Finite Group Databasebeta

← #11887258

Subgroups — #11887258

Order 1152.

983 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596277C211yesmaximal, characteristic
2#10594825C211yesmaximal, characteristic, complemented
3C3×#5218C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591479C211yesmaximal, characteristic, complemented
6#10591466C211yesmaximal, characteristic, complemented
7#10591465C211yesmaximal, characteristic, complemented
8#10591445C211yesmaximal, characteristic, complemented
9#10591443C211yesmaximal, characteristic, complemented
10#10591425C211yesmaximal, characteristic, complemented
11#10591424C211yesmaximal, characteristic, complemented
12#10591403C211yesmaximal, characteristic, complemented
13#10591187C211yesmaximal, characteristic, complemented
14#10591148C211yesmaximal, characteristic, complemented
15#10591124C211yesmaximal, characteristic, complemented
16#80159—31nomaximal
17#78759—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×#3830C2211yescharacteristic
20#64162—21no—
21C2×#3757—21no—
22#64148—21no—
23#64147C2211yescharacteristic
24#64145C2211yescharacteristic
25#64144—21no—
26D4×C3⋊Dic3C2211yescharacteristic
27C4×#638C2211yescharacteristic
28#64133C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic
34#63966—21no—
35#63955—21no—
36#63872C2211yescharacteristic, complemented
37#63871C2211yescharacteristic, complemented
38#63849C2211yescharacteristic, complemented
39#63848—21no—
40#63846—21no—
41#63843C2211yescharacteristic, complemented
42C2×#3719C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5806—31no—
62#5806—31no—
63#5806—61no—
64#5642—31no—
65#5513—31no—
66C3×#450—31no—
67C2×C3×#102—31no—
68#5218D311yescharacteristic, complemented
69C2×#832D311yescharacteristic, complemented
70#5173—31no—
71#5171—31no—
72#5166—31no—
73Dic3×SD16—31no—
74#5116—31no—
75C8×#67—31no—
76#5051—31no—
77#4971—31no—
78#4784—31no—
79#4783—31no—
80#4779—31no—
81#4778—31no—
82#4772—31no—
83#4772—31no—
84#4768—31no—
85#4768—31no—
86#4767—31no—
87#4766—31no—
88#4763—31no—
89#4758—31no—
90#67⋊C8—31no—
91#4721—31no—
92C24×C32—21no—
93C2×C32×D4—22no—
94C2×C32×D4—21no—
95C2×C32×D4—41no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×#638—21no—
101C2×#638D411yescharacteristic
102C22×C3⋊Dic3—21no—
103C22×C3⋊Dic3—21no—
104#3830—22no—
105#3830—41no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C22×C3×Dic3—21no—
109C2×C3×Dic6C2311yescharacteristic
110#3757—21no—
111#3757—21no—
112#3757—21no—
113#3757—21no—
114#3757—21no—
115#3757D411yescharacteristic
116#3752D411yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750D411yescharacteristic
120C4×C3⋊Dic3C2311yescharacteristic
121C3×#217—21no—
122C3×#214—22no—
123C3×#214—41no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C2×C3×C3⋊C8—41no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139#3722—21no—
140Dic32—21no—
141Dic32—21no—
142#3719—41no—
143#3710—41no—
144#3296—91noSylow
145C22×C3×D4—21no—
146C22×C3×D4C2×D311yescharacteristic
147C22×C3×D4C2×D311yescharacteristic
148C2×#237—31no—
149C2×#237—31no—
150C2×#237—61no—
151C2×C3×SD16—31no—
152C2×C3×SD16—31no—
153C22×C3×C8—31no—
154C3×C22⋊Q8—31no—
155C2×C3×C4⋊C4—31no—
156#953—61no—
157#953—61no—
158#953—62no—
159C2×#217—61no—
160C2×#217—61no—
161C2×#217—62no—
162#946—31no—
163Q8×Dic3—31no—
164C2×#216—31no—
165#939—61no—
166#939—61no—
167#939—62no—
168#938—31no—
169#938—31no—
170#938—61no—
171#936—31no—
172#936—31no—
173#936—61no—
174#935—61no—
175#935—61no—
176#935—62no—
177D4×Dic3—31no—
178D4×Dic3—31no—
179D4×Dic3—61no—
180C2×#214C2×D311yescharacteristic
181C2×#214C2×D311yescharacteristic
182#929—61no—
183C4×#67—31no—
184C4×#67—31no—
185C4×#67—61no—
186#926—61no—
187C2×C4⋊Dic3C2×D311yescharacteristic
188#924—31no—
189#924—31no—
190#924—61no—
191#924C2×D311yescharacteristic
192C22×C3⋊C8C2×D311yescharacteristic
193C2×Dic12—31no—
194C2×D3×C8—31no—
195C2×D3×C8—31no—
196#898—61no—
197#898—61no—
198#897—31no—
199#892—31no—
200#892—31no—
201#890—31no—
202#890—31no—
203#890—61no—
204#889—61no—
205#887—31no—
206#886—61no—
207#877—61no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×C22⋊C8—31no—
215#835—31no—
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic
218#832C2×D311yescharacteristic
219#832C2×D311yescharacteristic
220#832C2×D311yescharacteristic
221#832C2×D311yescharacteristic
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#818—31no—
226#817—31no—
227#817—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232Dic3⋊C8—31no—
233Dic3⋊C8—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810—31no—
237#810—31no—
238#810—31no—
239#808—31no—
240#808—31no—
241#807—31no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—42no—
245C23×C32—42no—
246C23×C32—81no—
247C23×C32C2×D411yescharacteristic
248C22×C3⋊D3C2×D411yescharacteristic
249C32×D4—21no—
250C32×D4—21no—
251C32×D4—21no—
252C32×D4—42no—
253C32×D4#4112yes—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2411yescharacteristic
258#638—22no—
259#638—42no—
260#638—81no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—42no—
264C2×C3⋊Dic3—81no—
265C2×C3⋊Dic3C2×D411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C4×C3⋊D3—21no—
269C4×C3⋊D3—21no—
270#634—21no—
271#634—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—42no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#552—91no—
284#546—91no—
285#488—91no—
286#483—91no—
287#482—91no—
288#478—91no—
289#467—91no—
290#465—91no—
291#464—91no—
292#452—91no—
293#450—31no—
294C4×SD16—91no—
295C8×D4—91no—
296#416—91no—
297C2×#102—31no—
298C24×C3—22no—
299C24×C3—21no—
300C24×C3—21no—
301C2×C3×Q8—31no—
302C2×C3×D4—22no—
303C2×C3×D4—22no—
304C2×C3×D4—22no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—42no—
310C2×C3×D4—41no—
311C2×C3×D4—41no—
312C2×C3×D4—42no—
313C2×C3×D4C22×D311yescharacteristic
314C2×C3×D4C22×D311yescharacteristic
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C22×C3×C4—21no—
318C22×C3×C4—61no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C2×#67—31no—
322C2×#67—31no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—62no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—62no—
330C22×Dic3—21no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—62no—
336C22×Dic3—62no—
337#237—62no—
338#237—62no—
339#237—122no—
340#237—121no—
341#237—121no—
342#237—122no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—61no—
346C2×Dic6—31no—
347C2×Dic6—31no—
348C2×Dic6—61no—
349C2×Dic6C22×D311yescharacteristic
350C3×SD16—62no—
351C3×SD16—121no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8—121no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C22⋊C4—61no—
363#217—21no—
364#217—31no—
365#217—31no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—62no—
376#217—62no—
377#217—62no—
378#217—62no—
379#217—62no—
380#217—61no—
381#217—61no—
382#216—121no—
383#214—22no—
384#214—41no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—31no—
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—
392C4⋊Dic3—21no—
393C4⋊Dic3—31no—
394C4⋊Dic3—31no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3—61no—
400C4⋊Dic3C22×D311yescharacteristic
401C4⋊Dic3C22×D311yescharacteristic
402C4⋊Dic3C22×D311yescharacteristic
403Dic3⋊C4—21no—
404Dic3⋊C4—31no—
405Dic3⋊C4—31no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—62no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414C4×Dic3—31no—
415C4×Dic3—31no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C2×C3⋊C8—41no—
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426Dic12—121no—
427D3×C8—121no—
428D3×C8—121no—
429C22×C32—22no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32—84no—
438C22×C32#13512yes—
439C22×C32C22×D411yescharacteristic
440C2×C3⋊D3—21no—
441C2×C3⋊D3—21no—
442C2×C3⋊D3—21no—
443C32×C4—21no—
444C32×C4C2×#4111yescharacteristic
445C32×C4H(5,𝔽2)11yescharacteristic
446C3⋊Dic3—21no—
447C3⋊Dic3—21no—
448C3⋊Dic3—21no—
449C3⋊Dic3—41no—
450C3⋊Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41—91no—
456C22×D4D3211yescharacteristic
457C2×Q16—91no—
458C2×SD16—31no—
459C2×SD16—31no—
460C22×C8—31no—
461C22×C8—91no—
462#126—181no—
463#125—91no—
464#125—181no—
465#124—91no—
466#123—181no—
467#123—181no—
468C22⋊Q8—31no—
469C22⋊Q8—91no—
470C22⋊Q8—91no—
471#121—91no—
472#121—181no—
473#120—181no—
474C4×Q8—91no—
475C4×D4—91no—
476C4×D4—91no—
477#117—91no—
478#117—181no—
479C2×C4⋊C4—31no—
480C2×C22⋊C4—181no—
481#107—91no—
482#106—91no—
483#106—91no—
484C4⋊C8—91no—
485#103—91no—
486#103—91no—
487#103—91no—
488#103—91no—
489#102—31no—
490#102—31no—
491#102—31no—
492#102—31no—
493#102—31no—
494#102—31no—
495C22⋊C8—31no—
496C22⋊C8—91no—
497C4×C8—91no—
498C23×C3—22no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—22no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—42no—
506C23×C3—42no—
507C23×C3—44no—
508C23×C3—44no—
509C23×C3—42no—
510C23×C3—42no—
511C23×C3—81no—
512C23×C3—81no—
513C23×C3—82no—
514C23×C3D3×D411yescharacteristic
515C23×C3D3×D411yescharacteristic
516C22×D3—31no—
517C22×D3—31no—
518C22×D3—61no—
519C3×Q8—61no—
520C3×Q8—61no—
521C3×D4—22no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—22no—
529C3×D4—41no—
530C3×D4—41no—
531C3×D4—42no—
532C3×D4—42no—
533C3×D4—44no—
534C3×D4#23512yes—
535C3×D4#23712yes—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—122no—
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—62no—
554#67—62no—
555#67—122no—
556#67—122no—
557#67—122no—
558#67—124no—
559#67—241no—
560#67—241no—
561#67—242no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—42no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—62no—
577C2×Dic3—62no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—122no—
583C2×Dic3—122no—
584C2×Dic3—124no—
585C2×Dic3—241no—
586C2×Dic3—241no—
587C2×Dic3—242no—
588C4×D3—61no—
589C4×D3—61no—
590C4×D3—61no—
591C4×D3—61no—
592C4×D3—121no—
593C4×D3—121no—
594Dic6—21no—
595Dic6—21no—
596Dic6—61no—
597Dic6—61no—
598Dic6—61no—
599Dic6—61no—
600Dic6—121no—
601Dic6—121no—
602C3×C8—61no—
603C3×C8—61no—
604C3×C8—61no—
605C3×C8—61no—
606C3⋊C8—21no—
607C3⋊C8—21no—
608C3⋊C8—21no—
609C3⋊C8—21no—
610C2×C32—22no—
611C2×C32—42no—
612C2×C32—81no—
613C2×C32#54611yescharacteristic
614C2×C32C2×#13511yescharacteristic
615C2×C32#57711yescharacteristic
616C3⋊D3—41no—
617C24—21no—
618#41—182no—
619#41—361no—
620C2×Q8—31no—
621C2×Q8—91no—
622C2×D4—22no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—91no—
626C2×D4—181no—
627C2×D4—181no—
628C2×D4C2×D3211yescharacteristic
629C2×D4C2×D3211yescharacteristic
630C22×C4—61no—
631C22×C4—91no—
632C22×C4—181no—
633C22×C4—181no—
634C22×C4C2×D3211yescharacteristic
635Q16—361no—
636SD16—62no—
637SD16—121no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—121no—
643C2×C8—361no—
644C4⋊C4—31no—
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—91no—
650C4⋊C4—91no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C22⋊C4—61no—
657C22⋊C4—91no—
658C22⋊C4—91no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C42—91no—
667C42—181no—
668C42—181no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—24no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—21no—
677C22×C3—22no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—84no—
696C22×C3—84no—
697C22×C3—88no—
698C22×C3#91212yes—
699C22×C3#91612yes—
700C22×C3C2×D3×D411yescharacteristic
701C22×C3C2×D3×D411yescharacteristic
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—41no—
716C3×C4—121no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4—121no—
720C3×C4C2×#23511yescharacteristic
721C3×C4C2×#23711yescharacteristic
722C3×C4#100411yescharacteristic
723C3×C4#100411yescharacteristic
724Dic3—41no—
725Dic3—41no—
726Dic3—41no—
727Dic3—41no—
728Dic3—61no—
729Dic3—61no—
730Dic3—61no—
731Dic3—61no—
732Dic3—61no—
733Dic3—61no—
734Dic3—121no—
735Dic3—121no—
736Dic3—121no—
737Dic3—122no—
738Dic3—122no—
739Dic3—121no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743C32#329611yescharacteristic, complemented, Sylow
744C23—21no—
745C23—21no—
746C23—42no—
747C23—42no—
748C23—81no—
749C23—91no—
750C23#381111yescharacteristic
751Q8—61no—
752Q8—61no—
753Q8—181no—
754Q8—181no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—182no—
760D4—362no—
761D4—721no—
762D4#380412yes—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—91no—
770C2×C4—91no—
771C2×C4—91no—
772C2×C4—122no—
773C2×C4—181no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—362no—
778C2×C4—721no—
779C2×C4#381111yescharacteristic
780C2×C4C22×D3211yescharacteristic
781C8—61no—
782C8—61no—
783C8—61no—
784C8—61no—
785C2×C3—22no—
786C2×C3—22no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—42no—
791C2×C3—44no—
792C2×C3—42no—
793C2×C3—42no—
794C2×C3—82no—
795C2×C3—81no—
796C2×C3—81no—
797C2×C3#549011yescharacteristic
798C2×C3#559111yescharacteristic
799C2×C3C2×#91211yescharacteristic
800C2×C3C2×#91611yescharacteristic
801C2×C3#576211yescharacteristic
802C2×C3#577511yescharacteristic
803D3—121no—
804D3—121no—
805D3—241no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—84no—
815C22—181no—
816C22—181no—
817C22—181no—
818C22#6393612yes—
819C22C2×#381111yescharacteristic
820C4—21no—
821C4—121no—
822C4—121no—
823C4—121no—
824C4—121no—
825C4—181no—
826C4—181no—
827C4—181no—
828C4—361no—
829C4—361no—
830C4C2×#380411yescharacteristic
831C4#6433011yescharacteristic
832C3—21no—
833C3#7875911yescharacteristic, complemented
834C3#8015911yescharacteristic, complemented
835C2—22no—
836C2—42no—
837C2—81no—
838C2—361no—
839C2C2×#6393611yescharacteristic
840C2#1059511511yescharacteristic
841C2#1059550011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radical#10596277C2
hypercenterC22×D4D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594825C2semidirect
3. C3×#5218C2semidirect
4. C2×C3×#832C2semidirect
5. #10591479C2semidirect
6. #10591466C2semidirect
7. #10591465C2semidirect
8. #10591445C2semidirect
9. #10591443C2semidirect
10. #10591425C2semidirect
11. #10591424C2semidirect
12. #10591403C2semidirect
13. #10591187C2semidirect
14. #10591148C2semidirect
15. #10591124C2semidirect
36. #63872C22semidirect
37. #63871C22semidirect
38. #63849C22semidirect
41. #63843C22semidirect
42. C2×#3719C22semidirect
43. C2×#3710C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. #63573C22semidirect
54. #63572C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63567C22semidirect
58. #63566C22semidirect
59. #63557C22semidirect
60. #63553C22semidirect
68. #5218D3semidirect
69. C2×#832D3semidirect
743. C32#3296semidirect
833. C3#78759semidirect
834. C3#80159semidirect

Maximal subgroups

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

subgroupindex
#105962772
#105948252
C3×#52182
C2×C3×#8322
#105914792
#105914662
#105914652
#105914452
#105914432
#105914252
#105914242
#105914032
#105911872
#105911482
#105911242
#801593
#787593