Finite Group Databasebeta

← C4×#63891 #11802199

Subgroups — C4×#63891 #11802199

Order 1152.

1473 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#625C211yesmaximal, characteristic
2C2×#63891C211yesmaximal, characteristic
3C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
4C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#10591379C211yesmaximal, characteristic, complemented
8#10591363C211yesmaximal, characteristic
9#10591362C211yesmaximal, characteristic, complemented
10C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
11#10591316C211yesmaximal, characteristic, complemented
12#10591284C211yesmaximal, characteristic, complemented
13C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
14#10591271C211yesmaximal, characteristic, complemented
15#10591250C211yesmaximal, characteristic, complemented
16C4×#883—31nomaximal
17C4×#886—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#625C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C4×#625—24no—
44#63891C418yesdirect product factor
45C4×D3×Dic3—24no—
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×C4×#67—31no—
58C22×C4×Dic3—31no—
59C2×#886—31no—
60C2×#883—31no—
61C2×C42×D3—31no—
62C3×C4×C22⋊C4—31no—
63C3×C4×C22⋊C4—31no—
64C4×#217—31no—
65#4958—31no—
66#4956—31no—
67#4951—31no—
68#4950—31no—
69#4945—31no—
70#4943—31no—
71C4×(C2×D3)⋊C4—31no—
72C4×(C2×D3)⋊C4D311yescharacteristic, complemented
73C4×(C2×D3)⋊C4D311yescharacteristic, complemented
74C4×C4⋊Dic3—31no—
75C4×C4⋊Dic3—31no—
76C4×C4⋊Dic3—31no—
77C4×C4⋊Dic3—61no—
78C4×Dic3⋊C4—31no—
79#4670—31no—
80#4670—31no—
81#4668—31no—
82#4664—31no—
83#4654—31no—
84#4653—31no—
85#4653—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
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—22no—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3D414yes—
108C2×#625—22no—
109C2×#625—22no—
110C2×#625C2×C414yes—
111C2×D3×Dic3—22no—
112C2×D3×Dic3—22no—
113C2×D3×Dic3—22no—
114C2×D3×Dic3—22no—
115C2×D3×Dic3—22no—
116C2×D3×Dic3C2×C414yescomplemented
117C32×C42—22no—
118C4⋊(C3⋊Dic3)—22no—
119C4⋊(C3⋊Dic3)C2×C414yescomplemented
120C4×C3⋊Dic3—22no—
121C4×C3⋊Dic3—22no—
122C3×(C2×D3)⋊C4—22no—
123C3×(C2×D3)⋊C4—22no—
124C3×(C2×D3)⋊C4C2×C414yescomplemented
125C3×(C2×D3)⋊C4C2×C414yescomplemented
126C3×C4×Dic3—22no—
127C3×C4×Dic3—22no—
128#3724—22no—
129Dic3⋊Dic3—22no—
130Dic3⋊Dic3C2×C414yescomplemented
131(C2×D3)⋊Dic3—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—
139C23×C3×C4—31no—
140C22×#67—31no—
141C22×#67—31no—
142C23×Dic3—31no—
143C23×Dic3—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3C2×D311yescharacteristic
147C22×C4×D3C2×D311yescharacteristic
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—31no—
151C2×C3×C22⋊C4—31no—
152C2×C3×C42—21no—
153C2×C3×C42—31no—
154C2×C3×C42—31no—
155C2×C3×C42C2×D311yescharacteristic
156C2×C3×C42C2×D311yescharacteristic
157C2×#217—31no—
158C2×#217—31no—
159C2×#217—31no—
160C2×#217—31no—
161C4×#67—64no—
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)⋊C4C2×D311yescharacteristic
168C2×(C2×D3)⋊C4C2×D311yescharacteristic
169C2×(C2×D3)⋊C4C2×D311yescharacteristic
170C2×(C2×D3)⋊C4C2×D311yescharacteristic
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—61no—
178C2×C4⋊Dic3—61no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—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×Dic3—64no—
194C2×C4×Dic3C2×D311yescharacteristic
195C2×C4×Dic3C2×D311yescharacteristic
196#886—38no—
197#883—38no—
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×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3C22×C412yes—
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×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⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C22×C412yes—
255C2×C3⋊Dic3C22×C412yes—
256C2×C3⋊Dic3#4112yes—
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×Dic3C2×D412yes—
274C2×C3×Dic3#4112yes—
275C3×C4×D3—28no—
276C3×C4×D3—44no—
277#625—28no—
278D3×Dic3—28no—
279D3×Dic3—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—91no—
291C4×C4⋊C4—91no—
292C4×C22⋊C4—31no—
293C4×C22⋊C4—31no—
294C4×C22⋊C4—91no—
295C24×C3—31no—
296C24×C3—31no—
297C23×D3C22×D311yescharacteristic
298C23×D3C22×D311yescharacteristic
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—34no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—62no—
310C22×C3×C4—62no—
311C22×C3×C4—62no—
312C22×C3×C4—62no—
313C22×C3×C4—62no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—34no—
321C2×#67—34no—
322C2×#67—62no—
323C2×#67—62no—
324C2×#67—62no—
325C2×#67—62no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—34no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—62no—
340C22×Dic3—62no—
341C22×Dic3—62no—
342C22×Dic3—62no—
343C22×Dic3—62no—
344C22×Dic3C22×D311yescharacteristic
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D311yescharacteristic
350C2×C4×D3—22no—
351C2×C4×D3—22no—
352C2×C4×D3—22no—
353C2×C4×D3—22no—
354C2×C4×D3—22no—
355C2×C4×D3—34no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3D1214yes—
362C3×C22⋊C4—34no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—62no—
365C3×C22⋊C4—62no—
366C3×C42—24no—
367C3×C42—22no—
368C3×C42—22no—
369C3×C42—62no—
370C3×C42—62no—
371#217—34no—
372#217—62no—
373#217—62no—
374#217—62no—
375(C2×D3)⋊C4—22no—
376(C2×D3)⋊C4—22no—
377(C2×D3)⋊C4—34no—
378(C2×D3)⋊C4—62no—
379(C2×D3)⋊C4—62no—
380(C2×D3)⋊C4—62no—
381(C2×D3)⋊C4C4×D314yescomplemented
382(C2×D3)⋊C4C4×D314yescomplemented
383C4⋊Dic3—34no—
384C4⋊Dic3—34no—
385C4⋊Dic3—34no—
386C4⋊Dic3—64no—
387C4⋊Dic3—62no—
388C4⋊Dic3—62no—
389C4⋊Dic3—64no—
390C4⋊Dic3—62no—
391Dic3⋊C4—34no—
392Dic3⋊C4—62no—
393Dic3⋊C4—62no—
394Dic3⋊C4—62no—
395C4×Dic3—22no—
396C4×Dic3—22no—
397C4×Dic3—62no—
398C4×Dic3—62no—
399C4×Dic3—62no—
400C4×Dic3—62no—
401C4×Dic3—62no—
402C4×Dic3—62no—
403C4×Dic3—62no—
404C4×Dic3—62no—
405C4×Dic3—122no—
406C4×Dic3—122no—
407C22×C32C23×C411yescharacteristic
408C22×C32C22×D411yescharacteristic
409C22×C32C2×#4111yescharacteristic
410C22×C32C2×#4111yescharacteristic
411C22×C32C2×#4111yescharacteristic
412C22×C32C2×#4111yescharacteristic
413C22×C32C2×#4111yescharacteristic
414C2×C3×D3—22no—
415C2×C3×D3—22no—
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×D3—22no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3C4×D414yes—
428C32×C4—22no—
429C32×C4—41no—
430C32×C4#12314yescomplemented
431C3⋊Dic3—22no—
432C3⋊Dic3—22no—
433C3⋊Dic3—22no—
434C3⋊Dic3—41no—
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C22×D4—91no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—91no—
445C23×C4—91no—
446#123—98no—
447C4×D4—184no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4—91no—
451C2×C4⋊C4—91no—
452C2×C4⋊C4—91no—
453C2×C22⋊C4—31no—
454C2×C22⋊C4—31no—
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×C42—31no—
462C2×C42—31no—
463C2×C42—91no—
464C2×C42—91no—
465C2×C42—91no—
466C2×C42—91no—
467C2×C42—184no—
468C2×C42D3211yescharacteristic
469#95—31no—
470#95—31no—
471#95—31no—
472#95—31no—
473#95—91no—
474#95—91no—
475#95—91no—
476#95—91no—
477#95—91no—
478#95—91no—
479C23×C3—21no—
480C23×C3—32no—
481C23×C3—32no—
482C23×C3—32no—
483C23×C3—32no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3—61no—
493C23×C3—61no—
494C23×C3C23×D311yescharacteristic
495C23×C3C23×D311yescharacteristic
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—21no—
505C22×D3—21no—
506C22×D3C2×C4×D312yes—
507C22×D3C2×C4×D312yes—
508C22×D3C2×D1212yes—
509C22×D3#23512yes—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—22no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—32no—
528C2×C3×C4—32no—
529C2×C3×C4—32no—
530C2×C3×C4—32no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—68no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—124no—
549C2×C3×C4C2×C4×D312yes—
550C2×C3×C4C2×C4×D312yes—
551C2×C3×C4C2×D1212yes—
552C2×C3×C4#23512yes—
553C2×C3×C4D3×D412yes—
554C2×C3×C4#23712yes—
555C2×C3×C4#23712yes—
556C2×C3×C4#23712yes—
557#67—68no—
558#67—68no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—32no—
574C2×Dic3—32no—
575C2×Dic3—32no—
576C2×Dic3—32no—
577C2×Dic3—32no—
578C2×Dic3—32no—
579C2×Dic3—62no—
580C2×Dic3—62no—
581C2×Dic3—62no—
582C2×Dic3—68no—
583C2×Dic3—68no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—62no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—121no—
604C2×Dic3—121no—
605C2×Dic3—121no—
606C2×Dic3—121no—
607C2×Dic3—121no—
608C2×Dic3—121no—
609C2×Dic3—121no—
610C2×Dic3—121no—
611C2×Dic3C2×C4×D312yes—
612C2×Dic3C2×C4×D312yes—
613C2×Dic3C2×D1212yes—
614C2×Dic3#23512yes—
615C4×D3—28no—
616C4×D3—44no—
617C4×D3—68no—
618C4×D3—68no—
619C2×C32C2×C4×D411yescharacteristic
620C2×C32C4×#4111yescharacteristic
621C2×C32C4×#4111yescharacteristic
622C2×C32C2×#12311yescharacteristic
623C2×C32#52511yescharacteristic
624C2×C32#52911yescharacteristic
625C2×C32#52911yescharacteristic
626C3×D3—24no—
627C3×D3—42no—
628C24—31no—
629C24—31no—
630C2×D4—94no—
631C2×D4—182no—
632C2×D4—182no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—34no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—62no—
641C22×C4—62no—
642C22×C4—62no—
643C22×C4—62no—
644C22×C4—62no—
645C22×C4—94no—
646C22×C4—91no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4—182no—
651C22×C4—182no—
652C22×C4—182no—
653C22×C4—182no—
654C22×C4—182no—
655C22×C4C2×D3211yescharacteristic
656C22×C4C2×D3211yescharacteristic
657C22×C4C2×D3211yescharacteristic
658C4⋊C4—94no—
659C4⋊C4—94no—
660C4⋊C4—182no—
661C4⋊C4—182no—
662C4⋊C4—182no—
663C22⋊C4—34no—
664C22⋊C4—34no—
665C22⋊C4—62no—
666C22⋊C4—62no—
667C22⋊C4—94no—
668C22⋊C4—182no—
669C22⋊C4—182no—
670C22⋊C4—182no—
671C42—22no—
672C42—62no—
673C42—62no—
674C42—182no—
675C42—182no—
676C42—182no—
677C42—182no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—34no—
686C22×C3—62no—
687C22×C3—62no—
688C22×C3—62no—
689C22×C3—62no—
690C22×C3—62no—
691C22×C3—62no—
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×C3C22×D1211yescharacteristic
702C22×C3C2×#23511yescharacteristic
703C22×C3C2×#23511yescharacteristic
704C22×C3C2×#23511yescharacteristic
705C22×C3C2×D3×D411yescharacteristic
706C22×C3C2×#23711yescharacteristic
707C22×C3C2×#23711yescharacteristic
708C22×C3C2×#23711yescharacteristic
709C22×C3D3×#4111yescharacteristic
710C22×C3D3×#4111yescharacteristic
711C22×C3D3×#4111yescharacteristic
712C22×C3D3×#4111yescharacteristic
713C2×D3—22no—
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—22no—
718C2×D3—22no—
719C2×D3—22no—
720C2×D3—22no—
721C2×D3—22no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3C4×D1214yes—
727C3×C4—24no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—24no—
731C3×C4—42no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—62no—
735C3×C4—62no—
736C3×C4—62no—
737C3×C4—62no—
738C3×C4—121no—
739C3×C4—121no—
740C3×C4#88314yescomplemented
741C3×C4#88614yescomplemented
742Dic3—22no—
743Dic3—22no—
744Dic3—22no—
745Dic3—22no—
746Dic3—41no—
747Dic3—41no—
748Dic3—62no—
749Dic3—62no—
750Dic3—62no—
751Dic3—62no—
752Dic3—62no—
753Dic3—62no—
754Dic3—122no—
755Dic3—122no—
756Dic3—122no—
757Dic3—122no—
758Dic3—121no—
759Dic3—121no—
760C32C4×#12311yescharacteristic, complemented, Sylow
761C23—32no—
762C23—32no—
763C23—32no—
764C23—32no—
765C23—61no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—61no—
770C23—61no—
771C23—61no—
772C23—61no—
773C23—61no—
774C23—61no—
775C23C22×D3211yescharacteristic
776D4—188no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—68no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—92no—
802C2×C4—92no—
803C2×C4—92no—
804C2×C4—124no—
805C2×C4—188no—
806C2×C4—188no—
807C2×C4—181no—
808C2×C4—181no—
809C2×C4—181no—
810C2×C4—181no—
811C2×C4—181no—
812C2×C4—181no—
813C2×C4—181no—
814C2×C4—181no—
815C2×C4—181no—
816C2×C4#379512yes—
817C2×C4C4×D3212yes—
818C2×C4D3×D1212yes—
819C2×C4#380512yes—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—64no—
828C2×C3—122no—
829C2×C3C2×C4×D1211yescharacteristic
830C2×C3C4×#23511yescharacteristic
831C2×C3C2×#88311yescharacteristic
832C2×C3C2×#88611yescharacteristic
833C2×C3#552411yescharacteristic
834C2×C3#552811yescharacteristic
835C2×C3C4×#23711yescharacteristic
836C2×C3C4×#23711yescharacteristic
837C2×C3C4×#23711yescharacteristic
838C2×C3#553811yescharacteristic
839C2×C3#553811yescharacteristic
840C2×C3C4×D3×D411yescharacteristic
841C2×C3#554711yescharacteristic
842C2×C3#555711yescharacteristic
843D3—24no—
844D3—42no—
845C22—34no—
846C22—62no—
847C22—62no—
848C22—62no—
849C22—62no—
850C22—62no—
851C22—62no—
852C22—62no—
853C22—62no—
854C22—62no—
855C22—121no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22C2×#379511yescharacteristic
860C22C2×C4×D3211yescharacteristic
861C22C2×D3×D1211yescharacteristic
862C22D3×#23511yescharacteristic
863C22D3×#23511yescharacteristic
864C22#6430611yescharacteristic
865C22C2×#380511yescharacteristic
866C4—22no—
867C4—41no—
868C4—62no—
869C4—62no—
870C4—62no—
871C4—62no—
872C4—121no—
873C4—121no—
874C4—182no—
875C4—182no—
876C4—182no—
877C4—361no—
878C4#6389114yesdirect product factor
879C3—21no—
880C3C4×#88611yescharacteristic, complemented
881C3C4×#88311yescharacteristic, complemented
882C2—64no—
883C2—122no—
884C2C4×#379511yescharacteristic
885C2#1059391011yescharacteristic
886C2C4×D3×D1211yescharacteristic
887C2#1059399711yescharacteristic
888C2C4×#380511yescharacteristic
889C2C2×#6389111yescharacteristic
890C2#1059493411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
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
3. C2×C4×D3×Dic3C2semidirect
4. C4×C4⋊(C3⋊Dic3)C2semidirect
5. C3×C4×(C2×D3)⋊C4C2semidirect
6. C3×C4×(C2×D3)⋊C4C2semidirect
7. #10591379C2semidirect
9. #10591362C2semidirect
10. C4×Dic3⋊Dic3C2semidirect
11. #10591316C2semidirect
12. #10591284C2semidirect
13. C4×(C2×D3)⋊Dic3C2semidirect
14. #10591271C2semidirect
15. #10591250C2semidirect
44. #63891C4direct (N × H)
72. C4×(C2×D3)⋊C4D3semidirect
73. C4×(C2×D3)⋊C4D3semidirect
116. C2×D3×Dic3C2×C4semidirect
119. C4⋊(C3⋊Dic3)C2×C4semidirect
124. C3×(C2×D3)⋊C4C2×C4semidirect
125. C3×(C2×D3)⋊C4C2×C4semidirect
130. Dic3⋊Dic3C2×C4semidirect
134. (C2×D3)⋊Dic3C2×C4semidirect
381. (C2×D3)⋊C4C4×D3semidirect
382. (C2×D3)⋊C4C4×D3semidirect
430. C32×C4#123semidirect
740. C3×C4#883semidirect
741. C3×C4#886semidirect
760. C32C4×#123semidirect
878. C4#63891direct (N × H)
880. C3C4×#886semidirect
881. C3C4×#883semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6252
C2×#638912
C2×C4×D3×Dic32
C4×C4⋊(C3⋊Dic3)2
C3×C4×(C2×D3)⋊C42
#105913792
#105913632
#105913622
C4×Dic3⋊Dic32
#105913162
#105912842
C4×(C2×D3)⋊Dic32
#105912712
#105912502
C4×#8833
C4×#8863