Finite Group Databasebeta

← #11878519

Subgroups — #11878519

Order 1152.

861 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595044C211yesmaximal, characteristic, complemented
2#10594894C211yesmaximal, characteristic, complemented
3#10592435C211yesmaximal, characteristic, complemented
4C3×#4733C211yesmaximal, characteristic, complemented
5C3×#4727C211yesmaximal, characteristic, complemented
6#10591163C211yesmaximal, characteristic, complemented
7#10591103C211yesmaximal, characteristic, complemented
8#10590966C211yesmaximal, characteristic, complemented
9#10590851C211yesmaximal, characteristic, complemented
10#10590850C211yesmaximal, characteristic, complemented
11#10590833C211yesmaximal, characteristic, complemented
12#10590826C211yesmaximal, characteristic, complemented
13#10590823C211yesmaximal, characteristic, complemented
14#10590682C211yesmaximal, characteristic, complemented
15#10590680C211yesmaximal, characteristic, complemented
16#80239—31nomaximal
17#78676—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21#64139C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63980—21no—
29#63980—21no—
30#63971—21no—
31#63958—21no—
32#63909C2211yescharacteristic
33#63908—21no—
34#63908C2211yescharacteristic
35#63908C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63888—21no—
38#63886—21no—
39#63856—21no—
40#63856C2211yescharacteristic
41#63856C2211yescharacteristic
42#63856C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46#63648C2211yescharacteristic
47#63648C2211yescharacteristic
48#63645C2211yescharacteristic
49#63645C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×#816C2211yescharacteristic
55#63575C2211yescharacteristic
56#63575C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63563C2211yescharacteristic
61#5833—31no—
62#5833—31no—
63#5833—31no—
64#5629—31no—
65C3×#452—31no—
66C3×#408—31no—
67#5238—31no—
68#5188—31no—
69#5187—31no—
70#5174—31no—
71#5172—31no—
72#5134—31no—
73#5134—31no—
74#5116—31no—
75#5115—31no—
76#5044—31no—
77#4812—31no—
78#4811—31no—
79#4775—31no—
80#4774—31no—
81#4736—31no—
82#4736—31no—
83#4736—31no—
84#4736—61no—
85#4734—31no—
86#4734—31no—
87#4733—31no—
88#4733D311yescharacteristic, complemented
89#4727D311yescharacteristic, complemented
90#4722—31no—
91#4722—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C2×C3×#67D411yescharacteristic
99C3×#235—41no—
100C3×#235—41no—
101C3×#235—41no—
102C3×#235—41no—
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6D411yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117#3799—41no—
118#3799—41no—
119C2×C32×C8C2311yescharacteristic
120C2×C32×C8C2311yescharacteristic
121#3752—21no—
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C3×#217—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×Dic12—41no—
132C3×#204—41no—
133C3×ΓL(1,𝔽25)—41no—
134C3×D3×C8—41no—
135#3724—21no—
136#3724—21no—
137#3724—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145#3717—41no—
146#3714—41no—
147#3203—91noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×#239—31no—
151C2×#235—31no—
152C2×#235C2×D311yescharacteristic
153C2×#235C2×D311yescharacteristic
154C2×C3×Q16—31no—
155C2×C3×SD16—31no—
156C2×C3×M16—31no—
157C22×C3×C8—31no—
158C3×C22⋊Q8—31no—
159#946—31no—
160#946—31no—
161#946—31no—
162#946—61no—
163#946—61no—
164C2×#215—31no—
165#939—61no—
166#939—61no—
167#939—61no—
168#939—61no—
169#939—61no—
170#939—61no—
171#938—31no—
172#938—31no—
173#938—61no—
174#938—61no—
175C2×#213—31no—
176#930—31no—
177#930—31no—
178#930—31no—
179#930—31no—
180#930—31no—
181#930—61no—
182#930—61no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—61no—
187#924—31no—
188#924—31no—
189#924—31no—
190#924—61no—
191#924C2×D311yescharacteristic
192C2×Dic12C2×D311yescharacteristic
193C2×D24—31no—
194C2×#204—31no—
195C2×#204C2×D311yescharacteristic
196C2×ΓL(1,𝔽25)C2×D311yescharacteristic
197C2×D3×C8C2×D311yescharacteristic
198#896—61no—
199#895—31no—
200#895—61no—
201D3×C4⋊C4—31no—
202#884—61no—
203#884—61no—
204C3×#103—31no—
205C3×#102—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8C2×D311yescharacteristic
211C3×C22⋊C8C2×D311yescharacteristic
212#835—31no—
213#835—31no—
214#835—31no—
215#832—31no—
216#830C2×D311yescharacteristic
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—61no—
223#821—61no—
224#821C2×D311yescharacteristic
225(C2×D3)⋊C8C2×D311yescharacteristic
226(C2×D3)⋊C8C2×D311yescharacteristic
227#818—31no—
228#818—31no—
229#818—31no—
230#818—31no—
231#818—31no—
232#818—31no—
233#818—61no—
234#818—61no—
235#816—31no—
236#816—31no—
237#816—31no—
238#816C2×D311yescharacteristic
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—81no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—81no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C3×#67—41no—
258C3×#67—41no—
259C3×#67—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—41no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—42no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277C3×Dic6—41no—
278#626—42no—
279#626—81no—
280#625—81no—
281#625—81no—
282#624—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—91no—
293#480—91no—
294#468—91no—
295#468—91no—
296#467—91no—
297#466—91no—
298#452—31no—
299#452—91no—
300#449—91no—
301#449—91no—
302#408—31no—
303C3×#41—121no—
304C3×#41—121no—
305C3×#41—121no—
306C3×#41—121no—
307C2×C3×Q8—31no—
308C2×C3×Q8—31no—
309C2×C3×Q8—31no—
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—61no—
315C22×C3×C4—21no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C2×#67—21no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—121no—
331C2×#67D1211yescharacteristic
332C2×#67D1211yescharacteristic
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336C22×Dic3—121no—
337#239—121no—
338#239—121no—
339#235—41no—
340#235—41no—
341#235—41no—
342#235—41no—
343#235—121no—
344#235—121no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12—61no—
350C2×D12D1211yescharacteristic
351C2×D12C22×D311yescharacteristic
352C2×C4×D3—21no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3C22×D311yescharacteristic
357C2×C4×D3C22×D311yescharacteristic
358C2×Dic6D1211yescharacteristic
359C2×Dic6C22×D311yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C3×Q16—121no—
362C3×SD16—121no—
363C3×M16—121no—
364C2×C3×C8—21no—
365C2×C3×C8—21no—
366C2×C3×C8—31no—
367C2×C3×C8—31no—
368C2×C3×C8—121no—
369C2×C3×C8C22×D311yescharacteristic
370C2×C3×C8C22×D311yescharacteristic
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C3×C4⋊C4—31no—
374C3×C4⋊C4—61no—
375C3×C22⋊C4—61no—
376#217—21no—
377#217—61no—
378#217—61no—
379#217—61no—
380#217—61no—
381#217—61no—
382#215—121no—
383#213—121no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—121no—
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—31no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—31no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—121no—
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—
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418Dic12—41no—
419D24—121no—
420#204—41no—
421#204—121no—
422ΓL(1,𝔽25)—41no—
423D3×C8—41no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32C22×D411yescharacteristic
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C32×C4—21no—
441C32×C4H(5,𝔽2)11yescharacteristic
442C32×C4H(5,𝔽2)11yescharacteristic
443C3⋊Dic3—41no—
444C3⋊Dic3—41no—
445C3⋊Dic3—41no—
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C2×#41—31no—
452C2×#41—31no—
453C2×#41—91no—
454C2×Q16—31no—
455C2×SD16—31no—
456C2×SD16—91no—
457C2×D8—91no—
458C2×M16—31no—
459C22×C8—31no—
460C22⋊Q8—31no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463C22⋊Q8—91no—
464C22⋊Q8—181no—
465C22⋊Q8—181no—
466#121—91no—
467#121—91no—
468#121—91no—
469#121—91no—
470#121—181no—
471#121—181no—
472#121—181no—
473#121—181no—
474#121—181no—
475#121—181no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478#107—91no—
479#107—91no—
480#107—91no—
481#107—91no—
482#103—31no—
483#103—91no—
484#103—91no—
485#103—91no—
486#102—31no—
487#102—91no—
488#102—91no—
489#102—91no—
490C22⋊C8—31no—
491C22⋊C8—31no—
492C22⋊C8—31no—
493C22⋊C8D3211yescharacteristic
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—31no—
497C23×C3—61no—
498C23×C3C2×D1211yescharacteristic
499C23×C3D3×D411yescharacteristic
500C22×D3—21no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—121no—
504C22×D3C2×D1211yescharacteristic
505C22×D3C2×D1211yescharacteristic
506C3×Q8—61no—
507C3×Q8—61no—
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—122no—
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—122no—
535C2×C3×C4C2×D1211yescharacteristic
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539#67—41no—
540#67—41no—
541#67—42no—
542#67—122no—
543#67—241no—
544#67—241no—
545#67—241no—
546#67—241no—
547#67—241no—
548#67—241no—
549#67—241no—
550#67—242no—
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—121no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—241no—
564C2×Dic3—241no—
565C2×Dic3—241no—
566C2×Dic3—242no—
567C2×Dic3C2×D1211yescharacteristic
568C2×Dic3C2×D1211yescharacteristic
569D12—21no—
570D12—21no—
571D12—41no—
572D12—61no—
573D12—61no—
574D12—61no—
575D12—61no—
576D12—121no—
577D12—121no—
578D12—122no—
579D12—241no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—21no—
583C4×D3—21no—
584C4×D3—42no—
585C4×D3—122no—
586C4×D3—122no—
587C4×D3—241no—
588Dic6—21no—
589Dic6—21no—
590Dic6—21no—
591Dic6—21no—
592Dic6—41no—
593C3×C8—21no—
594C3×C8—21no—
595C3×C8—21no—
596C3×C8—21no—
597C3×C8—41no—
598C3×C8—41no—
599C3×C8—61no—
600C3×C8—61no—
601C3⋊C8—21no—
602C3⋊C8—21no—
603C2×C32—41no—
604C2×C32#53411yescharacteristic
605C2×C32#57611yescharacteristic
606C2×C32#57811yescharacteristic
607C3⋊D3—81no—
608C3×D3—41no—
609C3×D3—41no—
610C3×D3—81no—
611#41—121no—
612#41—121no—
613#41—121no—
614#41—121no—
615#41—361no—
616#41—361no—
617C2×Q8—31no—
618C2×Q8—31no—
619C2×Q8—31no—
620C2×D4—31no—
621C2×D4—31no—
622C2×D4—31no—
623C2×D4—31no—
624C2×D4—61no—
625C2×D4—91no—
626C2×D4—181no—
627C2×D4—181no—
628C2×D4—181no—
629C2×D4—181no—
630C2×D4—181no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—181no—
635C22×C4—181no—
636C22×C4—181no—
637C22×C4C2×D3211yescharacteristic
638Q16—121no—
639SD16—121no—
640SD16—361no—
641D8—361no—
642M16—121no—
643C2×C8—31no—
644C2×C8—31no—
645C2×C8—121no—
646C2×C8C2×D3211yescharacteristic
647C2×C8C2×D3211yescharacteristic
648C4⋊C4—31no—
649C4⋊C4—61no—
650C4⋊C4—91no—
651C4⋊C4—91no—
652C4⋊C4—91no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C4⋊C4—181no—
657C4⋊C4—181no—
658C22⋊C4—61no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22×C3—22no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3C22×D1211yescharacteristic
686C22×C3C2×D3×D411yescharacteristic
687C2×D3—21no—
688C2×D3—21no—
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—241no—
703C2×D3—241no—
704C2×D3—241no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—41no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—121no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4#100411yescharacteristic
716C3×C4#100411yescharacteristic
717C3×C4#100411yescharacteristic
718C3×C4#100411yescharacteristic
719Dic3—21no—
720Dic3—21no—
721Dic3—41no—
722Dic3—41no—
723Dic3—41no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—241no—
731Dic3—241no—
732Dic3—241no—
733C32#320311yescharacteristic, complemented, Sylow
734C23—31no—
735C23—31no—
736C23—61no—
737C23—181no—
738C23D3×D1211yescharacteristic
739Q8—61no—
740Q8—61no—
741Q8—61no—
742Q8—61no—
743Q8—121no—
744D4—61no—
745D4—61no—
746D4—121no—
747D4—121no—
748D4—121no—
749D4—122no—
750D4—181no—
751D4—181no—
752D4—362no—
753D4—721no—
754D4—721no—
755D4—721no—
756D4—721no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—122no—
769C2×C4—181no—
770C2×C4—181no—
771C2×C4—181no—
772C2×C4—362no—
773C2×C4—721no—
774C2×C4—721no—
775C2×C4D3×D1211yescharacteristic
776C2×C4C22×D3211yescharacteristic
777C8—21no—
778C8—21no—
779C8—61no—
780C8—61no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—42no—
785C2×C3—41no—
786C2×C3—41no—
787C2×C3—121no—
788C2×C3—121no—
789C2×C3—241no—
790C2×C3#549311yescharacteristic
791C2×C3#558911yescharacteristic
792C2×C3#575211yescharacteristic
793C2×C3#575311yescharacteristic
794C2×C3#576911yescharacteristic
795C2×C3#577911yescharacteristic
796D3—41no—
797D3—41no—
798D3—81no—
799D3—241no—
800D3—241no—
801D3—481no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—61no—
806C22—61no—
807C22—61no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—361no—
815C22—361no—
816C22—361no—
817C22C2×D3×D1211yescharacteristic
818C4—21no—
819C4—61no—
820C4—61no—
821C4—121no—
822C4—121no—
823C4—121no—
824C4—361no—
825C4—361no—
826C4—361no—
827C4#6431311yescharacteristic
828C4#6431311yescharacteristic
829C3—21no—
830C3#7867611yescharacteristic, complemented
831C3#8023911yescharacteristic, complemented
832C2—41no—
833C2—121no—
834C2—121no—
835C2—241no—
836C2—721no—
837C2#1059429011yescharacteristic
838C2#1059468011yescharacteristic
839C2#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. #10595044C2semidirect
2. #10594894C2semidirect
3. #10592435C2semidirect
4. C3×#4733C2semidirect
5. C3×#4727C2semidirect
6. #10591163C2semidirect
7. #10591103C2semidirect
8. #10590966C2semidirect
9. #10590851C2semidirect
10. #10590850C2semidirect
11. #10590833C2semidirect
12. #10590826C2semidirect
13. #10590823C2semidirect
14. #10590682C2semidirect
15. #10590680C2semidirect
88. #4733D3semidirect
89. #4727D3semidirect
733. C32#3203semidirect
830. C3#78676semidirect
831. C3#80239semidirect

Maximal subgroups

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

subgroupindex
#105950442
#105948942
#105924352
C3×#47332
C3×#47272
#105911632
#105911032
#105909662
#105908512
#105908502
#105908332
#105908262
#105908232
#105906822
#105906802
#802393
#786763