Finite Group Databasebeta

← #11817829

Subgroups — #11817829

Order 1152.

1179 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63874C211yesmaximal, characteristic, complemented
2C2×#63868C211yesmaximal, characteristic, complemented
3#10592364C211yesmaximal, characteristic
4C3×#4649C211yesmaximal, characteristic, complemented
5C3×#4647C211yesmaximal, characteristic, complemented
6#10591345C211yesmaximal, characteristic, complemented
7#10591321C211yesmaximal, characteristic
8#10591320C211yesmaximal, characteristic
9#10591290C211yesmaximal, characteristic, complemented
10#10591289C211yesmaximal, characteristic, complemented
11#10591289C211yesmaximal, characteristic, complemented
12#10591203C211yesmaximal, characteristic, complemented
13#10591203C211yesmaximal, characteristic, complemented
14#10591202C211yesmaximal, characteristic, complemented
15#10591193C211yesmaximal, characteristic, complemented
16#76027—31nomaximal
17#73681—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45#63874—24no—
46#63868—24no—
47C32×#95C2211yescharacteristic
48#63658C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#898—31no—
56C2×#876—31no—
57C2×#872—31no—
58C2×#872—31no—
59C3×#389—31no—
60C3×C4×C4⋊C4—31no—
61#4993—31no—
62#4993—31no—
63#4993—31no—
64#4993—31no—
65#4991—31no—
66#4990—31no—
67#4990—31no—
68#4989—31no—
69#4988—31no—
70#4982—31no—
71#4978—31no—
72#4940—31no—
73#4940—31no—
74#4940—31no—
75#4939—31no—
76#4933—31no—
77#4672—31no—
78#4669—31no—
79#4668—31no—
80#4665—31no—
81#4665—31no—
82#4665—61no—
83#4657—31no—
84#4649D311yescharacteristic, complemented
85#4647D311yescharacteristic, complemented
86C23×C3⋊D3C2311yescharacteristic
87C23×C3⋊D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C2×C4⋊(C3⋊D3)—22no—
94C2×C4⋊(C3⋊D3)—22no—
95C2×C4⋊(C3⋊D3)—41no—
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—22no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107#3752—22no—
108#3752—22no—
109#3752—41no—
110C3×C4⋊Dic3—41no—
111C3×Dic3⋊C4—22no—
112C3×Dic3⋊C4—22no—
113C3×Dic3⋊C4—22no—
114C3×Dic3⋊C4—22no—
115C3×Dic3⋊C4—41no—
116C3×C4×Dic3—22no—
117C3×C4×Dic3—22no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3—22no—
120#3724—22no—
121#3724—41no—
122#3724D414yescomplemented
123Dic3⋊Dic3—22no—
124#3722—22no—
125#3722—22no—
126#3722—22no—
127#3722—22no—
128#3722—22no—
129#3722—22no—
130#3722—22no—
131#3722—41no—
132#2479—91noSylow
133C22×D12—31no—
134C22×D12—31no—
135C22×D12—61no—
136C22×C4×D3—31no—
137C22×C4×D3—31no—
138C22×C4×D3—61no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C42—31no—
146C2×C3×C42—31no—
147C2×C3×C42—31no—
148C2×C3×C42—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—61no—
172C2×(C2×D3)⋊C4—61no—
173C2×(C2×D3)⋊C4—61no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3C2×D311yescharacteristic
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4C2×D311yescharacteristic
184C2×Dic3⋊C4C2×D311yescharacteristic
185C2×Dic3⋊C4C2×D311yescharacteristic
186C2×Dic3⋊C4C2×D311yescharacteristic
187C2×Dic3⋊C4C2×D311yescharacteristic
188C2×C4×Dic3C2×D311yescharacteristic
189C2×C4×Dic3C2×D311yescharacteristic
190C2×C4×Dic3C2×D311yescharacteristic
191C2×C4×Dic3C2×D311yescharacteristic
192#898—64no—
193#876—64no—
194#872—64no—
195#872—64no—
196C3×#95—21no—
197C3×#95—31no—
198C3×#95—31no—
199C3×#95C2×D311yescharacteristic
200C3×#95C2×D311yescharacteristic
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—61no—
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C23×C32C2411yescharacteristic
215C22×C3⋊D3—21no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3—21no—
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3—21no—
221C22×C3⋊D3—21no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3#4112yes—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4#4112yes—
237C2×C32×C4#4112yes—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3C2×D412yes—
244C4⋊(C3⋊D3)—44no—
245C4×C3⋊D3—28no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D412yes—
268C2×C3×Dic3C2×D412yes—
269C2×C3×Dic3#4112yes—
270C2×#126—91no—
271C2×#117—91no—
272#399—91no—
273#399—91no—
274#398—91no—
275#394—91no—
276#390—91no—
277#389—31no—
278#388—91no—
279#388—91no—
280#388—91no—
281#387—91no—
282#386—91no—
283#385—91no—
284C4×C4⋊C4—31no—
285C23×D3—31no—
286C23×D3—31no—
287C23×D3—31no—
288C23×D3—31no—
289C23×D3—61no—
290C23×D3—61no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C2×D12—62no—
323C2×D12—62no—
324C2×D12—64no—
325C2×D12—62no—
326C2×D12—62no—
327C2×D12—122no—
328C2×D12—121no—
329C2×D12—121no—
330C2×D12—122no—
331C2×C4×D3—62no—
332C2×C4×D3—62no—
333C2×C4×D3—62no—
334C2×C4×D3—62no—
335C2×C4×D3—62no—
336C2×C4×D3—62no—
337C2×C4×D3—122no—
338C2×C4×D3—122no—
339C2×C4×D3—122no—
340C3×C4⋊C4—62no—
341C3×C4⋊C4—62no—
342C3×C4⋊C4—62no—
343C3×C4⋊C4—62no—
344C3×C4⋊C4—121no—
345C3×C4⋊C4—121no—
346C3×C42—62no—
347C3×C42—62no—
348C3×C42—62no—
349C3×C42—62no—
350(C2×D3)⋊C4—62no—
351(C2×D3)⋊C4—62no—
352(C2×D3)⋊C4—62no—
353(C2×D3)⋊C4—62no—
354(C2×D3)⋊C4—62no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4—62no—
357(C2×D3)⋊C4—62no—
358(C2×D3)⋊C4—62no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—62no—
365(C2×D3)⋊C4—62no—
366(C2×D3)⋊C4—62no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—122no—
369(C2×D3)⋊C4—122no—
370(C2×D3)⋊C4—121no—
371(C2×D3)⋊C4—121no—
372(C2×D3)⋊C4—121no—
373(C2×D3)⋊C4—121no—
374(C2×D3)⋊C4—122no—
375C4⋊Dic3—41no—
376C4⋊Dic3—62no—
377Dic3⋊C4—22no—
378Dic3⋊C4—22no—
379Dic3⋊C4—22no—
380Dic3⋊C4—22no—
381Dic3⋊C4—34no—
382Dic3⋊C4—34no—
383Dic3⋊C4—41no—
384Dic3⋊C4—62no—
385Dic3⋊C4—62no—
386Dic3⋊C4—62no—
387Dic3⋊C4—121no—
388Dic3⋊C4—121no—
389C4×Dic3—22no—
390C4×Dic3—22no—
391C4×Dic3—22no—
392C4×Dic3—22no—
393C22×C32C22×D411yescharacteristic
394C22×C32C2×#4111yescharacteristic
395C22×C32C2×#4111yescharacteristic
396C22×C32C2×#4111yescharacteristic
397C22×C32C2×#4111yescharacteristic
398C22×C32H(5,𝔽2)11yescharacteristic
399C22×C322−1+411yescharacteristic
400C2×C3⋊D3—22no—
401C2×C3⋊D3—22no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C32×C4—22no—
415C32×C4—22no—
416C32×C4—41no—
417C3⋊Dic3—22no—
418C3⋊Dic3—41no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4—91no—
428C23×C4—91no—
429#126—184no—
430#117—184no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—31no—
437C2×C4⋊C4—91no—
438C2×C4⋊C4—91no—
439C2×C4⋊C4—91no—
440C2×C4⋊C4—91no—
441C2×C22⋊C4—91no—
442C2×C22⋊C4—91no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C22⋊C4—91no—
447C2×C22⋊C4—91no—
448C2×C22⋊C4—91no—
449C2×C22⋊C4—91no—
450C2×C22⋊C4—91no—
451C2×C22⋊C4—91no—
452C2×C42—31no—
453C2×C42—31no—
454C2×C42—31no—
455C2×C42—31no—
456#95—31no—
457#95—31no—
458#95—91no—
459#95—91no—
460#95—91no—
461#95—91no—
462#95—91no—
463#95D3211yescharacteristic
464C23×C3—21no—
465C23×C3C23×D311yescharacteristic
466C23×C3C23×D311yescharacteristic
467C22×D3—32no—
468C22×D3—32no—
469C22×D3—62no—
470C22×D3—62no—
471C22×D3—62no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—62no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—121no—
500C22×D3—121no—
501C22×D3—121no—
502C22×D3—121no—
503C22×D3—121no—
504C22×D3—121no—
505C22×D3—121no—
506C22×D3—121no—
507C22×D3—121no—
508C22×D3—121no—
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—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—22no—
524C2×C3×C4—22no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—32no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4#23512yes—
557C2×C3×C4#23512yes—
558C2×C3×C4#23512yes—
559C2×C3×C4#23912yes—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—32no—
582C2×Dic3—32no—
583C2×Dic3—62no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3#23512yes—
600C2×Dic3D3×D412yes—
601C2×Dic3D3×D412yes—
602D12—124no—
603D12—124no—
604D12—128no—
605C4×D3—68no—
606C4×D3—68no—
607C4×D3—128no—
608C2×C32#52511yescharacteristic
609C2×C32#52911yescharacteristic
610C2×C32#54211yescharacteristic
611C2×C32#54711yescharacteristic
612C2×C32#55011yescharacteristic
613C2×C32#55111yescharacteristic
614C2×C32#55211yescharacteristic
615C3⋊D3—42no—
616C3⋊D3—81no—
617C24—91no—
618C24—91no—
619C2×D4—182no—
620C2×D4—182no—
621C2×D4—361no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—91no—
631C22×C4—91no—
632C22×C4—182no—
633C22×C4—182no—
634C22×C4—182no—
635C22×C4C2×D3211yescharacteristic
636C22×C4C2×D3211yescharacteristic
637C22×C4C2×D3211yescharacteristic
638C4⋊C4—62no—
639C4⋊C4—62no—
640C4⋊C4—62no—
641C4⋊C4—62no—
642C4⋊C4—94no—
643C4⋊C4—121no—
644C4⋊C4—121no—
645C4⋊C4—182no—
646C4⋊C4—182no—
647C4⋊C4—361no—
648C22⋊C4—182no—
649C22⋊C4—182no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C22⋊C4—182no—
653C22⋊C4—182no—
654C22⋊C4—182no—
655C22⋊C4—182no—
656C22⋊C4—182no—
657C22⋊C4—361no—
658C22⋊C4—361no—
659C42—62no—
660C42—62no—
661C42—62no—
662C42—62no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3C2×#23511yescharacteristic
671C22×C3C2×#23511yescharacteristic
672C22×C3C2×#23511yescharacteristic
673C22×C3C2×#23511yescharacteristic
674C22×C3C2×D3×D411yescharacteristic
675C22×C3C2×D3×D411yescharacteristic
676C22×C3#100411yescharacteristic
677C22×C3C2×#23911yescharacteristic
678C22×C3#100711yescharacteristic
679C22×C3#100711yescharacteristic
680C22×C3D3×#4111yescharacteristic
681C22×C3D3×#4111yescharacteristic
682C22×C3D3×#4111yescharacteristic
683C22×C3#100911yescharacteristic
684C2×D3—64no—
685C2×D3—62no—
686C2×D3—62no—
687C2×D3—62no—
688C2×D3—62no—
689C2×D3—62no—
690C2×D3—62no—
691C2×D3—122no—
692C2×D3—122no—
693C2×D3—122no—
694C2×D3—122no—
695C2×D3—122no—
696C2×D3—122no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—122no—
706C2×D3—122no—
707C2×D3—122no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
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—121no—
721C2×D3—121no—
722C2×D3—241no—
723C2×D3—241no—
724C2×D3—241no—
725C2×D3—241no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—42no—
731C3×C4—42no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—62no—
735C3×C4—62no—
736C3×C4—62no—
737C3×C4—81no—
738C3×C4—121no—
739C3×C4—121no—
740C3×C4—121no—
741C3×C4—121no—
742C3×C4—121no—
743Dic3—22no—
744Dic3—22no—
745Dic3—22no—
746Dic3—41no—
747Dic3—41no—
748Dic3—41no—
749Dic3—41no—
750Dic3—41no—
751Dic3—62no—
752Dic3—62no—
753Dic3—122no—
754Dic3—121no—
755Dic3—121no—
756Dic3—241no—
757C32#247911yescharacteristic, complemented, Sylow
758C23—92no—
759C23—181no—
760C23—181no—
761C23—181no—
762C23—181no—
763C23—181no—
764C23—181no—
765C23—181no—
766C23—181no—
767C23—181no—
768C23—181no—
769C23—181no—
770C23—181no—
771C23—181no—
772C23C22×D3211yescharacteristic
773D4—364no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—32no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—92no—
806C2×C4—188no—
807C2×C4—181no—
808C2×C4—181no—
809C2×C4—181no—
810C2×C4—181no—
811C2×C4—181no—
812C2×C4#379812yes—
813C2×C4#379912yes—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3#547911yescharacteristic
822C2×C3#550711yescharacteristic
823C2×C3#550711yescharacteristic
824C2×C3#552711yescharacteristic
825C2×C3#554711yescharacteristic
826C2×C3#555311yescharacteristic
827C2×C3#555611yescharacteristic
828C2×C3#558011yescharacteristic
829C2×C3#558111yescharacteristic
830C2×C3#558211yescharacteristic
831C2×C3#559911yescharacteristic
832C2×C3#562711yescharacteristic
833C2×C3#569311yescharacteristic
834C2×C3#573311yescharacteristic
835D3—124no—
836D3—122no—
837D3—122no—
838D3—242no—
839D3—241no—
840D3—241no—
841C22—182no—
842C22—182no—
843C22—182no—
844C22—361no—
845C22—361no—
846C22—361no—
847C22—361no—
848C22—361no—
849C22—361no—
850C22—361no—
851C22—361no—
852C22—361no—
853C22—361no—
854C22—361no—
855C22C2×#379811yescharacteristic
856C22C2×#379911yescharacteristic
857C22D3×#23511yescharacteristic
858C22D32×D411yescharacteristic
859C22#6431211yescharacteristic
860C22#6431411yescharacteristic
861C22#6431611yescharacteristic
862C4—22no—
863C4—22no—
864C4—41no—
865C4—62no—
866C4—62no—
867C4—62no—
868C4—121no—
869C4—121no—
870C4—121no—
871C4—121no—
872C4—121no—
873C4—182no—
874C4—361no—
875C3—21no—
876C3#7368111yescharacteristic, complemented
877C3#7602711yescharacteristic, complemented
878C2—362no—
879C2—721no—
880C2#1059387011yescharacteristic
881C2#1059404011yescharacteristic
882C2#1059406611yescharacteristic
883C2#1059424611yescharacteristic
884C2#1059434911yescharacteristic
885C2#1059435211yescharacteristic
886C2#1059451211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#95D32
hypocenterC32#2479
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63874C2semidirect
2. C2×#63868C2semidirect
4. C3×#4649C2semidirect
5. C3×#4647C2semidirect
6. #10591345C2semidirect
9. #10591290C2semidirect
10. #10591289C2semidirect
11. #10591289C2semidirect
12. #10591203C2semidirect
13. #10591203C2semidirect
14. #10591202C2semidirect
15. #10591193C2semidirect
84. #4649D3semidirect
85. #4647D3semidirect
122. #3724D4semidirect
757. C32#2479semidirect
876. C3#73681semidirect
877. C3#76027semidirect

Maximal subgroups

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

subgroupindex
C2×#638742
C2×#638682
#105923642
C3×#46492
C3×#46472
#105913452
#105913212
#105913202
#105912902
#105912892
#105912032
#105912022
#105911932
#760273
#736813