Finite Group Databasebeta

← #11800882

Subgroups — #11800882

Order 1152.

1489 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63878C211yesmaximal, characteristic
2C2×#63877C211yesmaximal, characteristic
3C2×D3×Dic3⋊C4C211yesmaximal, characteristic
4C4×#3750C211yesmaximal, characteristic, complemented
5C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
6C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
7#10591368C211yesmaximal, characteristic
8Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic
9#10591257C211yesmaximal, characteristic, complemented
10#10591243C211yesmaximal, characteristic, complemented
11#10591243C211yesmaximal, characteristic, complemented
12#10591242C211yesmaximal, characteristic, complemented
13#10591241C211yesmaximal, characteristic, complemented
14Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#10591237C211yesmaximal, characteristic
16#73750—31nomaximal
17#73435—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45#63878C418yescomplemented
46#63877C418yescomplemented
47D3×Dic3⋊C4C418yescomplemented
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C22×Dic3⋊C4—31no—
57C2×#892—31no—
58C2×D3×C4⋊C4—31no—
59C2×#877—31no—
60C2×#877—31no—
61C2×#872—31no—
62C3×C4×C4⋊C4—31no—
63C3×C4×C22⋊C4—31no—
64C4×#217—31no—
65Dic3×C4⋊C4—31no—
66Dic3×C4⋊C4—31no—
67Dic3×C22⋊C4—31no—
68Dic3×C22⋊C4—31no—
69C4×(C2×D3)⋊C4—31no—
70C4×(C2×D3)⋊C4D311yescharacteristic
71C4×C4⋊Dic3—31no—
72C4×Dic3⋊C4—31no—
73C4×Dic3⋊C4—31no—
74C4×Dic3⋊C4—31no—
75C4×Dic3⋊C4—31no—
76C4×Dic3⋊C4—31no—
77C4×Dic3⋊C4—61no—
78C4×Dic3⋊C4D311yescharacteristic, complemented
79#4666—31no—
80#4666—31no—
81#4649—31no—
82#4649—31no—
83#4649—31no—
84#4649—31no—
85#4649—31no—
86#4649—31no—
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
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
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×C4×D3—41no—
103C2×C3×C4×D3—41no—
104C2×C3×C4×D3C2×C414yes—
105C2×D3×Dic3—41no—
106C2×D3×Dic3—41no—
107C2×D3×Dic3C2×C414yes—
108C2×D3×Dic3C2×C414yes—
109C2×D3×Dic3C2×C414yes—
110C2×D3×Dic3C2×C414yes—
111C32×C42—41no—
112#3750C2×C414yes—
113#3750C2×C414yescomplemented
114C4×C3⋊Dic3—41no—
115C4×C3⋊Dic3C2×C414yescomplemented
116C3×(C2×D3)⋊C4C2×C414yes—
117C3×(C2×D3)⋊C4C2×C414yes—
118C3×Dic3⋊C4C2×C414yes—
119C3×Dic3⋊C4C2×C414yescomplemented
120C3×C4×Dic3—41no—
121C3×C4×Dic3—41no—
122C3×C4×Dic3C2×C414yescomplemented
123#3724C2×C414yes—
124#3724C2×C414yescomplemented
125Dic3⋊Dic3C2×C414yes—
126Dic3⋊Dic3C2×C414yescomplemented
127(C2×D3)⋊Dic3C2×C414yes—
128(C2×D3)⋊Dic3C2×C414yes—
129Dic32—41no—
130Dic32—41no—
131Dic32—41no—
132Dic32—41no—
133Dic32C2×C414yescomplemented
134Dic32C2×C414yescomplemented
135#2274—91noSylow
136C23×C3×C4—31no—
137C23×Dic3—31no—
138C23×Dic3—31no—
139C22×C4×D3—31no—
140C22×C4×D3—31no—
141C22×C4×D3C2×D311yescharacteristic
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C42—21no—
147C2×C3×C42—31no—
148C2×C3×C42—31no—
149C2×C3×C42—31no—
150C2×C3×C42C2×D311yescharacteristic
151C2×C3×C42C2×D311yescharacteristic
152C2×#217—31no—
153C2×#217—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4C2×D311yescharacteristic
157C2×(C2×D3)⋊C4C2×D311yescharacteristic
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—38no—
171C2×Dic3⋊C4—61no—
172C2×Dic3⋊C4—61no—
173C2×Dic3⋊C4C2×D311yescharacteristic
174C2×Dic3⋊C4C2×D311yescharacteristic
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
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—31no—
191C2×C4×Dic3—61no—
192C2×C4×Dic3—61no—
193C2×C4×Dic3C2×D311yescharacteristic
194C2×C4×Dic3C2×D311yescharacteristic
195C2×C4×Dic3C2×D311yescharacteristic
196#892—38no—
197D3×C4⋊C4—38no—
198#877—38no—
199#877—38no—
200#872—38no—
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—31no—
213C3⋊#95—61no—
214C3⋊#95—61no—
215C3⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C23×C32C2411yescharacteristic
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3C22×C412yes—
225C22×C3×D3C22×C412yes—
226C22×C3×D3C22×C412yes—
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×C4C22×C412yes—
235C2×C32×C4C22×C412yes—
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⋊Dic3C22×C412yes—
243C2×C3⋊Dic3C22×C412yes—
244C2×C3⋊Dic3C22×C412yes—
245C2×C3⋊Dic3C22×C412yes—
246C2×C3⋊Dic3C22×C412yes—
247C2×C3⋊Dic3C22×C412yes—
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×Dic3C22×C412yes—
261C2×C3×Dic3C22×C412yes—
262C2×C3×Dic3C22×C412yes—
263C2×C3×Dic3C22×C412yes—
264C2×C3×Dic3C22×C412yes—
265C2×C3×Dic3C22×C412yes—
266C2×C3×Dic3C22×C412yes—
267C2×C3×Dic3C22×C412yes—
268C2×C3×Dic3C22×C412yes—
269C3×C4×D3—44no—
270D3×Dic3—44no—
271D3×Dic3C42116yescomplemented
272C2×#117—91no—
273C2×#117—91no—
274C22×C4⋊C4—91no—
275C4×C4⋊C4—31no—
276C4×C4⋊C4—91no—
277C4×C4⋊C4—91no—
278C4×C4⋊C4—91no—
279C4×C4⋊C4—91no—
280C4×C4⋊C4—91no—
281C4×C4⋊C4—91no—
282C4×C4⋊C4—91no—
283C4×C22⋊C4—31no—
284C4×C22⋊C4—91no—
285C4×C22⋊C4—91no—
286C4×C22⋊C4—91no—
287C24×C3—31no—
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—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—34no—
300C22×C3×C4—121no—
301C22×C3×C4—121no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—34no—
311C22×Dic3—34no—
312C22×Dic3—34no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—34no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—121no—
325C22×Dic3—121no—
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C2×C4×D3—34no—
334C2×C4×D3—34no—
335C2×C4×D3—34no—
336C2×C4×D3—34no—
337C2×C4×D3—41no—
338C2×C4×D3—41no—
339C2×C4×D3—121no—
340C2×C4×D3—121no—
341C2×C4×D3C4×D314yes—
342C3×C4⋊C4—34no—
343C3×C4⋊C4—34no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—34no—
346C3×C42—34no—
347C3×C42—41no—
348C3×C42—41no—
349C3×C42—42no—
350C3×C42—121no—
351C3×C42—121no—
352#217—34no—
353#217—34no—
354(C2×D3)⋊C4—34no—
355(C2×D3)⋊C4—34no—
356(C2×D3)⋊C4C4×D314yes—
357(C2×D3)⋊C4C4×D314yes—
358C4⋊Dic3—34no—
359C4⋊Dic3—34no—
360Dic3⋊C4—34no—
361Dic3⋊C4—34no—
362Dic3⋊C4—34no—
363Dic3⋊C4—34no—
364Dic3⋊C4—34no—
365Dic3⋊C4—34no—
366Dic3⋊C4—34no—
367Dic3⋊C4—34no—
368Dic3⋊C4—34no—
369Dic3⋊C4—34no—
370Dic3⋊C4—64no—
371Dic3⋊C4—64no—
372Dic3⋊C4C4×D314yes—
373Dic3⋊C4C4×D314yescomplemented
374C4×Dic3—34no—
375C4×Dic3—34no—
376C4×Dic3—34no—
377C4×Dic3—34no—
378C4×Dic3—34no—
379C4×Dic3—34no—
380C4×Dic3—41no—
381C4×Dic3—41no—
382C4×Dic3—64no—
383C4×Dic3—121no—
384C4×Dic3—121no—
385C4×Dic3—121no—
386C4×Dic3—121no—
387C4×Dic3—121no—
388C4×Dic3—121no—
389C4×Dic3—121no—
390C4×Dic3—121no—
391C4×Dic3—121no—
392C4×Dic3—121no—
393C4×Dic3—122no—
394C4×Dic3C4×D314yescomplemented
395C22×C32C23×C411yescharacteristic
396C22×C32C23×C411yescharacteristic
397C22×C32C23×C411yescharacteristic
398C22×C32H(5,𝔽2)11yescharacteristic
399C22×C32H(5,𝔽2)11yescharacteristic
400C22×C322−1+411yescharacteristic
401C22×C322−1+411yescharacteristic
402C2×C3×D3—22no—
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—22no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3C2×C4214yes—
409C32×C4—22no—
410C32×C4—22no—
411C32×C4—22no—
412C3⋊Dic3—22no—
413C3⋊Dic3—22no—
414C3⋊Dic3—22no—
415C3⋊Dic3C2×C4214yes—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3C2×C4214yes—
423C23×C4—31no—
424C23×C4—91no—
425C23×C4—91no—
426#117—98no—
427#117—98no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—98no—
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—91no—
440C2×C22⋊C4—91no—
441C2×C42—31no—
442C2×C42—31no—
443C2×C42—31no—
444C2×C42—91no—
445C2×C42—91no—
446C2×C42—91no—
447C2×C42—91no—
448C2×C42—91no—
449C2×C42—91no—
450C2×C42—91no—
451C2×C42—91no—
452C2×C42D3211yescharacteristic
453#95—31no—
454#95—31no—
455#95—31no—
456#95—31no—
457#95—91no—
458#95—91no—
459#95—91no—
460#95—91no—
461C23×C3—21no—
462C23×C3—32no—
463C23×C3—32no—
464C23×C3—32no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3C23×D311yescharacteristic
470C23×C3C23×D311yescharacteristic
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3C2×C4×D312yes—
476C22×D3C2×C4×D312yes—
477C22×D3C2×C4×D312yes—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—32no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—32no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
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—124no—
521C2×C3×C4C2×C4×D312yes—
522C2×C3×C4C2×C4×D312yes—
523C2×C3×C4C2×C4×D312yes—
524C2×C3×C4C2×C4×D312yes—
525C2×C3×C4C2×C4×D312yes—
526C2×C3×C4C2×C4×D312yes—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—32no—
540C2×Dic3—32no—
541C2×Dic3—32no—
542C2×Dic3—32no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—316no—
546C2×Dic3—32no—
547C2×Dic3—32no—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—32no—
551C2×Dic3—32no—
552C2×Dic3—62no—
553C2×Dic3—62no—
554C2×Dic3—62no—
555C2×Dic3—62no—
556C2×Dic3—62no—
557C2×Dic3—62no—
558C2×Dic3—61no—
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—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—121no—
571C2×Dic3—121no—
572C2×Dic3—121no—
573C2×Dic3—121no—
574C2×Dic3—121no—
575C2×Dic3—121no—
576C2×Dic3—124no—
577C2×Dic3C2×C4×D312yes—
578C2×Dic3C2×C4×D312yes—
579C2×Dic3C2×C4×D312yes—
580C2×Dic3C2×C4×D312yes—
581C2×Dic3C2×C4×D312yes—
582C2×Dic3C2×C4×D312yes—
583C2×Dic3C2×C4×D312yes—
584C2×Dic3C2×C4×D312yes—
585C2×Dic3C2×C4×D312yes—
586C4×D3—316no—
587C4×D3—44no—
588C4×D3—124no—
589C2×C32C22×C4211yescharacteristic
590C2×C32#51811yescharacteristic
591C2×C32#51911yescharacteristic
592C2×C32#52011yescharacteristic
593C2×C32#52011yescharacteristic
594C2×C32#52011yescharacteristic
595C2×C32#52011yescharacteristic
596C3×D3—24no—
597C24—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—34no—
606C22×C4—94no—
607C22×C4—94no—
608C22×C4—94no—
609C22×C4—94no—
610C22×C4—91no—
611C22×C4—91no—
612C22×C4—91no—
613C22×C4—91no—
614C22×C4—121no—
615C22×C4—121no—
616C22×C4—361no—
617C22×C4—361no—
618C22×C4C2×D3211yescharacteristic
619C22×C4C2×D3211yescharacteristic
620C22×C4C2×D3211yescharacteristic
621C4⋊C4—34no—
622C4⋊C4—34no—
623C4⋊C4—94no—
624C4⋊C4—94no—
625C4⋊C4—94no—
626C4⋊C4—94no—
627C4⋊C4—94no—
628C4⋊C4—94no—
629C22⋊C4—34no—
630C22⋊C4—34no—
631C22⋊C4—94no—
632C22⋊C4—94no—
633C42—34no—
634C42—41no—
635C42—94no—
636C42—94no—
637C42—94no—
638C42—121no—
639C42—121no—
640C42—361no—
641C42—361no—
642C42—361no—
643C42—361no—
644C42—361no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—34no—
653C22×C3—62no—
654C22×C3—62no—
655C22×C3—62no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—62no—
659C22×C3C22×C4×D311yescharacteristic
660C22×C3C22×C4×D311yescharacteristic
661C22×C3C22×C4×D311yescharacteristic
662C22×C3C22×C4×D311yescharacteristic
663C22×C3C22×C4×D311yescharacteristic
664C22×C3C22×C4×D311yescharacteristic
665C22×C3#100411yescharacteristic
666C22×C3#100411yescharacteristic
667C22×C3#100411yescharacteristic
668C22×C3#100711yescharacteristic
669C22×C3#100911yescharacteristic
670C22×C3#101011yescharacteristic
671C22×C3#101011yescharacteristic
672C22×C3#101011yescharacteristic
673C2×D3—22no—
674C2×D3—22no—
675C2×D3—22no—
676C2×D3—22no—
677C2×D3—22no—
678C2×D3—22no—
679C2×D3C42×D314yes—
680C3×C4—24no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—22no—
686C3×C4—22no—
687C3×C4—34no—
688C3×C4—42no—
689C3×C4—42no—
690C3×C4—62no—
691C3×C4—62no—
692C3×C4—62no—
693C3×C4—62no—
694C3×C4—62no—
695C3×C4—62no—
696Dic3—22no—
697Dic3—22no—
698Dic3—22no—
699Dic3—22no—
700Dic3—22no—
701Dic3—22no—
702Dic3—34no—
703Dic3—34no—
704Dic3—64no—
705Dic3—62no—
706Dic3—62no—
707Dic3—62no—
708Dic3—62no—
709Dic3—62no—
710Dic3—62no—
711Dic3—122no—
712Dic3—122no—
713Dic3—122no—
714Dic3C42×D314yes—
715C32#227411yescharacteristic, complemented, Sylow
716C23—32no—
717C23—32no—
718C23—32no—
719C23—61no—
720C23—61no—
721C23—61no—
722C23—61no—
723C23C22×D3211yescharacteristic
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—916no—
752C2×C4—92no—
753C2×C4—92no—
754C2×C4—92no—
755C2×C4—92no—
756C2×C4—92no—
757C2×C4—92no—
758C2×C4—124no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4—181no—
764C2×C4—181no—
765C2×C4—364no—
766C2×C4C4×D3212yes—
767C2×C4C4×D3212yes—
768C2×C4C4×D3212yes—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—64no—
777C2×C3C2×C42×D311yescharacteristic
778C2×C3C2×C42×D311yescharacteristic
779C2×C3#548611yescharacteristic
780C2×C3#550411yescharacteristic
781C2×C3#551611yescharacteristic
782C2×C3#552311yescharacteristic
783C2×C3#554511yescharacteristic
784C2×C3#554611yescharacteristic
785C2×C3#554611yescharacteristic
786C2×C3#554611yescharacteristic
787C2×C3#554611yescharacteristic
788C2×C3#554611yescharacteristic
789C2×C3#557211yescharacteristic
790C2×C3#557411yescharacteristic
791D3—24no—
792C22—34no—
793C22—62no—
794C22—62no—
795C22—62no—
796C22—62no—
797C22—62no—
798C22—62no—
799C22#6429711yescharacteristic
800C22#6429811yescharacteristic
801C22C2×C4×D3211yescharacteristic
802C22C2×C4×D3211yescharacteristic
803C22C2×C4×D3211yescharacteristic
804C22#6430711yescharacteristic
805C22#6433011yescharacteristic
806C4—22no—
807C4—22no—
808C4—22no—
809C4—34no—
810C4—62no—
811C4—62no—
812C4—62no—
813C4—62no—
814C4—62no—
815C4—62no—
816C4—94no—
817C4—182no—
818C4—182no—
819C4—182no—
820C3—21no—
821C3#7343511yescharacteristic, complemented
822C3#7375011yescharacteristic, complemented
823C2—64no—
824C2#1059388511yescharacteristic
825C2#1059388711yescharacteristic
826C2#1059388911yescharacteristic
827C2C42×D3211yescharacteristic
828C2#1059487411yescharacteristic
829C2#1059487611yescharacteristic
830C2#1059505611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2274
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C4×#3750C2semidirect
6. C3×C4×Dic3⋊C4C2semidirect
9. #10591257C2semidirect
10. #10591243C2semidirect
11. #10591243C2semidirect
12. #10591242C2semidirect
13. #10591241C2semidirect
14. Dic3×Dic3⋊C4C2semidirect
45. #63878C4semidirect
46. #63877C4semidirect
47. D3×Dic3⋊C4C4semidirect
78. C4×Dic3⋊C4D3semidirect
113. #3750C2×C4semidirect
115. C4×C3⋊Dic3C2×C4semidirect
119. C3×Dic3⋊C4C2×C4semidirect
122. C3×C4×Dic3C2×C4semidirect
124. #3724C2×C4semidirect
126. Dic3⋊Dic3C2×C4semidirect
133. Dic32C2×C4semidirect
134. Dic32C2×C4semidirect
271. D3×Dic3C42semidirect
373. Dic3⋊C4C4×D3semidirect
394. C4×Dic3C4×D3semidirect
715. C32#2274semidirect
821. C3#73435semidirect
822. C3#73750semidirect

Maximal subgroups

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

subgroupindex
C2×#638782
C2×#638772
C2×D3×Dic3⋊C42
C4×#37502
C3×C4×(C2×D3)⋊C42
C3×C4×Dic3⋊C42
#105913682
Dic3×(C2×D3)⋊C42
#105912572
#105912432
#105912422
#105912412
Dic3×Dic3⋊C42
#105912372
#737503
#734353