Finite Group Databasebeta

← #11872158

Subgroups — #11872158

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic, complemented
2C3×#5534C211yesmaximal, characteristic, complemented
3C3×#5000C211yesmaximal, characteristic, complemented
4#10591183C211yesmaximal, characteristic, complemented
5#10591168C211yesmaximal, characteristic
6#10591127C211yesmaximal, characteristic, complemented
7#10591093C211yesmaximal, characteristic, complemented
8#10590362C211yesmaximal, characteristic, complemented
9C4×#3717C211yesmaximal, characteristic, complemented
10#10590356C211yesmaximal, characteristic, complemented
11#10590356C211yesmaximal, characteristic, complemented
12#10590346C211yesmaximal, characteristic, complemented
13C4×#3714C211yesmaximal, characteristic, complemented
14#10590313C211yesmaximal, characteristic, complemented
15#10590300C211yesmaximal, characteristic, complemented
16#83460—31nomaximal
17#79383—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C32×#117C2211yescharacteristic
20#64135C2211yescharacteristic
21#64102—21no—
22#64102—21no—
23C22⋊C4×C3⋊D3—21no—
24C22⋊C4×C3⋊D3—21no—
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26C4×C4⋊(C3⋊D3)C2211yescharacteristic
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×#924C2211yescharacteristic
31C3×#898—21no—
32C3×#896—21no—
33C3×#885—21no—
34C3×#883—21no—
35C3×#875C2211yescharacteristic, complemented
36C3×C4×D12C2211yescharacteristic, complemented
37C3×#869C2211yescharacteristic, complemented
38C3×C4×Dic6C2211yescharacteristic, complemented
39C2×#3717C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#830C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
46C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×#803C2211yescharacteristic, complemented
48C3×C4×C3⋊C8C2211yescharacteristic, complemented
49#63575C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63573C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61C3×#542—31no—
62#5534D311yescharacteristic, complemented
63#5521—31no—
64#5521—31no—
65#5521—61no—
66C3×#433—31no—
67#5087—31no—
68#5084—31no—
69#5057—31no—
70#5057—31no—
71#5046—31no—
72#5045—31no—
73#5036—31no—
74#5035—31no—
75#5026—31no—
76C4×#215—31no—
77#5014—31no—
78C4×#213—31no—
79#5000D311yescharacteristic, complemented
80#4846—31no—
81#4844—31no—
82#4844—31no—
83#4842—31no—
84#4737—31no—
85#4732—31no—
86#4731—31no—
87#4723—31no—
88#4711—31no—
89#4710—31no—
90C4×D24—31no—
91C4×#204—31no—
92C23×C3⋊D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3—21no—
103C2×C3×#67—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C32×C4⋊C4D411yescharacteristic
109C32×C4⋊C4D411yescharacteristic
110C32×C22⋊C4D411yescharacteristic
111C32×C22⋊C4D411yescharacteristic
112C32×C42C2311yescharacteristic
113C32×C42C2311yescharacteristic
114#3757—21no—
115#3752—21no—
116#3752—21no—
117#3752—21no—
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4×C3⋊Dic3—21no—
122C3×#217—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3717—22no—
138#3717—22no—
139#3714—22no—
140#3714—22no—
141#3118—91noSylow
142C22×D12—31no—
143C22×D12—31no—
144C22×D12—61no—
145C3×C4⋊Q8—31no—
146C3×#126—61no—
147C3×#124—31no—
148C3×#124—61no—
149C3×#123—61no—
150C3×C22⋊Q8—31no—
151C3×C22⋊Q8—61no—
152C3×#121—31no—
153C3×C4×Q8—31no—
154C3×C4×D4—31no—
155C3×#117—21no—
156C3×#117C2×D311yescharacteristic
157C3×#117C2×D311yescharacteristic
158C2×#215—31no—
159C2×#215—31no—
160C2×#213—31no—
161C2×#213—31no—
162#930C2×D311yescharacteristic
163#926—31no—
164#926—31no—
165#926—61no—
166#924C2×D311yescharacteristic
167C2×D24—31no—
168C2×D24—31no—
169C2×#204—31no—
170C2×#204—31no—
171#898—21no—
172#896—21no—
173#893—62no—
174#893—62no—
175#893—61no—
176#893—61no—
177#893—61no—
178#893—61no—
179#885—21no—
180#883—21no—
181D3×C22⋊C4—62no—
182D3×C22⋊C4—62no—
183D3×C22⋊C4—61no—
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186D3×C22⋊C4—61no—
187#875C2×D311yescharacteristic, complemented
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—31no—
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—61no—
197C4×D12—61no—
198C4×D12—61no—
199C4×D12—61no—
200C4×D12C2×D311yescharacteristic, complemented
201#869C2×D311yescharacteristic, complemented
202C4×Dic6C2×D311yescharacteristic, complemented
203C3×C4⋊C8—31no—
204C3×C4⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×C22⋊C8—31no—
207C3×#97—31no—
208C3×C4×C8—31no—
209#835—31no—
210#835—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#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
237#803C2×D311yescharacteristic, complemented
238C4×C3⋊C8C2×D311yescharacteristic, complemented
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—24no—
243C22×C3⋊D3—81no—
244C22×C3⋊D3—81no—
245C22×C3×D3—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—24no—
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)#4112yes—
260C4⋊(C3⋊D3)#4112yes—
261C4×C3⋊D3—81no—
262C4×C3⋊D3—81no—
263C4×C3⋊D3—81no—
264C4×C3⋊D3—81no—
265C3×#67—81no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—81no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#542—31no—
280#518—91no—
281#485—91no—
282#482—91no—
283#476—91no—
284#474—91no—
285#463—91no—
286#463—91no—
287#450—91no—
288#447—91no—
289#442—91no—
290#440—91no—
291C4×SD16—91no—
292C4×D8—91no—
293#433—31no—
294C23×D3—62no—
295C23×D3—61no—
296C23×D3—61no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×D4—31no—
300C2×C3×D4—61no—
301C22×C3×C4—21no—
302C22×C3×C4—61no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C2×#67—21no—
306C2×D12—31no—
307C2×D12—31no—
308C2×D12—31no—
309C2×D12—31no—
310C2×D12—61no—
311C2×D12—61no—
312C2×D12—62no—
313C2×D12—62no—
314C2×D12—62no—
315C2×D12—62no—
316C2×D12—62no—
317C2×D12—64no—
318C2×D12—64no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—62no—
324C2×C4×D3—62no—
325C2×C4×D3—62no—
326C2×C4×D3—62no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×Dic6—21no—
336C2×Dic6C22×D311yescharacteristic
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4D1211yescharacteristic
349C3×C4⋊C4D1211yescharacteristic
350C3×C4⋊C4#6711yescharacteristic
351C3×C4⋊C4#6711yescharacteristic
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4D1211yescharacteristic
360C3×C22⋊C4D1211yescharacteristic
361C3×C22⋊C4#6711yescharacteristic
362C3×C22⋊C4#6711yescharacteristic
363C3×C42—21no—
364C3×C42—21no—
365C3×C42—61no—
366C3×C42C22×D311yescharacteristic
367C3×C42C22×D311yescharacteristic
368C3×C42C22×D311yescharacteristic
369C3×C42C22×D311yescharacteristic
370#217—21no—
371#217—62no—
372#217—61no—
373#217—61no—
374#215—62no—
375#215—62no—
376#213—62no—
377#213—62no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—62no—
383(C2×D3)⋊C4—62no—
384(C2×D3)⋊C4—62no—
385(C2×D3)⋊C4—62no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394C4⋊Dic3—21no—
395C4⋊Dic3—31no—
396C4⋊Dic3—31no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3C22×D311yescharacteristic
402C4⋊Dic3C22×D311yescharacteristic
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405C4×Dic3—21no—
406C4×Dic3—62no—
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—22no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—84no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4C2×#4111yescharacteristic
437C32×C4C2×#4111yescharacteristic
438C3⋊Dic3—41no—
439C3⋊Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C22×D4—91no—
444C2×SD16—91no—
445C2×SD16—91no—
446C2×D8—91no—
447C2×D8—91no—
448C4⋊Q8—31no—
449#126—61no—
450#124—31no—
451#124—61no—
452#123—61no—
453C22⋊Q8—31no—
454C22⋊Q8—61no—
455#121—31no—
456C4×Q8—31no—
457C4×D4—31no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—181no—
463C4×D4—181no—
464#117—91no—
465#117D3211yescharacteristic
466C2×C22⋊C4—181no—
467C2×C22⋊C4—181no—
468#107—91no—
469#107—91no—
470#106—91no—
471#106—91no—
472C4⋊C8—31no—
473C4⋊C8—31no—
474#103—91no—
475#103—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—31no—
483C22⋊C8—31no—
484#97—31no—
485C4×C8—31no—
486C23×C3—21no—
487C23×C3—61no—
488C23×C3C2×D1211yescharacteristic
489C23×C3C2×#6711yescharacteristic
490C22×D3—21no—
491C22×D3—62no—
492C22×D3—62no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—68no—
498C22×D3—64no—
499C22×D3—64no—
500C22×D3—241no—
501C22×D3—241no—
502C22×D3—241no—
503C22×D3—241no—
504C22×D3—242no—
505C22×D3—242no—
506C3×Q8—61no—
507C3×Q8—61no—
508C3×Q8—241no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—241no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—241no—
528C2×C3×C4C2×D1211yescharacteristic
529C2×C3×C4C2×D1211yescharacteristic
530C2×C3×C4C2×D1211yescharacteristic
531C2×C3×C4C2×D1211yescharacteristic
532C2×C3×C4C2×D1211yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C2×#6711yescharacteristic
535C2×C3×C4C2×#6711yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C2×#6711yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—81no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—62no—
545C2×Dic3—62no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550D12—21no—
551D12—21no—
552D12—32no—
553D12—32no—
554D12—32no—
555D12—32no—
556D12—62no—
557D12—62no—
558D12—68no—
559D12—64no—
560D12—64no—
561D12—62no—
562D12—62no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—61no—
567C4×D3—81no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575C4×D3—241no—
576C4×D3—242no—
577C4×D3—242no—
578C4×D3—242no—
579C4×D3—242no—
580Dic6—21no—
581Dic6—21no—
582Dic6—81no—
583C3×C8—61no—
584C3×C8—61no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C3⋊C8—21no—
591C2×C32—41no—
592C2×C32#52511yescharacteristic
593C2×C32#57611yescharacteristic
594C2×C32#57711yescharacteristic
595C3⋊D3—42no—
596C3⋊D3—42no—
597C3×D3—81no—
598C24—181no—
599C2×Q8—31no—
600C2×Q8—61no—
601C2×D4—31no—
602C2×D4—61no—
603C2×D4—91no—
604C2×D4—91no—
605C2×D4—182no—
606C2×D4—182no—
607C2×D4—181no—
608C22×C4—61no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4C2×D3211yescharacteristic
614SD16—182no—
615SD16—182no—
616D8—182no—
617D8—182no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—31no—
621C2×C8—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—91no—
628C4⋊C4—91no—
629C4⋊C4#62611yescharacteristic
630C4⋊C4#62611yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4#62611yescharacteristic
642C22⋊C4#62611yescharacteristic
643C42—61no—
644C42—181no—
645C42C2×D3211yescharacteristic
646C42C2×D3211yescharacteristic
647C22×C3—22no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3C22×D1211yescharacteristic
661C22×C3C22×#6711yescharacteristic
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—64no—
666C2×D3—64no—
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—122no—
672C2×D3—122no—
673C2×D3—122no—
674C2×D3—122no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—248no—
684C2×D3—244no—
685C2×D3—244no—
686C3×C4—22no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4D3×#4111yescharacteristic
707C3×C4D3×#4111yescharacteristic
708C3×C4D3×#4111yescharacteristic
709C3×C4D3×#4111yescharacteristic
710Dic3—41no—
711Dic3—41no—
712Dic3—41no—
713Dic3—122no—
714Dic3—122no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—121no—
719C32#311811yescharacteristic, complemented, Sylow
720C23—61no—
721C23—184no—
722C23—181no—
723C23—181no—
724C23—721no—
725C23—721no—
726C23C2×#62611yescharacteristic
727Q8—61no—
728Q8—61no—
729Q8—241no—
730D4—61no—
731D4—61no—
732D4—92no—
733D4—92no—
734D4—184no—
735D4—181no—
736D4—181no—
737D4—241no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—181no—
744C2×C4—181no—
745C2×C4—241no—
746C2×C4—721no—
747C2×C4—721no—
748C2×C4—721no—
749C2×C4—721no—
750C2×C4C2×#62611yescharacteristic
751C2×C4C2×#62611yescharacteristic
752C2×C4C2×#62611yescharacteristic
753C2×C4C2×#62611yescharacteristic
754C2×C4C2×#62611yescharacteristic
755C2×C4C22×D3211yescharacteristic
756C8—61no—
757C8—61no—
758C8—61no—
759C8—61no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—42no—
764C2×C3—41no—
765C2×C3—41no—
766C2×C3—241no—
767C2×C3#552411yescharacteristic
768C2×C3#575111yescharacteristic
769C2×C3#575211yescharacteristic
770C2×C3#582811yescharacteristic
771C2×C3#583511yescharacteristic
772C2×C3#583711yescharacteristic
773D3—81no—
774D3—124no—
775D3—124no—
776D3—122no—
777D3—122no—
778D3—122no—
779D3—122no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—182no—
787C22—182no—
788C22—361no—
789C22—361no—
790C22—361no—
791C22—361no—
792C22—724no—
793C22C22×#62611yescharacteristic
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—121no—
800C4—121no—
801C4—121no—
802C4—361no—
803C4—361no—
804C4#6430611yescharacteristic
805C4#6430611yescharacteristic
806C3—21no—
807C3#7938311yescharacteristic, complemented
808C3#8346011yescharacteristic, complemented
809C2—41no—
810C2—241no—
811C2—362no—
812C2—362no—
813C2#1059503411yescharacteristic
814C2#1059544811yescharacteristic
815C2#1059544911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10591168C2
hypercenter#117D32
hypocenterC32#3118
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. #10595992C2semidirect
2. C3×#5534C2semidirect
3. C3×#5000C2semidirect
4. #10591183C2semidirect
6. #10591127C2semidirect
7. #10591093C2semidirect
8. #10590362C2semidirect
9. C4×#3717C2semidirect
10. #10590356C2semidirect
11. #10590356C2semidirect
12. #10590346C2semidirect
13. C4×#3714C2semidirect
14. #10590313C2semidirect
15. #10590300C2semidirect
35. C3×#875C22semidirect
36. C3×C4×D12C22semidirect
37. C3×#869C22semidirect
38. C3×C4×Dic6C22semidirect
45. C3×C4⋊(C3⋊C8)C22semidirect
46. C3×C4⋊(C3⋊C8)C22semidirect
47. C3×#803C22semidirect
48. C3×C4×C3⋊C8C22semidirect
49. #63575C22semidirect
50. #63575C22semidirect
51. #63573C22semidirect
52. #63573C22semidirect
53. #63566C22semidirect
54. #63566C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
62. #5534D3semidirect
79. #5000D3semidirect
187. #875C2×D3semidirect
200. C4×D12C2×D3semidirect
201. #869C2×D3semidirect
202. C4×Dic6C2×D3semidirect
235. C4⋊(C3⋊C8)C2×D3semidirect
236. C4⋊(C3⋊C8)C2×D3semidirect
237. #803C2×D3semidirect
238. C4×C3⋊C8C2×D3semidirect
719. C32#3118semidirect
807. C3#79383semidirect
808. C3#83460semidirect

Maximal subgroups

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

subgroupindex
#105959922
C3×#55342
C3×#50002
#105911832
#105911682
#105911272
#105910932
#105903622
C4×#37172
#105903562
#105903462
C4×#37142
#105903132
#105903002
#834603
#793833