Finite Group Databasebeta

← #11878518

Subgroups — #11878518

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
1#10595043C211yesmaximal, characteristic, complemented
2#10595004C211yesmaximal, characteristic, complemented
3#10592432C211yesmaximal, characteristic, complemented
4C3×#4736C211yesmaximal, characteristic, complemented
5C3×#4727C211yesmaximal, characteristic, complemented
6#10591182C211yesmaximal, characteristic, complemented
7#10591135C211yesmaximal, characteristic, complemented
8#10590969C211yesmaximal, characteristic, complemented
9#10590968C211yesmaximal, characteristic, complemented
10#10590852C211yesmaximal, characteristic, complemented
11#10590838C211yesmaximal, characteristic, complemented
12#10590828C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590684C211yesmaximal, characteristic, complemented
15#10590679C211yesmaximal, characteristic, complemented
16#81301—31nomaximal
17#78676—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21#64133C2211yescharacteristic
22C2×#3746C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24C3×#930C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63978—21no—
29#63978—21no—
30#63970—21no—
31#63970—21no—
32#63916—21no—
33#63909C2211yescharacteristic
34#63909C2211yescharacteristic
35#63908C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63887—21no—
38#63885—21no—
39#63871—21no—
40#63857C2211yescharacteristic
41#63857C2211yescharacteristic
42#63857C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46#63648C2211yescharacteristic
47#63643C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#818C2211yescharacteristic
54C3×#818C2211yescharacteristic
55#63575C2211yescharacteristic
56#63575C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63567C2211yescharacteristic
60#63564C2211yescharacteristic
61#5833—31no—
62#5833—31no—
63#5608—31no—
64#5510—31no—
65C3×#480—31no—
66C3×#408—31no—
67#5134—31no—
68#5134—31no—
69#5116—31no—
70#5115—31no—
71#5037—31no—
72#4970—31no—
73#4887—31no—
74#4886—31no—
75#4884—31no—
76#4882—31no—
77#4783—31no—
78#4781—31no—
79#4780—31no—
80#4775—31no—
81#4736—31no—
82#4736D311yescharacteristic, complemented
83#4734—31no—
84#4734—31no—
85#4733—31no—
86#4733—31no—
87#4733—31no—
88#4733—61no—
89#4727D311yescharacteristic, complemented
90#4722—31no—
91#4722—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94#3828—41no—
95#3828—41no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C3×#235—41no—
105C3×#235—41no—
106C2×C3×D12D411yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6D411yescharacteristic
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3795—41no—
118#3795—41no—
119C2×C32×C8C2311yescharacteristic
120C2×C32×C8C2311yescharacteristic
121#3757—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124#3746—41no—
125#3744—41no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×ΓL(1,𝔽25)—41no—
134C3×D3×C8—41no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145#3716—41no—
146#3714—41no—
147#3203—91noSylow
148C2×C3×#41—31no—
149C2×#237—31no—
150C2×#235—31no—
151C2×#235—31no—
152C2×#235—31no—
153C2×#235—61no—
154C2×#235C2×D311yescharacteristic
155C2×C3×M16—31no—
156C22×C3×C8—31no—
157C3×#121—31no—
158C2×C3×C4⋊C4—31no—
159#946—61no—
160#946—61no—
161#939—61no—
162#939—61no—
163#939—61no—
164#939—61no—
165#939—61no—
166#938—31no—
167#938—61no—
168#938—61no—
169#938—61no—
170C2×#214—31no—
171C2×#213—31no—
172#930—31no—
173#930—31no—
174#930—31no—
175#930—61no—
176#930—61no—
177#930C2×D311yescharacteristic
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3C2×D311yescharacteristic
180#924—31no—
181#924—31no—
182#924—31no—
183#924—31no—
184#924—31no—
185#924—61no—
186C2×Dic12—31no—
187C2×Dic12—31no—
188C2×Dic12—61no—
189C2×D24—31no—
190C2×#204—31no—
191C2×#204—31no—
192C2×#204—31no—
193C2×#204—61no—
194C2×ΓL(1,𝔽25)C2×D311yescharacteristic
195C2×D3×C8C2×D311yescharacteristic
196#897—31no—
197#897—31no—
198#897—31no—
199#897—61no—
200#895—31no—
201#895—31no—
202#895—61no—
203D3×C4⋊C4—31no—
204#884—61no—
205#878—61no—
206C3×#107—31no—
207C3×#107—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×C22⋊C8—21no—
211C3×C22⋊C8—31no—
212C3×C22⋊C8—31no—
213C3×C22⋊C8—31no—
214C3×C22⋊C8C2×D311yescharacteristic
215C3×C22⋊C8C2×D311yescharacteristic
216#830C2×D311yescharacteristic
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#821C2×D311yescharacteristic
222#821C2×D311yescharacteristic
223(C2×D3)⋊C8C2×D311yescharacteristic
224(C2×D3)⋊C8C2×D311yescharacteristic
225#818—31no—
226#818—31no—
227#818C2×D311yescharacteristic
228#818C2×D311yescharacteristic
229#816—31no—
230#816—31no—
231#816—31no—
232#816—31no—
233#816—31no—
234#816—61no—
235#810—31no—
236#810—31no—
237#810—31no—
238#809—31no—
239#807—31no—
240#807—31no—
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—42no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4×C3⋊D3—42no—
257#634—21no—
258#634—21no—
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×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×Dic6—41no—
278#626—81no—
279#626—81no—
280#625—42no—
281#625—81no—
282D3×Dic3—42no—
283D3×Dic3—81no—
284C32×C8—21no—
285C32×C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288#537—91no—
289#537—91no—
290#484—91no—
291#484—91no—
292#480—31no—
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—31no—
303C3×#41—121no—
304C3×#41—121no—
305C2×C3×Q8—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—61no—
311C22×C3×C4—21no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C2×#67—21no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—121no—
327C2×#67D1211yescharacteristic
328C2×#67D1211yescharacteristic
329C22×Dic3—21no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332#237—121no—
333#237—121no—
334#235—41no—
335#235—41no—
336#235—121no—
337#235—121no—
338#235—121no—
339#235—121no—
340#235—121no—
341#235—121no—
342#235—122no—
343#235—122no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—61no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12D1211yescharacteristic
350C2×D12C22×D311yescharacteristic
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—121no—
356C2×C4×D3C22×D311yescharacteristic
357C2×C4×D3C22×D311yescharacteristic
358C2×Dic6—31no—
359C2×Dic6—31no—
360C2×Dic6—31no—
361C2×Dic6—31no—
362C2×Dic6—61no—
363C2×Dic6—61no—
364C2×Dic6D1211yescharacteristic
365C3×M16—121no—
366C2×C3×C8—21no—
367C2×C3×C8—21no—
368C2×C3×C8—31no—
369C2×C3×C8—31no—
370C2×C3×C8—121no—
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C2×C3×C8C22×D311yescharacteristic
374C2×C3×C8C22×D311yescharacteristic
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—61no—
379C3×C22⋊C4—61no—
380#217—61no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—121no—
387#214—121no—
388#213—121no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398C4⋊Dic3—21no—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3C22×D311yescharacteristic
407C4⋊Dic3C22×D311yescharacteristic
408C4⋊Dic3C22×D311yescharacteristic
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—121no—
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418Dic12—121no—
419Dic12—121no—
420Dic12—122no—
421D24—121no—
422#204—121no—
423#204—121no—
424#204—122no—
425#204—121no—
426ΓL(1,𝔽25)—41no—
427D3×C8—41no—
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×C4H(5,𝔽2)11yescharacteristic
446C32×C4H(5,𝔽2)11yescharacteristic
447C3⋊Dic3—41no—
448C3⋊Dic3—41no—
449C3⋊Dic3—41no—
450C3×Dic3—21no—
451C3×Dic3—21no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41—31no—
456C2×#41—91no—
457C2×#41—91no—
458C2×Q16—91no—
459C2×SD16—91no—
460C2×SD16—91no—
461C2×D8—91no—
462C2×M16—31no—
463C22×C8—31no—
464C22⋊Q8—91no—
465C22⋊Q8—91no—
466C22⋊Q8—91no—
467C22⋊Q8—91no—
468C22⋊Q8—181no—
469C22⋊Q8—181no—
470#121—31no—
471#121—91no—
472#121—91no—
473#121—91no—
474#121—181no—
475#121—181no—
476#121—181no—
477#121—181no—
478#121—181no—
479#121—181no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—91no—
482#107—31no—
483#107—31no—
484#107—91no—
485#107—91no—
486#103—91no—
487#103—91no—
488#103—91no—
489#103—91no—
490#102—31no—
491#102—31no—
492#102—91no—
493#102—91no—
494C22⋊C8—31no—
495C22⋊C8—31no—
496C22⋊C8—31no—
497C22⋊C8D3211yescharacteristic
498C23×C3—21no—
499C23×C3—31no—
500C23×C3—31no—
501C23×C3—61no—
502C23×C3C2×D1211yescharacteristic
503C23×C3D3×D411yescharacteristic
504C22×D3—21no—
505C22×D3—61no—
506C22×D3—61no—
507C22×D3—121no—
508C22×D3C2×D1211yescharacteristic
509C22×D3C2×D1211yescharacteristic
510C3×Q8—121no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—121no—
514C3×D4—121no—
515C3×D4—121no—
516C3×D4—241no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—241no—
535C2×C3×C4C2×D1211yescharacteristic
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539#67—41no—
540#67—41no—
541#67—81no—
542#67—122no—
543#67—122no—
544#67—122no—
545#67—122no—
546#67—124no—
547#67—241no—
548#67—241no—
549#67—241no—
550#67—241no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—81no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—122no—
565C2×Dic3—241no—
566C2×Dic3C2×D1211yescharacteristic
567C2×Dic3C2×D1211yescharacteristic
568D12—21no—
569D12—21no—
570D12—41no—
571D12—62no—
572D12—61no—
573D12—61no—
574D12—61no—
575D12—61no—
576D12—121no—
577D12—241no—
578D12—241no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—21no—
583C4×D3—122no—
584C4×D3—122no—
585C4×D3—124no—
586C4×D3—122no—
587C4×D3—241no—
588Dic6—41no—
589Dic6—62no—
590Dic6—61no—
591Dic6—61no—
592Dic6—61no—
593Dic6—61no—
594Dic6—61no—
595Dic6—61no—
596Dic6—61no—
597Dic6—61no—
598Dic6—121no—
599Dic6—121no—
600Dic6—121no—
601C3×C8—21no—
602C3×C8—21no—
603C3×C8—21no—
604C3×C8—21no—
605C3×C8—41no—
606C3×C8—41no—
607C3×C8—61no—
608C3×C8—61no—
609C3⋊C8—21no—
610C3⋊C8—21no—
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—361no—
622#41—361no—
623#41—361no—
624#41—361no—
625C2×Q8—31no—
626C2×Q8—91no—
627C2×Q8—91no—
628C2×D4—31no—
629C2×D4—31no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—61no—
633C2×D4—91no—
634C2×D4—181no—
635C2×D4—181no—
636C2×D4—181no—
637C2×D4—181no—
638C2×D4—181no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—61no—
642C22×C4—181no—
643C22×C4—181no—
644C22×C4—181no—
645C22×C4C2×D3211yescharacteristic
646Q16—361no—
647SD16—361no—
648SD16—361no—
649D8—361no—
650M16—121no—
651C2×C8—31no—
652C2×C8—31no—
653C2×C8—121no—
654C2×C8C2×D3211yescharacteristic
655C2×C8C2×D3211yescharacteristic
656C4⋊C4—31no—
657C4⋊C4—31no—
658C4⋊C4—31no—
659C4⋊C4—61no—
660C4⋊C4—91no—
661C4⋊C4—181no—
662C4⋊C4—181no—
663C4⋊C4—181no—
664C4⋊C4—181no—
665C4⋊C4—181no—
666C22⋊C4—61no—
667C22⋊C4—181no—
668C22⋊C4—181no—
669C22⋊C4—181no—
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×C3C22×D1211yescharacteristic
694C22×C3C2×D3×D411yescharacteristic
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—61no—
719C3×C4—61no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4#100411yescharacteristic
724C3×C4#100411yescharacteristic
725C3×C4#100911yescharacteristic
726C3×C4#100911yescharacteristic
727Dic3—21no—
728Dic3—21no—
729Dic3—41no—
730Dic3—41no—
731Dic3—41no—
732Dic3—122no—
733Dic3—121no—
734Dic3—121no—
735Dic3—121no—
736Dic3—121no—
737Dic3—121no—
738Dic3—121no—
739Dic3—241no—
740Dic3—241no—
741C32#320311yescharacteristic, complemented, Sylow
742C23—31no—
743C23—31no—
744C23—61no—
745C23—181no—
746C23D3×D1211yescharacteristic
747Q8—121no—
748Q8—181no—
749Q8—181no—
750Q8—181no—
751Q8—181no—
752D4—61no—
753D4—61no—
754D4—121no—
755D4—121no—
756D4—121no—
757D4—181no—
758D4—181no—
759D4—241no—
760D4—362no—
761D4—362no—
762D4—721no—
763D4—721no—
764D4—721no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—241no—
780C2×C4—362no—
781C2×C4—362no—
782C2×C4—721no—
783C2×C4D3×D1211yescharacteristic
784C2×C4C22×D3211yescharacteristic
785C8—21no—
786C8—21no—
787C8—61no—
788C8—61no—
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#549311yescharacteristic
799C2×C3#565311yescharacteristic
800C2×C3#575211yescharacteristic
801C2×C3#575311yescharacteristic
802C2×C3#575711yescharacteristic
803C2×C3#577911yescharacteristic
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×D1211yescharacteristic
826C4—21no—
827C4—61no—
828C4—61no—
829C4—121no—
830C4—121no—
831C4—121no—
832C4—361no—
833C4—361no—
834C4—361no—
835C4#6431411yescharacteristic
836C4#6431411yescharacteristic
837C3—21no—
838C3#7867611yescharacteristic, complemented
839C3#8130111yescharacteristic, complemented
840C2—41no—
841C2—121no—
842C2—121no—
843C2—241no—
844C2—721no—
845C2#1059429111yescharacteristic
846C2#1059467811yescharacteristic
847C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3203
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10595043C2semidirect
2. #10595004C2semidirect
3. #10592432C2semidirect
4. C3×#4736C2semidirect
5. C3×#4727C2semidirect
6. #10591182C2semidirect
7. #10591135C2semidirect
8. #10590969C2semidirect
9. #10590968C2semidirect
10. #10590852C2semidirect
11. #10590838C2semidirect
12. #10590828C2semidirect
13. #10590826C2semidirect
14. #10590684C2semidirect
15. #10590679C2semidirect
82. #4736D3semidirect
89. #4727D3semidirect
741. C32#3203semidirect
838. C3#78676semidirect
839. C3#81301semidirect

Maximal subgroups

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

subgroupindex
#105950432
#105950042
#105924322
C3×#47362
C3×#47272
#105911822
#105911352
#105909692
#105909682
#105908522
#105908382
#105908282
#105908262
#105906842
#105906792
#813013
#786763