Finite Group Databasebeta

← #11887068

Subgroups — #11887068

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
1#10594621C211yesmaximal, characteristic, complemented
2#10594515C211yesmaximal, characteristic, complemented
3#10592581C211yesmaximal, characteristic, complemented
4C3×#4882C211yesmaximal, characteristic, complemented
5C3×#4872C211yesmaximal, characteristic, complemented
6#10590945C211yesmaximal, characteristic, complemented
7#10590944C211yesmaximal, characteristic, complemented
8#10590878C211yesmaximal, characteristic, complemented
9#10590721C211yesmaximal, characteristic, complemented
10#10590593C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590555C211yesmaximal, characteristic, complemented
13#10590547C211yesmaximal, characteristic, complemented
14#10590509C211yesmaximal, characteristic, complemented
15#10590499C211yesmaximal, characteristic, complemented
16#81302—31nomaximal
17#79608—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3798—21no—
22#64104C2211yescharacteristic
23C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C3×D24C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#893C2211yescharacteristic, complemented
28C3×D3×C4⋊C4C2211yescharacteristic, complemented
29#63923—21no—
30#63922—21no—
31#63918C2211yescharacteristic, complemented
32#63916C2211yescharacteristic, complemented
33#63911C2211yescharacteristic
34#63908C2211yescharacteristic, complemented
35#63906—21no—
36#63905—21no—
37C4×#626C2211yescharacteristic
38#63853—21no—
39#63851—21no—
40C2×#3714C2211yescharacteristic, complemented
41C2×#3713C2211yescharacteristic, complemented
42C2×#3710C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#107C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63647C2211yescharacteristic, complemented
47#63636C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61#5609—31no—
62#5551—31no—
63D4×D12—31no—
64#5507—31no—
65C3×#480—31no—
66C3×C4×D8—31no—
67#5156—31no—
68#5156—31no—
69#5038—31no—
70#5015—31no—
71#5007—31no—
72C2×#809—31no—
73#4890—31no—
74#4883—31no—
75#4882—31no—
76#4882—31no—
77#4882—61no—
78#4882D311yescharacteristic, complemented
79#4872D311yescharacteristic, complemented
80#4786—31no—
81#4775—31no—
82#4775—31no—
83#4773—31no—
84D3×#102—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4760—31no—
88#4732—31no—
89#67⋊C8—31no—
90#4694—31no—
91C8×D12—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×#627—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626D411yescharacteristic
112C2×#625—21no—
113C2×#625—21no—
114#3802—22no—
115#3802—41no—
116D3×D12—22no—
117D3×D12—41no—
118D3×D12—44no—
119#3798—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×D24—22no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3D411yescharacteristic
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142#3714—41no—
143#3713—41no—
144#3710—41no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×#235—61no—
152C2×#235—61no—
153C22×D12—31no—
154C22×D12—61no—
155C2×C3×D8—31no—
156C3×#121—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C2×C3×C4⋊C4—31no—
160#940—31no—
161#938—31no—
162#938—31no—
163#937—61no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167#930—31no—
168#930—61no—
169#929—61no—
170C4×#67—31no—
171#924—61no—
172C22×C3⋊C8—31no—
173C2×D24—31no—
174C2×D24C2×D311yescharacteristic
175C2×D3×C8—31no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178#896—61no—
179#895—31no—
180#895—31no—
181#895—31no—
182#895—61no—
183#895C2×D311yescharacteristic
184#894—61no—
185#893C2×D311yescharacteristic
186#893C2×D311yescharacteristic, complemented
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—61no—
190D3×C4⋊C4C2×D311yescharacteristic, complemented
191#888—31no—
192#884—61no—
193#883—61no—
194#883—61no—
195#882—61no—
196#882—61no—
197#882—61no—
198#874—31no—
199C4×D12—31no—
200#869—31no—
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—
210C3×C4×C8—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—61no—
220#821C2×D311yescharacteristic, complemented
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—61no—
224(C2×D3)⋊C8C2×D311yescharacteristic, complemented
225Dic3⋊C8—31no—
226C8×Dic3C2×D311yescharacteristic, complemented
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—61no—
232#809C2×D311yescharacteristic
233#809C2×D311yescharacteristic, complemented
234#809C2×D311yescharacteristic, complemented
235#807—31no—
236#807—31no—
237#807—61no—
238#807C2×D311yescharacteristic, complemented
239C4⋊(C3⋊C8)—31no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3C2×D411yescharacteristic
242C22×C3×D3—21no—
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—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—42no—
260C4×C3⋊D3—21no—
261C4×C3⋊D3—21no—
262C4×C3⋊D3—42no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—42no—
273C3×D12#4112yescomplemented
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—42no—
277C3×C4×D3—42no—
278C3×C4×D3—42no—
279#627—42no—
280#626—42no—
281#626—42no—
282#626—42no—
283#626—81no—
284#626D814yescomplemented
285#625—42no—
286#625—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—91no—
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—31no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—61no—
314C22×C3×C4—31no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C2×#67—31no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327D3×D4—62no—
328D3×D4—62no—
329D3×D4—62no—
330D3×D4—121no—
331D3×D4—124no—
332D3×D4—121no—
333D3×D4—121no—
334#235—124no—
335#235—124no—
336C2×D12—21no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—31no—
340C2×D12—61no—
341C2×D12—62no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12—61no—
348C2×D12—121no—
349C2×D12—121no—
350C2×D12—124no—
351C2×D12C22×D311yescharacteristic
352C2×D12C22×D311yescharacteristic
353C2×D12C22×D311yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3—21no—
357C2×C4×D3—31no—
358C2×C4×D3—31no—
359C2×C4×D3—61no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—121no—
363C2×C4×D3C22×D311yescharacteristic
364C2×Dic6—61no—
365C2×Dic6—61no—
366C3×D8—62no—
367C2×C3×C8—21no—
368C2×C3×C8—31no—
369C2×C3×C8—31no—
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—
383C3×C42—31no—
384#217—31no—
385#217—61no—
386#217—61no—
387#213—121no—
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—31no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—121no—
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3C22×D311yescharacteristic
407Dic3⋊C4—21no—
408Dic3⋊C4—31no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—121no—
413C4×Dic3C22×D311yescharacteristic
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8—121no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420D24—22no—
421D24—121no—
422D3×C8—121no—
423D3×C8—121no—
424D3×C8—121no—
425C22×C32C22×D411yescharacteristic
426C2×C3⋊D3—21no—
427C2×C3⋊D3—21no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3C2×D812yes—
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×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×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—41no—
455C3×Dic3C2×D812yes—
456C2×#41—181no—
457C22×D4—91no—
458C22×D4—91no—
459C22×D4—181no—
460C2×D8—31no—
461C2×D8—91no—
462C2×D8—91no—
463C22×C8—91no—
464C22×C8—91no—
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—31no—
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—31no—
499C23×C3—31no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C22×D3—21no—
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—31no—
507C22×D3—31no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—61no—
511C22×D3—121no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—241no—
521C22×D3—241no—
522C22×D3—241no—
523C22×D3—241no—
524C22×D3D3×D411yescharacteristic
525C3×D4—32no—
526C3×D4—61no—
527C3×D4—61no—
528C3×D4—61no—
529C3×D4—61no—
530C3×D4—61no—
531C3×D4—122no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
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—122no—
546C2×C3×C4—122no—
547C2×C3×C4—122no—
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550#67—34no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—122no—
555#67—122no—
556#67—122no—
557#67—122no—
558#67—241no—
559C2×Dic3—21no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—121no—
566C2×Dic3D3×D411yescharacteristic
567C2×Dic3D3×D411yescharacteristic
568C2×Dic3D3×D411yescharacteristic
569D12—21no—
570D12—21no—
571D12—21no—
572D12—21no—
573D12—21no—
574D12—34no—
575D12—42no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—121no—
581D12—121no—
582D12—122no—
583D12—122no—
584D12—122no—
585D12—122no—
586D12—122no—
587D12—242no—
588D12—241no—
589D12#23512yescomplemented
590C4×D3—21no—
591C4×D3—21no—
592C4×D3—42no—
593C4×D3—42no—
594C4×D3—42no—
595C4×D3—61no—
596C4×D3—61no—
597C4×D3—61no—
598C4×D3—61no—
599C4×D3—121no—
600C4×D3—121no—
601C4×D3—122no—
602C4×D3—122no—
603C4×D3—242no—
604Dic6—122no—
605Dic6—122no—
606C3×C8—21no—
607C3×C8—21no—
608C3×C8—41no—
609C3×C8—61no—
610C3×C8—61no—
611C3⋊C8—21no—
612C3⋊C8—21no—
613C3⋊C8—61no—
614C3⋊C8—61no—
615C3⋊C8—121no—
616C2×C32#54611yescharacteristic
617C2×C32C22×D811yescharacteristic
618C2×C32#57711yescharacteristic
619C3⋊D3—22no—
620C3⋊D3—81no—
621C3×D3—22no—
622C3×D3—42no—
623C3×D3—81no—
624C3×D3—81no—
625C24—181no—
626C24—181no—
627#41—364no—
628C2×Q8—181no—
629C2×D4—31no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—61no—
633C2×D4—91no—
634C2×D4—91no—
635C2×D4—181no—
636C2×D4—181no—
637C2×D4—181no—
638C2×D4—181no—
639C2×D4—182no—
640C2×D4—181no—
641C2×D4—181no—
642C2×D4—182no—
643C2×D4—181no—
644C2×D4—361no—
645C2×D4—364no—
646C2×D4—361no—
647C22×C4—31no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—91no—
652C22×C4—181no—
653D8—62no—
654D8—361no—
655D8—361no—
656C2×C8—31no—
657C2×C8—31no—
658C2×C8—91no—
659C2×C8—361no—
660C2×C8—361no—
661C2×C8C2×D3211yescharacteristic
662C4⋊C4—31no—
663C4⋊C4—61no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C4⋊C4C2×D3211yescharacteristic
669C4⋊C4C2×D3211yescharacteristic
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—91no—
674C22⋊C4—91no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C42—31no—
679C22×C3—21no—
680C22×C3—32no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—62no—
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×C3C2×D3×D411yescharacteristic
693C22×C3C2×D3×D411yescharacteristic
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—22no—
697C2×D3—32no—
698C2×D3—32no—
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—62no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—241no—
721C2×D3—241no—
722C2×D3—241no—
723C2×D3—244no—
724C2×D3—244no—
725C2×D3—244no—
726C2×D3—244no—
727C2×D3D3×D812yes—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—32no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—41no—
735C3×C4—61no—
736C3×C4—61no—
737C3×C4—81no—
738C3×C4—81no—
739C3×C4—121no—
740C3×C4C2×#23511yescharacteristic
741C3×C4D3×#4111yescharacteristic
742C3×C4#100911yescharacteristic
743C3×C4#100911yescharacteristic
744Dic3—21no—
745Dic3—21no—
746Dic3—41no—
747Dic3—61no—
748Dic3—61no—
749Dic3—121no—
750Dic3—121no—
751Dic3—121no—
752Dic3—241no—
753Dic3D3×D812yes—
754C32#329411yescharacteristic, complemented, Sylow
755C23—31no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—91no—
760C23—181no—
761C23—362no—
762C23—362no—
763C23—362no—
764C23—362no—
765C23—721no—
766C23—721no—
767Q8—362no—
768D4—32no—
769D4—61no—
770D4—61no—
771D4—61no—
772D4—61no—
773D4—61no—
774D4—94no—
775D4—122no—
776D4—181no—
777D4—181no—
778D4—362no—
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—91no—
794C2×C4—122no—
795C2×C4—122no—
796C2×C4—122no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—362no—
801C2×C4C22×D3211yescharacteristic
802C8—21no—
803C8—61no—
804C8—61no—
805C8—181no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—62no—
810C2×C3—122no—
811C2×C3—241no—
812C2×C3—241no—
813C2×C3#555011yescharacteristic
814C2×C3#565411yescharacteristic
815C2×C3C2×D3×D811yescharacteristic
816C2×C3C2×D3×D811yescharacteristic
817C2×C3#577011yescharacteristic
818C2×C3#577811yescharacteristic
819D3—22no—
820D3—42no—
821D3—62no—
822D3—62no—
823D3—81no—
824D3—81no—
825D3—122no—
826D3—241no—
827D3—241no—
828D3—481no—
829C22—32no—
830C22—61no—
831C22—61no—
832C22—62no—
833C22—92no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—181no—
843C22—181no—
844C22—361no—
845C22—361no—
846C22—361no—
847C22—724no—
848C22—724no—
849C22D32×D411yescharacteristic
850C4—32no—
851C4—41no—
852C4—41no—
853C4—61no—
854C4—61no—
855C4—121no—
856C4—181no—
857C4—361no—
858C4D3×#23511yescharacteristic
859C4#6432011yescharacteristic
860C3—21no—
861C3#7960811yescharacteristic, complemented
862C3#8130211yescharacteristic, complemented
863C2—62no—
864C2—122no—
865C2—182no—
866C2—241no—
867C2—241no—
868C2—721no—
869C2#1059461911yescharacteristic
870C2D32×D811yescharacteristic
871C2#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. #10594621C2semidirect
2. #10594515C2semidirect
3. #10592581C2semidirect
4. C3×#4882C2semidirect
5. C3×#4872C2semidirect
6. #10590945C2semidirect
7. #10590944C2semidirect
8. #10590878C2semidirect
9. #10590721C2semidirect
10. #10590593C2semidirect
11. D3×#809C2semidirect
12. #10590555C2semidirect
13. #10590547C2semidirect
14. #10590509C2semidirect
15. #10590499C2semidirect
23. C4⋊C4×C3⋊D3C22semidirect
27. C3×#893C22semidirect
28. C3×D3×C4⋊C4C22semidirect
31. #63918C22semidirect
32. #63916C22semidirect
34. #63908C22semidirect
40. C2×#3714C22semidirect
41. C2×#3713C22semidirect
42. C2×#3710C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#107C22semidirect
45. #63648C22semidirect
46. #63647C22semidirect
47. #63636C22semidirect
48. #63634C22semidirect
49. C3×#821C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×C8×Dic3C22semidirect
53. C3×#809C22semidirect
54. C3×#809C22semidirect
55. C3×#807C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63564C22semidirect
59. #63563C22semidirect
78. #4882D3semidirect
79. #4872D3semidirect
186. #893C2×D3semidirect
190. D3×C4⋊C4C2×D3semidirect
203. C3×#107C2×D3semidirect
204. C3×#107C2×D3semidirect
220. #821C2×D3semidirect
224. (C2×D3)⋊C8C2×D3semidirect
226. C8×Dic3C2×D3semidirect
233. #809C2×D3semidirect
234. #809C2×D3semidirect
238. #807C2×D3semidirect
273. C3×D12#41semidirect
284. #626D8semidirect
484. #107D32semidirect
589. D12#235semidirect
754. C32#3294semidirect
861. C3#79608semidirect
862. C3#81302semidirect

Maximal subgroups

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

subgroupindex
#105946212
#105945152
#105925812
C3×#48822
C3×#48722
#105909452
#105909442
#105908782
#105907212
#105905932
D3×#8092
#105905552
#105905472
#105905092
#105904992
#813023
#796083