Finite Group Databasebeta

← #11803931

Subgroups — #11803931

Order 1152.

1141 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#896C211yesmaximal, characteristic
2#10592683C211yesmaximal, characteristic, complemented
3C3×#4980C211yesmaximal, characteristic, complemented
4#10591379C211yesmaximal, characteristic
5#10591379C211yesmaximal, characteristic
6#10591368C211yesmaximal, characteristic
7Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic
8D3×C3⋊#95C211yesmaximal, characteristic
9#10591313C211yesmaximal, characteristic
10#10591272C211yesmaximal, characteristic, complemented
11#10591268C211yesmaximal, characteristic, complemented
12#10591262C211yesmaximal, characteristic, complemented
13#10591261C211yesmaximal, characteristic, complemented
14#10591220C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#82745—31nomaximal
17#75299—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C3×#896C418yescomplemented
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×C22⋊Q8—31no—
55C2×#896D311yescharacteristic
56C3×#387—31no—
57#5229—31no—
58#5229—31no—
59#5212—31no—
60C2×C3⋊#95—31no—
61#4987—31no—
62#4984—31no—
63#4984—31no—
64#4984—31no—
65#4984—61no—
66#4980—31no—
67#4980—31no—
68#4980—31no—
69#4980D311yescharacteristic, complemented
70#4978—31no—
71#4950—31no—
72#4950—31no—
73Dic3×C22⋊C4—31no—
74Dic3×C22⋊C4—31no—
75C4×(C2×D3)⋊C4—31no—
76#4929—31no—
77#4668—31no—
78#4668—31no—
79#4666—31no—
80D3×#95—31no—
81#4655—31no—
82#4652—31no—
83#4647—31no—
84#4646—31no—
85C23×C3×D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
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—41no—
101C2×C3×C4×D3—41no—
102C2×C3×C4×D3C2×C414yes—
103C2×C3×Dic6—41no—
104C2×C3×Dic6—41no—
105C2×C3×Dic6C2×C414yescomplemented
106C2×D3×Dic3—22no—
107C2×D3×Dic3—41no—
108C2×D3×Dic3—41no—
109C2×D3×Dic3—41no—
110C2×D3×Dic3—41no—
111C2×D3×Dic3Q814yescomplemented
112C32×C4⋊C4C2×C414yescomplemented
113C4⋊(C3⋊Dic3)—41no—
114C4⋊(C3⋊Dic3)—41no—
115C4⋊(C3⋊Dic3)—41no—
116C4×C3⋊Dic3—41no—
117C3×(C2×D3)⋊C4C2×C414yes—
118C3×(C2×D3)⋊C4C2×C414yes—
119C3×C4⋊Dic3—41no—
120C3×Dic3⋊C4C2×C414yescomplemented
121C3×Dic3⋊C4C2×C414yescomplemented
122C3×C4×Dic3—41no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3—41no—
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—22no—
127Dic32—41no—
128Dic32—41no—
129#2329—91noSylow
130C22×C3×Q8—31no—
131C23×C3×C4—31no—
132C23×Dic3—31no—
133C23×Dic3—31no—
134C22×C4×D3—31no—
135C22×C4×D3—31no—
136C22×C4×D3C2×D311yescharacteristic
137C22×Dic6C2×D311yescharacteristic
138C3×C22⋊Q8—38no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4C2×D311yescharacteristic
144C2×C3×C4⋊C4C2×D311yescharacteristic
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C42—31no—
148C2×#217—31no—
149C2×#217—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4C2×D311yescharacteristic
153C2×(C2×D3)⋊C4C2×D311yescharacteristic
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—61no—
163C2×C4⋊Dic3—61no—
164C2×C4⋊Dic3—61no—
165C2×C4⋊Dic3C2×D311yescharacteristic
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4C2×D311yescharacteristic
169C2×Dic3⋊C4C2×D311yescharacteristic
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#896Dic318yescomplemented
179C3×#95—31no—
180C3×#95—31no—
181C3×#95—31no—
182C3×#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
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—61no—
204C3⋊#95—61no—
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C23×C32C2411yescharacteristic
210C22×C3×D3—21no—
211C22×C3×D3—21no—
212C22×C3×D3—21no—
213C22×C3×D3—21no—
214C22×C3×D3C22×C412yes—
215C22×C3×D3C2×Q812yes—
216C22×C3×D3#4112yes—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4C22×C412yes—
224C2×C32×C4C22×C412yes—
225C2×C32×C4C22×C412yes—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3C2×Q812yes—
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—
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×Dic3C22×C412yes—
256C2×C3×Dic3C22×C412yes—
257C2×C3×Dic3C22×C412yes—
258C2×C3×Dic3C2×Q812yes—
259C3×C4×D3—44no—
260C3×Dic6—44no—
261D3×Dic3—44no—
262D3×Dic3—44no—
263C2×C22⋊Q8—31no—
264#391—91no—
265#391—91no—
266#389—91no—
267#389—91no—
268#387—31no—
269#387—91no—
270#387—91no—
271#387—91no—
272#385—91no—
273#385—91no—
274#380—91no—
275C4×C22⋊C4—91no—
276C4×C22⋊C4—91no—
277C2×#95—91no—
278C24×C3—31no—
279C23×D3C22×D311yescharacteristic
280C2×C3×Q8—34no—
281C2×C3×Q8—121no—
282C2×C3×Q8—121no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—34no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—121no—
295C22×C3×C4—121no—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—34no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—62no—
316C22×Dic3—121no—
317C22×Dic3—121no—
318C22×Dic3—121no—
319C22×Dic3—121no—
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C2×C4×D3—34no—
328C2×C4×D3—41no—
329C2×C4×D3—41no—
330C2×C4×D3—62no—
331C2×C4×D3—121no—
332C2×C4×D3—121no—
333C2×C4×D3—121no—
334C2×C4×D3—121no—
335C2×C4×D3C2×Dic314yes—
336C2×Dic6—41no—
337C2×Dic6—41no—
338C2×Dic6C2×Dic314yescomplemented
339C3×C4⋊C4—24no—
340C3×C4⋊C4—34no—
341C3×C4⋊C4—34no—
342C3×C4⋊C4—121no—
343C3×C4⋊C4C4×D314yescomplemented
344C3×C4⋊C4C2×Dic314yescomplemented
345C3×C22⋊C4—34no—
346C3×C22⋊C4—34no—
347C3×C42—121no—
348#217—62no—
349#217—62no—
350(C2×D3)⋊C4—62no—
351(C2×D3)⋊C4—62no—
352(C2×D3)⋊C4C2×Dic314yes—
353(C2×D3)⋊C4C2×Dic314yes—
354C4⋊Dic3—41no—
355C4⋊Dic3—121no—
356C4⋊Dic3—121no—
357C4⋊Dic3—121no—
358C4⋊Dic3—121no—
359C4⋊Dic3—121no—
360C4⋊Dic3—121no—
361C4⋊Dic3—121no—
362C4⋊Dic3—121no—
363C4⋊Dic3—122no—
364C4⋊Dic3—122no—
365C4⋊Dic3—122no—
366Dic3⋊C4—121no—
367Dic3⋊C4—121no—
368Dic3⋊C4C2×Dic314yescomplemented
369Dic3⋊C4C2×Dic314yescomplemented
370C4×Dic3—41no—
371C4×Dic3—121no—
372C4×Dic3—121no—
373C4×Dic3—121no—
374C4×Dic3—121no—
375C4×Dic3—121no—
376C4×Dic3—121no—
377C4×Dic3—122no—
378C22×C32C23×C411yescharacteristic
379C22×C32C22×Q811yescharacteristic
380C22×C32C2×#4111yescharacteristic
381C22×C32H(5,𝔽2)11yescharacteristic
382C22×C32H(5,𝔽2)11yescharacteristic
383C22×C32H(5,𝔽2)11yescharacteristic
384C22×C322−1+411yescharacteristic
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3C4×Q814yes—
392C32×C4—22no—
393C32×C4—22no—
394C32×C4—22no—
395C3⋊Dic3—22no—
396C3⋊Dic3—41no—
397C3⋊Dic3—41no—
398C3⋊Dic3—41no—
399C3×Dic3—22no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C22×Q8—31no—
407C23×C4—31no—
408C23×C4—91no—
409C23×C4—91no—
410C22⋊Q8—38no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—91no—
415C2×C4⋊C4—91no—
416C2×C4⋊C4—91no—
417C2×C4⋊C4—91no—
418C2×C4⋊C4—91no—
419C2×C4⋊C4D3211yescharacteristic
420C2×C22⋊C4—31no—
421C2×C22⋊C4—31no—
422C2×C22⋊C4—91no—
423C2×C22⋊C4—91no—
424C2×C42—31no—
425C2×C42—91no—
426C2×C42—91no—
427C2×C42—91no—
428#95—31no—
429#95—31no—
430#95—31no—
431#95—31no—
432#95—91no—
433#95—91no—
434#95—91no—
435#95—91no—
436#95—91no—
437#95—91no—
438#95—91no—
439#95—91no—
440#95—91no—
441#95—91no—
442C23×C3—21no—
443C23×C3—32no—
444C23×C3—32no—
445C23×C3—32no—
446C23×C3—61no—
447C23×C3—61no—
448C23×C3—61no—
449C23×C3—61no—
450C23×C3C23×D311yescharacteristic
451C23×C3C23×D311yescharacteristic
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3D3×Q812yes—
457C22×D3#23912yes—
458C22×D3C22×Dic312yes—
459C3×Q8—124no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—32no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—124no—
503C2×C3×C4C2×C4×D312yes—
504C2×C3×C4C2×C4×D312yes—
505C2×C3×C4C2×C4×D312yes—
506C2×C3×C4C22×Dic312yes—
507C2×C3×C4C22×Dic312yes—
508C2×C3×C4C22×Dic312yes—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—32no—
527C2×Dic3—32no—
528C2×Dic3—62no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—62no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—121no—
553C2×Dic3—121no—
554C2×Dic3—121no—
555C2×Dic3—121no—
556C2×Dic3—121no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—124no—
563C2×Dic3—124no—
564C2×Dic3D3×Q812yes—
565C2×Dic3C22×Dic312yes—
566C2×Dic3C22×Dic312yes—
567C2×Dic3C22×Dic312yes—
568C4×D3—44no—
569C4×D3—124no—
570C4×D3—124no—
571Dic6—44no—
572C2×C32C2×C4×Q811yescharacteristic
573C2×C32#51811yescharacteristic
574C2×C32#52011yescharacteristic
575C2×C32#53811yescharacteristic
576C2×C32#53911yescharacteristic
577C2×C32#54311yescharacteristic
578C2×C32#54411yescharacteristic
579C3×D3—24no—
580C24—31no—
581C2×Q8—34no—
582C2×Q8—121no—
583C2×Q8—121no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—34no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—94no—
593C22×C4—91no—
594C22×C4—91no—
595C22×C4—91no—
596C22×C4—91no—
597C22×C4—121no—
598C22×C4—121no—
599C22×C4—182no—
600C22×C4—361no—
601C22×C4—361no—
602C22×C4—361no—
603C22×C4—361no—
604C22×C4C2×D3211yescharacteristic
605C22×C4C2×D3211yescharacteristic
606C22×C4C2×D3211yescharacteristic
607C4⋊C4—34no—
608C4⋊C4—34no—
609C4⋊C4—121no—
610C4⋊C4—361no—
611C4⋊C4—361no—
612C4⋊C4—361no—
613C4⋊C4—361no—
614C4⋊C4—361no—
615C4⋊C4D3×Dic314yescomplemented
616C22⋊C4—34no—
617C22⋊C4—34no—
618C22⋊C4—182no—
619C22⋊C4—182no—
620C42—121no—
621C42—361no—
622C42—361no—
623C42—361no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—34no—
632C22×C3—62no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3C22×C4×D311yescharacteristic
639C22×C3#100411yescharacteristic
640C22×C3#100411yescharacteristic
641C22×C3#100411yescharacteristic
642C22×C3C2×D3×Q811yescharacteristic
643C22×C3C2×D3×Q811yescharacteristic
644C22×C3C2×#23911yescharacteristic
645C22×C3D3×#4111yescharacteristic
646C22×C3#100911yescharacteristic
647C22×C3#100911yescharacteristic
648C22×C3#100911yescharacteristic
649C22×C3#101011yescharacteristic
650C22×C3#101011yescharacteristic
651C22×C3C23×Dic311yescharacteristic
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—22no—
657C2×D3—22no—
658C2×D3Q8×Dic314yes—
659C3×C4—24no—
660C3×C4—22no—
661C3×C4—22no—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—22no—
665C3×C4—22no—
666C3×C4—42no—
667C3×C4—42no—
668C3×C4—62no—
669C3×C4—62no—
670C3×C4—62no—
671C3×C4—62no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4—121no—
675Dic3—22no—
676Dic3—22no—
677Dic3—22no—
678Dic3—22no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—62no—
683Dic3—62no—
684Dic3—122no—
685Dic3—122no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—241no—
693Dic3—241no—
694C32#232911yescharacteristic, complemented, Sylow
695C23—32no—
696C23—32no—
697C23—32no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23C22×D3211yescharacteristic
703Q8—124no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—92no—
732C2×C4—124no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4—181no—
744C2×C4—364no—
745C2×C4—364no—
746C2×C4C2×D3×Dic312yes—
747C2×C4C2×D3×Dic312yes—
748C2×C4C2×D3×Dic312yes—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—64no—
757C2×C3#552311yescharacteristic
758C2×C3#554511yescharacteristic
759C2×C3C4×D3×Q811yescharacteristic
760C2×C3#562311yescharacteristic
761C2×C3#563411yescharacteristic
762C2×C3#563411yescharacteristic
763C2×C3#564411yescharacteristic
764C2×C3#564511yescharacteristic
765C2×C3#566011yescharacteristic
766C2×C3#568911yescharacteristic
767C2×C3#570411yescharacteristic
768C2×C3#579811yescharacteristic
769C2×C3C2×Q8×Dic311yescharacteristic
770C2×C3#582711yescharacteristic
771D3—24no—
772C22—34no—
773C22—62no—
774C22—62no—
775C22—62no—
776C22—62no—
777C22—62no—
778C22—62no—
779C22#6429811yescharacteristic
780C22#6430811yescharacteristic
781C22#6431311yescharacteristic
782C22#6431411yescharacteristic
783C22D32×Q811yescharacteristic
784C22D3×#23911yescharacteristic
785C22C22×D3×Dic311yescharacteristic
786C4—22no—
787C4—22no—
788C4—22no—
789C4—62no—
790C4—62no—
791C4—62no—
792C4—62no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4—182no—
797C4—361no—
798C4—361no—
799C4—361no—
800C3—21no—
801C3#7529911yescharacteristic, complemented
802C3#8274511yescharacteristic, complemented
803C2—64no—
804C2#1059439011yescharacteristic
805C2#1059445511yescharacteristic
806C2#1059463611yescharacteristic
807C2#1059465211yescharacteristic
808C2#1059499211yescharacteristic
809C2#1059521511yescharacteristic
810C2D3×Q8×Dic311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2329
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592683C2semidirect
3. C3×#4980C2semidirect
10. #10591272C2semidirect
11. #10591268C2semidirect
12. #10591262C2semidirect
13. #10591261C2semidirect
14. #10591220C2semidirect
15. #10591192C2semidirect
33. C3×#896C4semidirect
69. #4980D3semidirect
105. C2×C3×Dic6C2×C4semidirect
111. C2×D3×Dic3Q8semidirect
112. C32×C4⋊C4C2×C4semidirect
120. C3×Dic3⋊C4C2×C4semidirect
121. C3×Dic3⋊C4C2×C4semidirect
178. #896Dic3semidirect
338. C2×Dic6C2×Dic3semidirect
343. C3×C4⋊C4C4×D3semidirect
344. C3×C4⋊C4C2×Dic3semidirect
368. Dic3⋊C4C2×Dic3semidirect
369. Dic3⋊C4C2×Dic3semidirect
615. C4⋊C4D3×Dic3semidirect
694. C32#2329semidirect
801. C3#75299semidirect
802. C3#82745semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8962
#105926832
C3×#49802
#105913792
#105913682
Dic3×(C2×D3)⋊C42
D3×C3⋊#952
#105913132
#105912722
#105912682
#105912622
#105912612
#105912202
#105911922
#827453
#752993