Finite Group Databasebeta

← #11801547

Subgroups — #11801547

Order 1152.

1487 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63904C211yesmaximal, characteristic
2C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
3C2×#63836C211yesmaximal, characteristic, complemented
4#10592368C211yesmaximal, characteristic, complemented
5C3×#4666C211yesmaximal, characteristic, complemented
6C3×#4652C211yesmaximal, characteristic, complemented
7#10591373C211yesmaximal, characteristic, complemented
8#10591372C211yesmaximal, characteristic, complemented
9#10591364C211yesmaximal, characteristic
10#10591364C211yesmaximal, characteristic
11#10591243C211yesmaximal, characteristic, complemented
12#10591239C211yesmaximal, characteristic, complemented
13#10591233C211yesmaximal, characteristic, complemented
14#10591202C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#74937—31nomaximal
17#73438—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×#626C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63904C418yescomplemented
44C4×D3×Dic3—24no—
45#63836—24no—
46C32×#95C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C4×#67—31no—
57C22×C4×Dic3—31no—
58C2×#893—31no—
59C2×#892—31no—
60C2×#872—31no—
61C2×C42×D3—31no—
62C3×#387—31no—
63C3×C4×C22⋊C4—31no—
64#4989—31no—
65#4980—31no—
66#4958—31no—
67#4958—31no—
68#4946—31no—
69#4946—31no—
70#4940—31no—
71C4×(C2×D3)⋊C4—31no—
72#4932—31no—
73C4×Dic3⋊C4—31no—
74#4669—31no—
75#4669—31no—
76#4669—31no—
77#4669—61no—
78#4668—31no—
79#4666—31no—
80#4666D311yescharacteristic, complemented
81#4665—31no—
82#4665—31no—
83#4652—31no—
84#4652D311yescharacteristic, complemented
85#4649—31no—
86#4648—31no—
87C23×C3⋊D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3C2×C414yes—
105C2×#626—22no—
106C2×#626—22no—
107C2×#626C2×C414yes—
108C2×#624—22no—
109C2×#624—22no—
110C2×#624C2×C414yescomplemented
111C2×D3×Dic3—22no—
112C2×D3×Dic3—22no—
113C2×D3×Dic3—22no—
114C2×D3×Dic3—22no—
115C2×D3×Dic3—22no—
116C2×D3×Dic3—22no—
117#3752—22no—
118#3752—22no—
119#3752C2×C414yescomplemented
120#3750—22no—
121C4×C3⋊Dic3—22no—
122C3×(C2×D3)⋊C4—22no—
123C3×(C2×D3)⋊C4—22no—
124C3×Dic3⋊C4—22no—
125C3×Dic3⋊C4C2×C414yescomplemented
126C3×C4×Dic3—22no—
127C3×C4×Dic3—22no—
128C3×C4×Dic3—22no—
129#3724—22no—
130Dic3⋊Dic3—22no—
131#3722—22no—
132#3722—22no—
133(C2×D3)⋊Dic3C2×C414yes—
134Dic32—22no—
135Dic32C2×C414yescomplemented
136Dic32D414yescomplemented
137#2290—91noSylow
138C23×C3×C4—31no—
139C22×#67—31no—
140C23×Dic3—31no—
141C23×Dic3—31no—
142C22×D12—31no—
143C22×C4×D3—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3C2×D311yescharacteristic
148C2×C3×C4⋊C4—31no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C22⋊C4—31no—
151C2×C3×C22⋊C4—31no—
152C2×C3×C42—31no—
153C2×C3×C42—31no—
154C2×C3×C42—31no—
155C2×#217—31no—
156C4×#67—38no—
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—61no—
169C2×(C2×D3)⋊C4—61no—
170C2×(C2×D3)⋊C4—61no—
171C2×(C2×D3)⋊C4C2×D311yescharacteristic
172C2×(C2×D3)⋊C4C2×D311yescharacteristic
173C2×C4⋊Dic3—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—61no—
180C2×Dic3⋊C4C2×D311yescharacteristic
181C2×Dic3⋊C4C2×D311yescharacteristic
182C2×C4×Dic3—31no—
183C2×C4×Dic3—31no—
184C2×C4×Dic3—31no—
185C2×C4×Dic3—31no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—61no—
191C2×C4×Dic3—64no—
192C2×C4×Dic3C2×D311yescharacteristic
193C2×C4×Dic3C2×D311yescharacteristic
194C2×C4×Dic3C2×D311yescharacteristic
195#893—38no—
196#892—64no—
197#872—64no—
198C42×D3—64no—
199C3×#95—21no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95C2×D311yescharacteristic
205C3×#95C2×D311yescharacteristic
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—61no—
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C23×C32C2411yescharacteristic
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⋊D3C22×C412yes—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3C22×C412yes—
234C22×C3×D3#4112yes—
235C22×C3×D3#4112yes—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C22×C412yes—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C22×C412yes—
252C2×C3⋊Dic3C2×D412yes—
253C2×C3⋊Dic3#4112yes—
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×Dic3—21no—
268C2×C3×Dic3C22×C412yes—
269C2×C3×Dic3C22×C412yes—
270C2×C3×Dic3C22×C412yes—
271C2×C3×Dic3C2×D412yes—
272C2×C3×Dic3C2×D412yes—
273C2×C3×Dic3#4112yes—
274C2×C3×Dic3#4112yes—
275C3×C4×D3—28no—
276#626—28no—
277#624—28no—
278D3×Dic3—28no—
279D3×Dic3—28no—
280C2×C4×D4—91no—
281C2×#117—91no—
282C22×C42—91no—
283#388—91no—
284#388—91no—
285#387—31no—
286#387—91no—
287#386—91no—
288#386—91no—
289#385—91no—
290#385—91no—
291C4×C4⋊C4—91no—
292C4×C22⋊C4—31no—
293C4×C22⋊C4—91no—
294#376—91no—
295C24×C3—31no—
296C23×D3—31no—
297C23×D3—31no—
298C23×D3—61no—
299C23×D3C22×D311yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—34no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—62no—
312C22×C3×C4—62no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C2×#67—34no—
320C2×#67—62no—
321C2×#67—62no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—62no—
332C22×Dic3—62no—
333C22×Dic3—62no—
334C22×Dic3—62no—
335C22×Dic3—62no—
336C22×Dic3—62no—
337C22×Dic3C22×D311yescharacteristic
338C22×Dic3C22×D311yescharacteristic
339C22×Dic3C22×D311yescharacteristic
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D311yescharacteristic
343C22×Dic3C22×D311yescharacteristic
344C2×D12—34no—
345C2×D12—62no—
346C2×D12—62no—
347C2×C4×D3—22no—
348C2×C4×D3—22no—
349C2×C4×D3—34no—
350C2×C4×D3—34no—
351C2×C4×D3—62no—
352C2×C4×D3—62no—
353C2×C4×D3—62no—
354C2×C4×D3—62no—
355C2×C4×D3—62no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3C4×D314yes—
362C3×C4⋊C4—34no—
363C3×C4⋊C4—62no—
364C3×C22⋊C4—62no—
365C3×C22⋊C4—62no—
366C3×C42—62no—
367C3×C42—62no—
368C3×C42—62no—
369#217—34no—
370(C2×D3)⋊C4—22no—
371(C2×D3)⋊C4—22no—
372(C2×D3)⋊C4—34no—
373(C2×D3)⋊C4—34no—
374(C2×D3)⋊C4—34no—
375(C2×D3)⋊C4—64no—
376(C2×D3)⋊C4—62no—
377(C2×D3)⋊C4—62no—
378(C2×D3)⋊C4—62no—
379(C2×D3)⋊C4—62no—
380(C2×D3)⋊C4—62no—
381(C2×D3)⋊C4—62no—
382(C2×D3)⋊C4—62no—
383(C2×D3)⋊C4—62no—
384(C2×D3)⋊C4—122no—
385(C2×D3)⋊C4—122no—
386C4⋊Dic3—62no—
387Dic3⋊C4—22no—
388Dic3⋊C4—62no—
389Dic3⋊C4—62no—
390Dic3⋊C4—62no—
391Dic3⋊C4—62no—
392Dic3⋊C4—62no—
393Dic3⋊C4—122no—
394Dic3⋊C4C4×D314yescomplemented
395C4×Dic3—22no—
396C4×Dic3—22no—
397C4×Dic3—22no—
398C4×Dic3—34no—
399C4×Dic3—34no—
400C4×Dic3—34no—
401C4×Dic3—34no—
402C4×Dic3—62no—
403C4×Dic3—62no—
404C4×Dic3—62no—
405C4×Dic3—62no—
406C4×Dic3—122no—
407C22×C32C23×C411yescharacteristic
408C22×C32C22×D411yescharacteristic
409C22×C32C2×#4111yescharacteristic
410C22×C32C2×#4111yescharacteristic
411C22×C32C2×#4111yescharacteristic
412C22×C32C2×#4111yescharacteristic
413C22×C32C2×#4111yescharacteristic
414C2×C3⋊D3—22no—
415C2×C3⋊D3—22no—
416C2×C3⋊D3—22no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3#11714yescomplemented
428C32×C4—22no—
429C32×C4—41no—
430C32×C4—41no—
431C3⋊Dic3—22no—
432C3⋊Dic3—22no—
433C3⋊Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3C4×D414yes—
441C22×D4—91no—
442C23×C4—31no—
443C23×C4—91no—
444C23×C4—91no—
445C23×C4—91no—
446C4×D4—98no—
447#117—184no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—91no—
451C2×C4⋊C4—91no—
452C2×C4⋊C4—91no—
453C2×C22⋊C4—31no—
454C2×C22⋊C4—31no—
455C2×C22⋊C4—91no—
456C2×C22⋊C4—91no—
457C2×C22⋊C4—91no—
458C2×C22⋊C4—91no—
459C2×C22⋊C4—91no—
460C2×C22⋊C4—91no—
461C2×C42—31no—
462C2×C42—31no—
463C2×C42—31no—
464C2×C42—91no—
465C2×C42—91no—
466C2×C42—91no—
467C2×C42—91no—
468C2×C42—184no—
469#95—31no—
470#95—31no—
471#95—31no—
472#95—31no—
473#95—91no—
474#95—91no—
475#95—91no—
476#95—91no—
477#95—91no—
478#95D3211yescharacteristic
479C23×C3—21no—
480C23×C3—32no—
481C23×C3—32no—
482C23×C3—32no—
483C23×C3—61no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3C23×D311yescharacteristic
488C23×C3C23×D311yescharacteristic
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—32no—
494C22×D3—32no—
495C22×D3—62no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—61no—
506C22×D3—61no—
507C22×D3—61no—
508C22×D3—121no—
509C22×D3—121no—
510C22×D3—121no—
511C22×D3—121no—
512C22×D3—121no—
513C22×D3—121no—
514C22×D3C2×C4×D312yes—
515C22×D3#23512yes—
516C22×D3#23512yes—
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—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—22no—
534C2×C3×C4—32no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—32no—
538C2×C3×C4—32no—
539C2×C3×C4—32no—
540C2×C3×C4—32no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—68no—
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—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4C2×C4×D312yes—
565C2×C3×C4C2×C4×D312yes—
566#67—68no—
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—32no—
584C2×Dic3—32no—
585C2×Dic3—32no—
586C2×Dic3—32no—
587C2×Dic3—62no—
588C2×Dic3—62no—
589C2×Dic3—62no—
590C2×Dic3—68no—
591C2×Dic3—68no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—121no—
605C2×Dic3—121no—
606C2×Dic3—121no—
607C2×Dic3—121no—
608C2×Dic3—121no—
609C2×Dic3—121no—
610C2×Dic3C2×C4×D312yes—
611C2×Dic3C2×C4×D312yes—
612C2×Dic3C2×C4×D312yes—
613C2×Dic3D3×D412yes—
614C2×Dic3D3×D412yes—
615C2×Dic3#23712yes—
616C2×Dic3#23912yes—
617D12—68no—
618C4×D3—28no—
619C4×D3—68no—
620C4×D3—68no—
621C4×D3—68no—
622C4×D3—68no—
623C2×C32C2×#11711yescharacteristic
624C2×C32C2×C4×D411yescharacteristic
625C2×C32C4×#4111yescharacteristic
626C2×C32#52511yescharacteristic
627C2×C32#52511yescharacteristic
628C2×C32#52911yescharacteristic
629C2×C32#52911yescharacteristic
630C3⋊D3—42no—
631C3×D3—24no—
632C24—31no—
633C24—91no—
634C2×D4—94no—
635C2×D4—182no—
636C2×D4—182no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—34no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—62no—
646C22×C4—62no—
647C22×C4—94no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4—182no—
652C22×C4—182no—
653C22×C4—182no—
654C22×C4—182no—
655C22×C4—182no—
656C22×C4—182no—
657C22×C4—182no—
658C22×C4—182no—
659C22×C4C2×D3211yescharacteristic
660C22×C4C2×D3211yescharacteristic
661C22×C4C2×D3211yescharacteristic
662C4⋊C4—34no—
663C4⋊C4—62no—
664C4⋊C4—182no—
665C4⋊C4—182no—
666C4⋊C4—182no—
667C22⋊C4—62no—
668C22⋊C4—62no—
669C22⋊C4—94no—
670C22⋊C4—94no—
671C22⋊C4—182no—
672C22⋊C4—182no—
673C22⋊C4—182no—
674C22⋊C4—182no—
675C42—62no—
676C42—62no—
677C42—62no—
678C42—94no—
679C42—94no—
680C42—182no—
681C42—182no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—34no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—62no—
695C22×C3—62no—
696C22×C3C22×C4×D311yescharacteristic
697C22×C3C22×C4×D311yescharacteristic
698C22×C3C2×#23511yescharacteristic
699C22×C3C2×#23511yescharacteristic
700C22×C3C2×D3×D411yescharacteristic
701C22×C3C2×D3×D411yescharacteristic
702C22×C3C2×#23711yescharacteristic
703C22×C3C2×#23911yescharacteristic
704C22×C3D3×#4111yescharacteristic
705C22×C3D3×#4111yescharacteristic
706C22×C3D3×#4111yescharacteristic
707C22×C3D3×#4111yescharacteristic
708C22×C3D3×#4111yescharacteristic
709C22×C3D3×#4111yescharacteristic
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—122no—
723C2×D3—122no—
724C2×D3—122no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—241no—
734C2×D3—241no—
735C2×D3—241no—
736C2×D3—241no—
737C2×D3#87214yescomplemented
738C3×C4—22no—
739C3×C4—22no—
740C3×C4—34no—
741C3×C4—42no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—41no—
746C3×C4—62no—
747C3×C4—62no—
748C3×C4—62no—
749C3×C4—62no—
750C3×C4—81no—
751C3×C4—81no—
752C3×C4—121no—
753C3×C4—121no—
754Dic3—22no—
755Dic3—22no—
756Dic3—22no—
757Dic3—22no—
758Dic3—41no—
759Dic3—41no—
760Dic3—62no—
761Dic3—62no—
762Dic3—62no—
763Dic3—62no—
764Dic3—62no—
765Dic3—62no—
766Dic3—122no—
767Dic3—122no—
768Dic3—122no—
769Dic3#67⋊C414yes—
770C32#229011yescharacteristic, complemented, Sylow
771C23—32no—
772C23—32no—
773C23—32no—
774C23—61no—
775C23—61no—
776C23—61no—
777C23—61no—
778C23—92no—
779C23—181no—
780C23—181no—
781C23—181no—
782C23—181no—
783C23—181no—
784C23—181no—
785C23C22×D3211yescharacteristic
786D4—188no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—32no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—32no—
799C2×C4—32no—
800C2×C4—32no—
801C2×C4—32no—
802C2×C4—68no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—92no—
818C2×C4—92no—
819C2×C4—92no—
820C2×C4—188no—
821C2×C4—188no—
822C2×C4—188no—
823C2×C4—181no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4—181no—
827C2×C4—181no—
828C2×C4—181no—
829C2×C4C4×D3212yes—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—64no—
838C2×C3C2×#87211yescharacteristic
839C2×C3C2×#67⋊C411yescharacteristic
840C2×C3D3×#11711yescharacteristic
841C2×C3#552211yescharacteristic
842C2×C3#553811yescharacteristic
843C2×C3#553811yescharacteristic
844C2×C3C4×D3×D411yescharacteristic
845C2×C3#554711yescharacteristic
846C2×C3#554711yescharacteristic
847C2×C3C4×#23911yescharacteristic
848C2×C3#562711yescharacteristic
849C2×C3#565611yescharacteristic
850C2×C3#569111yescharacteristic
851C2×C3#570611yescharacteristic
852D3—24no—
853D3—122no—
854D3—122no—
855D3—242no—
856C22—34no—
857C22—62no—
858C22—62no—
859C22—62no—
860C22—62no—
861C22—62no—
862C22—62no—
863C22—182no—
864C22—182no—
865C22—182no—
866C22—361no—
867C22—361no—
868C22—361no—
869C22—361no—
870C22C2×C4×D3211yescharacteristic
871C22D3×#23511yescharacteristic
872C22D3×#23511yescharacteristic
873C22D32×D411yescharacteristic
874C22D3×#23711yescharacteristic
875C22#6431211yescharacteristic
876C22D3×#23911yescharacteristic
877C4—22no—
878C4—34no—
879C4—41no—
880C4—41no—
881C4—62no—
882C4—62no—
883C4—62no—
884C4—62no—
885C4—121no—
886C4—121no—
887C4—182no—
888C4—182no—
889C4—182no—
890C3—21no—
891C3#7343811yescharacteristic, complemented
892C3#7493711yescharacteristic, complemented
893C2—64no—
894C2—362no—
895C2D3×#87211yescharacteristic
896C2#1059408911yescharacteristic
897C2D3×#67⋊C411yescharacteristic
898C2#1059426611yescharacteristic
899C2#1059436211yescharacteristic
900C2#1059440311yescharacteristic
901C2#1059462311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2290
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×Dic3C2semidirect
3. C2×#63836C2semidirect
4. #10592368C2semidirect
5. C3×#4666C2semidirect
6. C3×#4652C2semidirect
7. #10591373C2semidirect
8. #10591372C2semidirect
11. #10591243C2semidirect
12. #10591239C2semidirect
13. #10591233C2semidirect
14. #10591202C2semidirect
15. #10591192C2semidirect
43. #63904C4semidirect
80. #4666D3semidirect
84. #4652D3semidirect
110. C2×#624C2×C4semidirect
119. #3752C2×C4semidirect
125. C3×Dic3⋊C4C2×C4semidirect
135. Dic32C2×C4semidirect
136. Dic32D4semidirect
394. Dic3⋊C4C4×D3semidirect
427. C2×C3×D3#117semidirect
737. C2×D3#872semidirect
770. C32#2290semidirect
891. C3#73438semidirect
892. C3#74937semidirect

Maximal subgroups

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

subgroupindex
C2×#639042
C2×C4×D3×Dic32
C2×#638362
#105923682
C3×#46662
C3×#46522
#105913732
#105913722
#105913642
#105912432
#105912392
#105912332
#105912022
#105911922
#749373
#734383