Finite Group Databasebeta

← #11887011

Subgroups — #11887011

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D12×#67C211yesmaximal, characteristic, complemented
2#10594907C211yesmaximal, characteristic, complemented
3#10592435C211yesmaximal, characteristic, complemented
4C3×#4732C211yesmaximal, characteristic, complemented
5C3×#67⋊C8C211yesmaximal, characteristic, complemented
6#10591164C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590944C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590878C211yesmaximal, characteristic, complemented
11#10590831C211yesmaximal, characteristic, complemented
12#10590762C211yesmaximal, characteristic, complemented
13Dic3×D24C211yesmaximal, characteristic, complemented
14#10590753C211yesmaximal, characteristic, complemented
15#10590680C211yesmaximal, characteristic, complemented
16#80014—31nomaximal
17#79438—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3805—21no—
21C2×D3×D12C2211yescharacteristic
22#64139C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
24C3×#930C2211yescharacteristic, complemented
25C3×C4×#67C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic, complemented
27C2×C3×D24C2211yescharacteristic
28C2×C3×D24C2211yescharacteristic, complemented
29C2×C3×D3×C8C2211yescharacteristic, complemented
30#63977—21no—
31#63962—21no—
32#63922—21no—
33#63918C2211yescharacteristic, complemented
34#63911C2211yescharacteristic
35#63908C2211yescharacteristic
36#63908C2211yescharacteristic, complemented
37#63893—21no—
38Dic3×D12C2211yescharacteristic
39Dic3×D12C2211yescharacteristic, complemented
40#63891—21no—
41D3×C4⋊Dic3C2211yescharacteristic, complemented
42#63886—21no—
43C2×#3714C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63648C2211yescharacteristic, complemented
47#63645C2211yescharacteristic, complemented
48#63645C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61D4×#67—31no—
62#5611—31no—
63#5555—31no—
64D4×D12—31no—
65C3×#447—31no—
66C3×C8×D4—31no—
67C2×#832—31no—
68#5157—31no—
69#5156—31no—
70#5150—31no—
71Dic3×D8—31no—
72#5115—31no—
73#5115—31no—
74C2×#821—31no—
75C2×#821—31no—
76#5038—31no—
77#4846—31no—
78#4843—31no—
79#4774—31no—
80D3×#102—31no—
81#4760—31no—
82#4759—31no—
83#4736—31no—
84#4736—31no—
85#4736—31no—
86#4736—61no—
87#4732—31no—
88#4732D311yescharacteristic, complemented
89#67⋊C8D311yescharacteristic, complemented
90#4694—31no—
91C4×D24—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67D411yescharacteristic
100C2×C3×D12—22no—
101C2×C3×D12—21no—
102C2×C3×D12—41no—
103C2×C3×D12C2311yescharacteristic
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×#625—21no—
113C2×#625—21no—
114#3805—44no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118D3×D12—22no—
119D3×D12—41no—
120C2×C32×C8C2311yescharacteristic
121C2×C32×C8C2311yescharacteristic
122#3752—21no—
123C4⋊(C3⋊Dic3)—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127C3×#217D411yescharacteristic
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8—41no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×D24—22no—
137C3×D24—41no—
138C3×D3×C8—41no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145#3714—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×#67—61no—
149C2×#237—61no—
150C2×#237—61no—
151C2×D3×D4—31no—
152C2×D3×D4—61no—
153C22×D12—31no—
154C22×D12C2×D311yescharacteristic
155C2×C3×D8—31no—
156C2×C3×D8—31no—
157C22×C3×C8—31no—
158C22×C3×C8—31no—
159C3×#121—31no—
160C3×C4×D4—31no—
161#953—61no—
162#940—31no—
163#939—61no—
164#938—31no—
165#938—31no—
166#937—61no—
167#935—61no—
168D4×Dic3—31no—
169D4×Dic3—31no—
170C2×#213—31no—
171#930—31no—
172#930—31no—
173#930—31no—
174#930—31no—
175#930—61no—
176#930C2×D311yescharacteristic, complemented
177C4×#67C2×D311yescharacteristic
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—31no—
181C2×C4⋊Dic3—61no—
182C22×C3⋊C8C2×D311yescharacteristic, complemented
183C2×D24—31no—
184C2×D24C2×D311yescharacteristic
185C2×D24C2×D311yescharacteristic, complemented
186C2×D3×C8C2×D311yescharacteristic, complemented
187#897—61no—
188#895—61no—
189D3×C4⋊C4—31no—
190#888—31no—
191#886—61no—
192#886—61no—
193#883—61no—
194#882—61no—
195#882—61no—
196#878—61no—
197#874—31no—
198C4×D12—31no—
199C4×D12—31no—
200#869—31no—
201C3×C4⋊C8—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—21no—
205C3×C22⋊C8—31no—
206C3×C22⋊C8C2×D311yescharacteristic, complemented
207C3×C22⋊C8C2×D311yescharacteristic, complemented
208C3×C4×C8—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
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—31no—
223#821—31no—
224#821—61no—
225#821—61no—
226#821C2×D311yescharacteristic
227#821C2×D311yescharacteristic, complemented
228(C2×D3)⋊C8C2×D311yescharacteristic, complemented
229#818—31no—
230#818—31no—
231#818—31no—
232#818—31no—
233#818—31no—
234#818—61no—
235#818—61no—
236Dic3⋊C8C2×D311yescharacteristic, complemented
237C8×Dic3C2×D311yescharacteristic, complemented
238#809—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—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—42no—
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—21no—
263C3×#67—42no—
264C3×#67D814yescomplemented
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12—21no—
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—81no—
282#625—42no—
283#625—42no—
284D3×Dic3—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—31no—
301#447—91no—
302C4×D8—91no—
303C8×D4—31no—
304C2×#102—91no—
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—31no—
314C2×C3×D4—62no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4—121no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C2×#67—21no—
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—61no—
332C2×#67—121no—
333C2×#67—124no—
334C2×#67D1211yescharacteristic
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—121no—
341#237—124no—
342#237—124no—
343D3×D4—62no—
344D3×D4—121no—
345D3×D4—124no—
346C2×D12—22no—
347C2×D12—21no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12—41no—
351C2×D12—61no—
352C2×D12—62no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—121no—
357C2×D12C22×D311yescharacteristic
358C2×D12C22×D311yescharacteristic
359C2×D12C22×D311yescharacteristic
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3C22×D311yescharacteristic
364C2×Dic6—61no—
365C2×Dic6—61no—
366C3×D8—62no—
367C3×D8—121no—
368C2×C3×C8—21no—
369C2×C3×C8—21no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
372C2×C3×C8—121no—
373C2×C3×C8—121no—
374C2×C3×C8C22×D311yescharacteristic
375C2×C3×C8C22×D311yescharacteristic
376C2×C3×C8C22×D311yescharacteristic
377C2×C3×C8C22×D311yescharacteristic
378C3×C4⋊C4—31no—
379C3×C4⋊C4—31no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—31no—
382C3×C22⋊C4—61no—
383C3×C42—31no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—61no—
388#217D1211yescharacteristic
389#213—121no—
390(C2×D3)⋊C4—21no—
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—121no—
398(C2×D3)⋊C4D1211yescharacteristic
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3—61no—
412C4⋊Dic3—121no—
413C4⋊Dic3C22×D311yescharacteristic
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4D1211yescharacteristic
417C4×Dic3C22×D311yescharacteristic
418C2×C3⋊C8—41no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421D24—22no—
422D24—41no—
423D24—121no—
424D3×C8—41no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32C2×D812yes—
428C22×C32C22×D411yescharacteristic
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—22no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—84no—
444C2×C3×D3C2×D812yes—
445D32—84no—
446C32×C4—21no—
447C32×C4C2×#4111yescharacteristic
448C32×C4H(5,𝔽2)11yescharacteristic
449C3⋊Dic3—41no—
450C3⋊Dic3—41no—
451C3⋊Dic3—41no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—41no—
455C3×Dic3C2×D812yes—
456C2×#41—181no—
457C22×D4—31no—
458C22×D4—91no—
459C22×D4—181no—
460C2×D8—31no—
461C2×D8—31no—
462C2×D8—91no—
463C22×C8—31no—
464C22×C8—31no—
465C4⋊Q8—91no—
466#127—91no—
467#123—181no—
468#123—181no—
469C22⋊Q8—181no—
470#121—31no—
471#121—91no—
472#121—91no—
473#121—91no—
474#121—181no—
475#120—181no—
476#120—181no—
477C4×D4—31no—
478C4×D4—91no—
479C4×D4—91no—
480C2×C4⋊C4—91no—
481C2×C4⋊C4—91no—
482#107—91no—
483#107—91no—
484#107—91no—
485C4⋊C8—31no—
486#102—31no—
487#102—31no—
488#102—91no—
489#102—91no—
490#102—91no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496C22⋊C8—31no—
497C22⋊C8D3211yescharacteristic, complemented
498C4×C8—31no—
499C23×C3—21no—
500C23×C3—31no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—122no—
505C23×C3—122no—
506C23×C3—241no—
507C23×C3C2×D1211yescharacteristic
508C23×C3D3×D411yescharacteristic
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—42no—
513C22×D3—42no—
514C22×D3—61no—
515C22×D3—61no—
516C22×D3—81no—
517C22×D3—121no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3—241no—
523C22×D3—241no—
524C22×D3C2×D1211yescharacteristic
525C3×D4—34no—
526C3×D4—32no—
527C3×D4—61no—
528C3×D4—61no—
529C3×D4—61no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—122no—
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×C4C2×D1211yescharacteristic
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4C23×D311yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552#67—42no—
553#67—122no—
554#67—122no—
555#67—122no—
556#67—122no—
557#67—122no—
558#67—122no—
559#67—122no—
560#67—122no—
561#67—242no—
562#67—241no—
563#67D2414yescomplemented
564C2×Dic3—21no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—121no—
572C2×Dic3—121no—
573C2×Dic3—121no—
574C2×Dic3—122no—
575C2×Dic3—122no—
576C2×Dic3—122no—
577C2×Dic3—122no—
578C2×Dic3—122no—
579C2×Dic3—242no—
580C2×Dic3C2×D1211yescharacteristic
581C2×Dic3C2×D1211yescharacteristic
582C2×Dic3C2×D1211yescharacteristic
583D12—21no—
584D12—21no—
585D12—21no—
586D12—21no—
587D12—21no—
588D12—42no—
589D12—61no—
590D12—61no—
591D12—61no—
592D12—61no—
593D12—121no—
594D12—121no—
595D12—122no—
596D12—122no—
597D12—241no—
598D12#23712yescomplemented
599C4×D3—21no—
600C4×D3—21no—
601C4×D3—122no—
602C4×D3—122no—
603C4×D3—122no—
604Dic6—122no—
605Dic6—122no—
606C3×C8—21no—
607C3×C8—21no—
608C3×C8—21no—
609C3×C8—21no—
610C3×C8—41no—
611C3×C8—41no—
612C3×C8—61no—
613C3×C8—61no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C2×C32—22no—
617C2×C32#54611yescharacteristic
618C2×C32C22×D811yescharacteristic
619C2×C32#57711yescharacteristic
620C3⋊D3—81no—
621C3×D3—22no—
622C3×D3—42no—
623C3×D3—81no—
624C3×D3—81no—
625C24—61no—
626C24—181no—
627#41—364no—
628C2×Q8—181no—
629C2×D4—31no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—62no—
634C2×D4—61no—
635C2×D4—61no—
636C2×D4—91no—
637C2×D4—121no—
638C2×D4—181no—
639C2×D4—181no—
640C2×D4—181no—
641C2×D4—182no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—181no—
645C2×D4—361no—
646C2×D4—364no—
647C22×C4—31no—
648C22×C4—181no—
649C22×C4—181no—
650C22×C4—181no—
651C22×C4—181no—
652C22×C4C2×D3211yescharacteristic
653D8—62no—
654D8—121no—
655D8—361no—
656C2×C8—31no—
657C2×C8—31no—
658C2×C8—121no—
659C2×C8—121no—
660C2×C8C2×D3211yescharacteristic
661C2×C8C2×D3211yescharacteristic
662C4⋊C4—31no—
663C4⋊C4—31no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—91no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C22⋊C4—31no—
671C22⋊C4—31no—
672C22⋊C4—61no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C42—31no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—22no—
685C22×C3—32no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—61no—
689C22×C3—61no—
690C22×C3—62no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—244no—
700C22×C3C2×D2412yes—
701C22×C3D3×D812yes—
702C22×C3C22×D1211yescharacteristic
703C22×C3C2×D3×D411yescharacteristic
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—22no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—84no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—241no—
723C2×D3—241no—
724C2×D3—241no—
725C2×D3—244no—
726C2×D3—244no—
727C2×D3C2×D2412yes—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—32no—
733C3×C4—41no—
734C3×C4—61no—
735C3×C4—61no—
736C3×C4—121no—
737C3×C4C2×#23711yescharacteristic
738C3×C4#100411yescharacteristic
739C3×C4#100411yescharacteristic
740C3×C4D3×#4111yescharacteristic
741Dic3—21no—
742Dic3—21no—
743Dic3—41no—
744Dic3—121no—
745Dic3—121no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749Dic3—121no—
750Dic3—241no—
751Dic3—241no—
752Dic3—241no—
753Dic3C2×D2412yes—
754C32#329411yescharacteristic, complemented, Sylow
755C23—31no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—122no—
760C23—122no—
761C23—181no—
762C23—241no—
763C23—362no—
764C23—362no—
765C23—721no—
766C23D3×D1211yescharacteristic
767Q8—362no—
768D4—34no—
769D4—32no—
770D4—61no—
771D4—61no—
772D4—61no—
773D4—61no—
774D4—61no—
775D4—122no—
776D4—122no—
777D4—181no—
778D4—181no—
779D4—362no—
780D4—362no—
781D4—362no—
782D4—362no—
783D4—362no—
784D4—721no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—31no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4—362no—
797C2×C4—362no—
798C2×C4—362no—
799C2×C4—362no—
800C2×C4D3×D1211yescharacteristic
801C2×C4C22×D3211yescharacteristic
802C8—21no—
803C8—21no—
804C8—61no—
805C8—61no—
806C2×C3—22no—
807C2×C3—22no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—42no—
812C2×C3—62no—
813C2×C3—122no—
814C2×C3—241no—
815C2×C3—241no—
816C2×C3#555411yescharacteristic
817C2×C3#559111yescharacteristic
818C2×C3C22×D2411yescharacteristic
819C2×C3#575111yescharacteristic
820C2×C3C2×D3×D811yescharacteristic
821C2×C3#577511yescharacteristic
822D3—22no—
823D3—42no—
824D3—81no—
825D3—81no—
826D3—241no—
827D3—241no—
828D3—481no—
829C22—21no—
830C22—21no—
831C22—32no—
832C22—61no—
833C22—61no—
834C22—62no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—244no—
844C22—361no—
845C22—361no—
846C22—361no—
847C22—724no—
848C22D3×D2412yes—
849C22C2×D3×D1211yescharacteristic
850C4—21no—
851C4—32no—
852C4—61no—
853C4—61no—
854C4—121no—
855C4—361no—
856C4—361no—
857C4—361no—
858C4D3×#23711yescharacteristic
859C4#6431311yescharacteristic
860C3—21no—
861C3#7943811yescharacteristic, complemented
862C3#8001411yescharacteristic, complemented
863C2—22no—
864C2—62no—
865C2—122no—
866C2—241no—
867C2—241no—
868C2—721no—
869C2#1059429211yescharacteristic
870C2C2×D3×D2411yescharacteristic
871C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊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. #10594907C2semidirect
3. #10592435C2semidirect
4. C3×#4732C2semidirect
5. C3×#67⋊C8C2semidirect
6. #10591164C2semidirect
7. C2×#63563C2semidirect
8. #10590944C2semidirect
9. D3×#821C2semidirect
10. #10590878C2semidirect
11. #10590831C2semidirect
12. #10590762C2semidirect
13. Dic3×D24C2semidirect
14. #10590753C2semidirect
15. #10590680C2semidirect
23. C2×C4⋊(C3⋊Dic3)C22semidirect
24. C3×#930C22semidirect
26. C22×C3×C3⋊C8C22semidirect
28. C2×C3×D24C22semidirect
29. C2×C3×D3×C8C22semidirect
33. #63918C22semidirect
36. #63908C22semidirect
39. Dic3×D12C22semidirect
41. D3×C4⋊Dic3C22semidirect
43. C2×#3714C22semidirect
44. C32×C22⋊C8C22semidirect
45. #63648C22semidirect
46. #63648C22semidirect
47. #63645C22semidirect
48. #63645C22semidirect
50. C3×#821C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63575C22semidirect
55. #63564C22semidirect
58. #63563C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
88. #4732D3semidirect
89. #67⋊C8D3semidirect
176. #930C2×D3semidirect
182. C22×C3⋊C8C2×D3semidirect
185. C2×D24C2×D3semidirect
186. C2×D3×C8C2×D3semidirect
206. C3×C22⋊C8C2×D3semidirect
207. C3×C22⋊C8C2×D3semidirect
227. #821C2×D3semidirect
228. (C2×D3)⋊C8C2×D3semidirect
236. Dic3⋊C8C2×D3semidirect
237. C8×Dic3C2×D3semidirect
264. C3×#67D8semidirect
275. C3×D12#41semidirect
497. C22⋊C8D32semidirect
563. #67D24semidirect
598. D12#237semidirect
754. C32#3294semidirect
861. C3#79438semidirect
862. C3#80014semidirect

Maximal subgroups

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

subgroupindex
D12×#672
#105949072
#105924352
C3×#47322
C3×#67⋊C82
#105911642
C2×#635632
#105909442
D3×#8212
#105908782
#105908312
#105907622
Dic3×D242
#105907532
#105906802
#800143
#794383