Finite Group Databasebeta

← #11805656

Subgroups — #11805656

Order 1152.

1485 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic, complemented
2C2×#63881C211yesmaximal, characteristic
3C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C3×#4933C211yesmaximal, characteristic, complemented
6#10591382C211yesmaximal, characteristic
7#10591369C211yesmaximal, characteristic, complemented
8#10591368C211yesmaximal, characteristic, complemented
9#10591364C211yesmaximal, characteristic
10#10591355C211yesmaximal, characteristic, complemented
11#10591289C211yesmaximal, characteristic, complemented
12#10591259C211yesmaximal, characteristic, complemented
13#10591247C211yesmaximal, characteristic, complemented
14#10591243C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#75305—31nomaximal
17#73461—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29#64081—24no—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44#63881C418yescomplemented
45D3×Dic3⋊C4—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
56C22×Dic3⋊C4—31no—
57C2×#893—31no—
58C2×D3×C4⋊C4—31no—
59C2×#67⋊C4—31no—
60C2×#872—31no—
61C2×#872—31no—
62C2×#872—61no—
63C3×#387—31no—
64C3×C4×C22⋊C4—31no—
65#5213—31no—
66#4990—31no—
67#4980—31no—
68#4958—31no—
69#4942—31no—
70Dic3×C22⋊C4—31no—
71#4940—31no—
72C4×(C2×D3)⋊C4D311yescharacteristic, complemented
73#4933D311yescharacteristic, complemented
74C4×Dic3⋊C4—31no—
75#4670—31no—
76#4669—31no—
77#4667—31no—
78#4667—31no—
79#4667—31no—
80#4666—31no—
81#4665—31no—
82#4665—31no—
83#4652—31no—
84#4650—31no—
85#4650—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
94C22×C3⋊Dic3C2311yescharacteristic
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3C2×C414yescomplemented
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—41no—
108C2×#626—22no—
109C2×#626—22no—
110C2×#626C2×C414yes—
111C2×D3×Dic3—22no—
112C2×D3×Dic3—22no—
113C2×D3×Dic3—22no—
114C2×D3×Dic3—22no—
115C2×D3×Dic3—41no—
116C2×D3×Dic3C2×C414yes—
117C32×C42—22no—
118#3752—22no—
119#3752—22no—
120#3750—22no—
121#3750D414yescomplemented
122C4×C3⋊Dic3—22no—
123C3×(C2×D3)⋊C4—22no—
124C3×(C2×D3)⋊C4C2×C414yes—
125C3×Dic3⋊C4—22no—
126C3×Dic3⋊C4C2×C414yescomplemented
127C3×C4×Dic3—41no—
128#3724—22no—
129#3724—22no—
130Dic3⋊Dic3—22no—
131#3722—41no—
132#3722—41no—
133#3722C2×C414yescomplemented
134(C2×D3)⋊Dic3—22no—
135Dic32—41no—
136Dic32C2×C414yescomplemented
137#2352—91noSylow
138C23×C3×C4—31no—
139C22×#67—31no—
140C23×Dic3—31no—
141C23×Dic3—31no—
142C22×D12—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×C42C2×D311yescharacteristic
156C2×C3×C42C2×D311yescharacteristic
157C2×#217—31no—
158C2×(C2×D3)⋊C4—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—61no—
170C2×(C2×D3)⋊C4—61no—
171C2×(C2×D3)⋊C4C2×D311yescharacteristic
172C2×(C2×D3)⋊C4C2×D311yescharacteristic
173C2×C4⋊Dic3—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—61no—
184C2×Dic3⋊C4—61no—
185C2×Dic3⋊C4—64no—
186C2×Dic3⋊C4C2×D311yescharacteristic
187C2×Dic3⋊C4C2×D311yescharacteristic
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—61no—
195C2×C4×Dic3C2×D311yescharacteristic
196#893—38no—
197D3×C4⋊C4—64no—
198#67⋊C4—38no—
199#872—64no—
200#872—64no—
201#872—68no—
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⋊D3C22×C412yes—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3C22×C412yes—
235C22×C3×D3#4112yes—
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×C4—21no—
244C2×C32×C4C22×C412yes—
245C2×C32×C4C2×D412yes—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C22×C412yes—
252C2×C3⋊Dic3C2×D412yes—
253C2×C3⋊Dic3C2×D412yes—
254C2×C3⋊Dic3#4112yes—
255C4×C3⋊D3—28no—
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×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3C22×C412yes—
275C2×C3×Dic3C22×C412yes—
276C2×C3×Dic3C22×C412yes—
277C3×C4×D3—44no—
278#626—28no—
279D3×Dic3—28no—
280D3×Dic3—44no—
281C2×C4×D4—91no—
282C2×#117—91no—
283C22×C4⋊C4—91no—
284#388—91no—
285#388—91no—
286#387—31no—
287#387—91no—
288#386—91no—
289#386—91no—
290#382—91no—
291#380—91no—
292#380—91no—
293C4×C4⋊C4—91no—
294C4×C22⋊C4—31no—
295C4×C22⋊C4—91no—
296C24×C3—31no—
297C23×D3—31no—
298C23×D3—31no—
299C23×D3—61no—
300C23×D3C22×D311yescharacteristic
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
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—31no—
311C22×C3×C4—62no—
312C22×C3×C4—62no—
313C22×C3×C4—121no—
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—62no—
322C2×#67—62no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—34no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—62no—
334C22×Dic3—62no—
335C22×Dic3—62no—
336C22×Dic3—62no—
337C22×Dic3—121no—
338C22×Dic3C22×D311yescharacteristic
339C22×Dic3C22×D311yescharacteristic
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D311yescharacteristic
343C22×Dic3C22×D311yescharacteristic
344C22×Dic3C22×D311yescharacteristic
345C2×D12—34no—
346C2×D12—62no—
347C2×D12—62no—
348C2×C4×D3—22no—
349C2×C4×D3—22no—
350C2×C4×D3—34no—
351C2×C4×D3—34no—
352C2×C4×D3—34no—
353C2×C4×D3—41no—
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—64no—
362C2×C4×D3—64no—
363C2×C4×D3—62no—
364C2×C4×D3—62no—
365C2×C4×D3—121no—
366C3×C4⋊C4—34no—
367C3×C4⋊C4—62no—
368C3×C22⋊C4—34no—
369C3×C22⋊C4—62no—
370C3×C42—24no—
371C3×C42—22no—
372C3×C42—22no—
373C3×C42—121no—
374#217—62no—
375(C2×D3)⋊C4—22no—
376(C2×D3)⋊C4—34no—
377(C2×D3)⋊C4—34no—
378(C2×D3)⋊C4—62no—
379(C2×D3)⋊C4—62no—
380(C2×D3)⋊C4—64no—
381(C2×D3)⋊C4—64no—
382(C2×D3)⋊C4—62no—
383(C2×D3)⋊C4—62no—
384(C2×D3)⋊C4—62no—
385(C2×D3)⋊C4—121no—
386(C2×D3)⋊C4—121no—
387(C2×D3)⋊C4—121no—
388(C2×D3)⋊C4—121no—
389(C2×D3)⋊C4C4×D314yes—
390C4⋊Dic3—62no—
391Dic3⋊C4—22no—
392Dic3⋊C4—34no—
393Dic3⋊C4—34no—
394Dic3⋊C4—64no—
395Dic3⋊C4—62no—
396Dic3⋊C4—62no—
397Dic3⋊C4—62no—
398Dic3⋊C4—62no—
399Dic3⋊C4—62no—
400Dic3⋊C4—62no—
401Dic3⋊C4—62no—
402Dic3⋊C4—64no—
403Dic3⋊C4C4×D314yescomplemented
404C4×Dic3—34no—
405C4×Dic3—34no—
406C4×Dic3—41no—
407C4×Dic3—62no—
408C4×Dic3—62no—
409C4×Dic3—64no—
410C4×Dic3—121no—
411C4×Dic3—121no—
412C22×C32C23×C411yescharacteristic
413C22×C32C22×D411yescharacteristic
414C22×C32C2×#4111yescharacteristic
415C22×C32C2×#4111yescharacteristic
416C22×C32C2×#4111yescharacteristic
417C22×C32H(5,𝔽2)11yescharacteristic
418C22×C322−1+411yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—22no—
421C2×C3⋊D3—22no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3#11714yescomplemented
433C32×C4—22no—
434C32×C4—22no—
435C32×C4—41no—
436C3⋊Dic3—22no—
437C3⋊Dic3—41no—
438C3⋊Dic3C4×D414yes—
439C3×Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—22no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—91no—
447C23×C4—31no—
448C23×C4—91no—
449C23×C4—91no—
450C23×C4—91no—
451C4×D4—98no—
452#117—184no—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4—91no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—91no—
460C2×C4⋊C4—184no—
461C2×C22⋊C4—31no—
462C2×C22⋊C4—31no—
463C2×C22⋊C4—91no—
464C2×C22⋊C4—91no—
465C2×C22⋊C4—91no—
466C2×C22⋊C4—91no—
467C2×C22⋊C4—91no—
468C2×C22⋊C4—91no—
469C2×C42—31no—
470C2×C42—91no—
471C2×C42—91no—
472C2×C42—91no—
473C2×C42D3211yescharacteristic
474#95—31no—
475#95—31no—
476#95—31no—
477#95—31no—
478#95—31no—
479#95—31no—
480#95—91no—
481#95—91no—
482#95—91no—
483#95—91no—
484C23×C3—21no—
485C23×C3—32no—
486C23×C3—32no—
487C23×C3—32no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3C23×D311yescharacteristic
493C23×C3C23×D311yescharacteristic
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—32no—
499C22×D3—32no—
500C22×D3—62no—
501C22×D3—62no—
502C22×D3—62no—
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—121no—
516C22×D3—121no—
517C22×D3—121no—
518C22×D3—121no—
519C22×D3C2×C4×D312yes—
520C22×D3#23512yes—
521C22×D3#23512yes—
522C2×C3×C4—22no—
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—21no—
531C2×C3×C4—21no—
532C2×C3×C4—22no—
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—22no—
540C2×C3×C4—22no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—32no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
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—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—124no—
567C2×C3×C4C2×C4×D312yes—
568C2×C3×C4C2×C4×D312yes—
569C2×C3×C4D3×D412yes—
570C2×C3×C4D3×D412yes—
571#67—68no—
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—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—68no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—62no—
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—124no—
619C2×Dic3C2×C4×D312yes—
620C2×Dic3C2×C4×D312yes—
621C2×Dic3C2×C4×D312yes—
622D12—68no—
623C4×D3—44no—
624C4×D3—68no—
625C4×D3—68no—
626C4×D3—68no—
627C4×D3—616no—
628C4×D3—124no—
629C2×C32C2×#11711yescharacteristic
630C2×C32C2×C4×D411yescharacteristic
631C2×C32#52011yescharacteristic
632C2×C32#54611yescharacteristic
633C2×C32#54811yescharacteristic
634C2×C32#55211yescharacteristic
635C2×C32#55311yescharacteristic
636C3⋊D3—42no—
637C3×D3—24no—
638C24—31no—
639C24—91no—
640C2×D4—94no—
641C2×D4—182no—
642C2×D4—182no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—62no—
651C22×C4—62no—
652C22×C4—94no—
653C22×C4—91no—
654C22×C4—91no—
655C22×C4—94no—
656C22×C4—91no—
657C22×C4—121no—
658C22×C4—182no—
659C22×C4—182no—
660C22×C4—182no—
661C22×C4—182no—
662C22×C4—182no—
663C22×C4—182no—
664C22×C4—361no—
665C22×C4C2×D3211yescharacteristic
666C22×C4C2×D3211yescharacteristic
667C22×C4C2×D3211yescharacteristic
668C4⋊C4—34no—
669C4⋊C4—62no—
670C4⋊C4—94no—
671C4⋊C4—182no—
672C4⋊C4—182no—
673C4⋊C4—182no—
674C4⋊C4—182no—
675C22⋊C4—34no—
676C22⋊C4—62no—
677C22⋊C4—94no—
678C22⋊C4—182no—
679C22⋊C4—182no—
680C22⋊C4—182no—
681C22⋊C4—361no—
682C22⋊C4—361no—
683C42—22no—
684C42—94no—
685C42—121no—
686C42—182no—
687C42—361no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—34no—
696C22×C3—62no—
697C22×C3—62no—
698C22×C3—62no—
699C22×C3—62no—
700C22×C3—62no—
701C22×C3—62no—
702C22×C3C22×C4×D311yescharacteristic
703C22×C3C22×C4×D311yescharacteristic
704C22×C3C2×#23511yescharacteristic
705C22×C3C2×#23511yescharacteristic
706C22×C3C2×D3×D411yescharacteristic
707C22×C3C2×D3×D411yescharacteristic
708C22×C3#100411yescharacteristic
709C22×C3#100711yescharacteristic
710C22×C3D3×#4111yescharacteristic
711C22×C3D3×#4111yescharacteristic
712C22×C3D3×#4111yescharacteristic
713C22×C3D3×#4111yescharacteristic
714C22×C3#100911yescharacteristic
715C22×C3#101011yescharacteristic
716C2×D3—22no—
717C2×D3—22no—
718C2×D3—22no—
719C2×D3—22no—
720C2×D3—22no—
721C2×D3—22no—
722C2×D3—64no—
723C2×D3—62no—
724C2×D3—62no—
725C2×D3—62no—
726C2×D3—62no—
727C2×D3—62no—
728C2×D3—62no—
729C2×D3—122no—
730C2×D3—122no—
731C2×D3—122no—
732C2×D3—122no—
733C2×D3—122no—
734C2×D3—122no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3#87214yescomplemented
744C3×C4—24no—
745C3×C4—22no—
746C3×C4—22no—
747C3×C4—22no—
748C3×C4—22no—
749C3×C4—42no—
750C3×C4—42no—
751C3×C4—41no—
752C3×C4—41no—
753C3×C4—62no—
754C3×C4—62no—
755C3×C4—62no—
756C3×C4—121no—
757C3×C4—121no—
758C3×C4—121no—
759C3×C4—121no—
760Dic3—22no—
761Dic3—22no—
762Dic3—22no—
763Dic3—34no—
764Dic3—34no—
765Dic3—41no—
766Dic3—41no—
767Dic3—41no—
768Dic3—41no—
769Dic3—64no—
770Dic3—62no—
771Dic3—62no—
772Dic3—122no—
773Dic3—122no—
774Dic3—121no—
775Dic3—121no—
776C32#235211yescharacteristic, complemented, Sylow
777C23—32no—
778C23—32no—
779C23—32no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—61no—
784C23—92no—
785C23—181no—
786C23—181no—
787C23—181no—
788C23—181no—
789C23—181no—
790C23—181no—
791C23C22×D3211yescharacteristic
792D4—188no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—32no—
801C2×C4—32no—
802C2×C4—32no—
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—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—92no—
822C2×C4—92no—
823C2×C4—92no—
824C2×C4—92no—
825C2×C4—124no—
826C2×C4—188no—
827C2×C4—188no—
828C2×C4—181no—
829C2×C4—181no—
830C2×C4—181no—
831C2×C4—181no—
832C2×C4—181no—
833C2×C4—364no—
834C2×C4C4×D3212yes—
835C2×C4#381112yes—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—64no—
844C2×C3C2×#87211yescharacteristic
845C2×C3#549011yescharacteristic
846C2×C3D3×#11711yescharacteristic
847C2×C3#553111yescharacteristic
848C2×C3#554011yescharacteristic
849C2×C3C4×D3×D411yescharacteristic
850C2×C3C4×D3×D411yescharacteristic
851C2×C3#554611yescharacteristic
852C2×C3#555211yescharacteristic
853C2×C3#557411yescharacteristic
854C2×C3#563311yescharacteristic
855C2×C3#565411yescharacteristic
856C2×C3#569311yescharacteristic
857C2×C3#570911yescharacteristic
858D3—24no—
859D3—124no—
860D3—122no—
861D3—122no—
862C22—34no—
863C22—62no—
864C22—62no—
865C22—62no—
866C22—62no—
867C22—62no—
868C22—62no—
869C22—182no—
870C22—182no—
871C22—182no—
872C22—361no—
873C22—361no—
874C22—361no—
875C22—361no—
876C22#6429711yescharacteristic
877C22C2×C4×D3211yescharacteristic
878C22D3×#23511yescharacteristic
879C22D3×#23511yescharacteristic
880C22#6430611yescharacteristic
881C22#6430711yescharacteristic
882C22C2×#381111yescharacteristic
883C4—22no—
884C4—22no—
885C4—41no—
886C4—62no—
887C4—62no—
888C4—62no—
889C4—94no—
890C4—121no—
891C4—121no—
892C4—121no—
893C4—121no—
894C4—182no—
895C4—361no—
896C3—21no—
897C3#7346111yescharacteristic, complemented
898C3#7530511yescharacteristic, complemented
899C2—64no—
900C2—362no—
901C2#1059388911yescharacteristic
902C2#1059391811yescharacteristic
903C2#1059392411yescharacteristic
904C2D3×#87211yescharacteristic
905C2#1059491611yescharacteristic
906C2C4×#381111yescharacteristic
907C2#1059507711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C42D32
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64081C2semidirect
3. C2×D3×Dic3⋊C4C2semidirect
4. C3×C4×(C2×D3)⋊C4C2semidirect
5. C3×#4933C2semidirect
7. #10591369C2semidirect
8. #10591368C2semidirect
10. #10591355C2semidirect
11. #10591289C2semidirect
12. #10591259C2semidirect
13. #10591247C2semidirect
14. #10591243C2semidirect
15. #10591192C2semidirect
44. #63881C4semidirect
72. C4×(C2×D3)⋊C4D3semidirect
73. #4933D3semidirect
97. C2×C4×C3⋊D3C2×C4semidirect
121. #3750D4semidirect
126. C3×Dic3⋊C4C2×C4semidirect
133. #3722C2×C4semidirect
136. Dic32C2×C4semidirect
403. Dic3⋊C4C4×D3semidirect
432. C2×C3×D3#117semidirect
743. C2×D3#872semidirect
776. C32#2352semidirect
897. C3#73461semidirect
898. C3#75305semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C2×#638812
C2×D3×Dic3⋊C42
C3×C4×(C2×D3)⋊C42
C3×#49332
#105913822
#105913692
#105913682
#105913642
#105913552
#105912892
#105912592
#105912472
#105912432
#105911922
#753053
#734613