Finite Group Databasebeta

← #11887064

Subgroups — #11887064

Order 1152.

1042 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594618C211yesmaximal, characteristic, complemented
2#10594370C211yesmaximal, characteristic, complemented
3#10592589C211yesmaximal, characteristic, complemented
4C3×#4883C211yesmaximal, characteristic, complemented
5C3×#4882C211yesmaximal, characteristic, complemented
6#10590944C211yesmaximal, characteristic, complemented
7D3×#821C211yesmaximal, characteristic, complemented
8#10590749C211yesmaximal, characteristic, complemented
9#10590717C211yesmaximal, characteristic, complemented
10#10590595C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590552C211yesmaximal, characteristic, complemented
13#10590499C211yesmaximal, characteristic, complemented
14#10590459C211yesmaximal, characteristic, complemented
15#10590438C211yesmaximal, characteristic, complemented
16#81302—31nomaximal
17#80731—31nomaximal
18C2×#3802—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3795—21no—
22#64102C2211yescharacteristic
23#64097C2211yescharacteristic, complemented
24C2×C3×D24C2211yescharacteristic, complemented
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C3×#895C2211yescharacteristic
27C3×#895C2211yescharacteristic
28C3×#895C2211yescharacteristic, complemented
29C3×D3×C4⋊C4C2211yescharacteristic, complemented
30#63922—21no—
31#63922—21no—
32#63914C2211yescharacteristic
33#63912—21no—
34#63908C2211yescharacteristic, complemented
35#63905—21no—
36C4×#625C2211yescharacteristic
37#63898C2211yescharacteristic, complemented
38#63896—21no—
39D3×C4⋊Dic3C2211yescharacteristic, complemented
40#63884—21no—
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#107C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63641C2211yescharacteristic, complemented
47#63636C2211yescharacteristic
48#63634C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic, complemented
54C3×#807C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5611—31no—
62#5609—31no—
63#5609—31no—
64#5507—31no—
65C3×#480—31no—
66C3×#466—31no—
67#5156—31no—
68#5150—31no—
69C2×#821—31no—
70C8×#67—31no—
71#5038—31no—
72#5036—31no—
73#5033—31no—
74C2×#809—31no—
75#4890—31no—
76#4890—31no—
77#4890—61no—
78#4883D311yescharacteristic, complemented
79#4882—31no—
80#4882D311yescharacteristic, complemented
81#4872—31no—
82#4786—31no—
83#4775—31no—
84#4773—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4760—31no—
88#4760—31no—
89#4756—31no—
90#4732—31no—
91#67⋊C8—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634—21no—
97C2×C3×D12—21no—
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#625—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×#625D411yescharacteristic
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114#3802—44no—
115D3×D12—22no—
116D3×D12—22no—
117D3×D12—41no—
118D3×D12—41no—
119#3795—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126C4×C3⋊Dic3C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×D24—41no—
136C3×D3×C8—41no—
137#3724D411yescharacteristic
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143#3714—22no—
144#3713—41no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C2×#237—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4—61no—
152C2×#235—61no—
153C22×D12—31no—
154C22×D12—31no—
155C2×C3×D8—31no—
156C22×C3×C8—31no—
157C3×#121—31no—
158C3×#121—31no—
159C3×#121—31no—
160C2×C3×C4⋊C4—31no—
161#940—31no—
162#940—31no—
163#938—31no—
164#937—61no—
165#937—61no—
166#935—61no—
167D4×Dic3—31no—
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—31no—
171#930—31no—
172#929—61no—
173C4×#67—31no—
174C4×#67—31no—
175C2×C4⋊Dic3—31no—
176C22×C3⋊C8—31no—
177C2×D24—31no—
178C2×D24C2×D311yescharacteristic, complemented
179C2×D3×C8—31no—
180C2×D3×C8C2×D311yescharacteristic, complemented
181#896—61no—
182#895C2×D311yescharacteristic
183#895C2×D311yescharacteristic
184#895C2×D311yescharacteristic, complemented
185#894—61no—
186#893—31no—
187#893—31no—
188#893—31no—
189#893—61no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4C2×D311yescharacteristic, complemented
192#888—31no—
193#888—31no—
194#888—61no—
195#884—61no—
196#884—61no—
197#883—61no—
198#882—61no—
199#882—61no—
200#878—61no—
201C3×#107—21no—
202C3×#107—31no—
203C3×#107C2×D311yescharacteristic, complemented
204C3×#107C2×D311yescharacteristic, complemented
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×C22⋊C8—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#830—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821C2×D311yescharacteristic, complemented
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8C2×D311yescharacteristic, complemented
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—61no—
226C8×Dic3—31no—
227C8×Dic3—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#809C2×D311yescharacteristic, complemented
234#809C2×D311yescharacteristic, complemented
235#809C2×D311yescharacteristic, complemented
236#807—31no—
237#807—31no—
238#807—61no—
239#807C2×D311yescharacteristic, complemented
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—42no—
250C2×D32—81no—
251C2×D32—81no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)#4112yescomplemented
260C4×C3⋊D3—42no—
261#634—42no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—42no—
272C3×D12—42no—
273C3×D12—42no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—42no—
279#626—42no—
280#626—42no—
281#625—42no—
282#625—42no—
283#625—81no—
284#625D814yescomplemented
285D3×Dic3—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—31no—
295#480—91no—
296#474—91no—
297#466—31no—
298#466—91no—
299#459—91no—
300#447—91no—
301#447—91no—
302C4×D8—91no—
303C8×D4—91no—
304C2×#102—91no—
305C2×#102—91no—
306C23×D3—61no—
307C23×D3—61no—
308C23×D3—61no—
309C23×D3—61no—
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C2×#67—31no—
320C2×#67—31no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331#237—124no—
332D3×D4—62no—
333D3×D4—62no—
334D3×D4—121no—
335D3×D4—121no—
336D3×D4—124no—
337D3×D4—124no—
338#235—124no—
339C2×D12—21no—
340C2×D12—21no—
341C2×D12—21no—
342C2×D12—31no—
343C2×D12—31no—
344C2×D12—61no—
345C2×D12—62no—
346C2×D12—62no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12—121no—
350C2×D12—121no—
351C2×D12C22×D311yescharacteristic
352C2×D12C22×D311yescharacteristic
353C2×D12C22×D311yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C2×C4×D3—121no—
360C2×C4×D3C22×D311yescharacteristic
361C2×C4×D3C22×D311yescharacteristic
362C2×Dic6—61no—
363C2×Dic6—61no—
364C2×Dic6—121no—
365C3×D8—121no—
366C2×C3×C8—21no—
367C2×C3×C8—31no—
368C2×C3×C8—31no—
369C2×C3×C8—121no—
370C2×C3×C8C22×D311yescharacteristic
371C2×C3×C8C22×D311yescharacteristic
372C3×C4⋊C4—21no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C4⋊C4C22×D311yescharacteristic
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383#217—31no—
384#217—31no—
385#217—61no—
386#217—61no—
387#213—62no—
388#213—121no—
389#213—121no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—121no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3C22×D311yescharacteristic
405Dic3⋊C4—21no—
406Dic3⋊C4—31no—
407Dic3⋊C4—31no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—121no—
412C4×Dic3—31no—
413C4×Dic3—31no—
414C4×Dic3—61no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—61no—
418C2×C3⋊C8—121no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421D24—41no—
422D24—62no—
423D3×C8—41no—
424D3×C8—121no—
425C22×C32C22×D411yescharacteristic
426C2×C3⋊D3—22no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
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×D3C2×D812yes—
443C2×C3×D3C2×D812yes—
444D32—84no—
445D32—84no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4C2×#4111yescharacteristic
449C32×C4H(5,𝔽2)11yescharacteristic
450C3⋊Dic3—21no—
451C3⋊Dic3—41no—
452C3⋊Dic3C2×D812yes—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—41no—
456C2×#41—181no—
457C22×D4—91no—
458C22×D4—91no—
459C22×D4—181no—
460C2×D8—31no—
461C2×D8—91no—
462C2×D8—91no—
463C22×C8—31no—
464C22×C8—91no—
465C4⋊Q8—91no—
466#127—91no—
467#123—181no—
468#123—181no—
469C22⋊Q8—181no—
470#121—31no—
471#121—31no—
472#121—31no—
473#121—91no—
474#121—181no—
475#120—181no—
476#120—181no—
477C4×D4—91no—
478C4×D4—91no—
479C4×D4—91no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—91no—
482#107—31no—
483#107—91no—
484#107D3211yescharacteristic, complemented
485C4⋊C8—91no—
486#102—31no—
487#102—31no—
488#102—31no—
489#102—31no—
490#102—91no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496C22⋊C8—31no—
497C22⋊C8—91no—
498C4×C8—91no—
499C23×C3—31no—
500C23×C3—31no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—21no—
507C22×D3—61no—
508C22×D3—61no—
509C22×D3—121no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—241no—
519C22×D3—241no—
520C22×D3—241no—
521C22×D3—241no—
522C22×D3D3×D411yescharacteristic
523C22×D3D3×D411yescharacteristic
524C3×D4—61no—
525C3×D4—61no—
526C3×D4—61no—
527C3×D4—61no—
528C3×D4—61no—
529C3×D4—61no—
530C3×D4—122no—
531C3×D4—122no—
532C3×D4—122no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—122no—
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550#67—34no—
551#67—34no—
552#67—122no—
553#67—122no—
554#67—122no—
555#67—122no—
556#67—122no—
557#67—122no—
558#67—241no—
559#67—241no—
560C2×Dic3—21no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—121no—
570C2×Dic3—122no—
571C2×Dic3—122no—
572C2×Dic3D3×D411yescharacteristic
573C2×Dic3D3×D411yescharacteristic
574D12—21no—
575D12—21no—
576D12—21no—
577D12—21no—
578D12—21no—
579D12—21no—
580D12—32no—
581D12—32no—
582D12—42no—
583D12—42no—
584D12—42no—
585D12—62no—
586D12—61no—
587D12—61no—
588D12—121no—
589D12—122no—
590D12—122no—
591C4×D3—21no—
592C4×D3—21no—
593C4×D3—21no—
594C4×D3—21no—
595C4×D3—42no—
596C4×D3—122no—
597C4×D3—122no—
598C4×D3—122no—
599C4×D3—122no—
600C4×D3—242no—
601Dic6—122no—
602Dic6—122no—
603Dic6—242no—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8—41no—
607C3×C8—61no—
608C3×C8—61no—
609C3⋊C8—21no—
610C3⋊C8—21no—
611C3⋊C8—61no—
612C3⋊C8—61no—
613C3⋊C8—121no—
614C2×C32#54611yescharacteristic
615C2×C32C22×D811yescharacteristic
616C2×C32#57711yescharacteristic
617C3⋊D3—42no—
618C3×D3—22no—
619C3×D3—22no—
620C3×D3—81no—
621C3×D3—81no—
622C3×D3—81no—
623C24—181no—
624C24—181no—
625#41—364no—
626C2×Q8—181no—
627C2×D4—31no—
628C2×D4—31no—
629C2×D4—31no—
630C2×D4—61no—
631C2×D4—61no—
632C2×D4—61no—
633C2×D4—91no—
634C2×D4—91no—
635C2×D4—181no—
636C2×D4—181no—
637C2×D4—182no—
638C2×D4—182no—
639C2×D4—181no—
640C2×D4—181no—
641C2×D4—181no—
642C2×D4—361no—
643C2×D4—361no—
644C2×D4—364no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—61no—
648C22×C4—181no—
649C22×C4—181no—
650C22×C4—181no—
651D8—121no—
652D8—182no—
653D8—361no—
654C2×C8—31no—
655C2×C8—31no—
656C2×C8—91no—
657C2×C8—121no—
658C2×C8—361no—
659C2×C8C2×D3211yescharacteristic
660C4⋊C4—31no—
661C4⋊C4—61no—
662C4⋊C4—91no—
663C4⋊C4—91no—
664C4⋊C4—181no—
665C4⋊C4—181no—
666C4⋊C4C2×D3211yescharacteristic
667C4⋊C4C2×D3211yescharacteristic
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—91no—
672C22⋊C4—91no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C42—91no—
677C22×C3—21no—
678C22×C3—32no—
679C22×C3—32no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3C2×D3×D411yescharacteristic
694C22×C3C2×D3×D411yescharacteristic
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—62no—
709C2×D3—62no—
710C2×D3—122no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—241no—
716C2×D3—241no—
717C2×D3—244no—
718C2×D3—244no—
719C2×D3—244no—
720C2×D3—244no—
721C2×D3D3×D812yes—
722C2×D3D3×D812yes—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—61no—
730C3×C4—61no—
731C3×C4—81no—
732C3×C4—81no—
733C3×C4—121no—
734C3×C4#100411yescharacteristic
735C3×C4D3×#4111yescharacteristic
736C3×C4D3×#4111yescharacteristic
737C3×C4#100911yescharacteristic
738Dic3—21no—
739Dic3—21no—
740Dic3—32no—
741Dic3—32no—
742Dic3—41no—
743Dic3—62no—
744Dic3—61no—
745Dic3—61no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749Dic3—241no—
750C32#329411yescharacteristic, complemented, Sylow
751C23—31no—
752C23—31no—
753C23—61no—
754C23—61no—
755C23—61no—
756C23—181no—
757C23—362no—
758C23—362no—
759C23—362no—
760C23—362no—
761C23—721no—
762C23—721no—
763Q8—362no—
764D4—61no—
765D4—61no—
766D4—61no—
767D4—61no—
768D4—61no—
769D4—61no—
770D4—94no—
771D4—92no—
772D4—122no—
773D4—122no—
774D4—122no—
775D4—181no—
776D4—362no—
777D4—362no—
778D4—362no—
779D4—362no—
780D4—721no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—91no—
791C2×C4—91no—
792C2×C4—122no—
793C2×C4—181no—
794C2×C4—362no—
795C2×C4—362no—
796C2×C4—362no—
797C2×C4C22×D3211yescharacteristic
798C8—21no—
799C8—61no—
800C8—61no—
801C8—181no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—62no—
806C2×C3—62no—
807C2×C3—241no—
808C2×C3—241no—
809C2×C3—241no—
810C2×C3#561011yescharacteristic
811C2×C3#565411yescharacteristic
812C2×C3C2×D3×D811yescharacteristic
813C2×C3C2×D3×D811yescharacteristic
814C2×C3#577011yescharacteristic
815C2×C3#577811yescharacteristic
816D3—22no—
817D3—22no—
818D3—81no—
819D3—81no—
820D3—81no—
821D3—122no—
822D3—122no—
823D3—242no—
824C22—32no—
825C22—32no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22—61no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22—121no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22—182no—
840C22—361no—
841C22—361no—
842C22—724no—
843C22—724no—
844C22D32×D411yescharacteristic
845C4—41no—
846C4—41no—
847C4—61no—
848C4—61no—
849C4—92no—
850C4—121no—
851C4—181no—
852C4—361no—
853C4#6430711yescharacteristic
854C4#6431911yescharacteristic
855C3—21no—
856C3#8073111yescharacteristic, complemented
857C3#8130211yescharacteristic, complemented
858C2—62no—
859C2—62no—
860C2—241no—
861C2—241no—
862C2—241no—
863C2—362no—
864C2#1059461711yescharacteristic
865C2D32×D811yescharacteristic
866C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10594618C2semidirect
2. #10594370C2semidirect
3. #10592589C2semidirect
4. C3×#4883C2semidirect
5. C3×#4882C2semidirect
6. #10590944C2semidirect
7. D3×#821C2semidirect
8. #10590749C2semidirect
9. #10590717C2semidirect
10. #10590595C2semidirect
11. D3×#809C2semidirect
12. #10590552C2semidirect
13. #10590499C2semidirect
14. #10590459C2semidirect
15. #10590438C2semidirect
23. #64097C22semidirect
24. C2×C3×D24C22semidirect
25. C2×C3×D3×C8C22semidirect
28. C3×#895C22semidirect
29. C3×D3×C4⋊C4C22semidirect
34. #63908C22semidirect
37. #63898C22semidirect
39. D3×C4⋊Dic3C22semidirect
42. C2×#3713C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#107C22semidirect
46. #63641C22semidirect
48. #63634C22semidirect
49. C3×#821C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#809C22semidirect
52. C3×#809C22semidirect
53. C3×#809C22semidirect
54. C3×#807C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63553C22semidirect
78. #4883D3semidirect
80. #4882D3semidirect
178. C2×D24C2×D3semidirect
180. C2×D3×C8C2×D3semidirect
184. #895C2×D3semidirect
191. D3×C4⋊C4C2×D3semidirect
203. C3×#107C2×D3semidirect
204. C3×#107C2×D3semidirect
220. #821C2×D3semidirect
222. (C2×D3)⋊C8C2×D3semidirect
233. #809C2×D3semidirect
234. #809C2×D3semidirect
235. #809C2×D3semidirect
239. #807C2×D3semidirect
259. C4⋊(C3⋊D3)#41semidirect
284. #625D8semidirect
484. #107D32semidirect
750. C32#3294semidirect
856. C3#80731semidirect
857. C3#81302semidirect

Maximal subgroups

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

subgroupindex
#105946182
#105943702
#105925892
C3×#48832
C3×#48822
#105909442
D3×#8212
#105907492
#105907172
#105905952
D3×#8092
#105905522
#105904992
#105904592
#105904382
#813023
#807313