Finite Group Databasebeta

← #11878509

Subgroups — #11878509

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5629C211yesmaximal, characteristic, complemented
2#10595043C211yesmaximal, characteristic, complemented
3#10592746C211yesmaximal, characteristic, complemented
4C3×#5044C211yesmaximal, characteristic, complemented
5#10591599C211yesmaximal, characteristic, complemented
6#10591596C211yesmaximal, characteristic, complemented
7#10591589C211yesmaximal, characteristic, complemented
8#10591588C211yesmaximal, characteristic, complemented
9#10591182C211yesmaximal, characteristic, complemented
10#10591145C211yesmaximal, characteristic, complemented
11#10591089C211yesmaximal, characteristic, complemented
12#10590588C211yesmaximal, characteristic, complemented
13#10590576C211yesmaximal, characteristic, complemented
14#10590427C211yesmaximal, characteristic, complemented
15#10590422C211yesmaximal, characteristic, complemented
16#83426—31nomaximal
17#81484—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#930C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C3×#896—21no—
28C3×#895—21no—
29C3×#895C2211yescharacteristic
30C3×D3×C4⋊C4C2211yescharacteristic
31C3×#884—21no—
32C3×#884—21no—
33#63978—21no—
34#63978—21no—
35#63916—21no—
36#63909C2211yescharacteristic
37#63909C2211yescharacteristic
38#63871—21no—
39#63857C2211yescharacteristic
40#63857C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63657C2211yescharacteristic
46#63637C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63576C2211yescharacteristic
54#63576C2211yescharacteristic
55#63567C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#537—31no—
62#5833—31no—
63#5629D311yescharacteristic, complemented
64#5510—31no—
65C3×#484—31no—
66#5239—31no—
67#5238—31no—
68#5234—31no—
69#5051—31no—
70#5049—31no—
71#5047—31no—
72#5047—31no—
73#5047—61no—
74#5044D311yescharacteristic, complemented
75#5042—31no—
76#5038—31no—
77#5037—31no—
78#5033—31no—
79#4970—31no—
80#4967—31no—
81#4967—31no—
82#4886—31no—
83#4884—31no—
84#4883—31no—
85#4882—31no—
86#4813—31no—
87#4812—31no—
88#4810—31no—
89#4808—31no—
90#4734—31no—
91#4727—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95#3828—41no—
96#3828—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C3×#239—41no—
105C3×#239—41no—
106C3×#235—41no—
107C3×#235—41no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12D411yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6D411yescharacteristic
117C2×#626—21no—
118C2×#626—21no—
119C32×C4⋊C4—21no—
120C32×C4⋊C4C2311yescharacteristic
121C32×C22⋊C4—21no—
122#3756—41no—
123#3755—41no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3716—41no—
144#3714—41no—
145#3711—41no—
146D3×C3⋊C8—41no—
147#3203—91noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×#239C2×D311yescharacteristic
151C2×#235—31no—
152C2×#235—31no—
153C2×#235—61no—
154C2×#235C2×D311yescharacteristic
155C3×C22⋊Q8—21no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8C2×D311yescharacteristic
159C3×C22⋊Q8C2×D311yescharacteristic
160C3×#121—31no—
161C3×#121—31no—
162C3×#121—61no—
163C3×#121—61no—
164C3×#121—61no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167#946—61no—
168#946C2×D311yescharacteristic
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—61no—
172C2×#215—31no—
173C2×#215—31no—
174C2×#215—61no—
175#939—61no—
176#939—61no—
177#938—61no—
178C2×#214—31no—
179C2×#213—31no—
180#930—31no—
181#930—31no—
182#930—61no—
183#930—61no—
184#930C2×D311yescharacteristic
185C2×C4⋊Dic3C2×D311yescharacteristic
186#924—31no—
187#924—31no—
188C2×#208—31no—
189C22×C3⋊C8—31no—
190C2×D24—31no—
191C2×#204—31no—
192C2×ΓL(1,𝔽25)—31no—
193C2×D3×C8—31no—
194#897—31no—
195#897—31no—
196#897—61no—
197#896—21no—
198#895—21no—
199#895—31no—
200#895—31no—
201#895—61no—
202#895C2×D311yescharacteristic
203D3×C4⋊C4C2×D311yescharacteristic
204#884—21no—
205#884—21no—
206C3×#107—31no—
207C3×#107—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×C22⋊C8—31no—
211#835C2×D311yescharacteristic
212#835C2×D311yescharacteristic
213#832—31no—
214#832—31no—
215#830—31no—
216#830—31no—
217#830—31no—
218#830—31no—
219#830—61no—
220#830C2×D311yescharacteristic
221#821—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224#816—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—61no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#807—31no—
236#807—31no—
237#807—31no—
238#807—31no—
239#807C2×D311yescharacteristic
240#807C2×D311yescharacteristic
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C4×C3⋊D3—42no—
259#634—21no—
260#634—21no—
261C3×#67—41no—
262C3×#67—41no—
263C3×#67—81no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—81no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—41no—
273C3×D12—42no—
274C3×D12—81no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—42no—
280C3×C4×D3—81no—
281C3×Dic6—41no—
282#626—81no—
283#626—81no—
284C3⋊(C3⋊C8)—21no—
285C3⋊(C3⋊C8)—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288#537—31no—
289#537—91no—
290#484—31no—
291#484—91no—
292#480—91no—
293#480—91no—
294#468—91no—
295#468—91no—
296#467—91no—
297#466—91no—
298#452—91no—
299#452—91no—
300#449—91no—
301#449—91no—
302#408—91no—
303C3×#41—121no—
304C3×#41—121no—
305C3×#41—121no—
306C3×#41—121no—
307C2×C3×Q8—21no—
308C2×C3×Q8—31no—
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C2×#67—21no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—121no—
332C2×#67#6711yescharacteristic
333C2×#67#6711yescharacteristic
334C22×Dic3—21no—
335#239—41no—
336#239—41no—
337#235—41no—
338#235—41no—
339#235—121no—
340#235—121no—
341#235—121no—
342#235—121no—
343#235—122no—
344#235—122no—
345C2×D12—21no—
346C2×D12—21no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12#6711yescharacteristic
353C2×D12C22×D311yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3—121no—
359C2×C4×D3C22×D311yescharacteristic
360C2×C4×D3C22×D311yescharacteristic
361C2×Dic6—31no—
362C2×Dic6—31no—
363C2×Dic6—61no—
364C2×Dic6#6711yescharacteristic
365C2×C3×C8—31no—
366C2×C3×C8—31no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—41no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C22⋊C4—21no—
380C3×C22⋊C4—21no—
381C3×C22⋊C4—41no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385#217—61no—
386#217—61no—
387#216—121no—
388#216—121no—
389#216—122no—
390#215—121no—
391#215—121no—
392#215—122no—
393#214—121no—
394#213—121no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404C4⋊Dic3—21no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3C22×D311yescharacteristic
408C4⋊Dic3C22×D311yescharacteristic
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414#208—121no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8—61no—
421C2×C3⋊C8—121no—
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424D24—121no—
425#204—121no—
426ΓL(1,𝔽25)—121no—
427D3×C8—121no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32C22×D411yescharacteristic
432C2×C3⋊D3—41no—
433C2×C3⋊D3—41no—
434C2×C3⋊D3—41no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C32×C4—21no—
445C32×C4—41no—
446C32×C4—41no—
447C32×C4H(5,𝔽2)11yescharacteristic
448C32×C4H(5,𝔽2)11yescharacteristic
449C3⋊Dic3—41no—
450C3×Dic3—21no—
451C3×Dic3—21no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41—31no—
456C2×#41—31no—
457C2×#41—91no—
458C2×Q16—91no—
459C2×SD16—91no—
460C2×SD16—91no—
461C2×D8—91no—
462C2×M16—91no—
463C22×C8—91no—
464C22⋊Q8—31no—
465C22⋊Q8—61no—
466C22⋊Q8—91no—
467C22⋊Q8—91no—
468C22⋊Q8—181no—
469C22⋊Q8D3211yescharacteristic
470#121—31no—
471#121—31no—
472#121—61no—
473#121—61no—
474#121—61no—
475#121—91no—
476#121—91no—
477#121—181no—
478#121—181no—
479#121—181no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482#107—31no—
483#107—31no—
484#107—91no—
485#107—91no—
486#103—31no—
487#103—31no—
488#103—91no—
489#103—91no—
490#102—91no—
491#102—91no—
492#102—91no—
493#102—91no—
494C22⋊C8—31no—
495C22⋊C8—91no—
496C22⋊C8—91no—
497C22⋊C8—91no—
498C23×C3—21no—
499C23×C3—31no—
500C23×C3—31no—
501C23×C3—61no—
502C23×C3D3×D411yescharacteristic
503C23×C3C2×#6711yescharacteristic
504C22×D3—21no—
505C22×D3—61no—
506C22×D3—61no—
507C22×D3—121no—
508C22×D3C2×#6711yescharacteristic
509C22×D3C2×#6711yescharacteristic
510C3×Q8—21no—
511C3×Q8—21no—
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—41no—
515C3×Q8—41no—
516C3×Q8—121no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—121no—
520C3×D4—122no—
521C3×D4—121no—
522C3×D4—121no—
523C3×D4—241no—
524C3×D4—241no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—122no—
549C2×C3×C4—241no—
550C2×C3×C4—241no—
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4C2×#6711yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555#67—41no—
556#67—41no—
557#67—81no—
558#67—122no—
559#67—122no—
560#67—124no—
561#67—241no—
562#67—241no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—81no—
569C2×Dic3—121no—
570C2×Dic3C2×#6711yescharacteristic
571C2×Dic3C2×#6711yescharacteristic
572D12—21no—
573D12—21no—
574D12—41no—
575D12—42no—
576D12—62no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—61no—
581D12—81no—
582D12—121no—
583D12—241no—
584D12—241no—
585C4×D3—21no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—21no—
589C4×D3—42no—
590C4×D3—81no—
591C4×D3—122no—
592C4×D3—122no—
593C4×D3—124no—
594Dic6—41no—
595Dic6—62no—
596Dic6—61no—
597Dic6—61no—
598Dic6—61no—
599Dic6—61no—
600Dic6—121no—
601C3×C8—61no—
602C3×C8—61no—
603C3⋊C8—21no—
604C3⋊C8—21no—
605C3⋊C8—61no—
606C3⋊C8—61no—
607C3⋊C8—61no—
608C3⋊C8—61no—
609C3⋊C8—121no—
610C3⋊C8—121no—
611C2×C32—41no—
612C2×C32#53411yescharacteristic
613C2×C32#57611yescharacteristic
614C2×C32#57811yescharacteristic
615C3⋊D3—81no—
616C3×D3—41no—
617C3×D3—41no—
618C3×D3—81no—
619#41—121no—
620#41—121no—
621#41—121no—
622#41—121no—
623#41—361no—
624#41—361no—
625C2×Q8—31no—
626C2×Q8—91no—
627C2×Q8C2×D3211yescharacteristic
628C2×D4—31no—
629C2×D4—31no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—61no—
633C2×D4—61no—
634C2×D4—61no—
635C2×D4—91no—
636C2×D4—181no—
637C2×D4—181no—
638C2×D4—181no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—181no—
645C22×C4C2×D3211yescharacteristic
646Q16—361no—
647SD16—361no—
648SD16—361no—
649D8—361no—
650M16—361no—
651C2×C8—31no—
652C2×C8—31no—
653C2×C8—91no—
654C2×C8—91no—
655C2×C8—361no—
656C4⋊C4—21no—
657C4⋊C4—31no—
658C4⋊C4—31no—
659C4⋊C4—31no—
660C4⋊C4—61no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4—181no—
664C4⋊C4—181no—
665C4⋊C4C2×D3211yescharacteristic
666C22⋊C4—21no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—181no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—61no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3C2×D3×D411yescharacteristic
694C22×C3C22×#6711yescharacteristic
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—122no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—241no—
712C2×D3—241no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—61no—
723C3×C4—61no—
724C3×C4—81no—
725C3×C4—81no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4#100411yescharacteristic
730C3×C4#100411yescharacteristic
731C3×C4#100911yescharacteristic
732C3×C4#100911yescharacteristic
733Dic3—21no—
734Dic3—21no—
735Dic3—41no—
736Dic3—41no—
737Dic3—41no—
738Dic3—122no—
739Dic3—121no—
740Dic3—121no—
741C32#320311yescharacteristic, complemented, Sylow
742C23—31no—
743C23—31no—
744C23—61no—
745C23—181no—
746C23D3×#6711yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—121no—
750Q8—181no—
751Q8—181no—
752D4—61no—
753D4—61no—
754D4—121no—
755D4—122no—
756D4—121no—
757D4—121no—
758D4—181no—
759D4—181no—
760D4—241no—
761D4—241no—
762D4—362no—
763D4—721no—
764D4—721no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—122no—
779C2×C4—181no—
780C2×C4—241no—
781C2×C4—241no—
782C2×C4—362no—
783C2×C4D3×#6711yescharacteristic
784C2×C4C22×D3211yescharacteristic
785C8—61no—
786C8—61no—
787C8—181no—
788C8—181no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—81no—
795C2×C3—121no—
796C2×C3—121no—
797C2×C3—241no—
798C2×C3#565311yescharacteristic
799C2×C3#576611yescharacteristic
800C2×C3#577411yescharacteristic
801C2×C3#580411yescharacteristic
802C2×C3#583511yescharacteristic
803C2×C3#583811yescharacteristic
804D3—41no—
805D3—41no—
806D3—81no—
807D3—242no—
808D3—241no—
809D3—241no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—61no—
814C22—61no—
815C22—61no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—361no—
823C22—361no—
824C22—361no—
825C22C2×D3×#6711yescharacteristic
826C4—21no—
827C4—41no—
828C4—41no—
829C4—61no—
830C4—61no—
831C4—121no—
832C4—121no—
833C4—121no—
834C4—361no—
835C4#6431411yescharacteristic
836C4#6431411yescharacteristic
837C3—21no—
838C3#8148411yescharacteristic, complemented
839C3#8342611yescharacteristic, complemented
840C2—41no—
841C2—121no—
842C2—121no—
843C2—241no—
844C2—721no—
845C2#1059523411yescharacteristic
846C2#1059532711yescharacteristic
847C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3203
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5629C2semidirect
2. #10595043C2semidirect
3. #10592746C2semidirect
4. C3×#5044C2semidirect
5. #10591599C2semidirect
6. #10591596C2semidirect
7. #10591589C2semidirect
8. #10591588C2semidirect
9. #10591182C2semidirect
10. #10591145C2semidirect
11. #10591089C2semidirect
12. #10590588C2semidirect
13. #10590576C2semidirect
14. #10590427C2semidirect
15. #10590422C2semidirect
63. #5629D3semidirect
74. #5044D3semidirect
741. C32#3203semidirect
838. C3#81484semidirect
839. C3#83426semidirect

Maximal subgroups

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

subgroupindex
C3×#56292
#105950432
#105927462
C3×#50442
#105915992
#105915962
#105915892
#105915882
#105911822
#105911452
#105910892
#105905882
#105905762
#105904272
#105904222
#834263
#814843