Finite Group Databasebeta

← #11887070

Subgroups — #11887070

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
1#10595136C211yesmaximal, characteristic, complemented
2#10594621C211yesmaximal, characteristic, complemented
3#10592474C211yesmaximal, characteristic, complemented
4C3×#4775C211yesmaximal, characteristic, complemented
5C3×#4756C211yesmaximal, characteristic, complemented
6#10591516C211yesmaximal, characteristic, complemented
7#10591515C211yesmaximal, characteristic, complemented
8#10591481C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10D3×#821C211yesmaximal, characteristic, complemented
11#10590878C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13#10590555C211yesmaximal, characteristic, complemented
14#10590442C211yesmaximal, characteristic, complemented
15#10590438C211yesmaximal, characteristic, complemented
16#80731—31nomaximal
17#79608—31nomaximal
18C2×#3804—21no—
19C2×#3802C2211yescharacteristic
20C2×D3×D12—21no—
21C2×D3×D12C2211yescharacteristic
22#64147C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic, complemented
24C2×C8×C3⋊D3C2211yescharacteristic, complemented
25#64104C2211yescharacteristic
26C3×#938C2211yescharacteristic, complemented
27C3×D4×Dic3C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic, complemented
30C2×C3×D3×C8C2211yescharacteristic, complemented
31C3×#895C2211yescharacteristic
32C3×#893C2211yescharacteristic
33#63975—21no—
34#63969—21no—
35#63964—21no—
36#63923—21no—
37#63922—21no—
38#63918C2211yescharacteristic, complemented
39#63911C2211yescharacteristic
40#63906—21no—
41C4×#626C2211yescharacteristic
42#63900C2211yescharacteristic, complemented
43D3×C4⋊Dic3C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic, complemented
49C3×C8×Dic3C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63564C2211yescharacteristic, complemented
54#63564C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5611—31no—
62#5609—31no—
63#5551—31no—
64D4×D12—31no—
65C3×#466—31no—
66C3×C4×D8—31no—
67#5156—31no—
68#5156—31no—
69#5156—31no—
70#5150—31no—
71C2×#821—31no—
72C8×#67—31no—
73#5036—31no—
74#5033—31no—
75#5015—31no—
76#5007—31no—
77#4890—31no—
78#4882—31no—
79#4882—31no—
80#4882—31no—
81#4775—31no—
82#4775—31no—
83#4775—61no—
84#4775D311yescharacteristic, complemented
85D3×#102—31no—
86D3×#102—31no—
87D3×#102—31no—
88#4760—31no—
89#4756D311yescharacteristic, complemented
90#4694—31no—
91C8×D12—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×#627—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626D411yescharacteristic
111C2×#625—21no—
112C2×#624—21no—
113#3804—44no—
114C2×D3×Dic3—21no—
115#3802—22no—
116#3802—41no—
117D3×D12—22no—
118D3×D12—41no—
119D3×D12—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122#3757—21no—
123#3753—41no—
124#3752—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C8×C3⋊D3—41no—
128C3×#217—21no—
129C3×#217—21no—
130C3×#213—22no—
131C3×#213—41no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×D3×C8—41no—
140#3724—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3D411yescharacteristic
144#3722D411yescharacteristic
145(C2×D3)⋊Dic3D411yescharacteristic
146#3294—91noSylow
147C2×#237—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×#235—61no—
153C22×D12—31no—
154C22×D12—61no—
155C2×C3×D8—31no—
156C2×C3×D8—31no—
157C22×C3×C8—31no—
158C3×#121—31no—
159C3×#121—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162#940—31no—
163#938—31no—
164#938—31no—
165#938—61no—
166#938C2×D311yescharacteristic, complemented
167#937—61no—
168#935—61no—
169D4×Dic3C2×D311yescharacteristic, complemented
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—61no—
173C2×#213C2×D311yescharacteristic
174C2×#213C2×D311yescharacteristic, complemented
175#930—61no—
176C4×#67—31no—
177C2×C4⋊Dic3—31no—
178#924—61no—
179C2×D3×C8—31no—
180C2×D3×C8—31no—
181C2×D3×C8—61no—
182C2×D3×C8C2×D311yescharacteristic, complemented
183#895—31no—
184#895—31no—
185#895—61no—
186#895C2×D311yescharacteristic
187#893C2×D311yescharacteristic
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191#888—31no—
192#884—61no—
193#883—61no—
194#883—61no—
195#883—61no—
196#882—61no—
197#882—61no—
198#882—61no—
199#878—61no—
200#874—31no—
201C4×D12—31no—
202#869—31no—
203C3×#107—31no—
204C3×#107—31no—
205C3×#102—21no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102C2×D311yescharacteristic, complemented
209C3×#102C2×D311yescharacteristic, complemented
210C3×C4×C8—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#830—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—61no—
223#821C2×D311yescharacteristic
224#821C2×D311yescharacteristic, complemented
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228Dic3⋊C8—31no—
229C8×Dic3C2×D311yescharacteristic, complemented
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#807—31no—
235#807—31no—
236#807—61no—
237#807C2×D311yescharacteristic, complemented
238#807C2×D311yescharacteristic, complemented
239C4⋊(C3⋊C8)—31no—
240C23×C32—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3C2×D411yescharacteristic
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3C2×D411yescharacteristic
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—42no—
250C2×D32—81no—
251C2×D32—81no—
252C32×D4—21no—
253C32×D4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2411yescharacteristic
256#638—42no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3C2×D411yescharacteristic
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—42no—
262C4×C3⋊D3—21no—
263C4×C3⋊D3—21no—
264C3×#67—42no—
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—
278C3×C4×D3—42no—
279#627—42no—
280#626—42no—
281#626—42no—
282#626—81no—
283#626D814yescomplemented
284#625—42no—
285#624—42no—
286D3×Dic3—42no—
287C32×C8—21no—
288C3⋊(C3⋊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—31no—
298#466—91no—
299#459—91no—
300#447—91no—
301#447—91no—
302C4×D8—31no—
303C8×D4—91no—
304C2×#102—91no—
305C2×#102—91no—
306C23×D3—61no—
307C23×D3—61no—
308C23×D3—61no—
309C23×D3—61no—
310C2×C3×D4—21no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C2×#67—21no—
321C2×#67—31no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—121no—
330C22×Dic3—21no—
331C22×Dic3—61no—
332#237—124no—
333D3×D4—62no—
334D3×D4—62no—
335D3×D4—62no—
336D3×D4—121no—
337D3×D4—124no—
338D3×D4—121no—
339D3×D4—121no—
340#235—124no—
341C2×D12—21no—
342C2×D12—31no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—61no—
346C2×D12—62no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—121no—
353C2×D12—121no—
354C2×D12—124no—
355C2×D12C22×D311yescharacteristic
356C2×D12C22×D311yescharacteristic
357C2×C4×D3—21no—
358C2×C4×D3—31no—
359C2×C4×D3—31no—
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—
367C3×D8—62no—
368C3×D8—121no—
369C2×C3×C8—21no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
372C2×C3×C8—121no—
373C2×C3×C8C22×D311yescharacteristic
374C2×C3×C8C22×D311yescharacteristic
375C3×C4⋊C4—21no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C4⋊C4C22×D311yescharacteristic
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C42—31no—
385#217—21no—
386#217—21no—
387#217—31no—
388#217—61no—
389#217—61no—
390#217—121no—
391#213—22no—
392#213—41no—
393#213—121no—
394#213—121no—
395#213—122no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—121no—
404C4⋊Dic3—31no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3—61no—
410C4⋊Dic3C22×D311yescharacteristic
411C4⋊Dic3C22×D311yescharacteristic
412Dic3⋊C4—31no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417C4×Dic3C22×D311yescharacteristic
418C2×C3⋊C8—31no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—61no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423D3×C8—41no—
424D3×C8—121no—
425D3×C8—121no—
426D3×C8—122no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32C22×D411yescharacteristic
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—41no—
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3C2×D812yes—
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×D3C2×D812yes—
446D32—84no—
447D32—84no—
448C32×C4—41no—
449C32×C4C2×#4111yescharacteristic
450C32×C4H(5,𝔽2)11yescharacteristic
451C3⋊Dic3—21no—
452C3⋊Dic3—41no—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3C2×D812yes—
458C2×#41—181no—
459C22×D4—91no—
460C22×D4—91no—
461C22×D4—181no—
462C2×D8—31no—
463C2×D8—31no—
464C2×D8—91no—
465C22×C8—31no—
466C22×C8—91no—
467C4⋊Q8—91no—
468#127—91no—
469#123—181no—
470#123—181no—
471C22⋊Q8—181no—
472#121—31no—
473#121—31no—
474#121—91no—
475#121—91no—
476#121—181no—
477#120—181no—
478#120—181no—
479C4×D4—31no—
480C4×D4—31no—
481C4×D4—91no—
482C2×C4⋊C4—91no—
483C2×C4⋊C4—91no—
484#107—31no—
485#107—31no—
486#107—91no—
487C4⋊C8—91no—
488#102—31no—
489#102—31no—
490#102—91no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102D3211yescharacteristic, complemented
498C22⋊C8—91no—
499C22⋊C8—91no—
500C4×C8—31no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—31no—
504C23×C3—41no—
505C23×C3—61no—
506C23×C3—61no—
507C22×D3—21no—
508C22×D3—21no—
509C22×D3—31no—
510C22×D3—31no—
511C22×D3—61no—
512C22×D3—61no—
513C22×D3—61no—
514C22×D3—121no—
515C22×D3—122no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—241no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3D3×D411yescharacteristic
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—21no—
531C3×D4—21no—
532C3×D4—32no—
533C3×D4—41no—
534C3×D4—41no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—61no—
538C3×D4—122no—
539C3×D4—122no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—31no—
546C2×C3×C4—41no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—122no—
552C2×C3×C4—122no—
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555#67—34no—
556#67—42no—
557#67—122no—
558#67—122no—
559#67—122no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—242no—
564#67—241no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—42no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—121no—
574C2×Dic3—122no—
575C2×Dic3D3×D411yescharacteristic
576C2×Dic3D3×D411yescharacteristic
577C2×Dic3D3×D411yescharacteristic
578D12—21no—
579D12—21no—
580D12—21no—
581D12—34no—
582D12—42no—
583D12—61no—
584D12—61no—
585D12—61no—
586D12—61no—
587D12—121no—
588D12—121no—
589D12—122no—
590D12—122no—
591D12—122no—
592D12—122no—
593D12—242no—
594D12—241no—
595D12#23512yescomplemented
596C4×D3—21no—
597C4×D3—21no—
598C4×D3—42no—
599C4×D3—61no—
600C4×D3—61no—
601C4×D3—61no—
602C4×D3—61no—
603C4×D3—121no—
604C4×D3—121no—
605C4×D3—122no—
606C4×D3—122no—
607C4×D3—122no—
608Dic6—122no—
609Dic6—122no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—41no—
613C3×C8—61no—
614C3×C8—61no—
615C3⋊C8—21no—
616C3⋊C8—21no—
617C3⋊C8—62no—
618C3⋊C8—61no—
619C3⋊C8—61no—
620C2×C32—81no—
621C2×C32#54611yescharacteristic
622C2×C32C22×D811yescharacteristic
623C2×C32#57711yescharacteristic
624C3⋊D3—22no—
625C3⋊D3—81no—
626C3×D3—22no—
627C3×D3—42no—
628C3×D3—81no—
629C24—181no—
630C24—181no—
631#41—364no—
632C2×Q8—181no—
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—91no—
638C2×D4—91no—
639C2×D4—181no—
640C2×D4—181no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—182no—
644C2×D4—181no—
645C2×D4—182no—
646C2×D4—181no—
647C2×D4—361no—
648C2×D4—364no—
649C2×D4—361no—
650C2×D4C2×D3211yescharacteristic
651C22×C4—31no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—91no—
655C22×C4—181no—
656C22×C4—181no—
657D8—62no—
658D8—121no—
659D8—361no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—91no—
663C2×C8—121no—
664C2×C8—361no—
665C2×C8C2×D3211yescharacteristic
666C4⋊C4—31no—
667C4⋊C4—31no—
668C4⋊C4—91no—
669C4⋊C4—91no—
670C4⋊C4—181no—
671C4⋊C4—181no—
672C4⋊C4—181no—
673C4⋊C4C2×D3211yescharacteristic
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—91no—
679C22⋊C4—91no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C22×C3—21no—
684C22×C3—32no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—62no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C2×D3×D411yescharacteristic
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—22no—
707C2×D3—32no—
708C2×D3—32no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—62no—
715C2×D3—61no—
716C2×D3—61no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—121no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—241no—
728C2×D3—241no—
729C2×D3—241no—
730C2×D3—244no—
731C2×D3—244no—
732C2×D3—244no—
733C2×D3—244no—
734C2×D3D3×D812yes—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—32no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—61no—
741C3×C4—61no—
742C3×C4—81no—
743C3×C4—121no—
744C3×C4—121no—
745C3×C4C2×#23511yescharacteristic
746C3×C4#100411yescharacteristic
747C3×C4D3×#4111yescharacteristic
748C3×C4#100911yescharacteristic
749Dic3—21no—
750Dic3—21no—
751Dic3—41no—
752Dic3—41no—
753Dic3—61no—
754Dic3—61no—
755Dic3—121no—
756Dic3—121no—
757Dic3—121no—
758Dic3—241no—
759Dic3D3×D812yes—
760C32#329411yescharacteristic, complemented, Sylow
761C23—21no—
762C23—31no—
763C23—61no—
764C23—61no—
765C23—91no—
766C23—181no—
767C23—362no—
768C23—362no—
769C23—362no—
770C23—362no—
771C23—721no—
772C23—721no—
773Q8—362no—
774D4—21no—
775D4—21no—
776D4—32no—
777D4—61no—
778D4—61no—
779D4—61no—
780D4—94no—
781D4—122no—
782D4—122no—
783D4—181no—
784D4—181no—
785D4—362no—
786D4—362no—
787D4—362no—
788D4—362no—
789D4—362no—
790D4—721no—
791C2×C4—21no—
792C2×C4—31no—
793C2×C4—31no—
794C2×C4—31no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—91no—
800C2×C4—122no—
801C2×C4—122no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—181no—
805C2×C4—362no—
806C2×C4—362no—
807C2×C4C22×D3211yescharacteristic
808C8—21no—
809C8—61no—
810C8—61no—
811C8—181no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—62no—
816C2×C3—81no—
817C2×C3—81no—
818C2×C3—122no—
819C2×C3—161no—
820C2×C3—241no—
821C2×C3#555011yescharacteristic
822C2×C3#561011yescharacteristic
823C2×C3C2×D3×D811yescharacteristic
824C2×C3C2×D3×D811yescharacteristic
825C2×C3#577011yescharacteristic
826C2×C3#577011yescharacteristic
827D3—22no—
828D3—42no—
829D3—62no—
830D3—62no—
831D3—81no—
832D3—122no—
833D3—241no—
834D3—241no—
835D3—481no—
836C22—32no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—61no—
841C22—61no—
842C22—62no—
843C22—92no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—181no—
850C22—181no—
851C22—361no—
852C22—361no—
853C22—361no—
854C22—724no—
855C22—724no—
856C22D32×D411yescharacteristic
857C4—32no—
858C4—41no—
859C4—61no—
860C4—61no—
861C4—121no—
862C4—121no—
863C4—181no—
864C4—361no—
865C4D3×#23511yescharacteristic
866C4#6431411yescharacteristic
867C3—21no—
868C3#7960811yescharacteristic, complemented
869C3#8073111yescharacteristic, complemented
870C2—62no—
871C2—81no—
872C2—122no—
873C2—182no—
874C2—241no—
875C2—721no—
876C2#1059428311yescharacteristic
877C2D32×D811yescharacteristic
878C2#1059475711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595136C2semidirect
2. #10594621C2semidirect
3. #10592474C2semidirect
4. C3×#4775C2semidirect
5. C3×#4756C2semidirect
6. #10591516C2semidirect
7. #10591515C2semidirect
8. #10591481C2semidirect
9. #10590940C2semidirect
10. D3×#821C2semidirect
11. #10590878C2semidirect
12. C8×#626C2semidirect
13. #10590555C2semidirect
14. #10590442C2semidirect
15. #10590438C2semidirect
22. #64147C22semidirect
23. C2×#3753C22semidirect
24. C2×C8×C3⋊D3C22semidirect
26. C3×#938C22semidirect
27. C3×D4×Dic3C22semidirect
29. C2×C3×#213C22semidirect
30. C2×C3×D3×C8C22semidirect
38. #63918C22semidirect
42. #63900C22semidirect
43. D3×C4⋊Dic3C22semidirect
44. C32×#102C22semidirect
45. #63648C22semidirect
46. #63634C22semidirect
48. C3×#821C22semidirect
49. C3×C8×Dic3C22semidirect
50. C3×#807C22semidirect
51. C3×#807C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63564C22semidirect
54. #63564C22semidirect
56. #63563C22semidirect
58. #63562C22semidirect
59. #63557C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4775D3semidirect
89. #4756D3semidirect
166. #938C2×D3semidirect
169. D4×Dic3C2×D3semidirect
174. C2×#213C2×D3semidirect
182. C2×D3×C8C2×D3semidirect
208. C3×#102C2×D3semidirect
209. C3×#102C2×D3semidirect
224. #821C2×D3semidirect
229. C8×Dic3C2×D3semidirect
237. #807C2×D3semidirect
238. #807C2×D3semidirect
275. C3×D12#41semidirect
283. #626D8semidirect
497. #102D32semidirect
595. D12#235semidirect
760. C32#3294semidirect
868. C3#79608semidirect
869. C3#80731semidirect

Maximal subgroups

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

subgroupindex
#105951362
#105946212
#105924742
C3×#47752
C3×#47562
#105915162
#105915152
#105914812
#105909402
D3×#8212
#105908782
C8×#6262
#105905552
#105904422
#105904382
#807313
#796083