Finite Group Databasebeta

← #11805804

Subgroups — #11805804

Order 1152.

1253 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63879C211yesmaximal, characteristic
2#10592354C211yesmaximal, characteristic, complemented
3C3×#4670C211yesmaximal, characteristic, complemented
4C3×D3×#95C211yesmaximal, characteristic, complemented
5#10591381C211yesmaximal, characteristic
6#10591381C211yesmaximal, characteristic
7#10591368C211yesmaximal, characteristic, complemented
8#10591362C211yesmaximal, characteristic, complemented
9#10591316C211yesmaximal, characteristic, complemented
10#10591313C211yesmaximal, characteristic, complemented
11C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
12#10591263C211yesmaximal, characteristic, complemented
13#10591248C211yesmaximal, characteristic, complemented
14#10591239C211yesmaximal, characteristic, complemented
15#10591237C211yesmaximal, characteristic, complemented
16#75835—31nomaximal
17#73336—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#625C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39#63879C418yescomplemented
40C32×#95C2211yescharacteristic
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C4×#67—31no—
55C2×#67⋊C4—31no—
56C3×#388—31no—
57C2×C3×#95—31no—
58#5213—31no—
59#5213—31no—
60#5212—31no—
61C4×#217—31no—
62C4×#217—31no—
63#4987—31no—
64#4978—31no—
65#4956—31no—
66#4956—31no—
67#4951—31no—
68#4943—31no—
69Dic3×C22⋊C4—31no—
70C4×(C2×D3)⋊C4—31no—
71#4932—31no—
72#4670—31no—
73#4670D311yescharacteristic, complemented
74#4666—31no—
75#4666—31no—
76#4664—31no—
77D3×#95D311yescharacteristic, complemented
78#4655—31no—
79#4655—31no—
80#4655—31no—
81#4655—61no—
82#4651—31no—
83#4651—31no—
84#4648—31no—
85C23×C3×D3C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×C3×C4×D3—22no—
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—41no—
105C2×C3×C4×D3—41no—
106C2×C3×C4×D3—41no—
107C2×C3×C4×D3—41no—
108C2×C3×C4×D3C2×C414yes—
109C2×#625—22no—
110C2×#625—22no—
111C2×#625C2×C414yes—
112C2×D3×Dic3—41no—
113C2×D3×Dic3—41no—
114C2×D3×Dic3C2×C414yescomplemented
115C4⋊(C3⋊Dic3)—41no—
116#3750C2×C414yescomplemented
117C4×C3⋊Dic3—41no—
118C3×(C2×D3)⋊C4—22no—
119C3×(C2×D3)⋊C4—41no—
120C3×(C2×D3)⋊C4C2×C414yescomplemented
121C3×C4⋊Dic3—41no—
122C3×C4×Dic3—22no—
123(C2×D3)⋊Dic3—22no—
124(C2×D3)⋊Dic3—22no—
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—41no—
127(C2×D3)⋊Dic3C2×C414yes—
128Dic32—22no—
129Dic32—41no—
130Dic32C2×C414yescomplemented
131#2353—91noSylow
132C23×C3×C4—31no—
133C23×C3×C4—31no—
134C23×C3×C4—31no—
135C22×#67—31no—
136C22×#67—31no—
137C23×Dic3—31no—
138C22×C4×D3—31no—
139C22×C4×D3C2×D311yescharacteristic
140C22×C4×D3C2×D311yescharacteristic
141C22×C4×D3C2×D311yescharacteristic
142C2×C3×C4⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C42—31no—
147C2×#217—31no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C4×#67—38no—
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)⋊C4C2×D311yescharacteristic
159C2×(C2×D3)⋊C4C2×D311yescharacteristic
160C2×(C2×D3)⋊C4C2×D311yescharacteristic
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—61no—
164C2×C4⋊Dic3C2×D311yescharacteristic
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—61no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—61no—
177C2×C4×Dic3C2×D311yescharacteristic
178#67⋊C4—38no—
179C3×#95—21no—
180C3×#95—31no—
181C3×#95—31no—
182C3×#95—31no—
183C3×#95—31no—
184C3×#95C2×D311yescharacteristic
185C3×#95C2×D311yescharacteristic
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—61no—
205C3⋊#95—61no—
206C3⋊#95—61no—
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C23×C32C2411yescharacteristic
212C22×C3×D3—21no—
213C22×C3×D3—21no—
214C22×C3×D3—21no—
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×D3C22×C412yes—
223C22×C3×D3C22×C412yes—
224C22×C3×D3#4112yes—
225C22×C3×D3#4112yes—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4C22×C412yes—
234C2×C32×C4#4112yes—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C22×C412yes—
246C2×C3⋊Dic3C22×C412yes—
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×Dic3C22×C412yes—
263C2×C3×Dic3C22×C412yes—
264C2×C3×Dic3#4112yes—
265C3×C4×D3—44no—
266C3×C4×D3—44no—
267C3×C4×D3—44no—
268#625—28no—
269D3×Dic3—44no—
270C2×C4×D4—91no—
271#388—31no—
272#388—91no—
273#387—91no—
274#387—91no—
275#386—91no—
276#386—91no—
277#383—91no—
278#381—91no—
279#380—91no—
280C4×C22⋊C4—91no—
281C4×C22⋊C4—91no—
282C4×C22⋊C4—91no—
283#376—91no—
284C2×#95—31no—
285C24×C3—31no—
286C24×C3—31no—
287C23×D3C22×D311yescharacteristic
288C23×D3C22×D311yescharacteristic
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—34no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—62no—
300C22×C3×C4—62no—
301C22×C3×C4—62no—
302C22×C3×C4—62no—
303C22×C3×C4—121no—
304C22×C3×C4—121no—
305C22×C3×C4—121no—
306C22×C3×C4—121no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C2×#67—34no—
314C2×#67—34no—
315C2×#67—62no—
316C2×#67—62no—
317C2×#67—62no—
318C2×#67—62no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—34no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—121no—
333C22×Dic3—121no—
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D311yescharacteristic
338C22×Dic3C22×D311yescharacteristic
339C22×Dic3C22×D311yescharacteristic
340C2×C4×D3—22no—
341C2×C4×D3—22no—
342C2×C4×D3—22no—
343C2×C4×D3—22no—
344C2×C4×D3—34no—
345C2×C4×D3—41no—
346C2×C4×D3—41no—
347C2×C4×D3—41no—
348C2×C4×D3—41no—
349C2×C4×D3—121no—
350C2×C4×D3—121no—
351C2×C4×D3C4×D314yes—
352C3×C4⋊C4—121no—
353C3×C22⋊C4—34no—
354C3×C22⋊C4—62no—
355C3×C22⋊C4—121no—
356C3×C42—62no—
357#217—34no—
358#217—62no—
359#217—62no—
360#217—62no—
361#217—121no—
362(C2×D3)⋊C4—22no—
363(C2×D3)⋊C4—34no—
364(C2×D3)⋊C4—41no—
365(C2×D3)⋊C4—62no—
366(C2×D3)⋊C4—62no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—121no—
369(C2×D3)⋊C4C4×D314yescomplemented
370C4⋊Dic3—41no—
371C4⋊Dic3—121no—
372C4⋊Dic3—121no—
373C4⋊Dic3—122no—
374Dic3⋊C4—34no—
375Dic3⋊C4—34no—
376Dic3⋊C4—64no—
377C4×Dic3—22no—
378C4×Dic3—34no—
379C4×Dic3—34no—
380C4×Dic3—62no—
381C4×Dic3—62no—
382C4×Dic3—121no—
383C4×Dic3—121no—
384C4×Dic3—121no—
385C4×Dic3—121no—
386C4×Dic3—122no—
387C22×C32C23×C411yescharacteristic
388C22×C32C2×#4111yescharacteristic
389C22×C32C2×#4111yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32H(5,𝔽2)11yescharacteristic
393C22×C32H(5,𝔽2)11yescharacteristic
394C2×C3×D3—22no—
395C2×C3×D3—22no—
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3—22no—
399C2×C3×D3—22no—
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#11714yes—
408C32×C4—22no—
409C32×C4—22no—
410C32×C4—41no—
411C3⋊Dic3—22no—
412C3⋊Dic3—22no—
413C3⋊Dic3—41no—
414C3⋊Dic3—41no—
415C3×Dic3—22no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C22×D4—91no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—31no—
425C23×C4—91no—
426C4×D4—98no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—91no—
429C2×C4⋊C4—91no—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—91no—
434C2×C22⋊C4—91no—
435C2×C22⋊C4—91no—
436C2×C22⋊C4—91no—
437C2×C22⋊C4—91no—
438C2×C42—31no—
439C2×C42—91no—
440C2×C42—91no—
441C2×C42—91no—
442C2×C42—91no—
443#95—31no—
444#95—31no—
445#95—31no—
446#95—31no—
447#95—91no—
448#95—91no—
449#95—91no—
450#95—91no—
451#95—91no—
452#95—91no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95D3211yescharacteristic
457C23×C3—21no—
458C23×C3—32no—
459C23×C3—32no—
460C23×C3—32no—
461C23×C3—32no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3C23×D311yescharacteristic
473C23×C3C23×D311yescharacteristic
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3C2×C4×D312yes—
485C22×D3C2×C4×D312yes—
486C22×D3#23712yes—
487C22×D3#23912yes—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—32no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—124no—
530C2×C3×C4—124no—
531C2×C3×C4—124no—
532C2×C3×C4C2×C4×D312yes—
533C2×C3×C4C2×C4×D312yes—
534C2×C3×C4#23512yes—
535C2×C3×C4#23712yes—
536#67—68no—
537#67—68no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—32no—
554C2×Dic3—32no—
555C2×Dic3—32no—
556C2×Dic3—32no—
557C2×Dic3—62no—
558C2×Dic3—62no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—62no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—121no—
581C2×Dic3—121no—
582C2×Dic3—121no—
583C2×Dic3—121no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—124no—
590C2×Dic3C2×C4×D312yes—
591C2×Dic3C2×C4×D312yes—
592C2×Dic3#23512yes—
593C4×D3—44no—
594C4×D3—44no—
595C4×D3—44no—
596C4×D3—124no—
597C2×C32C2×#11711yescharacteristic
598C2×C32C4×#4111yescharacteristic
599C2×C32#51811yescharacteristic
600C2×C32#55111yescharacteristic
601C2×C32#55111yescharacteristic
602C2×C32#55311yescharacteristic
603C2×C32#55311yescharacteristic
604C3×D3—24no—
605C3×D3—42no—
606C24—31no—
607C24—31no—
608C2×D4—94no—
609C2×D4—182no—
610C2×D4—182no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—34no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—62no—
619C22×C4—62no—
620C22×C4—62no—
621C22×C4—62no—
622C22×C4—94no—
623C22×C4—91no—
624C22×C4—91no—
625C22×C4—91no—
626C22×C4—91no—
627C22×C4—121no—
628C22×C4—121no—
629C22×C4—121no—
630C22×C4—121no—
631C22×C4—361no—
632C22×C4—361no—
633C22×C4C2×D3211yescharacteristic
634C22×C4C2×D3211yescharacteristic
635C22×C4C2×D3211yescharacteristic
636C4⋊C4—94no—
637C4⋊C4—121no—
638C4⋊C4—361no—
639C22⋊C4—34no—
640C22⋊C4—62no—
641C22⋊C4—94no—
642C22⋊C4—121no—
643C22⋊C4—182no—
644C22⋊C4—182no—
645C22⋊C4—182no—
646C22⋊C4—361no—
647C42—62no—
648C42—94no—
649C42—182no—
650C42—361no—
651C42—361no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—34no—
660C22×C3—62no—
661C22×C3—62no—
662C22×C3—62no—
663C22×C3—62no—
664C22×C3—62no—
665C22×C3—62no—
666C22×C3—62no—
667C22×C3—62no—
668C22×C3—62no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3C22×C4×D311yescharacteristic
674C22×C3C22×C4×D311yescharacteristic
675C22×C3C2×#23511yescharacteristic
676C22×C3C2×#23511yescharacteristic
677C22×C3C2×#23711yescharacteristic
678C22×C3C2×#23711yescharacteristic
679C22×C3#100411yescharacteristic
680C22×C3#100411yescharacteristic
681C22×C3#100411yescharacteristic
682C22×C3C2×#23911yescharacteristic
683C22×C3D3×#4111yescharacteristic
684C22×C3D3×#4111yescharacteristic
685C22×C3D3×#4111yescharacteristic
686C22×C3#100911yescharacteristic
687C2×D3—22no—
688C2×D3—22no—
689C2×D3—22no—
690C2×D3—22no—
691C2×D3—22no—
692C2×D3—22no—
693C2×D3—22no—
694C2×D3—22no—
695C2×D3—22no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3#89214yes—
701C3×C4—22no—
702C3×C4—22no—
703C3×C4—22no—
704C3×C4—22no—
705C3×C4—42no—
706C3×C4—42no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4—62no—
710C3×C4—62no—
711C3×C4—62no—
712C3×C4—81no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4—121no—
716Dic3—22no—
717Dic3—22no—
718Dic3—22no—
719Dic3—41no—
720Dic3—41no—
721Dic3—41no—
722Dic3—62no—
723Dic3—62no—
724Dic3—62no—
725Dic3—62no—
726Dic3—122no—
727Dic3—122no—
728Dic3—122no—
729Dic3—121no—
730Dic3—121no—
731Dic3—121no—
732Dic3—121no—
733Dic3—241no—
734C32#235311yescharacteristic, complemented, Sylow
735C23—32no—
736C23—32no—
737C23—32no—
738C23—32no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—61no—
747C23—61no—
748C23—61no—
749C23C22×D3211yescharacteristic
750D4—188no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—32no—
759C2×C4—32no—
760C2×C4—32no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—92no—
777C2×C4—92no—
778C2×C4—124no—
779C2×C4—124no—
780C2×C4—124no—
781C2×C4—181no—
782C2×C4—181no—
783C2×C4—181no—
784C2×C4—181no—
785C2×C4—181no—
786C2×C4—181no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—364no—
792C2×C4#379512yes—
793C2×C4C4×D3212yes—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—64no—
802C2×C3—122no—
803C2×C3C4×#23511yescharacteristic
804C2×C3#548611yescharacteristic
805C2×C3#549511yescharacteristic
806C2×C3#549511yescharacteristic
807C2×C3C2×#89211yescharacteristic
808C2×C3#551411yescharacteristic
809C2×C3#551411yescharacteristic
810C2×C3D3×#11711yescharacteristic
811C2×C3C4×#23711yescharacteristic
812C2×C3#554511yescharacteristic
813C2×C3#561411yescharacteristic
814C2×C3#565811yescharacteristic
815C2×C3#567911yescharacteristic
816C2×C3#570911yescharacteristic
817D3—24no—
818D3—42no—
819C22—34no—
820C22—62no—
821C22—62no—
822C22—62no—
823C22—62no—
824C22—62no—
825C22—62no—
826C22—62no—
827C22—62no—
828C22—62no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22C2×#379511yescharacteristic
834C22C2×C4×D3211yescharacteristic
835C22D3×#23511yescharacteristic
836C22D3×#23711yescharacteristic
837C22#6431311yescharacteristic
838C22#6431411yescharacteristic
839C22D3×#23911yescharacteristic
840C4—22no—
841C4—22no—
842C4—41no—
843C4—62no—
844C4—62no—
845C4—62no—
846C4—121no—
847C4—121no—
848C4—121no—
849C4—182no—
850C4—182no—
851C4—361no—
852C4—361no—
853C3—21no—
854C3#7333611yescharacteristic, complemented
855C3#7583511yescharacteristic, complemented
856C2—64no—
857C2—122no—
858C2C4×#379511yescharacteristic
859C2#1059409211yescharacteristic
860C2#1059421111yescharacteristic
861C2#1059425411yescharacteristic
862C2#1059454511yescharacteristic
863C2#1059456011yescharacteristic
864C2D3×#89211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenter#95D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592354C2semidirect
3. C3×#4670C2semidirect
4. C3×D3×#95C2semidirect
7. #10591368C2semidirect
8. #10591362C2semidirect
9. #10591316C2semidirect
10. #10591313C2semidirect
11. C4×(C2×D3)⋊Dic3C2semidirect
12. #10591263C2semidirect
13. #10591248C2semidirect
14. #10591239C2semidirect
15. #10591237C2semidirect
39. #63879C4semidirect
73. #4670D3semidirect
77. D3×#95D3semidirect
114. C2×D3×Dic3C2×C4semidirect
116. #3750C2×C4semidirect
120. C3×(C2×D3)⋊C4C2×C4semidirect
130. Dic32C2×C4semidirect
369. (C2×D3)⋊C4C4×D3semidirect
734. C32#2353semidirect
854. C3#73336semidirect
855. C3#75835semidirect

Maximal subgroups

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

subgroupindex
C2×#638792
#105923542
C3×#46702
C3×D3×#952
#105913812
#105913682
#105913622
#105913162
#105913132
C4×(C2×D3)⋊Dic32
#105912632
#105912482
#105912392
#105912372
#758353
#733363