Finite Group Databasebeta

← #11887412

Subgroups — #11887412

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596277C211yesmaximal, characteristic, complemented
2#10594989C211yesmaximal, characteristic, complemented
3C3×#5217C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591479C211yesmaximal, characteristic, complemented
6#10591457C211yesmaximal, characteristic, complemented
7#10591455C211yesmaximal, characteristic, complemented
8#10591435C211yesmaximal, characteristic, complemented
9#10591434C211yesmaximal, characteristic, complemented
10#10591425C211yesmaximal, characteristic, complemented
11#10591424C211yesmaximal, characteristic, complemented
12#10591403C211yesmaximal, characteristic, complemented
13#10591175C211yesmaximal, characteristic, complemented
14#10591148C211yesmaximal, characteristic, complemented
15#10591135C211yesmaximal, characteristic, complemented
16#80015—31nomaximal
17#78760—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×#213C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C3×#930C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic
34#63978—21no—
35Dic3×#67—21no—
36#63916C2211yescharacteristic, complemented
37#63898C2211yescharacteristic, complemented
38#63890—21no—
39#63872C2211yescharacteristic, complemented
40#63858—21no—
41#63849C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63575C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5806—31no—
62#5806—31no—
63#5806—61no—
64#5618—31no—
65#5514—31no—
66C3×#447—31no—
67C2×C3×#102—31no—
68#5217D311yescharacteristic, complemented
69C2×#832D311yescharacteristic, complemented
70#5158—31no—
71#5157—31no—
72#5153—31no—
73Dic3×D8—31no—
74#5114—31no—
75C8×#67—31no—
76#5041—31no—
77#4970—31no—
78#4787—31no—
79#4784—31no—
80#4781—31no—
81#4779—31no—
82#4775—31no—
83#4772—31no—
84#4772—31no—
85#4768—31no—
86#4768—31no—
87#4766—31no—
88#4763—31no—
89#4756—31no—
90#67⋊C8—31no—
91#4722—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
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C2×C3×D12C2311yescharacteristic
111C2×#626—21no—
112C2×D3×Dic3—21no—
113#3757—21no—
114#3757—21no—
115#3757—21no—
116#3757—21no—
117#3757—21no—
118#3757D411yescharacteristic
119#3752D411yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122#3750D411yescharacteristic
123C4×C3⋊Dic3C2311yescharacteristic
124C3×#213—22no—
125C3×#213—41no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C2×C3×C3⋊C8—41no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3716—41no—
143#3710—41no—
144#3297—91noSylow
145C22×C3×D4—21no—
146C22×C3×D4C2×D311yescharacteristic
147C22×C3×D4C2×D311yescharacteristic
148C2×#237—31no—
149C2×#237—31no—
150C2×#237—61no—
151C2×C3×D8—31no—
152C2×C3×D8—31no—
153C22×C3×C8—31no—
154C3×#121—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#939—61no—
163#939—61no—
164#939—61no—
165#939—62no—
166#938—31no—
167#938—31no—
168#938—31no—
169#938—61no—
170#936—31no—
171#936—31no—
172#936—61no—
173#935—61no—
174#935—61no—
175#935—62no—
176D4×Dic3—31no—
177D4×Dic3—31no—
178D4×Dic3—31no—
179D4×Dic3—61no—
180D4×Dic3—61no—
181C2×#214—31no—
182C2×#213C2×D311yescharacteristic
183C2×#213C2×D311yescharacteristic
184#930—61no—
185#930C2×D311yescharacteristic
186C4×#67—31no—
187C4×#67—31no—
188C4×#67—61no—
189C4×#67—61no—
190C2×C4⋊Dic3C2×D311yescharacteristic
191#924—31no—
192#924—31no—
193#924—61no—
194C22×C3⋊C8C2×D311yescharacteristic
195C2×#204—31no—
196C2×D3×C8—31no—
197C2×D3×C8—31no—
198#898—61no—
199#895—31no—
200#894—61no—
201#893—31no—
202#892—31no—
203#892—31no—
204#890—31no—
205#890—31no—
206#886—61no—
207#879—61no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×C22⋊C8—31no—
215#832—31no—
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic
218#832C2×D311yescharacteristic
219#832C2×D311yescharacteristic
220#832C2×D311yescharacteristic
221#832C2×D311yescharacteristic
222#830C2×D311yescharacteristic
223#821—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226#818—31no—
227#818—31no—
228#817—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#807—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
249C22×C3×D3—21no—
250C32×D4—21no—
251C32×D4—21no—
252C32×D4—21no—
253C32×D4—42no—
254C32×D4#4112yes—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259#638—22no—
260#638—42no—
261#638—81no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—42no—
265C2×C3⋊Dic3—81no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4×C3⋊D3—21no—
270C4×C3⋊D3—21no—
271#634—21no—
272#634—21no—
273C3×#67—42no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—81no—
278C3×D12—21no—
279C3×D12—21no—
280#626—81no—
281D3×Dic3—81no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285C3×C3⋊C8—21no—
286#553—91no—
287#546—91no—
288#488—91no—
289#484—91no—
290#482—91no—
291#478—91no—
292#466—91no—
293#465—91no—
294#463—91no—
295#449—91no—
296#447—31no—
297C4×D8—91no—
298C8×D4—91no—
299#416—91no—
300C2×#102—31no—
301C24×C3—22no—
302C24×C3—21no—
303C24×C3—21no—
304C2×C3×D4—22no—
305C2×C3×D4—22no—
306C2×C3×D4—22no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—31no—
312C2×C3×D4—42no—
313C2×C3×D4—41no—
314C2×C3×D4—41no—
315C2×C3×D4—42no—
316C2×C3×D4—61no—
317C2×C3×D4C22×D311yescharacteristic
318C2×C3×D4C22×D311yescharacteristic
319C2×C3×D4C22×D311yescharacteristic
320C2×C3×D4C22×D311yescharacteristic
321C22×C3×C4—21no—
322C22×C3×C4—61no—
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—21no—
326C2×#67—31no—
327C2×#67—31no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—62no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—62no—
336C22×Dic3—21no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342C22×Dic3—62no—
343C22×Dic3—62no—
344#237—62no—
345#237—62no—
346#237—122no—
347#237—121no—
348#237—121no—
349#237—122no—
350C2×D12—61no—
351C2×D12C22×D311yescharacteristic
352C2×C4×D3—31no—
353C2×C4×D3—31no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×Dic6—31no—
357C2×Dic6—31no—
358C2×Dic6—61no—
359C3×D8—62no—
360C3×D8—121no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C2×C3×C8—121no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—61no—
370C3×C22⋊C4—61no—
371#217—31no—
372#217—31no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217—61no—
378#217—61no—
379#217—61no—
380#217—61no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—62no—
385#217—62no—
386#217—62no—
387#217—62no—
388#217—62no—
389#217—61no—
390#217—61no—
391#214—121no—
392#213—22no—
393#213—41no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402C4⋊Dic3—21no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3C22×D311yescharacteristic
409C4⋊Dic3C22×D311yescharacteristic
410C4⋊Dic3C22×D311yescharacteristic
411Dic3⋊C4—31no—
412Dic3⋊C4—31no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—62no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C2×C3⋊C8—41no—
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428C2×C3⋊C8C22×D311yescharacteristic
429#204—121no—
430D3×C8—121no—
431D3×C8—121no—
432C22×C32—22no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—84no—
441C22×C32#13512yes—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—21no—
444C2×C3⋊D3—21no—
445C2×C3⋊D3—21no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C32×C4—21no—
450C32×C4C2×#4111yescharacteristic
451C32×C4H(5,𝔽2)11yescharacteristic
452C3⋊Dic3—21no—
453C3⋊Dic3—21no—
454C3⋊Dic3—21no—
455C3⋊Dic3—41no—
456C3⋊Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3—41no—
460C2×#41—91no—
461C22×D4D3211yescharacteristic
462C2×SD16—91no—
463C2×D8—31no—
464C2×D8—31no—
465C22×C8—31no—
466C22×C8—91no—
467#126—181no—
468#125—91no—
469#124—91no—
470#123—181no—
471#123—181no—
472C22⋊Q8—91no—
473#121—31no—
474#121—91no—
475#121—91no—
476#121—181no—
477#121—181no—
478#120—181no—
479C4×D4—91no—
480C4×D4—91no—
481C4×D4—91no—
482C4×D4—181no—
483#117—91no—
484C2×C4⋊C4—31no—
485C2×C22⋊C4—181no—
486#107—91no—
487#107—91no—
488#106—91no—
489C4⋊C8—91no—
490#103—91no—
491#103—91no—
492#103—91no—
493#102—31no—
494#102—31no—
495#102—31no—
496#102—31no—
497#102—31no—
498#102—31no—
499#102—91no—
500C22⋊C8—31no—
501C22⋊C8—91no—
502C4×C8—91no—
503C23×C3—22no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—22no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—42no—
511C23×C3—42no—
512C23×C3—44no—
513C23×C3—44no—
514C23×C3—42no—
515C23×C3—42no—
516C23×C3—61no—
517C23×C3—81no—
518C23×C3—81no—
519C23×C3—82no—
520C23×C3D3×D411yescharacteristic
521C23×C3D3×D411yescharacteristic
522C22×D3—21no—
523C22×D3—31no—
524C22×D3—31no—
525C22×D3—61no—
526C3×D4—22no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—21no—
531C3×D4—21no—
532C3×D4—21no—
533C3×D4—22no—
534C3×D4—41no—
535C3×D4—41no—
536C3×D4—42no—
537C3×D4—42no—
538C3×D4—44no—
539C3×D4—61no—
540C3×D4—61no—
541C3×D4—122no—
542C3×D4#23512yes—
543C3×D4#23712yes—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—241no—
556C2×C3×C4D3×D411yescharacteristic
557C2×C3×C4D3×D411yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559C2×C3×C4C23×D311yescharacteristic
560#67—42no—
561#67—62no—
562#67—62no—
563#67—122no—
564#67—122no—
565#67—122no—
566#67—124no—
567#67—241no—
568#67—241no—
569#67—241no—
570#67—242no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—62no—
584C2×Dic3—62no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—81no—
590C2×Dic3—122no—
591C2×Dic3—122no—
592C2×Dic3—124no—
593C2×Dic3—241no—
594C2×Dic3—241no—
595C2×Dic3—241no—
596C2×Dic3—242no—
597D12—21no—
598D12—21no—
599D12—241no—
600C4×D3—61no—
601C4×D3—61no—
602C4×D3—61no—
603C4×D3—61no—
604C4×D3—121no—
605C4×D3—121no—
606C4×D3—241no—
607Dic6—61no—
608Dic6—61no—
609Dic6—61no—
610Dic6—61no—
611Dic6—121no—
612Dic6—121no—
613C3×C8—61no—
614C3×C8—61no—
615C3×C8—61no—
616C3×C8—61no—
617C3⋊C8—21no—
618C3⋊C8—21no—
619C3⋊C8—21no—
620C3⋊C8—21no—
621C2×C32—22no—
622C2×C32—42no—
623C2×C32—81no—
624C2×C32#54611yescharacteristic
625C2×C32C2×#13511yescharacteristic
626C2×C32#57611yescharacteristic
627C3⋊D3—41no—
628C3×D3—81no—
629C24—21no—
630#41—182no—
631#41—361no—
632C2×Q8—91no—
633C2×D4—22no—
634C2×D4—21no—
635C2×D4—31no—
636C2×D4—41no—
637C2×D4—61no—
638C2×D4—91no—
639C2×D4—181no—
640C2×D4—181no—
641C2×D4—181no—
642C2×D4C2×D3211yescharacteristic
643C2×D4C2×D3211yescharacteristic
644C22×C4—61no—
645C22×C4—91no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4—181no—
649C22×C4C2×D3211yescharacteristic
650SD16—361no—
651D8—62no—
652D8—121no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—31no—
656C2×C8—31no—
657C2×C8—121no—
658C2×C8—361no—
659C4⋊C4—31no—
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—61no—
663C4⋊C4—91no—
664C4⋊C4—91no—
665C4⋊C4—181no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C22⋊C4—61no—
669C22⋊C4—91no—
670C22⋊C4—91no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—91no—
680C42—181no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—24no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—21no—
689C22×C3—22no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—84no—
708C22×C3—84no—
709C22×C3—88no—
710C22×C3—121no—
711C22×C3—121no—
712C22×C3—121no—
713C22×C3#91212yes—
714C22×C3#91612yes—
715C22×C3C2×D3×D411yescharacteristic
716C22×C3C2×D3×D411yescharacteristic
717C2×D3—41no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—61no—
721C2×D3—61no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—41no—
734C3×C4—121no—
735C3×C4—121no—
736C3×C4—121no—
737C3×C4C2×#23511yescharacteristic
738C3×C4C2×#23711yescharacteristic
739C3×C4#100411yescharacteristic
740C3×C4#100411yescharacteristic
741Dic3—41no—
742Dic3—41no—
743Dic3—41no—
744Dic3—61no—
745Dic3—61no—
746Dic3—61no—
747Dic3—61no—
748Dic3—61no—
749Dic3—61no—
750Dic3—121no—
751Dic3—121no—
752Dic3—121no—
753Dic3—122no—
754Dic3—122no—
755Dic3—121no—
756Dic3—121no—
757Dic3—121no—
758Dic3—121no—
759C32#329711yescharacteristic, complemented, Sylow
760C23—21no—
761C23—21no—
762C23—42no—
763C23—42no—
764C23—61no—
765C23—81no—
766C23—91no—
767C23#381111yescharacteristic
768Q8—181no—
769Q8—181no—
770D4—21no—
771D4—21no—
772D4—21no—
773D4—42no—
774D4—61no—
775D4—61no—
776D4—122no—
777D4—182no—
778D4—362no—
779D4—721no—
780D4—721no—
781D4#380412yes—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—91no—
788C2×C4—91no—
789C2×C4—91no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—241no—
795C2×C4—362no—
796C2×C4—721no—
797C2×C4—721no—
798C2×C4#381111yescharacteristic
799C2×C4C22×D3211yescharacteristic
800C8—61no—
801C8—61no—
802C8—61no—
803C8—61no—
804C2×C3—22no—
805C2×C3—22no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—42no—
810C2×C3—44no—
811C2×C3—42no—
812C2×C3—42no—
813C2×C3—82no—
814C2×C3—81no—
815C2×C3—81no—
816C2×C3—241no—
817C2×C3#549011yescharacteristic
818C2×C3#559111yescharacteristic
819C2×C3C2×#91211yescharacteristic
820C2×C3#575711yescharacteristic
821C2×C3C2×#91611yescharacteristic
822C2×C3#577411yescharacteristic
823D3—81no—
824D3—121no—
825D3—121no—
826D3—241no—
827C22—21no—
828C22—21no—
829C22—22no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—84no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22—181no—
840C22—181no—
841C22—181no—
842C22#6393612yes—
843C22C2×#381111yescharacteristic
844C4—21no—
845C4—121no—
846C4—121no—
847C4—121no—
848C4—181no—
849C4—181no—
850C4—181no—
851C4—361no—
852C4—361no—
853C4C2×#380411yescharacteristic
854C4#6433011yescharacteristic
855C3—21no—
856C3#7876011yescharacteristic, complemented
857C3#8001511yescharacteristic, complemented
858C2—22no—
859C2—42no—
860C2—81no—
861C2—241no—
862C2—361no—
863C2#1059510211yescharacteristic
864C2C2×#6393611yescharacteristic
865C2#1059550011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3297
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
1. #10596277C2semidirect
2. #10594989C2semidirect
3. C3×#5217C2semidirect
4. C2×C3×#832C2semidirect
5. #10591479C2semidirect
6. #10591457C2semidirect
7. #10591455C2semidirect
8. #10591435C2semidirect
9. #10591434C2semidirect
10. #10591425C2semidirect
11. #10591424C2semidirect
12. #10591403C2semidirect
13. #10591175C2semidirect
14. #10591148C2semidirect
15. #10591135C2semidirect
36. #63916C22semidirect
37. #63898C22semidirect
39. #63872C22semidirect
41. #63849C22semidirect
42. C2×#3716C22semidirect
43. C2×#3710C22semidirect
51. #63575C22semidirect
52. #63575C22semidirect
53. #63573C22semidirect
54. #63572C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63567C22semidirect
58. #63563C22semidirect
59. #63557C22semidirect
60. #63553C22semidirect
68. #5217D3semidirect
69. C2×#832D3semidirect
759. C32#3297semidirect
856. C3#78760semidirect
857. C3#80015semidirect

Maximal subgroups

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

subgroupindex
#105962772
#105949892
C3×#52172
C2×C3×#8322
#105914792
#105914572
#105914552
#105914352
#105914342
#105914252
#105914242
#105914032
#105911752
#105911482
#105911352
#800153
#787603