Finite Group Databasebeta

← C4×#63854 #11802197

Subgroups — C4×#63854 #11802197

Order 1152.

1505 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#626C211yesmaximal, characteristic
2C2×C4×#624C211yesmaximal, characteristic, complemented
3C2×#63854C211yesmaximal, characteristic
4C4×#3752C211yesmaximal, characteristic, complemented
5C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
7#10591378C211yesmaximal, characteristic, complemented
8#10591371C211yesmaximal, characteristic, complemented
9C4×#3724C211yesmaximal, characteristic, complemented
10#10591307C211yesmaximal, characteristic, complemented
11#10591282C211yesmaximal, characteristic, complemented
12C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic
14#10591270C211yesmaximal, characteristic, complemented
15#10591249C211yesmaximal, characteristic, complemented
16C4×#894—31nomaximal
17C4×#883—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C4×#626—24no—
44C4×#624—24no—
45#63854C418yesdirect product factor
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C4×#67—31no—
57C2×#894—31no—
58C2×#883—31no—
59C2×C4×D12—31no—
60C2×C42×D3—31no—
61C2×C42×D3—31no—
62C3×C4×C4⋊C4—31no—
63C3×C4×C22⋊C4—31no—
64C4×#217—31no—
65#4990—31no—
66#4989—31no—
67#4980—31no—
68#4956—31no—
69#4951—31no—
70#4945—31no—
71C4×(C2×D3)⋊C4—31no—
72C4×(C2×D3)⋊C4—31no—
73C4×(C2×D3)⋊C4—31no—
74C4×(C2×D3)⋊C4—61no—
75C4×(C2×D3)⋊C4D311yescharacteristic, complemented
76C4×C4⋊Dic3D311yescharacteristic, complemented
77C4×Dic3⋊C4—31no—
78C4×Dic3⋊C4—31no—
79#4669—31no—
80#4668—31no—
81#4665—31no—
82#4664—31no—
83#4664—31no—
84#4655—31no—
85#4654—31no—
86#4652—31no—
87C23×C3⋊D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3D414yes—
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×#626—22no—
109C2×#626—22no—
110C2×#626C2×C414yes—
111C2×#624—22no—
112C2×#624—22no—
113C2×#624—22no—
114C2×#624—22no—
115C2×#624—22no—
116C2×#624C2×C414yescomplemented
117C32×C42—22no—
118#3752—22no—
119#3752C2×C414yescomplemented
120C4×C3⋊Dic3—22no—
121C3×(C2×D3)⋊C4—22no—
122C3×(C2×D3)⋊C4C2×C414yescomplemented
123C3×C4⋊Dic3—22no—
124C3×C4⋊Dic3C2×C414yescomplemented
125C3×C4×Dic3—22no—
126C3×C4×Dic3—22no—
127C3×C4×Dic3—22no—
128#3724—22no—
129#3724C2×C414yescomplemented
130Dic3⋊Dic3—22no—
131#3722—22no—
132(C2×D3)⋊Dic3—22no—
133(C2×D3)⋊Dic3—22no—
134(C2×D3)⋊Dic3C2×C414yescomplemented
135Dic32—22no—
136Dic32—22no—
137C4×#123—91noSylow
138C23×C3×C4—31no—
139C22×#67—31no—
140C22×D12—31no—
141C22×C4×D3—31no—
142C22×C4×D3—31no—
143C22×C4×D3—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3—61no—
148C22×C4×D3C2×D311yescharacteristic
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C22⋊C4—31no—
152C2×C3×C22⋊C4—31no—
153C2×C3×C42—21no—
154C2×C3×C42—31no—
155C2×C3×C42—31no—
156C2×C3×C42—31no—
157C2×C3×C42C2×D311yescharacteristic
158C2×C3×C42C2×D311yescharacteristic
159C2×#217—31no—
160C2×#217—31no—
161C2×#217—31no—
162C4×#67—64no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—61no—
173C2×(C2×D3)⋊C4—61no—
174C2×(C2×D3)⋊C4C2×D311yescharacteristic
175C2×(C2×D3)⋊C4C2×D311yescharacteristic
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3C2×D311yescharacteristic
178C2×C4⋊Dic3C2×D311yescharacteristic
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—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—61no—
191C2×C4×Dic3C2×D311yescharacteristic
192C2×C4×Dic3C2×D311yescharacteristic
193C2×C4×Dic3C2×D311yescharacteristic
194#894—38no—
195#883—38no—
196C4×D12—64no—
197C42×D3—64no—
198C42×D3—64no—
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—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—61no—
216C3⋊#95—61no—
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C23×C32C2411yescharacteristic
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3C22×C412yes—
227C22×C3⋊D3C2×D412yes—
228C22×C3⋊D3#4112yes—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3C22×C412yes—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C22×C412yes—
242C2×C32×C4C2×D412yes—
243C2×C32×C4#4112yes—
244C2×C32×C4#4112yes—
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⋊Dic3C22×C412yes—
253C2×C3⋊Dic3C2×D412yes—
254C4×C3⋊D3—28no—
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×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3C22×C412yes—
272C2×C3×Dic3C22×C412yes—
273C2×C3×Dic3C22×C412yes—
274C2×C3×Dic3#4112yes—
275C2×C3×Dic3#4112yes—
276C3×C4×D3—44no—
277#626—28no—
278#624—28no—
279#624—28no—
280C2×#123—91no—
281C2×C4×D4—91no—
282C22×C42—91no—
283#388—91no—
284#388—91no—
285#387—91no—
286#387—91no—
287#386—91no—
288#385—91no—
289#381—91no—
290C4×C4⋊C4—31no—
291C4×C4⋊C4—91no—
292C4×C22⋊C4—31no—
293C4×C22⋊C4—91no—
294C4×C22⋊C4—91no—
295C24×C3—31no—
296C23×D3—31no—
297C23×D3—31no—
298C23×D3—61no—
299C23×D3C22×D311yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—62no—
311C22×C3×C4—62no—
312C22×C3×C4—62no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C2×#67—34no—
320C2×#67—62no—
321C2×#67—62no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D311yescharacteristic
338C2×D12—34no—
339C2×D12—62no—
340C2×D12—62no—
341C2×C4×D3—22no—
342C2×C4×D3—22no—
343C2×C4×D3—22no—
344C2×C4×D3—34no—
345C2×C4×D3—34no—
346C2×C4×D3—34no—
347C2×C4×D3—34no—
348C2×C4×D3—64no—
349C2×C4×D3—62no—
350C2×C4×D3—62no—
351C2×C4×D3—62no—
352C2×C4×D3—62no—
353C2×C4×D3—62no—
354C2×C4×D3—62no—
355C2×C4×D3—62no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3—62no—
362C2×C4×D3—62no—
363C2×C4×D3—122no—
364C2×C4×D3—122no—
365C3×C4⋊C4—34no—
366C3×C4⋊C4—62no—
367C3×C22⋊C4—34no—
368C3×C22⋊C4—62no—
369C3×C42—22no—
370C3×C42—22no—
371C3×C42—42no—
372C3×C42—62no—
373C3×C42—62no—
374C3×C42—62no—
375#217—34no—
376#217—62no—
377#217—62no—
378(C2×D3)⋊C4—22no—
379(C2×D3)⋊C4—34no—
380(C2×D3)⋊C4—34no—
381(C2×D3)⋊C4—34no—
382(C2×D3)⋊C4—64no—
383(C2×D3)⋊C4—62no—
384(C2×D3)⋊C4—62no—
385(C2×D3)⋊C4—62no—
386(C2×D3)⋊C4—62no—
387(C2×D3)⋊C4—62no—
388(C2×D3)⋊C4—64no—
389(C2×D3)⋊C4—62no—
390(C2×D3)⋊C4C4×D314yescomplemented
391C4⋊Dic3—22no—
392C4⋊Dic3—62no—
393C4⋊Dic3C4×D314yescomplemented
394Dic3⋊C4—34no—
395Dic3⋊C4—34no—
396Dic3⋊C4—62no—
397Dic3⋊C4—62no—
398Dic3⋊C4—62no—
399C4×Dic3—22no—
400C4×Dic3—22no—
401C4×Dic3—22no—
402C4×Dic3—62no—
403C4×Dic3—62no—
404C4×Dic3—62no—
405C4×Dic3—62no—
406C4×Dic3—62no—
407C4×Dic3—62no—
408C4×Dic3—122no—
409C22×C32C23×C411yescharacteristic
410C22×C32C22×D411yescharacteristic
411C22×C32C2×#4111yescharacteristic
412C22×C32C2×#4111yescharacteristic
413C22×C32C2×#4111yescharacteristic
414C22×C32C2×#4111yescharacteristic
415C22×C32C2×#4111yescharacteristic
416C2×C3⋊D3—22no—
417C2×C3⋊D3—22no—
418C2×C3⋊D3—22no—
419C2×C3⋊D3—22no—
420C2×C3⋊D3—22no—
421C2×C3⋊D3—22no—
422C2×C3⋊D3C4×D414yes—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C32×C4—22no—
431C32×C4—41no—
432C32×C4#12314yescomplemented
433C3⋊Dic3—22no—
434C3⋊Dic3—22no—
435C3⋊Dic3—41no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C22×D4—91no—
444C23×C4—31no—
445C23×C4—91no—
446C23×C4—91no—
447C23×C4—91no—
448#123—98no—
449C4×D4—184no—
450C2×C4⋊C4—31no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4—91no—
453C2×C4⋊C4—91no—
454C2×C4⋊C4—91no—
455C2×C22⋊C4—31no—
456C2×C22⋊C4—31no—
457C2×C22⋊C4—91no—
458C2×C22⋊C4—91no—
459C2×C22⋊C4—91no—
460C2×C22⋊C4—91no—
461C2×C22⋊C4—91no—
462C2×C22⋊C4—91no—
463C2×C42—31no—
464C2×C42—31no—
465C2×C42—31no—
466C2×C42—91no—
467C2×C42—91no—
468C2×C42—91no—
469C2×C42—184no—
470C2×C42D3211yescharacteristic
471#95—31no—
472#95—31no—
473#95—31no—
474#95—31no—
475#95—91no—
476#95—91no—
477#95—91no—
478#95—91no—
479#95—91no—
480#95—91no—
481C23×C3—21no—
482C23×C3—32no—
483C23×C3—61no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
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—32no—
498C22×D3—32no—
499C22×D3—32no—
500C22×D3—32no—
501C22×D3—32no—
502C22×D3—32no—
503C22×D3—62no—
504C22×D3—62no—
505C22×D3—62no—
506C22×D3—61no—
507C22×D3—61no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—61no—
511C22×D3—61no—
512C22×D3—61no—
513C22×D3—61no—
514C22×D3—121no—
515C22×D3—121no—
516C22×D3—121no—
517C22×D3—121no—
518C22×D3C2×C4×D312yes—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—22no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—32no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—32no—
538C2×C3×C4—32no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—124no—
560C2×C3×C4C2×C4×D312yes—
561C2×C3×C4C2×C4×D312yes—
562C2×C3×C4#23512yes—
563C2×C3×C4#23512yes—
564C2×C3×C4D3×D412yes—
565C2×C3×C4D3×D412yes—
566C2×C3×C4#23712yes—
567C2×C3×C4#23912yes—
568#67—68no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—32no—
586C2×Dic3—32no—
587C2×Dic3—32no—
588C2×Dic3—32no—
589C2×Dic3—62no—
590C2×Dic3—62no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—62no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—121no—
607C2×Dic3—121no—
608C2×Dic3—121no—
609C2×Dic3—121no—
610C2×Dic3—121no—
611C2×Dic3—121no—
612C2×Dic3C2×C4×D312yes—
613C2×Dic3C2×C4×D312yes—
614C2×Dic3C2×C4×D312yes—
615C2×Dic3#23512yes—
616C2×Dic3#23512yes—
617D12—68no—
618C4×D3—44no—
619C4×D3—68no—
620C4×D3—68no—
621C4×D3—68no—
622C4×D3—68no—
623C4×D3—68no—
624C4×D3—68no—
625C4×D3—128no—
626C2×C32C2×C4×D411yescharacteristic
627C2×C32C4×#4111yescharacteristic
628C2×C32C4×#4111yescharacteristic
629C2×C32C2×#12311yescharacteristic
630C2×C32#52511yescharacteristic
631C2×C32#52911yescharacteristic
632C2×C32#52911yescharacteristic
633C3⋊D3—24no—
634C3×D3—42no—
635C24—31no—
636C24—91no—
637C2×D4—94no—
638C2×D4—182no—
639C2×D4—182no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—62no—
648C22×C4—62no—
649C22×C4—62no—
650C22×C4—94no—
651C22×C4—91no—
652C22×C4—91no—
653C22×C4—94no—
654C22×C4—91no—
655C22×C4—182no—
656C22×C4—182no—
657C22×C4—182no—
658C22×C4—182no—
659C22×C4—182no—
660C22×C4—182no—
661C22×C4—182no—
662C22×C4C2×D3211yescharacteristic
663C22×C4C2×D3211yescharacteristic
664C22×C4C2×D3211yescharacteristic
665C4⋊C4—34no—
666C4⋊C4—62no—
667C4⋊C4—94no—
668C4⋊C4—182no—
669C4⋊C4—182no—
670C22⋊C4—34no—
671C22⋊C4—62no—
672C22⋊C4—94no—
673C22⋊C4—94no—
674C22⋊C4—182no—
675C22⋊C4—182no—
676C22⋊C4—182no—
677C22⋊C4—182no—
678C42—22no—
679C42—62no—
680C42—62no—
681C42—62no—
682C42—182no—
683C42—182no—
684C42—182no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—62no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3C22×C4×D311yescharacteristic
700C22×C3C22×C4×D311yescharacteristic
701C22×C3C2×#23511yescharacteristic
702C22×C3C2×#23511yescharacteristic
703C22×C3C2×#23511yescharacteristic
704C22×C3C2×#23511yescharacteristic
705C22×C3C2×D3×D411yescharacteristic
706C22×C3C2×D3×D411yescharacteristic
707C22×C3C2×#23711yescharacteristic
708C22×C3C2×#23911yescharacteristic
709C22×C3D3×#4111yescharacteristic
710C22×C3D3×#4111yescharacteristic
711C22×C3D3×#4111yescharacteristic
712C22×C3D3×#4111yescharacteristic
713C2×D3—22no—
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—34no—
717C2×D3—34no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—64no—
723C2×D3—62no—
724C2×D3—62no—
725C2×D3—62no—
726C2×D3—62no—
727C2×D3—62no—
728C2×D3—62no—
729C2×D3—62no—
730C2×D3—62no—
731C2×D3—62no—
732C2×D3—62no—
733C2×D3—62no—
734C2×D3—62no—
735C2×D3—122no—
736C2×D3—122no—
737C2×D3—122no—
738C2×D3—122no—
739C2×D3—122no—
740C2×D3—122no—
741C3×C4—22no—
742C3×C4—22no—
743C3×C4—24no—
744C3×C4—42no—
745C3×C4—42no—
746C3×C4—41no—
747C3×C4—41no—
748C3×C4—62no—
749C3×C4—62no—
750C3×C4—62no—
751C3×C4—62no—
752C3×C4—62no—
753C3×C4—121no—
754C3×C4—121no—
755C3×C4#88314yescomplemented
756C3×C4#89414yescomplemented
757Dic3—22no—
758Dic3—22no—
759Dic3—22no—
760Dic3—22no—
761Dic3—22no—
762Dic3—41no—
763Dic3—41no—
764Dic3—62no—
765Dic3—62no—
766Dic3—62no—
767Dic3—62no—
768Dic3—122no—
769Dic3—122no—
770Dic3—122no—
771Dic3—121no—
772Dic3—121no—
773C32C4×#12311yescharacteristic, complemented, Sylow
774C23—32no—
775C23—61no—
776C23—61no—
777C23—61no—
778C23—61no—
779C23—61no—
780C23—61no—
781C23—92no—
782C23—92no—
783C23—92no—
784C23—181no—
785C23—181no—
786C23—181no—
787C23—181no—
788C23C22×D3211yescharacteristic
789D4—188no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—32no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—32no—
799C2×C4—32no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—92no—
817C2×C4—92no—
818C2×C4—124no—
819C2×C4—188no—
820C2×C4—188no—
821C2×C4—181no—
822C2×C4—181no—
823C2×C4—181no—
824C2×C4—181no—
825C2×C4—188no—
826C2×C4—181no—
827C2×C4—181no—
828C2×C4—181no—
829C2×C4#379912yes—
830C2×C4C4×D3212yes—
831C2×C4#380212yes—
832C2×C4#380412yes—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—122no—
841C2×C3C4×#23511yescharacteristic
842C2×C3C4×#23511yescharacteristic
843C2×C3C2×#88311yescharacteristic
844C2×C3C2×#89411yescharacteristic
845C2×C3#552811yescharacteristic
846C2×C3#552811yescharacteristic
847C2×C3C4×#23711yescharacteristic
848C2×C3C4×D3×D411yescharacteristic
849C2×C3C4×D3×D411yescharacteristic
850C2×C3#554711yescharacteristic
851C2×C3#554711yescharacteristic
852C2×C3#555711yescharacteristic
853C2×C3C4×#23911yescharacteristic
854C2×C3#558011yescharacteristic
855D3—42no—
856D3—64no—
857D3—64no—
858D3—124no—
859C22—62no—
860C22—62no—
861C22—62no—
862C22—94no—
863C22—121no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—182no—
868C22—182no—
869C22—182no—
870C22—182no—
871C22—182no—
872C22—182no—
873C22C2×#379911yescharacteristic
874C22C2×C4×D3211yescharacteristic
875C22C2×#380211yescharacteristic
876C22D3×#23511yescharacteristic
877C22D3×#23511yescharacteristic
878C22#6430611yescharacteristic
879C22C2×#380411yescharacteristic
880C4—22no—
881C4—41no—
882C4—62no—
883C4—62no—
884C4—62no—
885C4—62no—
886C4—62no—
887C4—121no—
888C4—121no—
889C4—182no—
890C4—182no—
891C4—361no—
892C4#6385414yesdirect product factor
893C3—21no—
894C3C4×#88311yescharacteristic, complemented
895C3C4×#89411yescharacteristic, complemented
896C2—122no—
897C2—184no—
898C2#1059393411yescharacteristic
899C2C4×#379911yescharacteristic
900C2C4×#380211yescharacteristic
901C2#1059400611yescharacteristic
902C2C2×#6385411yescharacteristic
903C2#1059483611yescharacteristic
904C2C4×#380411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C42D32
hypocenterC32C4×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×#624C2semidirect
4. C4×#3752C2semidirect
5. C3×C4×(C2×D3)⋊C4C2semidirect
6. C3×C4×C4⋊Dic3C2semidirect
7. #10591378C2semidirect
8. #10591371C2semidirect
9. C4×#3724C2semidirect
10. #10591307C2semidirect
11. #10591282C2semidirect
12. C4×(C2×D3)⋊Dic3C2semidirect
14. #10591270C2semidirect
15. #10591249C2semidirect
45. #63854C4direct (N × H)
75. C4×(C2×D3)⋊C4D3semidirect
76. C4×C4⋊Dic3D3semidirect
116. C2×#624C2×C4semidirect
119. #3752C2×C4semidirect
122. C3×(C2×D3)⋊C4C2×C4semidirect
124. C3×C4⋊Dic3C2×C4semidirect
129. #3724C2×C4semidirect
134. (C2×D3)⋊Dic3C2×C4semidirect
390. (C2×D3)⋊C4C4×D3semidirect
393. C4⋊Dic3C4×D3semidirect
432. C32×C4#123semidirect
755. C3×C4#883semidirect
756. C3×C4#894semidirect
773. C32C4×#123semidirect
892. C4#63854direct (N × H)
894. C3C4×#883semidirect
895. C3C4×#894semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6262
C2×C4×#6242
C2×#638542
C4×#37522
C3×C4×(C2×D3)⋊C42
C3×C4×C4⋊Dic32
#105913782
#105913712
C4×#37242
#105913072
#105912822
C4×(C2×D3)⋊Dic32
#105912752
#105912702
#105912492
C4×#8943
C4×#8833