156—31no—
69#5156—31no—
70#5156—31no—
71#5156—31no—
72#5156—31no—
73#5156—61no—
74#5151—31no—
75#5151D311yescharacteristic, complemented
76#5150—31no—
77#5150—31no—
78#5150—31no—
79#5150D311yescharacteristic, complemented
80#5073—31no—
81#5072—31no—
82#5070—31no—
83#5015—31no—
84#4843—31no—
85#4833—31no—
86#4773—31no—
87#4773—31no—
88#4760—31no—
89#4760—31no—
90#4694—31no—
91#4685—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98D4×C3⋊D3—41no—
99D4×C3⋊D3—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C22×C3×Dic3—21no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112#3811—44no—
113#3811—44no—
114C2×#627—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#625—21no—
121C2×#624D411yescharacteristic
122C2×#624D411yescharacteristic
123#3804—44no—
124C2×D3×Dic3—21no—
125#3802—41no—
126#3802—41no—
127C32×D8—41no—
128C2×C32×C8C2311yescharacteristic
129#3757—21no—
130#3753—41no—
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C3×#217—21no—
134C3×#213—41no—
135C3×#213—41no—
136C3×#213—41no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—41no—
143Dic3⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146Dic32D411yescharacteristic
147Dic32D411yescharacteristic
148#3714—41no—
149#3713—41no—
150#3205—91noSylow
151C2×#237—61no—
152C2×D3×D4—31no—
153C2×D3×D4—31no—
154C2×D3×D4—31no—
155C2×D3×D4—31no—
156C2×D3×D4—61no—
157C2×D3×D4—61no—
158C2×D3×D4—61no—
159C2×D3×D4—61no—
160C2×D3×D4—61no—
161C2×#235—61no—
162C2×C3×D8—21no—
163C2×C3×D8—31no—
164C2×C3×D8—31no—
165C2×C3×D8—31no—
166C2×C3×D8—31no—
167C2×C3×D8C2×D311yescharacteristic, complemented
168C2×C3×D8C2×D311yescharacteristic, complemented
169C3×#127—31no—
170C3×#127—31no—
171C3×#127—31no—
172C3×C4×D4—31no—
173#940—31no—
174#940—31no—
175#940—61no—
176#940—61no—
177#940—61no—
178#940—61no—
179#940C2×D311yescharacteristic
180#940C2×D311yescharacteristic
181#940C2×D311yescharacteristic, complemented
182#938—31no—
183#938—31no—
184#938—31no—
185#938—61no—
186#938—61no—
187#936—61no—
188D4×Dic3—31no—
189D4×Dic3—61no—
190D4×Dic3C2×D311yescharacteristic, complemented
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—61no—
197C2×#213C2×D311yescharacteristic, complemented
198C2×#213C2×D311yescharacteristic, complemented
199C2×#213C2×D311yescharacteristic, complemented
200C4×#67—61no—
201C2×D24—31no—
202C2×D24C2×D311yescharacteristic, complemented
203#895—31no—
204#888—31no—
205#885—61no—
206#884—61no—
207#874—31no—
208#874—31no—
209C4×D12—31no—
210C42×D3—31no—
211C42×D3—31no—
212#869—31no—
213C3×C4⋊C8—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C4×C8—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#832—31no—
222#832—61no—
223#832C2×D311yescharacteristic, complemented
224#821—31no—
225#821—31no—
226#821—31no—
227#821—31no—
228#821—31no—
229#821—61no—
230#821C2×D311yescharacteristic, complemented
231(C2×D3)⋊C8—31no—
232(C2×D3)⋊C8—31no—
233(C2×D3)⋊C8—31no—
234(C2×D3)⋊C8—31no—
235(C2×D3)⋊C8—61no—
236Dic3⋊C8—31no—
237Dic3⋊C8C2×D311yescharacteristic, complemented
238C8×Dic3—31no—
239C8×Dic3C2×D311yescharacteristic, complemented
240#809—31no—
241#809—31no—
242C4⋊(C3⋊C8)—31no—
243C4×C3⋊C8—31no—
244C23×C32—21no—
245C23×C32—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—42no—
248C22×C3⋊D3—42no—
249C22×C3⋊D3—42no—
250C22×C3⋊D3C2×D411yescharacteristic
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C2×D32—42no—
255C2×D32—42no—
256C2×D32—42no—
257C32×D4—21no—
258C32×D4—21no—
259C32×D4—21no—
260C32×D4—21no—
261C2×C32×C4C2411yescharacteristic
262#638—42no—
263#638—42no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3C2×D411yescharacteristic
266C4⋊(C3⋊D3)—21no—
267C4⋊(C3⋊D3)—21no—
268C4×C3⋊D3—21no—
269C4×C3⋊D3—21no—
270C3×#67—42no—
271C3×#67—42no—
272C3×#67—42no—
273C3×#67—42no—
274C3×#67—42no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—42no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288#627—42no—
289#626—42no—
290#626—42no—
291#626—42no—
292#626—42no—
293#626—42no—
294#625—42no—
295#624—22no—
296#624D814yescomplemented
297D3×Dic3—42no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302#532—91no—
303C2×#127—91no—
304#493—31no—
305#493—91no—
306#486—91no—
307#486—91no—
308#459—31no—
309#459—91no—
310#459—91no—
311#459—91no—
312#447—91no—
313#447—91no—
314#447—91no—
315#447—91no—
316#431—91no—
317C23×D3—61no—
318C23×D3—61no—
319C23×D3—61no—
320C23×D3—61no—
321C23×D3—121no—
322C2×C3×D4—21no—
323C2×C3×D4—21no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C2×C3×D4C22×D311yescharacteristic
337C22×C3×C4—61no—
338C2×#67—21no—
339C2×#67—21no—
340C2×#67—21no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—121no—
356C2×#67—121no—
357C22×Dic3—21no—
358C22×Dic3—61no—
359#237—124no—
360D3×D4—124no—
361D3×D4—124no—
362D3×D4—121no—
363D3×D4—121no—
364D3×D4—121no—
365D3×D4—121no—
366D3×D4—121no—
367D3×D4—121no—
368D3×D4—121no—
369D3×D4—121no—
370D3×D4—124no—
371D3×D4—124no—
372D3×D4—122no—
373D3×D4—122no—
374#235—124no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12C22×D311yescharacteristic
384C2×D12C22×D311yescharacteristic
385C2×D12C22×D311yescharacteristic
386C2×C4×D3—31no—
387C2×C4×D3—31no—
388C2×C4×D3—31no—
389C2×C4×D3—31no—
390C2×C4×D3—31no—
391C2×C4×D3—31no—
392C2×C4×D3—61no—
393C2×C4×D3—61no—
394C2×Dic6—61no—
395C2×Dic6—61no—
396C3×D8—41no—
397C3×D8—41no—
398C3×D8—42no—
399C3×D8—121no—
400C3×D8—121no—
401C3×D8—121no—
402C3×D8—121no—
403C2×C3×C8—21no—
404C2×C3×C8—31no—
405C2×C3×C8—31no—
406C2×C3×C8C22×D311yescharacteristic
407C2×C3×C8C22×D311yescharacteristic
408C3×C4⋊C4—31no—
409C3×C22⋊C4—61no—
410C3×C42—31no—
411C3×C42—31no—
412#217—21no—
413#217—61no—
414#217—61no—
415#217—61no—
416#217—61no—
417#217—121no—
418#213—41no—
419#213—41no—
420#213—41no—
421#213—121no—
422#213—121no—
423#213—121no—
424#213—121no—
425#213—121no—
426#213—122no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429C4⋊Dic3—31no—
430C4⋊Dic3—31no—
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3C22×D311yescharacteristic
434Dic3⋊C4—61no—
435C4×Dic3—31no—
436C4×Dic3—31no—
437C4×Dic3—31no—
438C4×Dic3—31no—
439C4×Dic3C22×D311yescharacteristic
440C4×Dic3C22×D311yescharacteristic
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446D24—41no—
447D24—121no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—21no—
456C2×C3⋊D3—21no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—84no—
461C2×C3⋊D3C2×D812yes—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471D32—84no—
472C32×C4H(5,𝔽2)11yescharacteristic
473C32×C4H(5,𝔽2)11yescharacteristic
474C3⋊Dic3—21no—
475C3⋊Dic3—41no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3C2×D812yes—
479C3×Dic3C2×D812yes—
480C3×Dic3AGL(1,ℤ/8)12yes—
481C2×#41—181no—
482C22×D4—91no—
483C22×D4—91no—
484C22×D4—181no—
485C22×D4—181no—
486C2×D8—31no—
487C2×D8—31no—
488C2×D8—31no—
489C2×D8—31no—
490C2×D8—91no—
491C2×D8—91no—
492C2×D8—91no—
493C2×D8D3211yescharacteristic, complemented
494C4⋊Q8—91no—
495#127—31no—
496#127—31no—
497#127—31no—
498#127—91no—
499#127—91no—
500#127—181no—
501#127—181no—
502#124—181no—
503#121—91no—
504#121—91no—
505#121—181no—
506C4×D4—31no—
507C4×D4—91no—
508C4×D4—181no—
509C2×C42—91no—
510C4⋊C8—31no—
511C4⋊C8—91no—
512#102—31no—
513#102—31no—
514#102—91no—
515#102—91no—
516#102—91no—
517#102—91no—
518#102—91no—
519#102—91no—
520C22⋊C8—91no—
521C22⋊C8—91no—
522C4×C8—31no—
523C4×C8—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—61no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—121no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—124no—
555C22×D3—242no—
556C22×D3—242no—
557C3×D4—22no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—21no—
566C3×D4—41no—
567C3×D4—41no—
568C3×D4—41no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—61no—
575C3×D4—122no—
576C3×D4—122no—
577C3×D4—122no—
578C3×D4—122no—
579C3×D4—122no—
580C3×D4—122no—
581C2×C3×C4—21no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—61no—
587C2×C3×C4—122no—
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C23×D311yescharacteristic
590#67—42no—
591#67—42no—
592#67—42no—
593#67—42no—
594#67—42no—
595#67—42no—
596#67—122no—
597#67—122no—
598#67—122no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—124no—
605#67—122no—
606#67—122no—
607#67—122no—
608#67—242no—
609C2×Dic3—21no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—42no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—121no—
617C2×Dic3—122no—
618C2×Dic3D3×D411yescharacteristic
619C2×Dic3D3×D411yescharacteristic
620C2×Dic3D3×D411yescharacteristic
621C2×Dic3D3×D411yescharacteristic
622D12—21no—
623D12—21no—
624D12—21no—
625D12—21no—
626D12—21no—
627D12—21no—
628D12—62no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—121no—
634D12—122no—
635D12—122no—
636D12—122no—
637D12—122no—
638D12—122no—
639C4×D3—34no—
640C4×D3—34no—
641C4×D3—62no—
642C4×D3—61no—
643C4×D3—61no—
644C4×D3—61no—
645C4×D3—61no—
646C4×D3—62no—
647C4×D3—121no—
648C4×D3—121no—
649C4×D3—122no—
650Dic6—122no—
651Dic6—122no—
652C3×C8—21no—
653C3×C8—21no—
654C3×C8—41no—
655C3×C8—61no—
656C3×C8—61no—
657C3⋊C8—21no—
658C3⋊C8—21no—
659C3⋊C8—61no—
660C3⋊C8—61no—
661C3⋊C8—121no—
662C2×C32—81no—
663C2×C32—81no—
664C2×C32#53511yescharacteristic
665C2×C32C22×D811yescharacteristic
666C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
667C3⋊D3—22no—
668C3⋊D3—81no—
669C3×D3—81no—
670C3×D3—81no—
671C3×D3—81no—
672C24—181no—
673C24—181no—
674#41—364no—
675C2×Q8—181no—
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—91no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—364no—
695C2×D4—361no—
696C2×D4—361no—
697C2×D4—361no—
698C2×D4—361no—
699C2×D4—364no—
700C2×D4C2×D3211yescharacteristic
701C2×D4C2×D3211yescharacteristic
702C22×C4—61no—
703C22×C4—91no—
704C22×C4—91no—
705C22×C4—91no—
706C22×C4—181no—
707D8—41no—
708D8—121no—
709D8—121no—
710D8—121no—
711D8—121no—
712D8—361no—
713D8—361no—
714D8—361no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—91no—
718C2×C8C2×D3211yescharacteristic
719C4⋊C4—31no—
720C4⋊C4—91no—
721C4⋊C4—181no—
722C22⋊C4—61no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C42—31no—
727C42—31no—
728C42—91no—
729C42—91no—
730C22×C3—21no—
731C22×C3—42no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C2×D3×D411yescharacteristic
760C2×D3—32no—
761C2×D3—32no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—62no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—122no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—241no—
786C2×D3—241no—
787C2×D3—244no—
788C2×D3—244no—
789C2×D3—244no—
790C2×D3—244no—
791C2×D3—248no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—32no—
795C3×C4—32no—
796C3×C4—32no—
797C3×C4—61no—
798C3×C4—121no—
799C3×C4#100411yescharacteristic
800C3×C4#100411yescharacteristic
801C3×C4#100411yescharacteristic
802C3×C4#100911yescharacteristic
803Dic3—21no—
804Dic3—41no—
805Dic3—61no—
806Dic3—61no—
807Dic3—121no—
808Dic3—121no—
809Dic3—121no—
810Dic3—241no—
811Dic3D3×D812yes—
812Dic3D3×D812yes—
813Dic3#91112yes—
814C32#320511yescharacteristic, complemented, Sylow
815C23—21no—
816C23—21no—
817C23—61no—
818C23—61no—
819C23—61no—
820C23—91no—
821C23—181no—
822C23—362no—
823C23—362no—
824C23—362no—
825C23—362no—
826C23—362no—
827C23—362no—
828Q8—362no—
829D4—21no—
830D4—21no—
831D4—21no—
832D4—21no—
833D4—61no—
834D4—61no—
835D4—61no—
836D4—61no—
837D4—61no—
838D4—61no—
839D4—122no—
840D4—122no—
841D4—122no—
842D4—122no—
843D4—122no—
844D4—122no—
845D4—181no—
846D4—181no—
847D4—362no—
848D4—362no—
849D4—362no—
850D4—362no—
851D4—362no—
852D4—362no—
853D4—362no—
854D4—362no—
855C2×C4—31no—
856C2×C4—31no—
857C2×C4—31no—
858C2×C4—31no—
859C2×C4—61no—
860C2×C4—94no—
861C2×C4—91no—
862C2×C4—122no—
863C2×C4—182no—
864C2×C4—181no—
865C2×C4—181no—
866C2×C4—181no—
867C2×C4—362no—
868C2×C4C22×D3211yescharacteristic
869C8—21no—
870C8—61no—
871C8—61no—
872C8—181no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—82no—
877C2×C3—81no—
878C2×C3—81no—
879C2×C3—81no—
880C2×C3—81no—
881C2×C3—161no—
882C2×C3—241no—
883C2×C3—241no—
884C2×C3—241no—
885C2×C3#560711yescharacteristic
886C2×C3#571511yescharacteristic
887C2×C3C2×D3×D811yescharacteristic
888C2×C3C2×D3×D811yescharacteristic
889C2×C3C2×#91111yescharacteristic
890C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
891D3—62no—
892D3—62no—
893D3—81no—
894D3—81no—
895D3—81no—
896D3—122no—
897D3—242no—
898D3—241no—
899D3—241no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—92no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—121no—
912C22—121no—
913C22—121no—
914C22—121no—
915C22—121no—
916C22—181no—
917C22—181no—
918C22—361no—
919C22—361no—
920C22—361no—
921C22—724no—
922C22—724no—
923C22D32×D411yescharacteristic
924C4—32no—
925C4—32no—
926C4—32no—
927C4—61no—
928C4—121no—
929C4—181no—
930C4—361no—
931C4#6431411yescharacteristic
932C4#6433011yescharacteristic
933C3—21no—
934C3#8033611yescharacteristic, complemented
935C3#8178511yescharacteristic, complemented
936C2—81no—
937C2—81no—
938C2—182no—
939C2—241no—
940C2—241no—
941C2—241no—
942C2—721no—
943C2D32×D811yescharacteristic
944C2D3×#91111yescharacteristic
945C2#1059529911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595300C2semidirect
2. #10595139C2semidirect
3. #10592855C2semidirect
4. C3×#5151C2semidirect
5. C3×#5150C2semidirect
6. #10591516C2semidirect
7. #10591487C2semidirect
8. #10591482C2semidirect
9. #10591481C2semidirect
10. #10591456C2semidirect
11. #10591428C2semidirect
12. #10590945C2semidirect
13. #10590878C2semidirect
14. #10590753C2semidirect
15. #10590643C2semidirect
23. C2×C32×D8C22semidirect
25. C2×#3753C22semidirect
28. C3×#940C22semidirect
29. C3×D4×Dic3C22semidirect
30. C2×C3×#213C22semidirect
31. C2×C3×#213C22semidirect
32. C2×C3×#213C22semidirect
33. C2×C3×D24C22semidirect
39. #63918C22semidirect
43. Dic3×D12C22semidirect
45. C2×#3714C22semidirect
46. C2×#3713C22semidirect
47. #63659C22semidirect
48. #63648C22semidirect
50. C3×#832C22semidirect
51. C3×#821C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
75. #5151D3semidirect
79. #5150D3semidirect
167. C2×C3×D8C2×D3semidirect
168. C2×C3×D8C2×D3semidirect
181. #940C2×D3semidirect
190. D4×Dic3C2×D3semidirect
197. C2×#213C2×D3semidirect
198. C2×#213C2×D3semidirect
199. C2×#213C2×D3semidirect
202. C2×D24C2×D3semidirect
223. #832C2×D3semidirect
230. #821C2×D3semidirect
237. Dic3⋊C8C2×D3semidirect
239. C8×Dic3C2×D3semidirect
296. #624D8semidirect
493. C2×D8D32semidirect
814. C32#3205semidirect
934. C3#80336semidirect
935. C3#81785semidirect

Maximal subgroups

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

subgroupindex
#105953002
#105951392
#105928552
C3×#51512
C3×#51502
#105915162
#105914872
#105914822
#105914812
#105914562
#105914282
#105909452
#105908782
#105907532
#105906432
#817853
#803363