Finite Group Databasebeta

← #11887017

Subgroups — #11887017

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D12×#67C211yesmaximal, characteristic, complemented
2#10594906C211yesmaximal, characteristic, complemented
3#10592814C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591162C211yesmaximal, characteristic, complemented
7#10591133C211yesmaximal, characteristic, complemented
8#10590947C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590878C211yesmaximal, characteristic, complemented
11#10590826C211yesmaximal, characteristic, complemented
12#10590765C211yesmaximal, characteristic, complemented
13#10590762C211yesmaximal, characteristic, complemented
14#10590745C211yesmaximal, characteristic, complemented
15#10590680C211yesmaximal, characteristic, complemented
16#79438—31nomaximal
17#78757—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3804—21no—
21C2×D3×D12C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic, complemented
23#64139C2211yescharacteristic
24#64139C2211yescharacteristic, complemented
25C2×#3745C2211yescharacteristic, complemented
26C3×C4×#67C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
28C2×C3×D3×C8C2211yescharacteristic, complemented
29#63977—21no—
30#63966—21no—
31#63922—21no—
32#63918C2211yescharacteristic, complemented
33#63911C2211yescharacteristic
34#63909C2211yescharacteristic, complemented
35#63908C2211yescharacteristic
36#63895—21no—
37#63894C2211yescharacteristic, complemented
38Dic3×D12C2211yescharacteristic
39#63890—21no—
40D3×C4⋊Dic3C2211yescharacteristic, complemented
41#63886—21no—
42C2×#3714C2211yescharacteristic
43C2×#3714C2211yescharacteristic, complemented
44#63648C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63645C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61D4×#67—31no—
62#5555—31no—
63D4×D12—31no—
64#5507—31no—
65C3×C8×D4—31no—
66C2×C3×#102—31no—
67#5217—31no—
68#5115—31no—
69#5115—31no—
70#5115—31no—
71#5115—61no—
72C2×#821—31no—
73C2×#821D311yescharacteristic, complemented
74C8×#67D311yescharacteristic, complemented
75#4967—31no—
76#4846—31no—
77#4843—31no—
78#4786—31no—
79#4775—31no—
80#4774—31no—
81#4773—31no—
82D3×#102—31no—
83#4760—31no—
84#4759—31no—
85#4756—31no—
86#4736—31no—
87#4736—31no—
88#4732—31no—
89#4732—31no—
90#4694—31no—
91C4×D24—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C3×#67D411yescharacteristic
100C22×C3×Dic3—21no—
101C2×C3×D12—22no—
102C2×C3×D12—21no—
103C2×C3×D12—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107D3×#67—44no—
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×#624—21no—
115#3804—44no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118D3×D12—22no—
119D3×D12—41no—
120C2×C32×C8—41no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123#3752—21no—
124#3752—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3745—41no—
128C3×#217D411yescharacteristic
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×D3×C8—41no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144#3714—22no—
145#3714—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×#67—61no—
149C2×#237—61no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×#235—61no—
153C22×D12—31no—
154C22×D12C2×D311yescharacteristic
155C22×C3×C8—21no—
156C22×C3×C8—31no—
157C22×C3×C8C2×D311yescharacteristic, complemented
158C22×C3×C8C2×D311yescharacteristic, complemented
159C3×C4×D4—31no—
160C2×C3×C4⋊C4—31no—
161#953—61no—
162#940—31no—
163#939—61no—
164#938—31no—
165#937—61no—
166D4×Dic3—31no—
167C2×#213—31no—
168C2×#213—31no—
169#930—31no—
170#930—31no—
171#930—31no—
172#930—31no—
173#930—31no—
174#930—31no—
175#930—61no—
176#930—61no—
177#929—61no—
178C4×#67C2×D311yescharacteristic
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3C2×D311yescharacteristic, complemented
181C2×D24—31no—
182C2×D24—31no—
183C2×D24—31no—
184C2×D24—31no—
185C2×D24—61no—
186C2×D3×C8C2×D311yescharacteristic, complemented
187#897—61no—
188#896—61no—
189#895—31no—
190#895—61no—
191#894—61no—
192#893—31no—
193D3×C4⋊C4—31no—
194#888—31no—
195#886—61no—
196#886—61no—
197#882—61no—
198#882—61no—
199#874—31no—
200C4×D12—31no—
201C4×D12—31no—
202#869—31no—
203C3×C4⋊C8—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×C22⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C4×C8—31no—
211#832—31no—
212#832—31no—
213#830C2×D311yescharacteristic, complemented
214#821—31no—
215#821—31no—
216#821—31no—
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#821C2×D311yescharacteristic
226#821C2×D311yescharacteristic, complemented
227#821C2×D311yescharacteristic, complemented
228(C2×D3)⋊C8C2×D311yescharacteristic, complemented
229#818—31no—
230#818—31no—
231#818—31no—
232#818—31no—
233#818—61no—
234Dic3⋊C8C2×D311yescharacteristic, complemented
235C8×Dic3C2×D311yescharacteristic, complemented
236#809—31no—
237#809—31no—
238#807—31no—
239#807—31no—
240C23×C32C2×D411yescharacteristic
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—42no—
246C22×C3×D3—42no—
247C22×C3×D3—81no—
248C22×C3×D3C2×D411yescharacteristic
249C2×D32—42no—
250C2×D32—42no—
251C2×D32—81no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256#638—42no—
257#638—42no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—21no—
263C4⋊(C3⋊D3)—21no—
264C3×#67D814yescomplemented
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—42no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—42no—
275C3×D12#4112yescomplemented
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278#627—42no—
279#626—42no—
280#626—42no—
281#626—42no—
282#626—81no—
283#625—42no—
284#624—42no—
285D3×Dic3—42no—
286D3×Dic3—42no—
287C32×C8—21no—
288C32×C8—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#547—91no—
292D42—91no—
293#486—91no—
294#480—91no—
295#480—91no—
296#474—91no—
297#466—91no—
298#466—91no—
299#459—91no—
300#447—91no—
301#447—91no—
302C4×D8—91no—
303C8×D4—31no—
304C2×#102—31no—
305C2×#102—91no—
306C24×C3—61no—
307C23×D3—21no—
308C23×D3—61no—
309C23×D3—61no—
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—62no—
314C2×C3×D4—61no—
315C2×C3×D4—121no—
316C22×C3×C4—21no—
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C2×#67—61no—
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—61no—
331C2×#67—121no—
332C2×#67—121no—
333C2×#67—124no—
334C2×#67D1211yescharacteristic
335C22×Dic3—21no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338#237—124no—
339D3×D4—62no—
340D3×D4—121no—
341D3×D4—124no—
342#235—124no—
343C2×D12—22no—
344C2×D12—21no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—41no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—62no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—121no—
358C2×D12C22×D311yescharacteristic
359C2×D12C22×D311yescharacteristic
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3C22×D311yescharacteristic
365C2×Dic6—61no—
366C2×Dic6—61no—
367C2×C3×C8—21no—
368C2×C3×C8—21no—
369C2×C3×C8—31no—
370C2×C3×C8—31no—
371C2×C3×C8—41no—
372C2×C3×C8—41no—
373C2×C3×C8—42no—
374C2×C3×C8—121no—
375C2×C3×C8C22×D311yescharacteristic
376C2×C3×C8C22×D311yescharacteristic
377C2×C3×C8C22×D311yescharacteristic
378C2×C3×C8C22×D311yescharacteristic
379C3×C4⋊C4—31no—
380C3×C4⋊C4—31no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—61no—
383C3×C22⋊C4—31no—
384C3×C22⋊C4—31no—
385C3×C42—31no—
386#217—61no—
387#217—61no—
388#217D1211yescharacteristic
389#213—62no—
390#213—121no—
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—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—121no—
402(C2×D3)⋊C4—121no—
403(C2×D3)⋊C4D1211yescharacteristic
404C4⋊Dic3—21no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—31no—
408C4⋊Dic3—31no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3—61no—
412C4⋊Dic3—61no—
413C4⋊Dic3C22×D311yescharacteristic
414C4⋊Dic3C22×D311yescharacteristic
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417Dic3⋊C4D1211yescharacteristic
418C4×Dic3C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421D24—62no—
422D24—121no—
423D24—121no—
424D24—122no—
425D24—121no—
426D3×C8—41no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32C2×D812yes—
430C22×C32C22×D411yescharacteristic
431C2×C3⋊D3—41no—
432C2×C3⋊D3—41no—
433C2×C3⋊D3—41no—
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—22no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—84no—
446C2×C3×D3C2×D812yes—
447D32—84no—
448C32×C4—21no—
449C32×C4C2×#4111yescharacteristic
450C32×C4H(5,𝔽2)11yescharacteristic
451C3⋊Dic3—41no—
452C3⋊Dic3—41no—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3C2×D812yes—
458C2×#41—181no—
459C22×D4—31no—
460C22×D4—91no—
461C22×D4—181no—
462C2×D8—91no—
463C2×D8—91no—
464C2×D8—91no—
465C22×C8—31no—
466C22×C8D3211yescharacteristic, complemented
467C4⋊Q8—91no—
468#127—91no—
469#123—181no—
470#123—181no—
471C22⋊Q8—181no—
472#121—91no—
473#121—91no—
474#121—91no—
475#121—91no—
476#121—181no—
477#120—181no—
478#120—181no—
479C4×D4—31no—
480C4×D4—91no—
481C4×D4—91no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—91no—
484#107—91no—
485#107—91no—
486#107—91no—
487C4⋊C8—31no—
488#102—31no—
489#102—31no—
490#102—31no—
491#102—31no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498C22⋊C8—31no—
499C22⋊C8—31no—
500C4×C8—31no—
501C23×C3—21no—
502C23×C3—31no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—122no—
506C23×C3—122no—
507C23×C3—241no—
508C23×C3C2×D1211yescharacteristic
509C23×C3D3×D411yescharacteristic
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—42no—
513C22×D3—42no—
514C22×D3—61no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—81no—
519C22×D3—121no—
520C22×D3—121no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—122no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3C2×D1211yescharacteristic
528C3×D4—34no—
529C3×D4—32no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—61no—
533C3×D4—122no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—122no—
550C2×C3×C4C2×D1211yescharacteristic
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554#67—122no—
555#67—122no—
556#67—122no—
557#67—122no—
558#67—122no—
559#67—122no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—242no—
564#67—242no—
565#67—241no—
566#67D2414yescomplemented
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—42no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—121no—
575C2×Dic3—121no—
576C2×Dic3—122no—
577C2×Dic3—122no—
578C2×Dic3C2×D1211yescharacteristic
579C2×Dic3C2×D1211yescharacteristic
580C2×Dic3C2×D1211yescharacteristic
581D12—21no—
582D12—21no—
583D12—21no—
584D12—42no—
585D12—61no—
586D12—61no—
587D12—61no—
588D12—61no—
589D12—61no—
590D12—61no—
591D12—61no—
592D12—61no—
593D12—121no—
594D12—121no—
595D12—121no—
596D12—121no—
597D12—122no—
598D12—122no—
599D12—122no—
600D12—241no—
601D12#23512yescomplemented
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—122no—
605C4×D3—122no—
606C4×D3—122no—
607C4×D3—122no—
608Dic6—122no—
609Dic6—122no—
610C3×C8—22no—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—21no—
614C3×C8—21no—
615C3×C8—41no—
616C3×C8—61no—
617C3×C8—61no—
618C3⋊C8—21no—
619C3⋊C8—21no—
620C2×C32—22no—
621C2×C32#54611yescharacteristic
622C2×C32C22×D811yescharacteristic
623C2×C32#57711yescharacteristic
624C3⋊D3—81no—
625C3⋊D3—81no—
626C3×D3—22no—
627C3×D3—42no—
628C3×D3—81no—
629C24—61no—
630C24—181no—
631#41—364no—
632C2×Q8—181no—
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—62no—
637C2×D4—61no—
638C2×D4—91no—
639C2×D4—91no—
640C2×D4—121no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—182no—
645C2×D4—181no—
646C2×D4—181no—
647C2×D4—181no—
648C2×D4—181no—
649C2×D4—361no—
650C2×D4—364no—
651C22×C4—31no—
652C22×C4—61no—
653C22×C4—181no—
654C22×C4—181no—
655C22×C4—181no—
656C22×C4C2×D3211yescharacteristic
657D8—182no—
658D8—361no—
659D8—361no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—41no—
663C2×C8—121no—
664C2×C8C2×D3211yescharacteristic
665C2×C8C2×D3211yescharacteristic
666C4⋊C4—31no—
667C4⋊C4—31no—
668C4⋊C4—31no—
669C4⋊C4—61no—
670C4⋊C4—91no—
671C4⋊C4—91no—
672C4⋊C4—181no—
673C4⋊C4—181no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—22no—
689C22×C3—32no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—62no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—244no—
701C22×C3C2×D2412yes—
702C22×C3D3×D812yes—
703C22×C3C22×D1211yescharacteristic
704C22×C3C2×D3×D411yescharacteristic
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—22no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—84no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—241no—
727C2×D3—241no—
728C2×D3—241no—
729C2×D3—241no—
730C2×D3—241no—
731C2×D3—241no—
732C2×D3—244no—
733C2×D3—244no—
734C2×D3C2×D2412yes—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—32no—
740C3×C4—41no—
741C3×C4—61no—
742C3×C4—61no—
743C3×C4—121no—
744C3×C4—121no—
745C3×C4C2×#23511yescharacteristic
746C3×C4#100411yescharacteristic
747C3×C4#100411yescharacteristic
748C3×C4D3×#4111yescharacteristic
749Dic3—21no—
750Dic3—21no—
751Dic3—41no—
752Dic3—41no—
753Dic3—121no—
754Dic3—121no—
755Dic3—121no—
756Dic3—121no—
757Dic3—241no—
758Dic3—241no—
759Dic3C2×D2412yes—
760C32#329411yescharacteristic, complemented, Sylow
761C23—31no—
762C23—61no—
763C23—61no—
764C23—122no—
765C23—122no—
766C23—181no—
767C23—181no—
768C23—241no—
769C23—362no—
770C23—362no—
771C23—721no—
772C23D3×D1211yescharacteristic
773Q8—362no—
774D4—34no—
775D4—32no—
776D4—61no—
777D4—61no—
778D4—61no—
779D4—122no—
780D4—181no—
781D4—181no—
782D4—181no—
783D4—181no—
784D4—362no—
785D4—362no—
786D4—362no—
787D4—362no—
788D4—362no—
789D4—362no—
790D4—721no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—31no—
794C2×C4—31no—
795C2×C4—31no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—122no—
801C2×C4—181no—
802C2×C4—181no—
803C2×C4—362no—
804C2×C4—362no—
805C2×C4—362no—
806C2×C4D3×D1211yescharacteristic
807C2×C4C22×D3211yescharacteristic
808C8—21no—
809C8—21no—
810C8—61no—
811C8—61no—
812C2×C3—22no—
813C2×C3—22no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—42no—
818C2×C3—62no—
819C2×C3—122no—
820C2×C3—241no—
821C2×C3#549011yescharacteristic
822C2×C3#555411yescharacteristic
823C2×C3C22×D2411yescharacteristic
824C2×C3#575111yescharacteristic
825C2×C3C2×D3×D811yescharacteristic
826C2×C3#576211yescharacteristic
827D3—22no—
828D3—42no—
829D3—81no—
830D3—241no—
831D3—241no—
832D3—241no—
833D3—241no—
834D3—481no—
835D3—481no—
836C22—21no—
837C22—21no—
838C22—32no—
839C22—61no—
840C22—61no—
841C22—62no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—244no—
848C22—361no—
849C22—361no—
850C22—361no—
851C22—361no—
852C22—361no—
853C22—361no—
854C22—724no—
855C22D3×D2412yes—
856C22C2×D3×D1211yescharacteristic
857C4—21no—
858C4—32no—
859C4—61no—
860C4—61no—
861C4—121no—
862C4—121no—
863C4—361no—
864C4—361no—
865C4D3×#23511yescharacteristic
866C4#6433011yescharacteristic
867C3—21no—
868C3#7875711yescharacteristic, complemented
869C3#7943811yescharacteristic, complemented
870C2—22no—
871C2—62no—
872C2—122no—
873C2—241no—
874C2—721no—
875C2—721no—
876C2C2×D3×D2411yescharacteristic
877C2#1059467711yescharacteristic
878C2#1059507311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3294
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. D12×#67C2semidirect
2. #10594906C2semidirect
3. #10592814C2semidirect
4. C2×C3×#821C2semidirect
5. C3×C8×#67C2semidirect
6. #10591162C2semidirect
7. #10591133C2semidirect
8. #10590947C2semidirect
9. D3×#821C2semidirect
10. #10590878C2semidirect
11. #10590826C2semidirect
12. #10590765C2semidirect
13. #10590762C2semidirect
14. #10590745C2semidirect
15. #10590680C2semidirect
22. C22×C32×C8C22semidirect
24. #64139C22semidirect
25. C2×#3745C22semidirect
27. C2×C3×C4⋊Dic3C22semidirect
28. C2×C3×D3×C8C22semidirect
32. #63918C22semidirect
34. #63909C22semidirect
37. #63894C22semidirect
40. D3×C4⋊Dic3C22semidirect
43. C2×#3714C22semidirect
44. #63648C22semidirect
45. #63648C22semidirect
46. #63645C22semidirect
47. C3×#830C22semidirect
50. C3×#821C22semidirect
51. C3×#821C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63575C22semidirect
56. #63575C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
60. #63563C22semidirect
73. C2×#821D3semidirect
74. C8×#67D3semidirect
157. C22×C3×C8C2×D3semidirect
158. C22×C3×C8C2×D3semidirect
180. C2×C4⋊Dic3C2×D3semidirect
186. C2×D3×C8C2×D3semidirect
213. #830C2×D3semidirect
226. #821C2×D3semidirect
227. #821C2×D3semidirect
228. (C2×D3)⋊C8C2×D3semidirect
234. Dic3⋊C8C2×D3semidirect
235. C8×Dic3C2×D3semidirect
264. C3×#67D8semidirect
275. C3×D12#41semidirect
466. C22×C8D32semidirect
566. #67D24semidirect
601. D12#235semidirect
760. C32#3294semidirect
868. C3#78757semidirect
869. C3#79438semidirect

Maximal subgroups

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

subgroupindex
D12×#672
#105949062
#105928142
C2×C3×#8212
C3×C8×#672
#105911622
#105911332
#105909472
D3×#8212
#105908782
#105908262
#105907652
#105907622
#105907452
#105906802
#794383
#787573