Finite Group Databasebeta

← #11817782

Subgroups — #11817782

Order 1152.

1131 conjugacy classes of subgroups.

The subgroup lattice has 871 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#877C211yesmaximal, characteristic, complemented
2C2×#63862C211yesmaximal, characteristic, complemented
3#10592643C211yesmaximal, characteristic, complemented
4C3×#4957C211yesmaximal, characteristic
5#10591718C211yesmaximal, characteristic, complemented
6#10591715C211yesmaximal, characteristic, complemented
7#10591710C211yesmaximal, characteristic
8#10591709C211yesmaximal, characteristic
9#10591330C211yesmaximal, characteristic, complemented
10C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
11#10591305C211yesmaximal, characteristic, complemented
12#10591303C211yesmaximal, characteristic, complemented
13#10591279C211yesmaximal, characteristic, complemented
14#10591201C211yesmaximal, characteristic, complemented
15#10591200C211yesmaximal, characteristic, complemented
16#82253—31nomaximal
17#76332—31nomaximal
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C3×#877—24no—
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46#63862—24no—
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×C3×#117—31no—
56C2×#898—31no—
57C2×#879—31no—
58C2×#877D311yescharacteristic, complemented
59C3×#390—31no—
60#5222—31no—
61#5220—31no—
62#5213—31no—
63#5210—31no—
64#4993—31no—
65#4983—31no—
66#4982—31no—
67#4980—31no—
68#4976—31no—
69#4961—31no—
70#4957D311yescharacteristic
71#4951—31no—
72#4950—31no—
73#4949—31no—
74#4949—31no—
75#4949—31no—
76#4944—31no—
77#4944—31no—
78#4944—31no—
79#4944—61no—
80#4940—31no—
81#4940—31no—
82C4×C4⋊Dic3—31no—
83#4933—31no—
84C4×Dic3⋊C4—31no—
85#4928—31no—
86C24×C32C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C3×#67—22no—
95C2×C3×#67—22no—
96C2×C3×#67—41no—
97C22×C3×Dic3—22no—
98C22×C3×Dic3—22no—
99C22×C3×Dic3—22no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C32×C22⋊C4—22no—
108#3757—22no—
109#3757—41no—
110#3750—41no—
111C4×C3⋊Dic3—22no—
112C3×#217—22no—
113C3×#217—22no—
114C3×(C2×D3)⋊C4—22no—
115C3×(C2×D3)⋊C4—22no—
116C3×Dic3⋊C4—22no—
117C3×Dic3⋊C4—41no—
118C3×Dic3⋊C4D414yescomplemented
119C3×C4×Dic3—22no—
120C3×C4×Dic3—22no—
121C3×C4×Dic3—22no—
122#3724—41no—
123Dic3⋊Dic3—22no—
124Dic3⋊Dic3—22no—
125Dic3⋊Dic3—22no—
126Dic3⋊Dic3—22no—
127Dic3⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129(C2×D3)⋊Dic3—22no—
130(C2×D3)⋊Dic3—22no—
131(C2×D3)⋊Dic3—41no—
132#2479—91noSylow
133C22×C3×D4—31no—
134C23×C3×C4—31no—
135C22×#67C2×D311yescharacteristic
136C23×Dic3C2×D311yescharacteristic
137C3×#117—64no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4C2×D311yescharacteristic
147C2×C3×C22⋊C4C2×D311yescharacteristic
148C2×C3×C42—31no—
149C2×C3×C42—31no—
150C2×C3×C42—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×#217—31no—
155C2×#217—31no—
156C2×#217—31no—
157C2×#217—31no—
158C2×#217—31no—
159C2×#217—61no—
160C2×#217—61no—
161C2×#217C2×D311yescharacteristic
162C2×#217C2×D311yescharacteristic
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4C2×D311yescharacteristic
168C2×(C2×D3)⋊C4C2×D311yescharacteristic
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
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—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—61no—
184C2×Dic3⋊C4C2×D311yescharacteristic
185C2×Dic3⋊C4C2×D311yescharacteristic
186C2×Dic3⋊C4C2×D311yescharacteristic
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—61no—
190C2×C4×Dic3C2×D311yescharacteristic
191C2×C4×Dic3C2×D311yescharacteristic
192C2×C4×Dic3C2×D311yescharacteristic
193#898—64no—
194#879—64no—
195#877—24no—
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—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—61no—
213C3⋊#95—61no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32#4112yes—
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×D3—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4C2×D412yes—
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⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C3×#67—44no—
248C2×C3×Dic3—28no—
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×Dic3C2×D412yes—
266C2×C3×Dic3C2×D412yes—
267C2×C3×Dic3#4112yes—
268C2×C3×Dic3#4112yes—
269C2×C3×Dic3#4112yes—
270C2×#126—91no—
271C2×#117—31no—
272#399—91no—
273#399—91no—
274#398—91no—
275#394—91no—
276#390—31no—
277#389—91no—
278#388—91no—
279#388—91no—
280#388—91no—
281#387—91no—
282#386—91no—
283#385—91no—
284C4×C4⋊C4—91no—
285C24×C3—21no—
286C24×C3—31no—
287C24×C3C22×D311yescharacteristic
288C24×C3C22×D311yescharacteristic
289C23×D3C22×D311yescharacteristic
290C2×C3×D4—62no—
291C2×C3×D4—62no—
292C2×C3×D4—121no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
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×C4—62no—
303C22×C3×C4—62no—
304C22×C3×C4—62no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—22no—
310C2×#67—22no—
311C2×#67—41no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3—22no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C3×C4⋊C4—34no—
335C3×C4⋊C4—62no—
336C3×C4⋊C4—121no—
337C3×C22⋊C4—22no—
338C3×C22⋊C4—22no—
339C3×C22⋊C4—42no—
340C3×C22⋊C4—62no—
341C3×C22⋊C4—62no—
342C3×C22⋊C4—62no—
343C3×C22⋊C4—62no—
344C3×C42—62no—
345C3×C42—62no—
346C3×C42—62no—
347#217—22no—
348#217—22no—
349#217—64no—
350#217—62no—
351#217—62no—
352#217—62no—
353#217—62no—
354#217—62no—
355#217—121no—
356#217—121no—
357#217—121no—
358#217—122no—
359(C2×D3)⋊C4—22no—
360(C2×D3)⋊C4—22no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—121no—
365C4⋊Dic3—62no—
366C4⋊Dic3—62no—
367C4⋊Dic3—62no—
368C4⋊Dic3—62no—
369C4⋊Dic3—62no—
370Dic3⋊C4—22no—
371Dic3⋊C4—41no—
372Dic3⋊C4—62no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375Dic3⋊C4—62no—
376Dic3⋊C4—62no—
377Dic3⋊C4—121no—
378Dic3⋊C4—121no—
379Dic3⋊C4—121no—
380Dic3⋊C4—121no—
381Dic3⋊C4—122no—
382Dic3⋊C4#6714yescomplemented
383C4×Dic3—22no—
384C4×Dic3—22no—
385C4×Dic3—22no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C4×Dic3—122no—
389C22×C32—22no—
390C22×C32—22no—
391C22×C32—22no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32C22×D411yescharacteristic
397C22×C32C2×#4111yescharacteristic
398C22×C32C2×#4111yescharacteristic
399C22×C32C2×#4111yescharacteristic
400C22×C32C2×#4111yescharacteristic
401C22×C32H(5,𝔽2)11yescharacteristic
402C22×C322−1+411yescharacteristic
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—
410C32×C4—22no—
411C32×C4—41no—
412C3⋊Dic3—41no—
413C3⋊Dic3—41no—
414C3⋊Dic3—41no—
415C3⋊Dic3—41no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C22×D4—31no—
424C23×C4—31no—
425#126—184no—
426#117—64no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—91no—
431C2×C4⋊C4—91no—
432C2×C4⋊C4—91no—
433C2×C4⋊C4—91no—
434C2×C4⋊C4—91no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—91no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—31no—
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⋊C4D3211yescharacteristic
448C2×C42—31no—
449C2×C42—31no—
450C2×C42—31no—
451C2×C42—91no—
452#95—91no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459#95—91no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—22no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3#23512yes—
488C23×C3#23512yes—
489C23×C3C23×D311yescharacteristic
490C23×C3C23×D311yescharacteristic
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C3×D4—124no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—22no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—32no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—68no—
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—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4D3×D412yes—
538C2×C3×C4C2×#6712yes—
539#67—44no—
540C2×Dic3—28no—
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—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—62no—
558C2×Dic3—62no—
559C2×Dic3—62no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
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—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3—121no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3#23512yes—
594C2×Dic3#23712yes—
595C2×Dic3#23712yes—
596C2×Dic3C2×#6712yes—
597C2×Dic3C2×#6712yes—
598C2×C32—42no—
599C2×C32#52511yescharacteristic
600C2×C32#52911yescharacteristic
601C2×C32#54211yescharacteristic
602C2×C32#54711yescharacteristic
603C2×C32#55011yescharacteristic
604C2×C32#55111yescharacteristic
605C2×C32#55211yescharacteristic
606C3×D3—81no—
607C24—31no—
608C24C2×D3211yescharacteristic
609C2×D4—62no—
610C2×D4—62no—
611C2×D4—121no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—62no—
620C22×C4—62no—
621C22×C4—62no—
622C22×C4—91no—
623C22×C4—91no—
624C22×C4—91no—
625C22×C4—91no—
626C22×C4C2×D3211yescharacteristic
627C22×C4C2×D3211yescharacteristic
628C4⋊C4—34no—
629C4⋊C4—62no—
630C4⋊C4—121no—
631C4⋊C4—182no—
632C4⋊C4—182no—
633C4⋊C4—182no—
634C4⋊C4—182no—
635C4⋊C4—182no—
636C4⋊C4—361no—
637C4⋊C4—361no—
638C22⋊C4—22no—
639C22⋊C4—62no—
640C22⋊C4—62no—
641C22⋊C4—62no—
642C22⋊C4—62no—
643C22⋊C4—182no—
644C22⋊C4—182no—
645C22⋊C4—182no—
646C22⋊C4—182no—
647C22⋊C4—361no—
648C22⋊C4—361no—
649C42—62no—
650C42—62no—
651C42—62no—
652C42—182no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—81no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3C2×#23511yescharacteristic
689C22×C3C2×#23511yescharacteristic
690C22×C3C2×#23511yescharacteristic
691C22×C3C2×D3×D411yescharacteristic
692C22×C3C2×#23711yescharacteristic
693C22×C3C2×#23711yescharacteristic
694C22×C3#100411yescharacteristic
695C22×C3D3×#4111yescharacteristic
696C22×C3D3×#4111yescharacteristic
697C22×C3D3×#4111yescharacteristic
698C22×C3#100911yescharacteristic
699C22×C3#101011yescharacteristic
700C22×C3#101011yescharacteristic
701C22×C3C22×#6711yescharacteristic
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C3×C4—22no—
710C3×C4—22no—
711C3×C4—42no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—62no—
715C3×C4—62no—
716C3×C4—62no—
717C3×C4—62no—
718C3×C4—62no—
719C3×C4—81no—
720C3×C4—121no—
721C3×C4—121no—
722Dic3—22no—
723Dic3—22no—
724Dic3—22no—
725Dic3—22no—
726Dic3—22no—
727Dic3—41no—
728Dic3—41no—
729Dic3—122no—
730Dic3—122no—
731Dic3—122no—
732Dic3—121no—
733Dic3—121no—
734Dic3—121no—
735Dic3—121no—
736Dic3—121no—
737Dic3—121no—
738Dic3—121no—
739Dic3—121no—
740Dic3—241no—
741C32#247911yescharacteristic, complemented, Sylow
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—61no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23—61no—
755C23#379812yes—
756C23C22×D3211yescharacteristic
757D4—124no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—68no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—181no—
786C2×C4—181no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4D3×#6712yes—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—42no—
806C2×C3—42no—
807C2×C3—82no—
808C2×C3—241no—
809C2×C3#549511yescharacteristic
810C2×C3#552711yescharacteristic
811C2×C3#552811yescharacteristic
812C2×C3#553111yescharacteristic
813C2×C3#553411yescharacteristic
814C2×C3#554111yescharacteristic
815C2×C3#554711yescharacteristic
816C2×C3#560011yescharacteristic
817C2×C3#561111yescharacteristic
818C2×C3#566911yescharacteristic
819C2×C3#571811yescharacteristic
820C2×C3#579111yescharacteristic
821C2×C3#582411yescharacteristic
822C2×C3#583411yescharacteristic
823D3—81no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—121no—
832C22—121no—
833C22—121no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22C2×#379811yescharacteristic
839C22D3×#23511yescharacteristic
840C22#6430911yescharacteristic
841C22D3×#23711yescharacteristic
842C22D3×#23711yescharacteristic
843C22#6431411yescharacteristic
844C22C2×D3×#6711yescharacteristic
845C4—22no—
846C4—41no—
847C4—62no—
848C4—62no—
849C4—62no—
850C4—62no—
851C4—62no—
852C4—121no—
853C4—121no—
854C4—361no—
855C4—361no—
856C4—361no—
857C4—361no—
858C3—21no—
859C3#7633211yescharacteristic, complemented
860C3#8225311yescharacteristic, complemented
861C2—42no—
862C2—241no—
863C2#1059403711yescharacteristic
864C2#1059403911yescharacteristic
865C2#1059408611yescharacteristic
866C2#1059420711yescharacteristic
867C2#1059500211yescharacteristic
868C2#1059515111yescharacteristic
869C2#1059515811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2479
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#877C2semidirect
2. C2×#63862C2semidirect
3. #10592643C2semidirect
5. #10591718C2semidirect
6. #10591715C2semidirect
9. #10591330C2semidirect
10. C4×Dic3⋊Dic3C2semidirect
11. #10591305C2semidirect
12. #10591303C2semidirect
13. #10591279C2semidirect
14. #10591201C2semidirect
15. #10591200C2semidirect
58. C2×#877D3semidirect
118. C3×Dic3⋊C4D4semidirect
382. Dic3⋊C4#67semidirect
741. C32#2479semidirect
859. C3#76332semidirect
860. C3#82253semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8772
C2×#638622
#105926432
C3×#49572
#105917182
#105917152
#105917102
#105917092
#105913302
C4×Dic3⋊Dic32
#105913052
#105913032
#105912792
#105912012
#105912002
#822533
#763323