Finite Group Databasebeta

← #11878663

Subgroups — #11878663

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#10594518C211yesmaximal, characteristic, complemented
3#10592472C211yesmaximal, characteristic, complemented
4C3×#4786C211yesmaximal, characteristic, complemented
5C3×#4760C211yesmaximal, characteristic, complemented
6#10591482C211yesmaximal, characteristic, complemented
7#10591456C211yesmaximal, characteristic, complemented
8#10591429C211yesmaximal, characteristic, complemented
9#10590945C211yesmaximal, characteristic, complemented
10#10590880C211yesmaximal, characteristic, complemented
11#10590765C211yesmaximal, characteristic, complemented
12#10590643C211yesmaximal, characteristic, complemented
13#10590598C211yesmaximal, characteristic, complemented
14#10590548C211yesmaximal, characteristic, complemented
15#10590547C211yesmaximal, characteristic, complemented
16#81566—31nomaximal
17#80336—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3811—21no—
20C2×#3811—21no—
21C2×#3802C2211yescharacteristic
22C2×#3799—21no—
23C2×#3753C2211yescharacteristic, complemented
24C2×#3745C2211yescharacteristic, complemented
25#64104C2211yescharacteristic
26C3×#940C2211yescharacteristic
27C3×#940C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic, complemented
29C2×C3×D24C2211yescharacteristic, complemented
30C3×#893C2211yescharacteristic, complemented
31C3×#888C2211yescharacteristic, complemented
32#63979—21no—
33#63979—21no—
34#63916C2211yescharacteristic
35#63911C2211yescharacteristic
36#63911C2211yescharacteristic
37#63911C2211yescharacteristic, complemented
38#63910—21no—
39#63907—21no—
40#63904—21no—
41#63894C2211yescharacteristic, complemented
42C4×#624C2211yescharacteristic
43C2×#3714C2211yescharacteristic, complemented
44C2×#3714C2211yescharacteristic, complemented
45C2×#3714C2211yescharacteristic, complemented
46C2×#3713C2211yescharacteristic, complemented
47C32×#102C2211yescharacteristic, complemented
48#63647C2211yescharacteristic
49#63636C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5725—31no—
62D3×#127—31no—
63D3×#127—31no—
64#5548—31no—
65C3×#486—31no—
66C3×#459—31no—
67#5156—31no—
68#5156—31no—
69#5151—31no—
70#5151—31no—
71#5088—31no—
72#5073—31no—
73#5072—31no—
74#5015—31no—
75#4843—31no—
76#4833—31no—
77#4786—31no—
78#4786—31no—
79#4786—31no—
80#4786D311yescharacteristic, complemented
81#4773—31no—
82#4773—31no—
83#4773—31no—
84#4773—31no—
85#4773—31no—
86#4773—31no—
87#4773—61no—
88#4760—31no—
89#4760D311yescharacteristic, complemented
90#4695—31no—
91#4685—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96D4×C3⋊D3—41no—
97D4×C3⋊D3—41no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
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×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×Dic6—21no—
111#3811—44no—
112#3811—44no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#625—21no—
121C2×#624—21no—
122C2×#624D411yescharacteristic
123C2×#624D411yescharacteristic
124#3802—41no—
125#3802—41no—
126#3799—44no—
127C2×C32×C8C2311yescharacteristic
128C32×C4⋊C4C2311yescharacteristic
129#3753—41no—
130#3752—21no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3745—41no—
133C3×#213—41no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×C4×Dic3C2311yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—41no—
142#3722—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32D411yescharacteristic
145Dic32D411yescharacteristic
146#3714—41no—
147#3714—41no—
148#3714—41no—
149#3713—41no—
150#3205—91noSylow
151C2×#239—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—31no—
163C2×C3×D8—31no—
164C3×C4⋊Q8—31no—
165C3×#127—31no—
166C3×#127—31no—
167C3×C4×D4—31no—
168#947—61no—
169#940—31no—
170#940—31no—
171#940—31no—
172#940—61no—
173#940—61no—
174#940—61no—
175#940—61no—
176#940C2×D311yescharacteristic
177#940C2×D311yescharacteristic
178#938—31no—
179C2×#213—31no—
180C2×#213—31no—
181C2×#213—31no—
182C2×#213—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—61no—
187C2×#213C2×D311yescharacteristic, complemented
188C4×#67—61no—
189C2×D24—31no—
190C2×D24—31no—
191C2×D24—31no—
192C2×D24—31no—
193C2×D24—31no—
194C2×D24—61no—
195C2×D24C2×D311yescharacteristic, complemented
196#895—31no—
197#895—31no—
198#895—31no—
199#895—61no—
200#895—61no—
201#893—31no—
202#893—61no—
203#893C2×D311yescharacteristic, complemented
204#888C2×D311yescharacteristic, complemented
205#885—61no—
206#884—61no—
207#874—31no—
208#874—31no—
209#874—31no—
210C4×D12—31no—
211C42×D3—31no—
212C42×D3—31no—
213C3×C4⋊C8—31no—
214C3×#102—21no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102C2×D311yescharacteristic, complemented
220C3×#102C2×D311yescharacteristic, complemented
221C3×C4×C8—31no—
222#832—31no—
223#832C2×D311yescharacteristic, complemented
224#821—31no—
225#821C2×D311yescharacteristic, complemented
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—61no—
231Dic3⋊C8—31no—
232Dic3⋊C8C2×D311yescharacteristic, complemented
233C8×Dic3—31no—
234C8×Dic3C2×D311yescharacteristic, complemented
235#809—31no—
236#809—31no—
237#809—31no—
238#809—31no—
239#809—61no—
240#809C2×D311yescharacteristic, complemented
241#809C2×D311yescharacteristic, complemented
242C4⋊(C3⋊C8)—31no—
243C4×C3⋊C8—31no—
244C23×C32—21no—
245C22×C3⋊D3—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—
259C2×C32×C4—21no—
260C2×C32×C4C2411yescharacteristic
261#638—42no—
262C2×C3⋊Dic3C2×D411yescharacteristic
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—21no—
267C4⋊(C3⋊D3)—42no—
268C4×C3⋊D3—21no—
269C4×C3⋊D3—21no—
270C3×#67—42no—
271C3×#67—42no—
272C3×#67—42no—
273C3×#67—42no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×C4×D3—42no—
286C3×Dic6—42no—
287#626—42no—
288#626—42no—
289#626—42no—
290#626—42no—
291#626—42no—
292#626—42no—
293#626—42no—
294#625—42no—
295#624—22no—
296#624—42no—
297#624D814yescomplemented
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302#532—91no—
303C2×#127—91no—
304#493—91no—
305#493—91no—
306#486—31no—
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×Q8—61no—
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×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C22×C3×C4—61no—
334C2×#67—21no—
335C2×#67—21no—
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—121no—
350#239—124no—
351D3×D4—124no—
352D3×D4—124no—
353D3×D4—121no—
354D3×D4—121no—
355D3×D4—121no—
356D3×D4—121no—
357D3×D4—121no—
358D3×D4—121no—
359D3×D4—121no—
360D3×D4—121no—
361D3×D4—124no—
362D3×D4—124no—
363D3×D4—122no—
364D3×D4—122no—
365#235—124no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—121no—
382C2×D12C22×D311yescharacteristic
383C2×D12C22×D311yescharacteristic
384C2×D12C22×D311yescharacteristic
385C2×C4×D3—21no—
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×C4×D3—61no—
395C2×Dic6—21no—
396C3×D8—121no—
397C3×D8—121no—
398C2×C3×C8—21no—
399C2×C3×C8—31no—
400C2×C3×C8—31no—
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C22×D311yescharacteristic
403C3×C4⋊C4—21no—
404C3×C4⋊C4—31no—
405C3×C4⋊C4—61no—
406C3×C4⋊C4C22×D311yescharacteristic
407C3×C4⋊C4C22×D311yescharacteristic
408C3×C22⋊C4—61no—
409C3×C42—31no—
410C3×C42—31no—
411#217—61no—
412#213—41no—
413#213—121no—
414#213—121no—
415#213—121no—
416#213—121no—
417#213—121no—
418#213—121no—
419#213—121no—
420#213—122no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—121no—
428C4⋊Dic3C22×D311yescharacteristic
429Dic3⋊C4—21no—
430C4×Dic3—31no—
431C4×Dic3—31no—
432C4×Dic3—31no—
433C4×Dic3—31no—
434C4×Dic3C22×D311yescharacteristic
435C4×Dic3C22×D311yescharacteristic
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—61no—
439C2×C3⋊C8C22×D311yescharacteristic
440C2×C3⋊C8C22×D311yescharacteristic
441D24—41no—
442D24—121no—
443D24—121no—
444D24—122no—
445D24—121no—
446D24—121no—
447D24—121no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32C22×D411yescharacteristic
452C2×C3⋊D3—21no—
453C2×C3⋊D3—21no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
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×C4—41no—
473C32×C4H(5,𝔽2)11yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3⋊Dic3—21no—
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—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×D8—91no—
493C2×D8—91no—
494C4⋊Q8—31no—
495#127—31no—
496#127—31no—
497#127—91no—
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—31no—
515#102—31no—
516#102—91no—
517#102—91no—
518#102—91no—
519#102D3211yescharacteristic, complemented
520C22⋊C8—91no—
521C22⋊C8—91no—
522C4×C8—31no—
523C4×C8—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—41no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—61no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—31no—
534C22×D3—31no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—121no—
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×Q8—122no—
558C3×D4—22no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—41no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—122no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—122no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—41no—
582C2×C3×C4—61no—
583C2×C3×C4—122no—
584C2×C3×C4C23×D311yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586#67—42no—
587#67—42no—
588#67—42no—
589#67—42no—
590#67—122no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—124no—
597#67—122no—
598#67—122no—
599#67—122no—
600#67—122no—
601#67—122no—
602C2×Dic3—21no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—61no—
606C2×Dic3D3×D411yescharacteristic
607C2×Dic3D3×D411yescharacteristic
608C2×Dic3D3×D411yescharacteristic
609C2×Dic3D3×D411yescharacteristic
610D12—21no—
611D12—21no—
612D12—21no—
613D12—21no—
614D12—21no—
615D12—21no—
616D12—62no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—121no—
626D12—121no—
627D12—121no—
628D12—122no—
629D12—122no—
630D12—122no—
631D12—122no—
632D12—122no—
633D12—122no—
634D12—122no—
635D12—122no—
636D12—122no—
637D12—242no—
638C4×D3—34no—
639C4×D3—34no—
640C4×D3—42no—
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—
650C4×D3—122no—
651Dic6—42no—
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#53511yescharacteristic
664C2×C32C22×D811yescharacteristic
665C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
666C3⋊D3—22no—
667C3⋊D3—81no—
668C3⋊D3—81no—
669C3×D3—81no—
670C3×D3—81no—
671C3×D3—81no—
672C24—181no—
673C24—181no—
674#41—364no—
675C2×Q8—61no—
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—91no—
684C2×D4—91no—
685C2×D4—181no—
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—181no—
695C2×D4—364no—
696C2×D4—361no—
697C2×D4—361no—
698C2×D4—361no—
699C2×D4—361no—
700C2×D4—364no—
701C2×D4C2×D3211yescharacteristic
702C22×C4—61no—
703C22×C4—91no—
704C22×C4—91no—
705C22×C4—91no—
706C22×C4—181no—
707D8—121no—
708D8—121no—
709D8—361no—
710D8—361no—
711D8—361no—
712D8—361no—
713D8—361no—
714D8—361no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—91no—
718C2×C8C2×D3211yescharacteristic
719C4⋊C4—31no—
720C4⋊C4—61no—
721C4⋊C4C2×D3211yescharacteristic
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—81no—
739C22×C3—81no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3C2×D3×D411yescharacteristic
750C22×C3C2×D3×D411yescharacteristic
751C2×D3—32no—
752C2×D3—32no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—62no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—122no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—241no—
783C2×D3—241no—
784C2×D3—241no—
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—41no—
798C3×C4—41no—
799C3×C4—61no—
800C3×C4—81no—
801C3×C4—121no—
802C3×C4#100411yescharacteristic
803C3×C4#100911yescharacteristic
804C3×C4#100911yescharacteristic
805C3×C4#100911yescharacteristic
806Dic3—21no—
807Dic3—41no—
808Dic3—61no—
809Dic3—61no—
810Dic3—121no—
811Dic3D3×D812yes—
812Dic3D3×D812yes—
813Dic3#91412yes—
814C32#320511yescharacteristic, complemented, Sylow
815C23—21no—
816C23—61no—
817C23—61no—
818C23—61no—
819C23—91no—
820C23—181no—
821C23—181no—
822C23—362no—
823C23—362no—
824C23—362no—
825C23—362no—
826C23—362no—
827C23—362no—
828Q8—122no—
829D4—21no—
830D4—21no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—61no—
835D4—61no—
836D4—61no—
837D4—122no—
838D4—122no—
839D4—122no—
840D4—122no—
841D4—181no—
842D4—181no—
843D4—181no—
844D4—181no—
845D4—362no—
846D4—362no—
847D4—362no—
848D4—362no—
849D4—362no—
850D4—362no—
851D4—362no—
852D4—362no—
853D4—362no—
854D4—362no—
855C2×C4—21no—
856C2×C4—31no—
857C2×C4—31no—
858C2×C4—31no—
859C2×C4—31no—
860C2×C4—61no—
861C2×C4—94no—
862C2×C4—91no—
863C2×C4—122no—
864C2×C4—182no—
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—241no—
880C2×C3—241no—
881C2×C3—241no—
882C2×C3#560711yescharacteristic
883C2×C3#567411yescharacteristic
884C2×C3C2×D3×D811yescharacteristic
885C2×C3C2×D3×D811yescharacteristic
886C2×C3C2×#91411yescharacteristic
887C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
888D3—62no—
889D3—62no—
890D3—81no—
891D3—81no—
892D3—81no—
893D3—122no—
894D3—242no—
895D3—241no—
896D3—241no—
897D3—241no—
898D3—241no—
899D3—481no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—92no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—121no—
912C22—121no—
913C22—181no—
914C22—181no—
915C22—361no—
916C22—361no—
917C22—361no—
918C22—361no—
919C22—361no—
920C22—361no—
921C22—724no—
922C22—724no—
923C22D32×D411yescharacteristic
924C4—32no—
925C4—32no—
926C4—32no—
927C4—41no—
928C4—61no—
929C4—121no—
930C4—181no—
931C4#6430811yescharacteristic
932C4#6431411yescharacteristic
933C3—21no—
934C3#8033611yescharacteristic, complemented
935C3#8156611yescharacteristic, complemented
936C2—81no—
937C2—182no—
938C2—241no—
939C2—241no—
940C2—241no—
941C2—721no—
942C2—721no—
943C2#1059428711yescharacteristic
944C2D32×D811yescharacteristic
945C2D3×#91411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3205
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. #10595300C2semidirect
2. #10594518C2semidirect
3. #10592472C2semidirect
4. C3×#4786C2semidirect
5. C3×#4760C2semidirect
6. #10591482C2semidirect
7. #10591456C2semidirect
8. #10591429C2semidirect
9. #10590945C2semidirect
10. #10590880C2semidirect
11. #10590765C2semidirect
12. #10590643C2semidirect
13. #10590598C2semidirect
14. #10590548C2semidirect
15. #10590547C2semidirect
23. C2×#3753C22semidirect
24. C2×#3745C22semidirect
28. C2×C3×#213C22semidirect
29. C2×C3×D24C22semidirect
30. C3×#893C22semidirect
31. C3×#888C22semidirect
37. #63911C22semidirect
41. #63894C22semidirect
43. C2×#3714C22semidirect
44. C2×#3714C22semidirect
45. C2×#3714C22semidirect
46. C2×#3713C22semidirect
47. C32×#102C22semidirect
49. #63636C22semidirect
50. C3×#832C22semidirect
51. C3×#821C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×#809C22semidirect
55. C3×#809C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63564C22semidirect
58. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
80. #4786D3semidirect
89. #4760D3semidirect
187. C2×#213C2×D3semidirect
195. C2×D24C2×D3semidirect
203. #893C2×D3semidirect
204. #888C2×D3semidirect
219. C3×#102C2×D3semidirect
220. C3×#102C2×D3semidirect
223. #832C2×D3semidirect
225. #821C2×D3semidirect
232. Dic3⋊C8C2×D3semidirect
234. C8×Dic3C2×D3semidirect
240. #809C2×D3semidirect
241. #809C2×D3semidirect
297. #624D8semidirect
519. #102D32semidirect
814. C32#3205semidirect
934. C3#80336semidirect
935. C3#81566semidirect

Maximal subgroups

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

subgroupindex
#105953002
#105945182
#105924722
C3×#47862
C3×#47602
#105914822
#105914562
#105914292
#105909452
#105908802
#105907652
#105906432
#105905982
#105905482
#105905472
#815663
#803363