Finite Group Databasebeta

← C4×#63868 #11802439

Subgroups — C4×#63868 #11802439

Order 1152.

1161 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63868C211yesmaximal, characteristic
2C4×#3752C211yesmaximal, characteristic
3C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C3×C42×Dic3C211yesmaximal, characteristic, complemented
5C4×#3724C211yesmaximal, characteristic, complemented
6#10591331C211yesmaximal, characteristic, complemented
7C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8#10591289C211yesmaximal, characteristic
9C4×#3722C211yesmaximal, characteristic
10C4×#3722C211yesmaximal, characteristic
11#10591223C211yesmaximal, characteristic, complemented
12#10591202C211yesmaximal, characteristic
13#10591201C211yesmaximal, characteristic, complemented
14#10591194C211yesmaximal, characteristic
15#10591193C211yesmaximal, characteristic, complemented
16C4×#898—31nomaximal
17C4×#876—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C2×C32×C42C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41#63868C418yesdirect product factor
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×#898—31no—
55C2×#876—31no—
56C3×C4×C4⋊C4—31no—
57C3×C43—31no—
58#4990—31no—
59#4980—31no—
60#4978—31no—
61#4940—31no—
62#4940—31no—
63#4940—31no—
64C4×(C2×D3)⋊C4—31no—
65C4×(C2×D3)⋊C4—31no—
66C4×(C2×D3)⋊C4—31no—
67C4×(C2×D3)⋊C4—31no—
68C4×(C2×D3)⋊C4—31no—
69C4×(C2×D3)⋊C4—31no—
70C4×(C2×D3)⋊C4—61no—
71#4937—31no—
72C4×C4⋊Dic3—31no—
73#4933—31no—
74#4933—31no—
75#4933—31no—
76C4×Dic3⋊C4—31no—
77C4×Dic3⋊C4—31no—
78C4×Dic3⋊C4—31no—
79C4×Dic3⋊C4D311yescharacteristic, complemented
80C42×Dic3D311yescharacteristic, complemented
81#4670—31no—
82#4669—31no—
83#4654—31no—
84#4651—31no—
85C23×C3⋊D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C2×C4×C3⋊D3—22no—
93C2×C4×C3⋊D3—22no—
94C2×C4×C3⋊D3—22no—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C32×C42—22no—
104#3752—22no—
105#3752C2×C414yes—
106C4×C3⋊Dic3—22no—
107C3×Dic3⋊C4—22no—
108C3×Dic3⋊C4C2×C414yescomplemented
109C3×C4×Dic3—22no—
110C3×C4×Dic3—22no—
111C3×C4×Dic3—22no—
112C3×C4×Dic3—22no—
113C3×C4×Dic3—22no—
114C3×C4×Dic3—22no—
115C3×C4×Dic3—22no—
116C3×C4×Dic3C2×C414yescomplemented
117#3724—22no—
118#3724C2×C414yescomplemented
119Dic3⋊Dic3—22no—
120Dic3⋊Dic3C2×C414yescomplemented
121#3722—22no—
122#3722—22no—
123#3722C2×C414yes—
124#3722C2×C414yes—
125C4×#126—91noSylow
126C22×C4×D3—31no—
127C22×C4×D3—31no—
128C22×C4×D3—61no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C42—21no—
132C2×C3×C42—31no—
133C2×C3×C42—31no—
134C2×C3×C42—31no—
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137C2×C3×C42—31no—
138C2×C3×C42—31no—
139C2×C3×C42—31no—
140C2×C3×C42C2×D311yescharacteristic
141C2×C3×C42C2×D311yescharacteristic
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—31no—
144C2×(C2×D3)⋊C4—31no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—61no—
155C2×(C2×D3)⋊C4—61no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4C2×D311yescharacteristic
165C2×Dic3⋊C4C2×D311yescharacteristic
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—61no—
169C2×C4×Dic3C2×D311yescharacteristic
170C2×C4×Dic3C2×D311yescharacteristic
171C2×C4×Dic3C2×D311yescharacteristic
172C2×C4×Dic3C2×D311yescharacteristic
173C2×C4×Dic3C2×D311yescharacteristic
174C2×C4×Dic3C2×D311yescharacteristic
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177#898—38no—
178#876—38no—
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—61no—
202C3⋊#95—61no—
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C23×C32C2411yescharacteristic
206C22×C3⋊D3—21no—
207C22×C3⋊D3—21no—
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—21no—
211C22×C3⋊D3—21no—
212C22×C3⋊D3C22×C412yes—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4C22×C412yes—
218C2×C32×C4#4112yes—
219C2×C32×C4#4112yes—
220C2×C32×C4#4112yes—
221C2×C32×C4#4112yes—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3C22×C412yes—
231C4×C3⋊D3—44no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
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—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3C22×C412yes—
251C2×C3×Dic3C22×C412yes—
252C2×C3×Dic3C22×C412yes—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3#4112yes—
255C2×C3×Dic3#4112yes—
256C2×#126—91no—
257#388—91no—
258#388—91no—
259#388—91no—
260#387—91no—
261#387—91no—
262#387—91no—
263#383—91no—
264C4×C4⋊C4—31no—
265C4×C4⋊C4—91no—
266C4×C4⋊C4—91no—
267C4×C22⋊C4—91no—
268C4×C22⋊C4—91no—
269C4×C22⋊C4—91no—
270C43—31no—
271C23×D3—31no—
272C23×D3—31no—
273C23×D3—61no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300C22×Dic3C22×D311yescharacteristic
301C22×Dic3C22×D311yescharacteristic
302C22×Dic3C22×D311yescharacteristic
303C22×Dic3C22×D311yescharacteristic
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C2×C4×D3—64no—
309C2×C4×D3—62no—
310C2×C4×D3—62no—
311C2×C4×D3—62no—
312C2×C4×D3—62no—
313C2×C4×D3—62no—
314C2×C4×D3—62no—
315C2×C4×D3—122no—
316C2×C4×D3—122no—
317C3×C4⋊C4—34no—
318C3×C4⋊C4—62no—
319C3×C42—22no—
320C3×C42—22no—
321C3×C42—34no—
322C3×C42—42no—
323C3×C42—62no—
324C3×C42—62no—
325C3×C42—62no—
326C3×C42—62no—
327C3×C42—62no—
328C3×C42—62no—
329C3×C42—62no—
330(C2×D3)⋊C4—34no—
331(C2×D3)⋊C4—34no—
332(C2×D3)⋊C4—34no—
333(C2×D3)⋊C4—34no—
334(C2×D3)⋊C4—34no—
335(C2×D3)⋊C4—34no—
336(C2×D3)⋊C4—64no—
337(C2×D3)⋊C4—62no—
338(C2×D3)⋊C4—62no—
339(C2×D3)⋊C4—64no—
340(C2×D3)⋊C4—62no—
341(C2×D3)⋊C4—62no—
342(C2×D3)⋊C4—62no—
343(C2×D3)⋊C4—62no—
344C4⋊Dic3—34no—
345C4⋊Dic3—62no—
346Dic3⋊C4—22no—
347Dic3⋊C4—34no—
348Dic3⋊C4—34no—
349Dic3⋊C4—34no—
350Dic3⋊C4—62no—
351Dic3⋊C4—62no—
352Dic3⋊C4—62no—
353Dic3⋊C4C4×D314yescomplemented
354C4×Dic3—22no—
355C4×Dic3—22no—
356C4×Dic3—22no—
357C4×Dic3—22no—
358C4×Dic3—22no—
359C4×Dic3—22no—
360C4×Dic3—22no—
361C4×Dic3—62no—
362C4×Dic3—62no—
363C4×Dic3—122no—
364C4×Dic3C4×D314yescomplemented
365C22×C32C23×C411yescharacteristic
366C22×C32C2×#4111yescharacteristic
367C22×C32C2×#4111yescharacteristic
368C22×C32C2×#4111yescharacteristic
369C22×C32C2×#4111yescharacteristic
370C22×C32C2×#4111yescharacteristic
371C22×C32C2×#4111yescharacteristic
372C2×C3⋊D3—22no—
373C2×C3⋊D3—22no—
374C2×C3⋊D3—22no—
375C2×C3⋊D3—41no—
376C2×C3⋊D3—41no—
377C2×C3⋊D3—41no—
378C2×C3⋊D3—41no—
379C32×C4—22no—
380C32×C4—22no—
381C32×C4#12614yescomplemented
382C3⋊Dic3—22no—
383C3⋊Dic3—41no—
384C3⋊Dic3—41no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—22no—
389C3×Dic3—22no—
390C3×Dic3—22no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C23×C4—91no—
394#126—98no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—91no—
398C2×C4⋊C4—91no—
399C2×C4⋊C4—91no—
400C2×C4⋊C4—91no—
401C2×C22⋊C4—91no—
402C2×C22⋊C4—91no—
403C2×C22⋊C4—91no—
404C2×C22⋊C4—91no—
405C2×C22⋊C4—91no—
406C2×C22⋊C4—91no—
407C2×C42—31no—
408C2×C42—31no—
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—31no—
412C2×C42—31no—
413C2×C42—31no—
414C2×C42—31no—
415C2×C42—91no—
416C2×C42D3211yescharacteristic
417#95—31no—
418#95—31no—
419#95—91no—
420#95—91no—
421#95—91no—
422#95—91no—
423#95—91no—
424#95—91no—
425#95—91no—
426#95—91no—
427#95—91no—
428#95—91no—
429C23×C3—21no—
430C23×C3C23×D311yescharacteristic
431C23×C3C23×D311yescharacteristic
432C22×D3—32no—
433C22×D3—32no—
434C22×D3—62no—
435C22×D3—62no—
436C22×D3—62no—
437C22×D3—61no—
438C22×D3—61no—
439C22×D3—61no—
440C22×D3—61no—
441C22×D3—61no—
442C22×D3—61no—
443C22×D3—61no—
444C22×D3—61no—
445C22×D3—61no—
446C22×D3—61no—
447C22×D3—61no—
448C22×D3—61no—
449C22×D3—121no—
450C22×D3—121no—
451C22×D3—121no—
452C22×D3—121no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—32no—
469C2×C3×C4—32no—
470C2×C3×C4—32no—
471C2×C3×C4—32no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
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×C4C2×C4×D312yes—
495C2×C3×C4C2×C4×D312yes—
496C2×C3×C4#23512yes—
497C2×C3×C4#23512yes—
498C2×C3×C4#23512yes—
499C2×C3×C4#23512yes—
500C2×C3×C4#23512yes—
501C2×C3×C4#23512yes—
502C2×C3×C4#23712yes—
503C2×C3×C4#23912yes—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
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—32no—
523C2×Dic3—32no—
524C2×Dic3—62no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—62no—
530C2×Dic3—62no—
531C2×Dic3—61no—
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—121no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3C2×C4×D312yes—
550C2×Dic3C2×C4×D312yes—
551C2×Dic3C2×C4×D312yes—
552C2×Dic3C2×C4×D312yes—
553C2×Dic3#23512yes—
554C2×Dic3#23512yes—
555C4×D3—128no—
556C4×D3—124no—
557C4×D3—124no—
558C2×C32C4×#4111yescharacteristic
559C2×C32C4×#4111yescharacteristic
560C2×C32C4×#4111yescharacteristic
561C2×C32C2×#12611yescharacteristic
562C2×C32#52911yescharacteristic
563C2×C32#52911yescharacteristic
564C2×C32#52911yescharacteristic
565C3⋊D3—42no—
566C24—91no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—91no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—182no—
579C22×C4—182no—
580C22×C4—182no—
581C22×C4C2×D3211yescharacteristic
582C22×C4C2×D3211yescharacteristic
583C22×C4C2×D3211yescharacteristic
584C4⋊C4—34no—
585C4⋊C4—62no—
586C4⋊C4—94no—
587C4⋊C4—94no—
588C4⋊C4—182no—
589C4⋊C4—182no—
590C22⋊C4—94no—
591C22⋊C4—94no—
592C22⋊C4—94no—
593C22⋊C4—182no—
594C22⋊C4—182no—
595C22⋊C4—182no—
596C42—22no—
597C42—34no—
598C42—62no—
599C42—62no—
600C42—62no—
601C42—62no—
602C42—62no—
603C42—62no—
604C42—62no—
605C42—182no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3C22×C4×D311yescharacteristic
614C22×C3C22×C4×D311yescharacteristic
615C22×C3C2×#23511yescharacteristic
616C22×C3C2×#23511yescharacteristic
617C22×C3C2×#23511yescharacteristic
618C22×C3C2×#23511yescharacteristic
619C22×C3C2×#23511yescharacteristic
620C22×C3C2×#23511yescharacteristic
621C22×C3C2×#23511yescharacteristic
622C22×C3C2×#23511yescharacteristic
623C22×C3C2×#23711yescharacteristic
624C22×C3C2×#23911yescharacteristic
625C22×C3D3×#4111yescharacteristic
626C22×C3D3×#4111yescharacteristic
627C2×D3—64no—
628C2×D3—62no—
629C2×D3—62no—
630C2×D3—62no—
631C2×D3—62no—
632C2×D3—62no—
633C2×D3—62no—
634C2×D3—122no—
635C2×D3—122no—
636C2×D3—122no—
637C2×D3—122no—
638C2×D3—122no—
639C2×D3—122no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—22no—
652C3×C4—24no—
653C3×C4—42no—
654C3×C4—42no—
655C3×C4—62no—
656C3×C4—62no—
657C3×C4—62no—
658C3×C4—62no—
659C3×C4—62no—
660C3×C4—62no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4#87614yescomplemented
664C3×C4#89814yescomplemented
665Dic3—22no—
666Dic3—22no—
667Dic3—22no—
668Dic3—22no—
669Dic3—22no—
670Dic3—22no—
671Dic3—41no—
672Dic3—41no—
673Dic3—62no—
674Dic3—62no—
675Dic3—122no—
676Dic3—122no—
677Dic3—122no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682C32C4×#12611yescharacteristic, complemented, Sylow
683C23—92no—
684C23—181no—
685C23—181no—
686C23—181no—
687C23—181no—
688C23—181no—
689C23—181no—
690C23C22×D3211yescharacteristic
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—32no—
696C2×C4—32no—
697C2×C4—32no—
698C2×C4—32no—
699C2×C4—32no—
700C2×C4—32no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—92no—
720C2×C4—181no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—364no—
729C2×C4#379812yes—
730C2×C4#379812yes—
731C2×C4#379912yes—
732C2×C4C4×D3212yes—
733C2×C4#380412yes—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3C4×#23511yescharacteristic
742C2×C3C4×#23511yescharacteristic
743C2×C3C4×#23511yescharacteristic
744C2×C3C4×#23511yescharacteristic
745C2×C3C2×#87611yescharacteristic
746C2×C3#547911yescharacteristic
747C2×C3#547911yescharacteristic
748C2×C3#547911yescharacteristic
749C2×C3C2×#89811yescharacteristic
750C2×C3#552811yescharacteristic
751C2×C3C4×#23711yescharacteristic
752C2×C3#553811yescharacteristic
753C2×C3C4×#23911yescharacteristic
754C2×C3#558011yescharacteristic
755D3—124no—
756D3—122no—
757D3—122no—
758C22—182no—
759C22—182no—
760C22—182no—
761C22—361no—
762C22—361no—
763C22—361no—
764C22—361no—
765C22C2×#379811yescharacteristic
766C22C2×#379811yescharacteristic
767C22C2×#379911yescharacteristic
768C22C2×C4×D3211yescharacteristic
769C22D3×#23511yescharacteristic
770C22D3×#23511yescharacteristic
771C22C2×#380411yescharacteristic
772C4—22no—
773C4—22no—
774C4—62no—
775C4—62no—
776C4—62no—
777C4—62no—
778C4—62no—
779C4—62no—
780C4—121no—
781C4—121no—
782C4—182no—
783C4—361no—
784C4—361no—
785C4#6386814yesdirect product factor
786C3—21no—
787C3C4×#87611yescharacteristic, complemented
788C3C4×#89811yescharacteristic, complemented
789C2—362no—
790C2#1059387011yescharacteristic
791C2C4×#379811yescharacteristic
792C2C4×#379911yescharacteristic
793C2#1059397311yescharacteristic
794C2#1059483911yescharacteristic
795C2C2×#6386811yescharacteristic
796C2C4×#380411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32C4×#126
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×C4×Dic3⋊C4C2semidirect
4. C3×C42×Dic3C2semidirect
5. C4×#3724C2semidirect
6. #10591331C2semidirect
7. C4×Dic3⋊Dic3C2semidirect
11. #10591223C2semidirect
13. #10591201C2semidirect
15. #10591193C2semidirect
41. #63868C4direct (N × H)
79. C4×Dic3⋊C4D3semidirect
80. C42×Dic3D3semidirect
108. C3×Dic3⋊C4C2×C4semidirect
116. C3×C4×Dic3C2×C4semidirect
118. #3724C2×C4semidirect
120. Dic3⋊Dic3C2×C4semidirect
353. Dic3⋊C4C4×D3semidirect
364. C4×Dic3C4×D3semidirect
381. C32×C4#126semidirect
663. C3×C4#876semidirect
664. C3×C4#898semidirect
682. C32C4×#126semidirect
785. C4#63868direct (N × H)
787. C3C4×#876semidirect
788. C3C4×#898semidirect

Maximal subgroups

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

subgroupindex
C2×#638682
C4×#37522
C3×C4×Dic3⋊C42
C3×C42×Dic32
C4×#37242
#105913312
C4×Dic3⋊Dic32
#105912892
C4×#37222
#105912232
#105912022
#105912012
#105911942
#105911932
C4×#8983
C4×#8763