Finite Group Databasebeta

← #11802184

Subgroups — #11802184

Order 1152.

1547 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64103C211yesmaximal, characteristic
2C2×#63894C211yesmaximal, characteristic
3C2×C4×#624C211yesmaximal, characteristic, complemented
4C3×#4980C211yesmaximal, characteristic, complemented
5C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
6#10591380C211yesmaximal, characteristic
7#10591378C211yesmaximal, characteristic, complemented
8#10591266C211yesmaximal, characteristic, complemented
9#10591263C211yesmaximal, characteristic, complemented
10#10591243C211yesmaximal, characteristic, complemented
11#10591233C211yesmaximal, characteristic, complemented
12#10591233C211yesmaximal, characteristic, complemented
13#10591233C211yesmaximal, characteristic, complemented
14#10591219C211yesmaximal, characteristic, complemented
15#10591202C211yesmaximal, characteristic, complemented
16#74940—31nomaximal
17C4×#894—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28#64103C418yescomplemented
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44#63894—24no—
45C4×#624—24no—
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#894—31no—
57C2×#894—31no—
58C2×#894—61no—
59C2×#893—31no—
60C2×C4×D12—31no—
61C2×C42×D3—31no—
62C2×C42×D3—31no—
63C3×#387—31no—
64C3×C4×C4⋊C4—31no—
65#4990—31no—
66#4989—31no—
67#4980D311yescharacteristic, complemented
68#4978—31no—
69Dic3×C4⋊C4D311yescharacteristic, complemented
70#4940—31no—
71C4×(C2×D3)⋊C4—31no—
72C4×(C2×D3)⋊C4—31no—
73C4×(C2×D3)⋊C4—31no—
74C4×Dic3⋊C4—31no—
75#4670—31no—
76#4669—31no—
77#4668—31no—
78#4666—31no—
79#4666—31no—
80#4666—31no—
81#4665—31no—
82#4665—31no—
83#4664—31no—
84#4664—31no—
85#4655—31no—
86#4649—31no—
87C23×C3⋊D3C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—22no—
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)C2×C414yes—
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3C2×C414yescomplemented
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C2×#624—22no—
109C2×#624—22no—
110C2×#624—22no—
111C2×#624—22no—
112C2×#624—22no—
113C2×#624—22no—
114C2×#624—22no—
115C2×#624—22no—
116C2×#624D414yes—
117C32×C4⋊C4C2×C414yescomplemented
118#3752C2×C414yescomplemented
119#3752C2×C414yescomplemented
120#3752C2×C414yescomplemented
121#3750C2×C414yescomplemented
122C3×C4⋊Dic3—22no—
123C3×C4⋊Dic3—22no—
124C3×C4×Dic3—22no—
125C3×C4×Dic3—22no—
126C3×C4×Dic3—22no—
127C3×C4×Dic3—22no—
128#3724—22no—
129#3722—22no—
130#3722—22no—
131#3722—22no—
132#3722—22no—
133#3722—22no—
134Dic32—22no—
135Dic32—22no—
136Dic32—22no—
137C4×#123—91noSylow
138C22×D12—31no—
139C22×D12—31no—
140C22×D12—61no—
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—31no—
148C22×C4×D3—31no—
149C22×C4×D3—61no—
150C2×C3×C4⋊C4—21no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4C2×D311yescharacteristic
154C2×C3×C4⋊C4C2×D311yescharacteristic
155C2×C3×C42—31no—
156C2×C3×C42—31no—
157C2×C3×C42—31no—
158C2×C3×C42—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
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—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—61no—
176C2×(C2×D3)⋊C4—61no—
177C2×(C2×D3)⋊C4—61no—
178C2×C4⋊Dic3C2×D311yescharacteristic
179C2×C4⋊Dic3C2×D311yescharacteristic
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—61no—
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×Dic3C2×D311yescharacteristic
192C2×C4×Dic3C2×D311yescharacteristic
193C2×C4×Dic3C2×D311yescharacteristic
194C2×C4×Dic3C2×D311yescharacteristic
195#894—38no—
196#894—38no—
197#894—68no—
198#893—64no—
199C4×D12—64no—
200C42×D3—64no—
201C42×D3—64no—
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⋊#95C2×D311yescharacteristic
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C3⋊#95C2×D311yescharacteristic
222C23×C32C2411yescharacteristic
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⋊D3—21no—
233C22×C3⋊D3C22×C412yes—
234C22×C3⋊D3C22×C412yes—
235C22×C3⋊D3C2×D412yes—
236C22×C3⋊D3#4112yes—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C22×C412yes—
244C2×C32×C4C22×C412yes—
245C2×C32×C4C22×C412yes—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C22×C412yes—
251C2×C3⋊Dic3C22×C412yes—
252C4⋊(C3⋊D3)—28no—
253C4×C3⋊D3—28no—
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×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×Dic3—21no—
272C2×C3×Dic3C2×D412yes—
273C2×C3×Dic3C2×D412yes—
274C2×C3×Dic3#4112yes—
275C2×C3×Dic3#4112yes—
276C2×C3×Dic3#4112yes—
277C2×C3×Dic3#4112yes—
278#624—28no—
279#624—28no—
280#624—44no—
281C2×#123—91no—
282C2×C4×D4—91no—
283C22×C42—91no—
284#388—91no—
285#388—91no—
286#387—31no—
287#387—91no—
288#386—91no—
289#385—91no—
290#381—91no—
291C4×C4⋊C4—31no—
292C4×C4⋊C4—91no—
293C4×C22⋊C4—91no—
294C4×C22⋊C4—91no—
295C4×C22⋊C4—91no—
296C23×D3—31no—
297C23×D3—31no—
298C23×D3—31no—
299C23×D3—31no—
300C23×D3—61no—
301C23×D3—61no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C2×D12—34no—
334C2×D12—34no—
335C2×D12—64no—
336C2×D12—62no—
337C2×D12—62no—
338C2×D12—62no—
339C2×D12—62no—
340C2×D12—122no—
341C2×D12—122no—
342C2×C4×D3—34no—
343C2×C4×D3—34no—
344C2×C4×D3—34no—
345C2×C4×D3—34no—
346C2×C4×D3—64no—
347C2×C4×D3—62no—
348C2×C4×D3—62no—
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—62no—
364C2×C4×D3—62no—
365C2×C4×D3—62no—
366C2×C4×D3—62no—
367C2×C4×D3—122no—
368C2×C4×D3—122no—
369C3×C4⋊C4—24no—
370C3×C4⋊C4—62no—
371C3×C4⋊C4—62no—
372C3×C4⋊C4C4×D314yescomplemented
373C3×C4⋊C4C4×D314yescomplemented
374C3×C42—62no—
375C3×C42—62no—
376C3×C42—62no—
377C3×C42—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—34no—
384(C2×D3)⋊C4—64no—
385(C2×D3)⋊C4—64no—
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—
393(C2×D3)⋊C4—62no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397C4⋊Dic3—22no—
398C4⋊Dic3—22no—
399Dic3⋊C4—34no—
400Dic3⋊C4—34no—
401Dic3⋊C4—64no—
402Dic3⋊C4—62no—
403Dic3⋊C4—62no—
404C4×Dic3—22no—
405C4×Dic3—22no—
406C4×Dic3—22no—
407C4×Dic3—22no—
408C4×Dic3—62no—
409C4×Dic3—62no—
410C4×Dic3—62no—
411C4×Dic3—62no—
412C4×Dic3—62no—
413C4×Dic3—62no—
414C22×C32C23×C411yescharacteristic
415C22×C32C22×D411yescharacteristic
416C22×C32C2×#4111yescharacteristic
417C22×C32C2×#4111yescharacteristic
418C22×C32C2×#4111yescharacteristic
419C22×C32C2×#4111yescharacteristic
420C22×C32C2×#4111yescharacteristic
421C2×C3⋊D3—22no—
422C2×C3⋊D3—22no—
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⋊D3—22no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
432C2×C3⋊D3—41no—
433C2×C3⋊D3—41no—
434C2×C3⋊D3C4×D414yes—
435C32×C4—22no—
436C32×C4—22no—
437C32×C4—22no—
438C3⋊Dic3—22no—
439C3⋊Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—22no—
442C3×Dic3—22no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3#12314yescomplemented
448C22×D4—91no—
449C23×C4—91no—
450C23×C4—91no—
451C23×C4—91no—
452C23×C4—91no—
453#123—98no—
454C4×D4—184no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4—31no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4D3211yescharacteristic
460C2×C22⋊C4—91no—
461C2×C22⋊C4—91no—
462C2×C22⋊C4—91no—
463C2×C22⋊C4—91no—
464C2×C22⋊C4—91no—
465C2×C22⋊C4—91no—
466C2×C22⋊C4—91no—
467C2×C22⋊C4—91no—
468C2×C42—31no—
469C2×C42—31no—
470C2×C42—31no—
471C2×C42—31no—
472C2×C42—91no—
473C2×C42—91no—
474C2×C42—91no—
475C2×C42—184no—
476#95—31no—
477#95—31no—
478#95—31no—
479#95—31no—
480#95—31no—
481#95—31no—
482#95—91no—
483#95—91no—
484#95—91no—
485#95—91no—
486C23×C3—21no—
487C23×C3C23×D311yescharacteristic
488C23×C3C23×D311yescharacteristic
489C22×D3—32no—
490C22×D3—32no—
491C22×D3—32no—
492C22×D3—32no—
493C22×D3—32no—
494C22×D3—32no—
495C22×D3—32no—
496C22×D3—32no—
497C22×D3—62no—
498C22×D3—62no—
499C22×D3—62no—
500C22×D3—62no—
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—61no—
513C22×D3—61no—
514C22×D3—61no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—121no—
522C22×D3—121no—
523C22×D3—121no—
524C22×D3—121no—
525C22×D3—121no—
526C22×D3—121no—
527C22×D3—121no—
528C22×D3—121no—
529C22×D3—121no—
530C22×D3—121no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—32no—
547C2×C3×C4—32no—
548C2×C3×C4—32no—
549C2×C3×C4—32no—
550C2×C3×C4—32no—
551C2×C3×C4—32no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4C2×C4×D312yes—
577C2×C3×C4C2×C4×D312yes—
578C2×C3×C4C2×C4×D312yes—
579C2×C3×C4C2×C4×D312yes—
580C2×C3×C4C2×C4×D312yes—
581C2×C3×C4C2×C4×D312yes—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—32no—
601C2×Dic3—32no—
602C2×Dic3—32no—
603C2×Dic3—32no—
604C2×Dic3—62no—
605C2×Dic3—62no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—121no—
615C2×Dic3—121no—
616C2×Dic3—121no—
617C2×Dic3—121no—
618C2×Dic3#23512yes—
619C2×Dic3#23512yes—
620C2×Dic3D3×D412yes—
621C2×Dic3D3×D412yes—
622C2×Dic3#23912yes—
623C2×Dic3#23912yes—
624D12—68no—
625D12—68no—
626D12—128no—
627C4×D3—68no—
628C4×D3—68no—
629C4×D3—68no—
630C4×D3—68no—
631C4×D3—68no—
632C4×D3—68no—
633C4×D3—128no—
634C4×D3—124no—
635C4×D3—124no—
636C2×C32C2×C4×D411yescharacteristic
637C2×C32C4×#4111yescharacteristic
638C2×C32C4×#4111yescharacteristic
639C2×C32C2×#12311yescharacteristic
640C2×C32#52511yescharacteristic
641C2×C32#52911yescharacteristic
642C2×C32#52911yescharacteristic
643C3⋊D3—24no—
644C3⋊D3—42no—
645C24—91no—
646C24—91no—
647C2×D4—94no—
648C2×D4—182no—
649C2×D4—182no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—31no—
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—94no—
659C22×C4—91no—
660C22×C4—91no—
661C22×C4—94no—
662C22×C4—182no—
663C22×C4—182no—
664C22×C4—182no—
665C22×C4—182no—
666C22×C4—182no—
667C22×C4—182no—
668C22×C4—182no—
669C22×C4—182no—
670C22×C4—182no—
671C22×C4—182no—
672C22×C4C2×D3211yescharacteristic
673C22×C4C2×D3211yescharacteristic
674C22×C4C2×D3211yescharacteristic
675C4⋊C4—62no—
676C4⋊C4—62no—
677C4⋊C4—94no—
678C4⋊C4—182no—
679C4⋊C4#62414yescomplemented
680C22⋊C4—94no—
681C22⋊C4—94no—
682C22⋊C4—94no—
683C22⋊C4—182no—
684C22⋊C4—182no—
685C22⋊C4—182no—
686C22⋊C4—182no—
687C22⋊C4—182no—
688C42—62no—
689C42—62no—
690C42—62no—
691C42—62no—
692C42—182no—
693C42—182no—
694C42—182no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3C22×C4×D311yescharacteristic
703C22×C3C22×C4×D311yescharacteristic
704C22×C3C2×#23511yescharacteristic
705C22×C3C2×#23511yescharacteristic
706C22×C3C2×D3×D411yescharacteristic
707C22×C3C2×D3×D411yescharacteristic
708C22×C3C2×#23911yescharacteristic
709C22×C3C2×#23911yescharacteristic
710C22×C3D3×#4111yescharacteristic
711C22×C3D3×#4111yescharacteristic
712C22×C3D3×#4111yescharacteristic
713C22×C3D3×#4111yescharacteristic
714C22×C3D3×#4111yescharacteristic
715C22×C3D3×#4111yescharacteristic
716C2×D3—34no—
717C2×D3—34no—
718C2×D3—64no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—62no—
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—62no—
736C2×D3—62no—
737C2×D3—122no—
738C2×D3—122no—
739C2×D3—122no—
740C2×D3—122no—
741C2×D3—122no—
742C2×D3—122no—
743C2×D3—122no—
744C2×D3—122no—
745C2×D3—122no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—241no—
755C2×D3—241no—
756C2×D3—241no—
757C2×D3—241no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—34no—
765C3×C4—42no—
766C3×C4—42no—
767C3×C4—42no—
768C3×C4—62no—
769C3×C4—62no—
770C3×C4—62no—
771C3×C4—121no—
772C3×C4—121no—
773C3×C4—121no—
774C3×C4—121no—
775Dic3—22no—
776Dic3—22no—
777Dic3—22no—
778Dic3—41no—
779Dic3—41no—
780Dic3—41no—
781Dic3—41no—
782Dic3—62no—
783Dic3—62no—
784Dic3—62no—
785Dic3—62no—
786Dic3—122no—
787Dic3—122no—
788Dic3#89414yescomplemented
789C32C4×#12311yescharacteristic, complemented, Sylow
790C23—92no—
791C23—92no—
792C23—92no—
793C23—92no—
794C23—181no—
795C23—181no—
796C23—181no—
797C23—181no—
798C23—181no—
799C23—181no—
800C23—181no—
801C23—181no—
802C23—181no—
803C23—181no—
804C23C22×D3211yescharacteristic
805D4—188no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—32no—
817C2×C4—32no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—92no—
837C2×C4—92no—
838C2×C4—188no—
839C2×C4—188no—
840C2×C4—188no—
841C2×C4—181no—
842C2×C4—181no—
843C2×C4—181no—
844C2×C4—181no—
845C2×C4—364no—
846C2×C4C2×#62412yes—
847C2×C4C2×#62412yes—
848C2×C4C2×#62412yes—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3C4×#23511yescharacteristic
857C2×C3C2×#89411yescharacteristic
858C2×C3#552211yescharacteristic
859C2×C3#552811yescharacteristic
860C2×C3C4×D3×D411yescharacteristic
861C2×C3C4×D3×D411yescharacteristic
862C2×C3#554711yescharacteristic
863C2×C3C4×#23911yescharacteristic
864C2×C3C4×#23911yescharacteristic
865C2×C3#558011yescharacteristic
866C2×C3#562711yescharacteristic
867C2×C3D3×#12311yescharacteristic
868C2×C3#569111yescharacteristic
869C2×C3#570611yescharacteristic
870D3—64no—
871D3—64no—
872D3—124no—
873D3—122no—
874D3—122no—
875D3—242no—
876C22—94no—
877C22—182no—
878C22—182no—
879C22—182no—
880C22—182no—
881C22—182no—
882C22—182no—
883C22—182no—
884C22—182no—
885C22—182no—
886C22—361no—
887C22—361no—
888C22—361no—
889C22—361no—
890C22D3×#23511yescharacteristic
891C22D3×#23511yescharacteristic
892C22D32×D411yescharacteristic
893C22#6431211yescharacteristic
894C22D3×#23911yescharacteristic
895C22D3×#23911yescharacteristic
896C22C22×#62411yescharacteristic
897C4—22no—
898C4—22no—
899C4—22no—
900C4—34no—
901C4—62no—
902C4—62no—
903C4—62no—
904C4—121no—
905C4—121no—
906C4—121no—
907C4—121no—
908C4—182no—
909C4—182no—
910C3—21no—
911C3C4×#89411yescharacteristic, complemented
912C3#7494011yescharacteristic, complemented
913C2—184no—
914C2—362no—
915C2#1059442211yescharacteristic
916C2#1059442311yescharacteristic
917C2D3×#89411yescharacteristic
918C2#1059462311yescharacteristic
919C2#1059495411yescharacteristic
920C2D4×#62411yescharacteristic
921C2#1059538611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32C4×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#624C2semidirect
4. C3×#4980C2semidirect
5. C3×Dic3×C4⋊C4C2semidirect
7. #10591378C2semidirect
8. #10591266C2semidirect
9. #10591263C2semidirect
10. #10591243C2semidirect
11. #10591233C2semidirect
12. #10591233C2semidirect
13. #10591233C2semidirect
14. #10591219C2semidirect
15. #10591202C2semidirect
28. #64103C4semidirect
67. #4980D3semidirect
69. Dic3×C4⋊C4D3semidirect
99. C2×C4×C3⋊D3C2×C4semidirect
117. C32×C4⋊C4C2×C4semidirect
118. #3752C2×C4semidirect
119. #3752C2×C4semidirect
120. #3752C2×C4semidirect
121. #3750C2×C4semidirect
372. C3×C4⋊C4C4×D3semidirect
373. C3×C4⋊C4C4×D3semidirect
447. C3×Dic3#123semidirect
679. C4⋊C4#624semidirect
788. Dic3#894semidirect
789. C32C4×#123semidirect
911. C3C4×#894semidirect
912. C3#74940semidirect

Maximal subgroups

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

subgroupindex
C2×#641032
C2×#638942
C2×C4×#6242
C3×#49802
C3×Dic3×C4⋊C42
#105913802
#105913782
#105912662
#105912632
#105912432
#105912332
#105912192
#105912022
#749403
C4×#8943