Finite Group Databasebeta

← #11872312

Subgroups — #11872312

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595994C211yesmaximal, characteristic, complemented
2C3×#5535C211yesmaximal, characteristic, complemented
3C3×#5000C211yesmaximal, characteristic, complemented
4#10591182C211yesmaximal, characteristic, complemented
5#10591182C211yesmaximal, characteristic, complemented
6#10591094C211yesmaximal, characteristic, complemented
7#10591092C211yesmaximal, characteristic, complemented
8#10590377C211yesmaximal, characteristic, complemented
9#10590360C211yesmaximal, characteristic, complemented
10C4×#3716C211yesmaximal, characteristic, complemented
11#10590355C211yesmaximal, characteristic, complemented
12#10590346C211yesmaximal, characteristic, complemented
13C4×#3714C211yesmaximal, characteristic, complemented
14#10590308C211yesmaximal, characteristic, complemented
15#10590292C211yesmaximal, characteristic, complemented
16#83434—31nomaximal
17#79384—31nomaximal
18C2×#3828C2211yescharacteristic
19C32×#117C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21#64101—21no—
22C4⋊C4×C3⋊D3—21no—
23#64090—21no—
24#64090—21no—
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26C4×C4⋊(C3⋊D3)C2211yescharacteristic
27C4×#634C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×#930C2211yescharacteristic
31C3×#894—21no—
32C3×#894—21no—
33C3×#884—21no—
34C3×#884—21no—
35C3×#874C2211yescharacteristic
36C3×C4×D12C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×#870C2211yescharacteristic
39C2×#3716C2211yescharacteristic
40C2×#3716C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#830C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×C4⋊(C3⋊C8)C2211yescharacteristic
46C3×C4⋊(C3⋊C8)C2211yescharacteristic
47C3×#803C2211yescharacteristic
48C3×C4×C3⋊C8C2211yescharacteristic
49#63575C2211yescharacteristic
50#63575C2211yescharacteristic
51#63573C2211yescharacteristic
52#63573C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61C3×#540—31no—
62#5535D311yescharacteristic, complemented
63#5523—31no—
64#5523—31no—
65#5523—61no—
66C3×#433—31no—
67#5075—31no—
68#5072—31no—
69#5066—31no—
70#5063—31no—
71#5037—31no—
72#5037—31no—
73#5034—31no—
74#5033—31no—
75#5018—31no—
76C4×#214—31no—
77#5014—31no—
78C4×#213—31no—
79#5000D311yescharacteristic, complemented
80#4848—31no—
81#4847—31no—
82#4843—31no—
83#4829—31no—
84#4736—31no—
85#4735—31no—
86#4734—31no—
87#4734—31no—
88#4711—31no—
89#4710—31no—
90C4×D24—31no—
91C4×#204—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C22×C3⋊Dic3—21no—
95#3828—22no—
96#3828—22no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×#634C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C32×C4⋊C4D411yescharacteristic
111C32×C4⋊C4D411yescharacteristic
112C32×C22⋊C4D411yescharacteristic
113C32×C22⋊C4D411yescharacteristic
114C32×C42C2311yescharacteristic
115C32×C42C2311yescharacteristic
116#3752—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122#3750—21no—
123C4×C3⋊Dic3—21no—
124C4×C3⋊Dic3—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3716—22no—
138#3716—22no—
139#3714—22no—
140#3714—22no—
141#3119—91noSylow
142C2×#235—31no—
143C2×#235—31no—
144C2×#235—61no—
145C3×#127—31no—
146C3×#125—31no—
147C3×#123—61no—
148C3×#123—61no—
149C3×#121—31no—
150C3×#121—31no—
151C3×#121—61no—
152C3×#121—61no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C3×#117—21no—
156C3×#117C2×D311yescharacteristic
157C3×#117C2×D311yescharacteristic
158C2×#214—31no—
159C2×#214—31no—
160C2×#213—31no—
161C2×#213—31no—
162#930C2×D311yescharacteristic
163#930C2×D311yescharacteristic
164C2×C4⋊Dic3—31no—
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—61no—
167C2×D24—31no—
168C2×D24—31no—
169C2×#204—31no—
170C2×#204—31no—
171#894—21no—
172#894—21no—
173#892—62no—
174#892—61no—
175#892—61no—
176D3×C4⋊C4—62no—
177D3×C4⋊C4—61no—
178D3×C4⋊C4—61no—
179#884—21no—
180#884—21no—
181#67⋊C4—62no—
182#67⋊C4—62no—
183#67⋊C4—61no—
184#67⋊C4—61no—
185#67⋊C4—61no—
186#67⋊C4—61no—
187#874C2×D311yescharacteristic
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12—61no—
194C4×D12C2×D311yescharacteristic
195C4×D12C2×D311yescharacteristic
196#870C2×D311yescharacteristic
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—31no—
201C4×Dic6—61no—
202C4×Dic6—61no—
203C3×C4⋊C8—31no—
204C3×C4⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×C22⋊C8—31no—
207C3×#97—31no—
208C3×C4×C8—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#830C2×D311yescharacteristic
214#830C2×D311yescharacteristic
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#818—31no—
222#818—31no—
223#817—31no—
224#817—31no—
225#816—31no—
226#816—31no—
227#810—31no—
228#810—31no—
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235C4⋊(C3⋊C8)C2×D311yescharacteristic
236C4⋊(C3⋊C8)C2×D311yescharacteristic
237#803C2×D311yescharacteristic
238C4×C3⋊C8C2×D311yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251#638—24no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—81no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)#4112yes—
258C4×C3⋊D3—24no—
259C4×C3⋊D3—81no—
260C4×C3⋊D3—81no—
261#634—21no—
262#634#4112yes—
263C3×#67—81no—
264C3×#67—81no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—81no—
272C3×D12—81no—
273C3×C4×D3—81no—
274C3×C4×D3—81no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#540—31no—
280#520—91no—
281#481—91no—
282#480—91no—
283#479—91no—
284#478—91no—
285#460—91no—
286#459—91no—
287#449—91no—
288#449—91no—
289#442—91no—
290#440—91no—
291C4×SD16—91no—
292C4×D8—91no—
293#433—31no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C22×C3×C4—21no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C2×#67—21no—
306C2×#67—21no—
307C2×#67—62no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—62no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313#235—62no—
314#235—62no—
315#235—62no—
316#235—62no—
317#235—64no—
318#235—64no—
319C2×D12—21no—
320C2×D12—21no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—61no—
324C2×D12C22×D311yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3—62no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—62no—
332C2×C4×D3—62no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×Dic6—31no—
338C2×Dic6—31no—
339C2×Dic6—61no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4D1211yescharacteristic
351C3×C4⋊C4D1211yescharacteristic
352C3×C4⋊C4#6711yescharacteristic
353C3×C4⋊C4#6711yescharacteristic
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4D1211yescharacteristic
361C3×C22⋊C4D1211yescharacteristic
362C3×C22⋊C4#6711yescharacteristic
363C3×C22⋊C4#6711yescharacteristic
364C3×C42—21no—
365C3×C42—21no—
366C3×C42C22×D311yescharacteristic
367C3×C42C22×D311yescharacteristic
368C3×C42C22×D311yescharacteristic
369C3×C42C22×D311yescharacteristic
370#214—62no—
371#214—62no—
372#213—62no—
373#213—62no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—62no—
379(C2×D3)⋊C4—62no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—62no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—62no—
398Dic3⋊C4—62no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403C4×Dic3—62no—
404C4×Dic3—62no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413D24—62no—
414D24—62no—
415#204—62no—
416#204—62no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—22no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4C2×#4111yescharacteristic
436C32×C4C2×#4111yescharacteristic
437C3⋊Dic3—22no—
438C3⋊Dic3—41no—
439C3⋊Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—91no—
443C2×SD16—91no—
444C2×SD16—91no—
445C2×D8—91no—
446C2×D8—91no—
447#127—31no—
448#125—31no—
449#123—61no—
450#123—61no—
451#121—31no—
452#121—31no—
453#121—61no—
454#121—61no—
455C4×Q8—91no—
456C4×Q8—91no—
457C4×D4—31no—
458C4×D4—31no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C4×D4—181no—
463#117—181no—
464#117D3211yescharacteristic
465C2×C4⋊C4—91no—
466C2×C4⋊C4—181no—
467#107—91no—
468#107—91no—
469#106—91no—
470#106—91no—
471C4⋊C8—31no—
472C4⋊C8—31no—
473#103—91no—
474#103—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481C22⋊C8—31no—
482C22⋊C8—31no—
483#97—31no—
484C4×C8—31no—
485C23×C3—21no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3C2×D1211yescharacteristic
489C23×C3C2×#6711yescharacteristic
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—62no—
493C22×D3—61no—
494C22×D3—61no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—241no—
500C3×D4—241no—
501C3×D4—241no—
502C3×D4—241no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—241no—
518C2×C3×C4—241no—
519C2×C3×C4C2×D1211yescharacteristic
520C2×C3×C4C2×D1211yescharacteristic
521C2×C3×C4C2×D1211yescharacteristic
522C2×C3×C4C2×D1211yescharacteristic
523C2×C3×C4C2×D1211yescharacteristic
524C2×C3×C4C2×#6711yescharacteristic
525C2×C3×C4C2×#6711yescharacteristic
526C2×C3×C4C2×#6711yescharacteristic
527C2×C3×C4C2×#6711yescharacteristic
528C2×C3×C4C2×#6711yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—68no—
532#67—64no—
533#67—64no—
534#67—81no—
535#67—81no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—62no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—241no—
548C2×Dic3—241no—
549C2×Dic3—242no—
550D12—21no—
551D12—21no—
552D12—21no—
553D12—21no—
554D12—32no—
555D12—32no—
556D12—62no—
557D12—62no—
558D12—61no—
559D12—61no—
560D12—81no—
561D12—81no—
562C4×D3—68no—
563C4×D3—64no—
564C4×D3—64no—
565C4×D3—81no—
566C4×D3—81no—
567C4×D3—241no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—242no—
572C4×D3—242no—
573Dic6—32no—
574Dic6—32no—
575Dic6—62no—
576Dic6—62no—
577Dic6—61no—
578Dic6—61no—
579C3×C8—61no—
580C3×C8—61no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C2×C32—41no—
588C2×C32#52511yescharacteristic
589C2×C32#57611yescharacteristic
590C2×C32#57711yescharacteristic
591C3⋊D3—42no—
592C3×D3—81no—
593C3×D3—81no—
594#41—182no—
595#41—182no—
596C2×Q8—91no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—91no—
604C2×D4—181no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4C2×D3211yescharacteristic
612SD16—182no—
613SD16—182no—
614D8—182no—
615D8—182no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4#62611yescharacteristic
630C4⋊C4#62611yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4#62611yescharacteristic
638C22⋊C4#62611yescharacteristic
639C42—181no—
640C42—181no—
641C42C2×D3211yescharacteristic
642C42C2×D3211yescharacteristic
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3C22×D1211yescharacteristic
660C22×C3C22×#6711yescharacteristic
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—64no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—122no—
671C2×D3—122no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C3×C4—22no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—121no—
694C3×C4—121no—
695C3×C4D3×#4111yescharacteristic
696C3×C4D3×#4111yescharacteristic
697C3×C4D3×#4111yescharacteristic
698C3×C4D3×#4111yescharacteristic
699Dic3—41no—
700Dic3—41no—
701Dic3—64no—
702Dic3—62no—
703Dic3—62no—
704Dic3—122no—
705Dic3—122no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710C32#311911yescharacteristic, complemented, Sylow
711C23—61no—
712C23—61no—
713C23—181no—
714C23C2×#62611yescharacteristic
715Q8—92no—
716Q8—181no—
717D4—61no—
718D4—61no—
719D4—61no—
720D4—61no—
721D4—92no—
722D4—184no—
723D4—181no—
724D4—241no—
725D4—241no—
726D4—241no—
727D4—241no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—184no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—241no—
737C2×C4—241no—
738C2×C4—721no—
739C2×C4—721no—
740C2×C4—721no—
741C2×C4C2×#62611yescharacteristic
742C2×C4C2×#62611yescharacteristic
743C2×C4C2×#62611yescharacteristic
744C2×C4C2×#62611yescharacteristic
745C2×C4C2×#62611yescharacteristic
746C2×C4C22×D3211yescharacteristic
747C8—61no—
748C8—61no—
749C8—61no—
750C8—61no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—41no—
756C2×C3—41no—
757C2×C3—241no—
758C2×C3—241no—
759C2×C3#552411yescharacteristic
760C2×C3#575111yescharacteristic
761C2×C3#575211yescharacteristic
762C2×C3#582811yescharacteristic
763C2×C3#583511yescharacteristic
764C2×C3#583611yescharacteristic
765D3—81no—
766D3—81no—
767D3—124no—
768D3—122no—
769D3—122no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—182no—
780C22—361no—
781C22—361no—
782C22C22×#62611yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—121no—
789C4—121no—
790C4—182no—
791C4—361no—
792C4—361no—
793C4#6430611yescharacteristic
794C4#6430611yescharacteristic
795C3—21no—
796C3#7938411yescharacteristic, complemented
797C3#8343411yescharacteristic, complemented
798C2—41no—
799C2—241no—
800C2—241no—
801C2—362no—
802C2#1059503411yescharacteristic
803C2#1059544711yescharacteristic
804C2#1059544911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595994C2semidirect
2. C3×#5535C2semidirect
3. C3×#5000C2semidirect
4. #10591182C2semidirect
5. #10591182C2semidirect
6. #10591094C2semidirect
7. #10591092C2semidirect
8. #10590377C2semidirect
9. #10590360C2semidirect
10. C4×#3716C2semidirect
11. #10590355C2semidirect
12. #10590346C2semidirect
13. C4×#3714C2semidirect
14. #10590308C2semidirect
15. #10590292C2semidirect
62. #5535D3semidirect
79. #5000D3semidirect
710. C32#3119semidirect
796. C3#79384semidirect
797. C3#83434semidirect

Maximal subgroups

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

subgroupindex
#105959942
C3×#55352
C3×#50002
#105911822
#105910942
#105910922
#105903772
#105903602
C4×#37162
#105903552
#105903462
C4×#37142
#105903082
#105902922
#834343
#793843