Finite Group Databasebeta

← #11878571

Subgroups — #11878571

Order 1152.

866 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595004C211yesmaximal, characteristic, complemented
2#10594894C211yesmaximal, characteristic, complemented
3#10592813C211yesmaximal, characteristic, complemented
4C3×#5114C211yesmaximal, characteristic, complemented
5C3×#5110C211yesmaximal, characteristic, complemented
6#10591165C211yesmaximal, characteristic, complemented
7#10591121C211yesmaximal, characteristic, complemented
8#10590970C211yesmaximal, characteristic, complemented
9#10590968C211yesmaximal, characteristic, complemented
10#10590960C211yesmaximal, characteristic, complemented
11#10590823C211yesmaximal, characteristic, complemented
12#10590677C211yesmaximal, characteristic, complemented
13#10590676C211yesmaximal, characteristic, complemented
14#10590675C211yesmaximal, characteristic, complemented
15#10590674C211yesmaximal, characteristic, complemented
16#80670—31nomaximal
17#78677—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic
22#64139C2211yescharacteristic
23#64133C2211yescharacteristic
24C2×#3744C2211yescharacteristic
25C3×#930C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29#63971—21no—
30#63970—21no—
31#63970—21no—
32#63958—21no—
33#63909C2211yescharacteristic
34#63908C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63888—21no—
38#63887—21no—
39#63886—21no—
40#63885—21no—
41#63857C2211yescharacteristic
42#63856C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45#63648C2211yescharacteristic
46#63644C2211yescharacteristic
47#63643C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#817C2211yescharacteristic
54C3×#816C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5833—31no—
62#5833—31no—
63#5629—31no—
64#5608—31no—
65C3×#465—31no—
66C3×#408—31no—
67#5173—31no—
68#5172—31no—
69#5137—31no—
70#5135—31no—
71#5114—31no—
72#5114—31no—
73#5114—61no—
74#5114D311yescharacteristic, complemented
75#5110D311yescharacteristic, complemented
76#5052—31no—
77#5039—31no—
78#4863—31no—
79#4862—31no—
80#4808—31no—
81#4805—31no—
82#4781—31no—
83#4777—31no—
84#4735—31no—
85#4735—31no—
86#4734—31no—
87#4734—31no—
88#4733—31no—
89#4733—31no—
90#4721—31no—
91#4721—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C2×C3×#67D411yescharacteristic
99C3×#235—41no—
100C3×#235—41no—
101C2×C3×D12D411yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6D411yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×#624—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3—21no—
115#3799—41no—
116#3799—41no—
117#3795—41no—
118#3795—41no—
119C2×C32×C8—41no—
120C2×C32×C8C2311yescharacteristic
121C2×C32×C8C2311yescharacteristic
122#3757—21no—
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127#3744—41no—
128C3×#217—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×#208—41no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×#204—41no—
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145#3719—41no—
146#3714—41no—
147#3204—91noSylow
148C2×C3×#41—31no—
149C2×#239—31no—
150C2×#237—31no—
151C2×#235—31no—
152C2×#235—31no—
153C2×#235C2×D311yescharacteristic
154C2×C3×SD16—31no—
155C2×C3×M16—31no—
156C22×C3×C8—21no—
157C22×C3×C8C2×D311yescharacteristic
158C22×C3×C8C2×D311yescharacteristic
159C3×C22⋊Q8—31no—
160C3×#121—31no—
161#946—31no—
162#946—61no—
163#946—61no—
164C2×#216—31no—
165#939—61no—
166#939—61no—
167#939—61no—
168#939—61no—
169#939—61no—
170#938—31no—
171#938—61no—
172#938—61no—
173#938—61no—
174C2×#213—31no—
175#930—31no—
176#930—31no—
177#930—31no—
178#930—31no—
179#930—61no—
180#930C2×D311yescharacteristic
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183#924—31no—
184#924—31no—
185#924—31no—
186#924—31no—
187#924—61no—
188#924C2×D311yescharacteristic
189C2×#208C2×D311yescharacteristic
190C2×Dic12—31no—
191C2×D24—31no—
192C2×#204—31no—
193C2×#204—31no—
194C2×#204—61no—
195C2×#204C2×D311yescharacteristic
196#897—31no—
197#896—61no—
198#895—31no—
199#895—61no—
200D3×C4⋊C4—31no—
201D3×C4⋊C4—31no—
202#884—61no—
203#884—61no—
204#884—61no—
205#878—61no—
206C3×#106—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211C3×C22⋊C8—31no—
212C3×C22⋊C8—31no—
213#835—31no—
214#832—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821C2×D311yescharacteristic
221(C2×D3)⋊C8C2×D311yescharacteristic
222(C2×D3)⋊C8C2×D311yescharacteristic
223(C2×D3)⋊C8C2×D311yescharacteristic
224(C2×D3)⋊C8C2×D311yescharacteristic
225#817—31no—
226#817—31no—
227#817—31no—
228#817—31no—
229#817—61no—
230#817C2×D311yescharacteristic
231#816—31no—
232#816—31no—
233#816—31no—
234#816—31no—
235#816—61no—
236#816C2×D311yescharacteristic
237#810—31no—
238#809—31no—
239#808—31no—
240#808—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—81no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256#634—21no—
257#634—21no—
258C3×#67—41no—
259C3×#67—41no—
260C3×#67—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—41no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3×Dic6—41no—
276#626—42no—
277#626—81no—
278#625—42no—
279#625—81no—
280#624—42no—
281D3×Dic3—42no—
282D3×Dic3—81no—
283D3×Dic3—81no—
284C32×C8—21no—
285C32×C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288#537—91no—
289#537—91no—
290#483—91no—
291#483—91no—
292#481—91no—
293#481—91no—
294#470—91no—
295#469—91no—
296#465—31no—
297#465—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×Q8—31no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—61no—
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
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—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332#239—121no—
333#239—121no—
334#237—121no—
335#237—121no—
336#235—41no—
337#235—41no—
338#235—121no—
339#235—121no—
340#235—121no—
341#235—121no—
342C2×D12—31no—
343C2×D12—31no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12D1211yescharacteristic
348C2×D12C22×D311yescharacteristic
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3C22×D311yescharacteristic
355C2×C4×D3C22×D311yescharacteristic
356C2×Dic6—31no—
357C2×Dic6—31no—
358C2×Dic6—61no—
359C2×Dic6D1211yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C3×SD16—121no—
362C3×M16—121no—
363C2×C3×C8—21no—
364C2×C3×C8—21no—
365C2×C3×C8—31no—
366C2×C3×C8—31no—
367C2×C3×C8—41no—
368C2×C3×C8—41no—
369C2×C3×C8—42no—
370C2×C3×C8C22×D311yescharacteristic
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C2×C3×C8C22×D311yescharacteristic
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379#217—21no—
380#217—61no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—121no—
386#216—121no—
387#213—121no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—61no—
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—121no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
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
408Dic3⋊C4—21no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—121no—
417#208—41no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420Dic12—121no—
421D24—121no—
422#204—41no—
423#204—121no—
424#204—121no—
425#204—122no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32C22×D411yescharacteristic
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
432C2×C3⋊D3—41no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C32×C4—21no—
443C32×C4H(5,𝔽2)11yescharacteristic
444C32×C4H(5,𝔽2)11yescharacteristic
445C3⋊Dic3—41no—
446C3⋊Dic3—41no—
447C3⋊Dic3—41no—
448C3×Dic3—21no—
449C3×Dic3—21no—
450C3×Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C2×#41—31no—
454C2×#41—91no—
455C2×#41—91no—
456C2×Q16—91no—
457C2×SD16—31no—
458C2×SD16—91no—
459C2×D8—91no—
460C2×M16—31no—
461C22×C8D3211yescharacteristic
462C22⋊Q8—31no—
463C22⋊Q8—91no—
464C22⋊Q8—91no—
465C22⋊Q8—91no—
466C22⋊Q8—181no—
467C22⋊Q8—181no—
468#121—31no—
469#121—91no—
470#121—91no—
471#121—91no—
472#121—181no—
473#121—181no—
474#121—181no—
475#121—181no—
476#121—181no—
477#121—181no—
478C2×C4⋊C4—91no—
479C2×C4⋊C4—91no—
480#106—31no—
481#106—91no—
482#106—91no—
483#106—91no—
484#103—31no—
485#103—91no—
486#103—91no—
487#103—91no—
488#102—31no—
489#102—91no—
490#102—91no—
491#102—91no—
492C22⋊C8—31no—
493C22⋊C8—31no—
494C22⋊C8—31no—
495C22⋊C8—31no—
496C23×C3—21no—
497C23×C3—31no—
498C23×C3—31no—
499C23×C3—61no—
500C23×C3C2×D1211yescharacteristic
501C23×C3D3×D411yescharacteristic
502C22×D3—21no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—121no—
506C22×D3C2×D1211yescharacteristic
507C22×D3C2×D1211yescharacteristic
508C3×Q8—61no—
509C3×Q8—61no—
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×C4C2×D1211yescharacteristic
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538#67—41no—
539#67—41no—
540#67—81no—
541#67—122no—
542#67—122no—
543#67—122no—
544#67—241no—
545#67—241no—
546#67—241no—
547#67—241no—
548#67—241no—
549#67—242no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—122no—
563C2×Dic3—241no—
564C2×Dic3—241no—
565C2×Dic3C2×D1211yescharacteristic
566C2×Dic3C2×D1211yescharacteristic
567D12—21no—
568D12—21no—
569D12—41no—
570D12—61no—
571D12—61no—
572D12—61no—
573D12—61no—
574D12—121no—
575D12—121no—
576D12—122no—
577D12—241no—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—122no—
583C4×D3—122no—
584C4×D3—122no—
585C4×D3—241no—
586C4×D3—241no—
587Dic6—21no—
588Dic6—21no—
589Dic6—41no—
590Dic6—61no—
591Dic6—61no—
592Dic6—61no—
593Dic6—61no—
594Dic6—121no—
595Dic6—121no—
596C3×C8—22no—
597C3×C8—21no—
598C3×C8—21no—
599C3×C8—21no—
600C3×C8—21no—
601C3×C8—41no—
602C3×C8—61no—
603C3×C8—61no—
604C3⋊C8—21no—
605C3⋊C8—21no—
606C2×C32—41no—
607C2×C32#53411yescharacteristic
608C2×C32#57711yescharacteristic
609C2×C32#57711yescharacteristic
610C3⋊D3—81no—
611C3×D3—41no—
612C3×D3—41no—
613C3×D3—81no—
614#41—121no—
615#41—121no—
616#41—361no—
617#41—361no—
618#41—361no—
619#41—361no—
620C2×Q8—31no—
621C2×Q8—31no—
622C2×Q8—91no—
623C2×D4—31no—
624C2×D4—31no—
625C2×D4—31no—
626C2×D4—31no—
627C2×D4—61no—
628C2×D4—91no—
629C2×D4—181no—
630C2×D4—181no—
631C2×D4—181no—
632C2×D4—181no—
633C2×D4—181no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—181no—
637C22×C4—181no—
638C22×C4—181no—
639C22×C4—181no—
640C22×C4C2×D3211yescharacteristic
641Q16—361no—
642SD16—121no—
643SD16—361no—
644D8—361no—
645M16—121no—
646C2×C8—31no—
647C2×C8—31no—
648C2×C8—41no—
649C2×C8C2×D3211yescharacteristic
650C2×C8C2×D3211yescharacteristic
651C4⋊C4—31no—
652C4⋊C4—31no—
653C4⋊C4—61no—
654C4⋊C4—91no—
655C4⋊C4—91no—
656C4⋊C4—181no—
657C4⋊C4—181no—
658C4⋊C4—181no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C22⋊C4—61no—
662C22⋊C4—61no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C22⋊C4—181no—
669C22×C3—22no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3C22×D1211yescharacteristic
689C22×C3C2×D3×D411yescharacteristic
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—241no—
706C2×D3—241no—
707C2×D3—241no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—41no—
713C3×C4—61no—
714C3×C4—61no—
715C3×C4—121no—
716C3×C4—121no—
717C3×C4—121no—
718C3×C4#100411yescharacteristic
719C3×C4#100411yescharacteristic
720C3×C4#100411yescharacteristic
721C3×C4#100911yescharacteristic
722Dic3—21no—
723Dic3—21no—
724Dic3—41no—
725Dic3—41no—
726Dic3—41no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731Dic3—121no—
732Dic3—121no—
733Dic3—241no—
734Dic3—241no—
735Dic3—241no—
736C32#320411yescharacteristic, complemented, Sylow
737C23—31no—
738C23—31no—
739C23—61no—
740C23—181no—
741C23D3×D1211yescharacteristic
742Q8—61no—
743Q8—61no—
744Q8—121no—
745Q8—181no—
746Q8—181no—
747D4—61no—
748D4—61no—
749D4—121no—
750D4—121no—
751D4—121no—
752D4—181no—
753D4—181no—
754D4—241no—
755D4—362no—
756D4—362no—
757D4—721no—
758D4—721no—
759D4—721no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—31no—
763C2×C4—31no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—181no—
772C2×C4—181no—
773C2×C4—181no—
774C2×C4—362no—
775C2×C4—362no—
776C2×C4—721no—
777C2×C4—721no—
778C2×C4D3×D1211yescharacteristic
779C2×C4C22×D3211yescharacteristic
780C8—21no—
781C8—21no—
782C8—61no—
783C8—61no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—42no—
788C2×C3—41no—
789C2×C3—41no—
790C2×C3—121no—
791C2×C3—121no—
792C2×C3—241no—
793C2×C3#549311yescharacteristic
794C2×C3#560511yescharacteristic
795C2×C3#575111yescharacteristic
796C2×C3#575111yescharacteristic
797C2×C3#576211yescharacteristic
798C2×C3#577011yescharacteristic
799D3—41no—
800D3—41no—
801D3—81no—
802D3—241no—
803D3—241no—
804D3—481no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—361no—
818C22—361no—
819C22—361no—
820C22C2×D3×D1211yescharacteristic
821C4—21no—
822C4—61no—
823C4—61no—
824C4—121no—
825C4—121no—
826C4—121no—
827C4—361no—
828C4—361no—
829C4—361no—
830C4#6430711yescharacteristic
831C4#6433011yescharacteristic
832C3—21no—
833C3#7867711yescharacteristic, complemented
834C3#8067011yescharacteristic, complemented
835C2—41no—
836C2—121no—
837C2—121no—
838C2—241no—
839C2—721no—
840C2#1059467711yescharacteristic
841C2#1059467911yescharacteristic
842C2#1059507211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3204
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. #10595004C2semidirect
2. #10594894C2semidirect
3. #10592813C2semidirect
4. C3×#5114C2semidirect
5. C3×#5110C2semidirect
6. #10591165C2semidirect
7. #10591121C2semidirect
8. #10590970C2semidirect
9. #10590968C2semidirect
10. #10590960C2semidirect
11. #10590823C2semidirect
12. #10590677C2semidirect
13. #10590676C2semidirect
14. #10590675C2semidirect
15. #10590674C2semidirect
74. #5114D3semidirect
75. #5110D3semidirect
736. C32#3204semidirect
833. C3#78677semidirect
834. C3#80670semidirect

Maximal subgroups

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

subgroupindex
#105950042
#105948942
#105928132
C3×#51142
C3×#51102
#105911652
#105911212
#105909702
#105909682
#105909602
#105908232
#105906772
#105906762
#105906752
#105906742
#806703
#786773