Finite Group Databasebeta

← C4×#63850 #11802192

Subgroups — C4×#63850 #11802192

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×C3×C42×D3C211yesmaximal, characteristic, complemented
2C2×C4×#626C211yesmaximal, characteristic
3C2×#63850C211yesmaximal, characteristic
4C4×#3752C211yesmaximal, characteristic, complemented
5C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
6#10591382C211yesmaximal, characteristic
7C4×#3724C211yesmaximal, characteristic, complemented
8#10591333C211yesmaximal, characteristic, complemented
9#10591294C211yesmaximal, characteristic, complemented
10#10591289C211yesmaximal, characteristic, complemented
11C4×#3722C211yesmaximal, characteristic, complemented
12#10591277C211yesmaximal, characteristic, complemented
13C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
14#10591202C211yesmaximal, characteristic, complemented
15#10591201C211yesmaximal, characteristic, complemented
16C4×#929—31nomaximal
17C4×#894—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×C42×D3—24no—
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C4×#626—24no—
45#63850C418yesdirect product factor
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C22×C3×C42—31no—
57C2×#929—31no—
58C2×C4×#67—31no—
59C2×#894—31no—
60C2×C4×D12—31no—
61C2×C42×D3D311yescharacteristic, complemented
62C3×C4×C4⋊C4—31no—
63#5213—31no—
64#5211—31no—
65#5210—31no—
66C4×#217—31no—
67#4990—31no—
68#4989—31no—
69#4980—31no—
70#4940—31no—
71#4940—31no—
72C4×(C2×D3)⋊C4—31no—
73C4×(C2×D3)⋊C4—31no—
74C4×(C2×D3)⋊C4—31no—
75C4×(C2×D3)⋊C4—31no—
76C4×(C2×D3)⋊C4—31no—
77C4×(C2×D3)⋊C4—61no—
78#4933—31no—
79#4933—31no—
80C4×Dic3⋊C4—31no—
81C4×Dic3⋊C4—31no—
82C4×Dic3⋊C4D311yescharacteristic, complemented
83#4669—31no—
84#4665—31no—
85#4664—31no—
86#4655—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⋊D3—22no—
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×C3×C4×D3—22no—
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3C2×C414yescomplemented
113C2×C3×C4×D3D414yes—
114C2×#626—22no—
115C2×#626—22no—
116C2×#626C2×C414yes—
117C32×C42—22no—
118#3752—22no—
119#3752C2×C414yescomplemented
120C4×C3⋊Dic3—22no—
121C3×Dic3⋊C4—22no—
122C3×Dic3⋊C4C2×C414yescomplemented
123C3×C4×Dic3—22no—
124C3×C4×Dic3—22no—
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#3722—22no—
133#3722C2×C414yescomplemented
134(C2×D3)⋊Dic3—22no—
135(C2×D3)⋊Dic3—22no—
136(C2×D3)⋊Dic3C2×C414yescomplemented
137C4×#123—91noSylow
138C23×C3×C4—31no—
139C23×C3×C4—31no—
140C23×C3×C4—31no—
141C22×#67—31no—
142C22×D12—31no—
143C22×C4×D3—31no—
144C22×C4×D3—31no—
145C22×C4×D3—61no—
146C22×C4×D3C2×D311yescharacteristic
147C22×C4×D3C2×D311yescharacteristic
148C22×C4×D3C2×D311yescharacteristic
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C42—21no—
152C2×C3×C42—31no—
153C2×C3×C42—31no—
154C2×C3×C42—31no—
155C2×C3×C42—31no—
156C2×C3×C42—31no—
157C2×C3×C42—64no—
158C2×C3×C42C2×D311yescharacteristic
159C2×C3×C42C2×D311yescharacteristic
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—31no—
163#929—38no—
164C4×#67—64no—
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—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—61no—
179C2×(C2×D3)⋊C4—61no—
180C2×C4⋊Dic3—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4C2×D311yescharacteristic
187C2×Dic3⋊C4C2×D311yescharacteristic
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—61no—
191C2×C4×Dic3C2×D311yescharacteristic
192C2×C4×Dic3C2×D311yescharacteristic
193C2×C4×Dic3C2×D311yescharacteristic
194C2×C4×Dic3C2×D311yescharacteristic
195C2×C4×Dic3C2×D311yescharacteristic
196#894—38no—
197C4×D12—64no—
198C42×D3—24no—
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—31no—
216C3⋊#95—31no—
217C3⋊#95—61no—
218C3⋊#95—61no—
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⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3C22×C412yes—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3C22×C412yes—
234C22×C3×D3C2×D412yes—
235C22×C3×D3#4112yes—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C22×C412yes—
241C2×C32×C4C2×D412yes—
242C2×C32×C4#4112yes—
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⋊Dic3—21no—
253C2×C3⋊Dic3C22×C412yes—
254C4×C3⋊D3—44no—
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×Dic3C2×D412yes—
275C2×C3×Dic3#4112yes—
276C3×C4×D3—28no—
277C3×C4×D3—28no—
278C3×C4×D3—28no—
279#626—28no—
280C2×#123—91no—
281C2×C4×D4—91no—
282C22×C42—31no—
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—91no—
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—34no—
309C22×C3×C4—34no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—62no—
313C22×C3×C4—62no—
314C22×C3×C4—62no—
315C22×C3×C4—62no—
316C22×C3×C4—62no—
317C22×C3×C4—62no—
318C22×C3×C4—62no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—34no—
326C2×#67—62no—
327C2×#67—62no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3C22×D311yescharacteristic
338C22×Dic3C22×D311yescharacteristic
339C22×Dic3C22×D311yescharacteristic
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D311yescharacteristic
343C22×Dic3C22×D311yescharacteristic
344C2×D12—34no—
345C2×D12—62no—
346C2×D12—62no—
347C2×C4×D3—22no—
348C2×C4×D3—22no—
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C2×C4×D3—22no—
352C2×C4×D3—22no—
353C2×C4×D3—22no—
354C2×C4×D3—64no—
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—122no—
362C2×C4×D3—122no—
363C2×C4×D3C4×D314yescomplemented
364C2×C4×D3#6714yes—
365C3×C4⋊C4—34no—
366C3×C4⋊C4—62no—
367C3×C42—22no—
368C3×C42—22no—
369C3×C42—42no—
370C3×C42—62no—
371C3×C42—62no—
372C3×C42—62no—
373C3×C42—62no—
374C3×C42—62no—
375#217—34no—
376#217—62no—
377#217—62no—
378(C2×D3)⋊C4—34no—
379(C2×D3)⋊C4—34no—
380(C2×D3)⋊C4—34no—
381(C2×D3)⋊C4—34no—
382(C2×D3)⋊C4—34no—
383(C2×D3)⋊C4—64no—
384(C2×D3)⋊C4—62no—
385(C2×D3)⋊C4—62no—
386(C2×D3)⋊C4—64no—
387(C2×D3)⋊C4—62no—
388(C2×D3)⋊C4—62no—
389(C2×D3)⋊C4—62no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—62no—
392(C2×D3)⋊C4—62no—
393C4⋊Dic3—62no—
394Dic3⋊C4—22no—
395Dic3⋊C4—34no—
396Dic3⋊C4—34no—
397Dic3⋊C4—62no—
398Dic3⋊C4—62no—
399Dic3⋊C4—62no—
400Dic3⋊C4C4×D314yescomplemented
401C4×Dic3—22no—
402C4×Dic3—22no—
403C4×Dic3—22no—
404C4×Dic3—22no—
405C4×Dic3—22no—
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—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3C4×D414yes—
430C32×C4—22no—
431C32×C4—22no—
432C32×C4#12314yescomplemented
433C3⋊Dic3—22no—
434C3⋊Dic3—41no—
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—31no—
446C23×C4—31no—
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—91no—
456C2×C22⋊C4—91no—
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—31no—
467C2×C42—31no—
468C2×C42—64no—
469C2×C42—91no—
470C2×C42D3211yescharacteristic
471#95—31no—
472#95—31no—
473#95—91no—
474#95—91no—
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—32no—
484C23×C3—32no—
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—32no—
496C22×D3—32no—
497C22×D3—62no—
498C22×D3—62no—
499C22×D3—62no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—61no—
506C22×D3—61no—
507C22×D3—61no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—61no—
511C22×D3—61no—
512C22×D3—121no—
513C22×D3—121no—
514C22×D3—121no—
515C22×D3—121no—
516C22×D3C2×C4×D312yes—
517C22×D3#23512yes—
518C22×D3C2×#6712yes—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—32no—
533C2×C3×C4—32no—
534C2×C3×C4—32no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—68no—
542C2×C3×C4—68no—
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—68no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4C2×C4×D312yes—
561C2×C3×C4C2×C4×D312yes—
562C2×C3×C4#23512yes—
563C2×C3×C4#23512yes—
564C2×C3×C4#23512yes—
565C2×C3×C4#23512yes—
566C2×C3×C4#23512yes—
567C2×C3×C4D3×D412yes—
568C2×C3×C4#23912yes—
569C2×C3×C4C2×#6712yes—
570#67—68no—
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—21no—
586C2×Dic3—21no—
587C2×Dic3—32no—
588C2×Dic3—32no—
589C2×Dic3—62no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—62no—
595C2×Dic3—62no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—121no—
609C2×Dic3—121no—
610C2×Dic3—121no—
611C2×Dic3—121no—
612C2×Dic3—121no—
613C2×Dic3—121no—
614C2×Dic3C2×C4×D312yes—
615C2×Dic3C2×C4×D312yes—
616C2×Dic3C2×C4×D312yes—
617C2×Dic3#23512yes—
618C2×Dic3C2×#6712yes—
619D12—68no—
620C4×D3—28no—
621C4×D3—28no—
622C4×D3—28no—
623C4×D3—128no—
624C4×D3—124no—
625C4×D3—124no—
626C2×C32C2×C4×D411yescharacteristic
627C2×C32C4×#4111yescharacteristic
628C2×C32C4×#4111yescharacteristic
629C2×C32C2×#12311yescharacteristic
630C2×C32#52511yescharacteristic
631C2×C32#52911yescharacteristic
632C2×C32#52911yescharacteristic
633C3⋊D3—42no—
634C3×D3—24no—
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—34no—
646C22×C4—34no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—62no—
650C22×C4—62no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—91no—
657C22×C4—91no—
658C22×C4—91no—
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—94no—
671C22⋊C4—94no—
672C22⋊C4—94no—
673C22⋊C4—182no—
674C22⋊C4—182no—
675C22⋊C4—182no—
676C22⋊C4—182no—
677C22⋊C4—182no—
678C42—22no—
679C42—62no—
680C42—62no—
681C42—62no—
682C42—62no—
683C42—62no—
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—34no—
693C22×C3—62no—
694C22×C3—62no—
695C22×C3—62no—
696C22×C3—62no—
697C22×C3—62no—
698C22×C3—62no—
699C22×C3C22×C4×D311yescharacteristic
700C22×C3C22×C4×D311yescharacteristic
701C22×C3C2×#23511yescharacteristic
702C22×C3C2×#23511yescharacteristic
703C22×C3C2×#23511yescharacteristic
704C22×C3C2×#23511yescharacteristic
705C22×C3C2×#23511yescharacteristic
706C22×C3C2×#23511yescharacteristic
707C22×C3C2×#23511yescharacteristic
708C22×C3C2×D3×D411yescharacteristic
709C22×C3C2×#23911yescharacteristic
710C22×C3D3×#4111yescharacteristic
711C22×C3D3×#4111yescharacteristic
712C22×C3C22×#6711yescharacteristic
713C2×D3—22no—
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—22no—
718C2×D3—22no—
719C2×D3—64no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—62no—
723C2×D3—62no—
724C2×D3—62no—
725C2×D3—62no—
726C2×D3—122no—
727C2×D3—122no—
728C2×D3—122no—
729C2×D3—122no—
730C2×D3—122no—
731C2×D3—122no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—121no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3C4×#6714yes—
741C3×C4—22no—
742C3×C4—22no—
743C3×C4—22no—
744C3×C4—22no—
745C3×C4—24no—
746C3×C4—42no—
747C3×C4—42no—
748C3×C4—62no—
749C3×C4—62no—
750C3×C4—62no—
751C3×C4—62no—
752C3×C4—62no—
753C3×C4—121no—
754C3×C4—121no—
755C3×C4#89414yescomplemented
756C3×C4#92914yescomplemented
757Dic3—22no—
758Dic3—22no—
759Dic3—22no—
760Dic3—22no—
761Dic3—22no—
762Dic3—41no—
763Dic3—41no—
764Dic3—62no—
765Dic3—62no—
766Dic3—122no—
767Dic3—122no—
768Dic3—122no—
769Dic3—121no—
770Dic3—121no—
771Dic3—121no—
772Dic3—121no—
773C32C4×#12311yescharacteristic, complemented, Sylow
774C23—32no—
775C23—32no—
776C23—32no—
777C23—61no—
778C23—61no—
779C23—61no—
780C23—61no—
781C23—92no—
782C23—181no—
783C23—181no—
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—32no—
795C2×C4—32no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—32no—
799C2×C4—68no—
800C2×C4—68no—
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—68no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—92no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—181no—
823C2×C4—181no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4—181no—
827C2×C4—364no—
828C2×C4#379812yes—
829C2×C4#379812yes—
830C2×C4#379912yes—
831C2×C4C4×D3212yes—
832C2×C4D3×#6712yes—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—64no—
841C2×C3C4×#23511yescharacteristic
842C2×C3C4×#23511yescharacteristic
843C2×C3C4×#23511yescharacteristic
844C2×C3#547911yescharacteristic
845C2×C3#547911yescharacteristic
846C2×C3C2×#89411yescharacteristic
847C2×C3#552811yescharacteristic
848C2×C3C4×D3×D411yescharacteristic
849C2×C3#554711yescharacteristic
850C2×C3C4×#23911yescharacteristic
851C2×C3#558011yescharacteristic
852C2×C3C2×C4×#6711yescharacteristic
853C2×C3C2×#92911yescharacteristic
854C2×C3#579111yescharacteristic
855D3—24no—
856D3—124no—
857D3—122no—
858D3—122no—
859C22—34no—
860C22—62no—
861C22—62no—
862C22—62no—
863C22—62no—
864C22—62no—
865C22—62no—
866C22—182no—
867C22—182no—
868C22—182no—
869C22—361no—
870C22—361no—
871C22—361no—
872C22—361no—
873C22C2×#379811yescharacteristic
874C22C2×#379811yescharacteristic
875C22C2×#379911yescharacteristic
876C22C2×C4×D3211yescharacteristic
877C22D3×#23511yescharacteristic
878C22D3×#23511yescharacteristic
879C22C2×D3×#6711yescharacteristic
880C4—22no—
881C4—22no—
882C4—62no—
883C4—62no—
884C4—62no—
885C4—62no—
886C4—62no—
887C4—121no—
888C4—121no—
889C4—182no—
890C4—361no—
891C4—361no—
892C4#6385014yesdirect product factor
893C3—21no—
894C3C4×#89411yescharacteristic, complemented
895C3C4×#92911yescharacteristic, complemented
896C2—64no—
897C2—362no—
898C2#1059387011yescharacteristic
899C2C4×#379811yescharacteristic
900C2C4×#379911yescharacteristic
901C2#1059397311yescharacteristic
902C2C2×#6385011yescharacteristic
903C2#1059500211yescharacteristic
904C2C4×D3×#6711yescharacteristic
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
1. C2×C3×C42×D3C2semidirect
4. C4×#3752C2semidirect
5. C3×C4×Dic3⋊C4C2semidirect
7. C4×#3724C2semidirect
8. #10591333C2semidirect
9. #10591294C2semidirect
10. #10591289C2semidirect
11. C4×#3722C2semidirect
12. #10591277C2semidirect
13. C4×(C2×D3)⋊Dic3C2semidirect
14. #10591202C2semidirect
15. #10591201C2semidirect
45. #63850C4direct (N × H)
61. C2×C42×D3D3semidirect
82. C4×Dic3⋊C4D3semidirect
112. C2×C3×C4×D3C2×C4semidirect
119. #3752C2×C4semidirect
122. C3×Dic3⋊C4C2×C4semidirect
129. #3724C2×C4semidirect
133. #3722C2×C4semidirect
136. (C2×D3)⋊Dic3C2×C4semidirect
363. C2×C4×D3C4×D3semidirect
400. Dic3⋊C4C4×D3semidirect
432. C32×C4#123semidirect
755. C3×C4#894semidirect
756. C3×C4#929semidirect
773. C32C4×#123semidirect
892. C4#63850direct (N × H)
894. C3C4×#894semidirect
895. C3C4×#929semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C42×D32
C2×C4×#6262
C2×#638502
C4×#37522
C3×C4×Dic3⋊C42
#105913822
C4×#37242
#105913332
#105912942
#105912892
C4×#37222
#105912772
C4×(C2×D3)⋊Dic32
#105912022
#105912012
C4×#9293
C4×#8943