Finite Group Databasebeta

← #11803929

Subgroups — #11803929

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#896C211yesmaximal, characteristic
2#10592679C211yesmaximal, characteristic, complemented
3C3×#4984C211yesmaximal, characteristic, complemented
4#10591377C211yesmaximal, characteristic
5#10591377C211yesmaximal, characteristic
6#10591368C211yesmaximal, characteristic
7Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic
8D3×C3⋊#95C211yesmaximal, characteristic
9#10591313C211yesmaximal, characteristic
10#10591272C211yesmaximal, characteristic, complemented
11#10591265C211yesmaximal, characteristic, complemented
12#10591262C211yesmaximal, characteristic, complemented
13#10591261C211yesmaximal, characteristic, complemented
14#10591221C211yesmaximal, characteristic, complemented
15#10591201C211yesmaximal, characteristic, complemented
16#82745—31nomaximal
17#76199—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⋊Dic3C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
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
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
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×#389—31no—
57#5229—31no—
58#5229—31no—
59#5212—31no—
60C2×C3⋊#95—31no—
61#4989—31no—
62#4989—31no—
63#4987—31no—
64#4984—31no—
65#4984D311yescharacteristic, complemented
66#4980—31no—
67#4980—31no—
68#4980—31no—
69#4980—31no—
70#4980—31no—
71#4980—61no—
72#4978—31no—
73#4976—31no—
74#4973—31no—
75#4950—31no—
76#4950—31no—
77Dic3×C22⋊C4—31no—
78Dic3×C22⋊C4—31no—
79C4×(C2×D3)⋊C4—31no—
80#4933—31no—
81#4666—31no—
82D3×#95—31no—
83#4655—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—
115C3×(C2×D3)⋊C4C2×C414yes—
116C3×(C2×D3)⋊C4C2×C414yes—
117C3×C4⋊Dic3—41no—
118C3×C4⋊Dic3—41no—
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⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4C2×D311yescharacteristic
146C2×C3×C4⋊C4C2×D311yescharacteristic
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C42—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4C2×D311yescharacteristic
155C2×(C2×D3)⋊C4C2×D311yescharacteristic
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—61no—
161C2×C4⋊Dic3C2×D311yescharacteristic
162C2×C4⋊Dic3C2×D311yescharacteristic
163C2×C4⋊Dic3C2×D311yescharacteristic
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4C2×D311yescharacteristic
167C2×Dic3⋊C4C2×D311yescharacteristic
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—61no—
175C2×C4×Dic3C2×D311yescharacteristic
176#896Dic318yescomplemented
177C3×#95—31no—
178C3×#95—31no—
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⋊#95—61no—
206C3⋊#95—61no—
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—31no—
267#389—91no—
268#387—91no—
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⋊C4—121no—
344C3×C4⋊C4—121no—
345C3×C4⋊C4C4×D314yescomplemented
346C3×C4⋊C4C2×Dic314yescomplemented
347C3×C22⋊C4—34no—
348C3×C22⋊C4—34no—
349C3×C42—121no—
350#217—62no—
351#217—62no—
352(C2×D3)⋊C4—62no—
353(C2×D3)⋊C4—62no—
354(C2×D3)⋊C4C2×Dic314yes—
355(C2×D3)⋊C4C2×Dic314yes—
356C4⋊Dic3—41no—
357C4⋊Dic3—41no—
358C4⋊Dic3—41no—
359C4⋊Dic3—121no—
360C4⋊Dic3—121no—
361C4⋊Dic3—121no—
362C4⋊Dic3—121no—
363C4⋊Dic3—122no—
364Dic3⋊C4—121no—
365Dic3⋊C4—121no—
366Dic3⋊C4C2×Dic314yescomplemented
367Dic3⋊C4C2×Dic314yescomplemented
368C4×Dic3—41no—
369C4×Dic3—121no—
370C4×Dic3—121no—
371C4×Dic3—121no—
372C4×Dic3—121no—
373C4×Dic3—121no—
374C4×Dic3—121no—
375C4×Dic3—122no—
376C22×C32C23×C411yescharacteristic
377C22×C32C22×Q811yescharacteristic
378C22×C32C2×#4111yescharacteristic
379C22×C32H(5,𝔽2)11yescharacteristic
380C22×C32H(5,𝔽2)11yescharacteristic
381C22×C32H(5,𝔽2)11yescharacteristic
382C22×C322−1+411yescharacteristic
383C2×C3×D3—22no—
384C2×C3×D3—22no—
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3C4×Q814yes—
390C32×C4—22no—
391C32×C4—22no—
392C32×C4—22no—
393C3⋊Dic3—22no—
394C3⋊Dic3—41no—
395C3⋊Dic3—41no—
396C3⋊Dic3—41no—
397C3×Dic3—22no—
398C3×Dic3—22no—
399C3×Dic3—22no—
400C3×Dic3—22no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C22×Q8—31no—
405C23×C4—31no—
406C23×C4—91no—
407C23×C4—91no—
408C22⋊Q8—38no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—31no—
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⋊C4D3211yescharacteristic
418C2×C22⋊C4—31no—
419C2×C22⋊C4—31no—
420C2×C22⋊C4—91no—
421C2×C22⋊C4—91no—
422C2×C42—31no—
423C2×C42—91no—
424C2×C42—91no—
425C2×C42—91no—
426#95—31no—
427#95—31no—
428#95—91no—
429#95—91no—
430#95—91no—
431#95—91no—
432#95—91no—
433#95—91no—
434#95—91no—
435#95—91no—
436#95—91no—
437#95—91no—
438#95—91no—
439#95—91no—
440C23×C3—21no—
441C23×C3—32no—
442C23×C3—32no—
443C23×C3—32no—
444C23×C3—61no—
445C23×C3—61no—
446C23×C3—61no—
447C23×C3—61no—
448C23×C3C23×D311yescharacteristic
449C23×C3C23×D311yescharacteristic
450C22×D3—21no—
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3D3×Q812yes—
455C22×D3#23912yes—
456C22×D3C22×Dic312yes—
457C3×Q8—124no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
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—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—32no—
474C2×C3×C4—32no—
475C2×C3×C4—32no—
476C2×C3×C4—32no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
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—124no—
501C2×C3×C4C2×C4×D312yes—
502C2×C3×C4C2×C4×D312yes—
503C2×C3×C4C2×C4×D312yes—
504C2×C3×C4C22×Dic312yes—
505C2×C3×C4C22×Dic312yes—
506C2×C3×C4C22×Dic312yes—
507C2×Dic3—21no—
508C2×Dic3—21no—
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—32no—
525C2×Dic3—32no—
526C2×Dic3—62no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—62no—
532C2×Dic3—61no—
533C2×Dic3—61no—
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—121no—
551C2×Dic3—121no—
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—124no—
561C2×Dic3—124no—
562C2×Dic3D3×Q812yes—
563C2×Dic3C22×Dic312yes—
564C2×Dic3C22×Dic312yes—
565C2×Dic3C22×Dic312yes—
566C4×D3—44no—
567C4×D3—124no—
568C4×D3—124no—
569Dic6—44no—
570C2×C32C2×C4×Q811yescharacteristic
571C2×C32#51811yescharacteristic
572C2×C32#52011yescharacteristic
573C2×C32#53811yescharacteristic
574C2×C32#53911yescharacteristic
575C2×C32#54311yescharacteristic
576C2×C32#54411yescharacteristic
577C3×D3—24no—
578C24—31no—
579C2×Q8—34no—
580C2×Q8—121no—
581C2×Q8—121no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—34no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—94no—
591C22×C4—91no—
592C22×C4—91no—
593C22×C4—91no—
594C22×C4—91no—
595C22×C4—121no—
596C22×C4—121no—
597C22×C4—182no—
598C22×C4—361no—
599C22×C4—361no—
600C22×C4—361no—
601C22×C4—361no—
602C22×C4C2×D3211yescharacteristic
603C22×C4C2×D3211yescharacteristic
604C22×C4C2×D3211yescharacteristic
605C4⋊C4—34no—
606C4⋊C4—34no—
607C4⋊C4—121no—
608C4⋊C4—121no—
609C4⋊C4—121no—
610C4⋊C4—361no—
611C4⋊C4—361no—
612C4⋊C4—361no—
613C4⋊C4D3×Dic314yescomplemented
614C22⋊C4—34no—
615C22⋊C4—34no—
616C22⋊C4—182no—
617C22⋊C4—182no—
618C42—121no—
619C42—361no—
620C42—361no—
621C42—361no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—34no—
630C22×C3—62no—
631C22×C3—62no—
632C22×C3—62no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3C22×C4×D311yescharacteristic
637C22×C3#100411yescharacteristic
638C22×C3#100411yescharacteristic
639C22×C3#100411yescharacteristic
640C22×C3#100411yescharacteristic
641C22×C3C2×D3×Q811yescharacteristic
642C22×C3C2×D3×Q811yescharacteristic
643C22×C3C2×#23911yescharacteristic
644C22×C3#100711yescharacteristic
645C22×C3D3×#4111yescharacteristic
646C22×C3#100911yescharacteristic
647C22×C3#100911yescharacteristic
648C22×C3#101011yescharacteristic
649C22×C3C23×Dic311yescharacteristic
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—22no—
655C2×D3—22no—
656C2×D3Q8×Dic314yes—
657C3×C4—22no—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—22no—
662C3×C4—22no—
663C3×C4—42no—
664C3×C4—42no—
665C3×C4—42no—
666C3×C4—62no—
667C3×C4—62no—
668C3×C4—62no—
669C3×C4—62no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673Dic3—22no—
674Dic3—22no—
675Dic3—22no—
676Dic3—22no—
677Dic3—41no—
678Dic3—41no—
679Dic3—41no—
680Dic3—62no—
681Dic3—62no—
682Dic3—122no—
683Dic3—122no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691Dic3—241no—
692C32#232911yescharacteristic, complemented, Sylow
693C23—32no—
694C23—32no—
695C23—32no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23C22×D3211yescharacteristic
701Q8—124no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—32no—
709C2×C4—32no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—61no—
713C2×C4—61no—
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—92no—
730C2×C4—124no—
731C2×C4—181no—
732C2×C4—181no—
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—364no—
743C2×C4—364no—
744C2×C4C2×D3×Dic312yes—
745C2×C4C2×D3×Dic312yes—
746C2×C4C2×D3×Dic312yes—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—64no—
755C2×C3#550411yescharacteristic
756C2×C3#554511yescharacteristic
757C2×C3C4×D3×Q811yescharacteristic
758C2×C3#561311yescharacteristic
759C2×C3#562311yescharacteristic
760C2×C3#563411yescharacteristic
761C2×C3#563411yescharacteristic
762C2×C3#564411yescharacteristic
763C2×C3#564511yescharacteristic
764C2×C3#569211yescharacteristic
765C2×C3#572911yescharacteristic
766C2×C3#579811yescharacteristic
767C2×C3C2×Q8×Dic311yescharacteristic
768C2×C3#582711yescharacteristic
769D3—24no—
770C22—34no—
771C22—62no—
772C22—62no—
773C22—62no—
774C22—62no—
775C22—62no—
776C22—62no—
777C22#6429711yescharacteristic
778C22#6430711yescharacteristic
779C22#6431311yescharacteristic
780C22#6431411yescharacteristic
781C22D32×Q811yescharacteristic
782C22D3×#23911yescharacteristic
783C22C22×D3×Dic311yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—62no—
788C4—62no—
789C4—62no—
790C4—62no—
791C4—121no—
792C4—121no—
793C4—121no—
794C4—182no—
795C4—361no—
796C4—361no—
797C4—361no—
798C3—21no—
799C3#7619911yescharacteristic, complemented
800C3#8274511yescharacteristic, complemented
801C2—64no—
802C2#1059439111yescharacteristic
803C2#1059445411yescharacteristic
804C2#1059463511yescharacteristic
805C2#1059465111yescharacteristic
806C2#1059498611yescharacteristic
807C2#1059521511yescharacteristic
808C2D3×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. #10592679C2semidirect
3. C3×#4984C2semidirect
10. #10591272C2semidirect
11. #10591265C2semidirect
12. #10591262C2semidirect
13. #10591261C2semidirect
14. #10591221C2semidirect
15. #10591201C2semidirect
33. C3×#896C4semidirect
65. #4984D3semidirect
105. C2×C3×Dic6C2×C4semidirect
111. C2×D3×Dic3Q8semidirect
112. C32×C4⋊C4C2×C4semidirect
120. C3×Dic3⋊C4C2×C4semidirect
121. C3×Dic3⋊C4C2×C4semidirect
176. #896Dic3semidirect
338. C2×Dic6C2×Dic3semidirect
345. C3×C4⋊C4C4×D3semidirect
346. C3×C4⋊C4C2×Dic3semidirect
366. Dic3⋊C4C2×Dic3semidirect
367. Dic3⋊C4C2×Dic3semidirect
613. C4⋊C4D3×Dic3semidirect
692. C32#2329semidirect
799. C3#76199semidirect
800. 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
#105926792
C3×#49842
#105913772
#105913682
Dic3×(C2×D3)⋊C42
D3×C3⋊#952
#105913132
#105912722
#105912652
#105912622
#105912612
#105912212
#105912012
#827453
#761993