Finite Group Databasebeta

← #11805453

Subgroups — #11805453

Order 1152.

1669 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63904C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic, complemented
3C2×#63881C211yesmaximal, characteristic
4C2×#63880C211yesmaximal, characteristic
5C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
6#10592366C211yesmaximal, characteristic, complemented
7C3×#4668C211yesmaximal, characteristic, complemented
8C3×#4647C211yesmaximal, characteristic, complemented
9#10591377C211yesmaximal, characteristic, complemented
10#10591375C211yesmaximal, characteristic, complemented
11#10591374C211yesmaximal, characteristic, complemented
12#10591369C211yesmaximal, characteristic, complemented
13#10591265C211yesmaximal, characteristic, complemented
14#10591244C211yesmaximal, characteristic, complemented
15#10591243C211yesmaximal, characteristic, complemented
16#76202—31nomaximal
17#74393—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×#3724C2211yescharacteristic
39C2×#3724C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47#63904—24no—
48#63900—24no—
49#63881C418yescomplemented
50#63880—24no—
51D3×Dic3⋊C4—24no—
52C32×#95C2211yescharacteristic
53#63658C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58C2×C4×#67—31no—
59C22×Dic3⋊C4—31no—
60C2×#893—31no—
61C2×#893—31no—
62C2×D3×C4⋊C4—31no—
63C2×D3×C4⋊C4—31no—
64C2×D3×C4⋊C4—31no—
65C2×#67⋊C4—31no—
66C2×#67⋊C4—31no—
67C2×C4×D12—31no—
68C3×#389—31no—
69C3×#385—31no—
70#4989—31no—
71#4989—31no—
72#4989—31no—
73#4984—31no—
74#4976—31no—
75#4975—31no—
76#4975—31no—
77#4950—31no—
78#4942—31no—
79C4×Dic3⋊C4—31no—
80#4668—31no—
81#4668—31no—
82#4668D311yescharacteristic, complemented
83#4667—31no—
84#4667—31no—
85#4667—31no—
86#4667—61no—
87#4649—31no—
88#4647D311yescharacteristic, complemented
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
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
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—41no—
110C2×#626C2×C414yes—
111C2×#626D414yes—
112C2×#626Q814yes—
113C2×#624—22no—
114C2×#624—22no—
115C2×#624—22no—
116C2×#624—22no—
117C2×#624—41no—
118C2×#624—41no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—41no—
124C2×D3×Dic3C2×C414yescomplemented
125#3752—22no—
126#3752—22no—
127#3750—22no—
128#3750—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4C2×C414yescomplemented
131C3×C4⋊Dic3—22no—
132C3×C4⋊Dic3—22no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4—22no—
135C3×Dic3⋊C4—41no—
136C3×Dic3⋊C4C2×C414yescomplemented
137C3×C4×Dic3—22no—
138#3724—22no—
139#3724D414yescomplemented
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3—22no—
142Dic3⋊Dic3—41no—
143#3722C2×C414yescomplemented
144(C2×D3)⋊Dic3—22no—
145Dic32—22no—
146Dic32C2×C414yescomplemented
147D4×C4⋊C4—91noSylow
148C23×C3×C4—31no—
149C22×#67—31no—
150C23×Dic3—31no—
151C23×Dic3—31no—
152C22×D12—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C22×C4×D3—61no—
162C22×C4×D3C2×D311yescharacteristic
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C42—31no—
172C2×#217—31no—
173C4×#67—64no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—61no—
182C2×(C2×D3)⋊C4—61no—
183C2×(C2×D3)⋊C4C2×D311yescharacteristic
184C2×(C2×D3)⋊C4C2×D311yescharacteristic
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—31no—
187C2×C4⋊Dic3—31no—
188C2×C4⋊Dic3C2×D311yescharacteristic
189C2×C4⋊Dic3C2×D311yescharacteristic
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—31no—
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—61no—
202C2×Dic3⋊C4—61no—
203C2×Dic3⋊C4—64no—
204C2×Dic3⋊C4C2×D311yescharacteristic
205C2×Dic3⋊C4C2×D311yescharacteristic
206C2×Dic3⋊C4C2×D311yescharacteristic
207C2×Dic3⋊C4C2×D311yescharacteristic
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3C2×D311yescharacteristic
213#893—38no—
214#893—64no—
215D3×C4⋊C4—64no—
216D3×C4⋊C4—64no—
217D3×C4⋊C4—64no—
218#67⋊C4—38no—
219#67⋊C4—64no—
220C4×D12—64no—
221C3×#95—21no—
222C3×#95—31no—
223C3×#95—31no—
224C3×#95C2×D311yescharacteristic
225C3×#95C2×D311yescharacteristic
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—61no—
233C3⋊#95C2×D311yescharacteristic
234C3⋊#95C2×D311yescharacteristic
235C23×C32C2411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C22×C412yes—
241C22×C3⋊D3C2×D412yes—
242C22×C3⋊D3C2×Q812yes—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3C22×C412yes—
248C22×C3×D3C2×D412yes—
249C22×C3×D3C2×Q812yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4C22×C412yes—
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⋊Dic3C22×C412yes—
266C2×C3⋊Dic3C2×D412yes—
267C2×C3⋊Dic3#4112yes—
268C4×C3⋊D3—28no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3C22×C412yes—
284C2×C3×Dic3C22×C412yes—
285C2×C3×Dic3C22×C412yes—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3C2×Q812yes—
290C3×C4×D3—44no—
291#626C4⋊C4116yescomplemented
292#624—44no—
293#624—44no—
294D3×Dic3—28no—
295D3×Dic3—44no—
296C2×C4×D4—91no—
297C2×C4×D4—91no—
298C2×C4×D4—91no—
299C22×C4⋊C4—91no—
300C22×C4⋊C4—91no—
301#389—31no—
302#389—91no—
303#385—31no—
304#385—91no—
305#385—91no—
306#385—91no—
307#384—91no—
308#380—91no—
309#380—91no—
310C4×C4⋊C4—91no—
311C24×C3—31no—
312C23×D3—31no—
313C23×D3—31no—
314C23×D3—61no—
315C23×D3C22×D311yescharacteristic
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—62no—
327C22×C3×C4—62no—
328C22×C3×C4—121no—
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C2×#67—34no—
336C2×#67—34no—
337C2×#67—34no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—34no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—62no—
349C22×Dic3—62no—
350C22×Dic3—62no—
351C22×Dic3—62no—
352C22×Dic3—121no—
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C2×D12—34no—
361C2×D12—34no—
362C2×D12—34no—
363C2×C4×D3—22no—
364C2×C4×D3—22no—
365C2×C4×D3—34no—
366C2×C4×D3—34no—
367C2×C4×D3—34no—
368C2×C4×D3—41no—
369C2×C4×D3—64no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—122no—
387C2×C4×D3—122no—
388C2×C4×D3—121no—
389C2×C4×D3—121no—
390C2×C4×D3—121no—
391C2×C4×D3—121no—
392C2×C4×D3—121no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—62no—
395C3×C4⋊C4—62no—
396C3×C4⋊C4—62no—
397C3×C4⋊C4—62no—
398C3×C4⋊C4—121no—
399C3×C22⋊C4—34no—
400C3×C22⋊C4—62no—
401C3×C42—62no—
402#217—62no—
403(C2×D3)⋊C4—22no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—122no—
412(C2×D3)⋊C4—122no—
413(C2×D3)⋊C4C4×D314yescomplemented
414C4⋊Dic3—22no—
415C4⋊Dic3—22no—
416C4⋊Dic3—62no—
417C4⋊Dic3—62no—
418C4⋊Dic3—121no—
419Dic3⋊C4—22no—
420Dic3⋊C4—22no—
421Dic3⋊C4—34no—
422Dic3⋊C4—34no—
423Dic3⋊C4—41no—
424Dic3⋊C4—62no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—122no—
433Dic3⋊C4—122no—
434Dic3⋊C4—121no—
435Dic3⋊C4C4×D314yescomplemented
436C4×Dic3—22no—
437C4×Dic3—34no—
438C4×Dic3—34no—
439C4×Dic3—62no—
440C4×Dic3—62no—
441C22×C32C23×C411yescharacteristic
442C22×C32C22×D411yescharacteristic
443C22×C32C22×D411yescharacteristic
444C22×C32C22×Q811yescharacteristic
445C22×C32C2×#4111yescharacteristic
446C22×C32H(5,𝔽2)11yescharacteristic
447C22×C322−1+411yescharacteristic
448C2×C3⋊D3—22no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—22no—
454C2×C3⋊D3C2×C4⋊C414yescomplemented
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3C2×C4⋊C414yescomplemented
462C32×C4—22no—
463C32×C4—41no—
464C32×C4—41no—
465C3⋊Dic3—41no—
466C3⋊Dic3—41no—
467C3⋊Dic3C4×D414yescomplemented
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—41no—
473C3×Dic3—41no—
474C3×Dic3C2×C4⋊C414yescomplemented
475C22×D4—91no—
476C23×C4—31no—
477C23×C4—91no—
478C23×C4—91no—
479C23×C4—91no—
480C23×C4—91no—
481C23×C4—91no—
482C4×D4—98no—
483C4×D4—184no—
484C4×D4—184no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—184no—
499C2×C4⋊C4—184no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C42—31no—
507C2×C42—91no—
508C2×C42—91no—
509#95—31no—
510#95—31no—
511#95—91no—
512#95—91no—
513#95—91no—
514#95D3211yescharacteristic
515C23×C3—21no—
516C23×C3—32no—
517C23×C3—32no—
518C23×C3—32no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3C23×D311yescharacteristic
524C23×C3C23×D311yescharacteristic
525C22×D3—21no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—32no—
530C22×D3—32no—
531C22×D3—32no—
532C22×D3—32no—
533C22×D3—32no—
534C22×D3—32no—
535C22×D3—62no—
536C22×D3—62no—
537C22×D3—62no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—121no—
547C22×D3—121no—
548C22×D3—121no—
549C22×D3—121no—
550C22×D3C2×C4×D312yes—
551C22×D3D3×D412yes—
552C22×D3D3×Q812yes—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—22no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—32no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—124no—
600C2×C3×C4C2×C4×D312yes—
601C2×C3×C4C2×C4×D312yes—
602#67—316no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—62no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—68no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—121no—
640C2×Dic3—121no—
641C2×Dic3—121no—
642C2×Dic3—121no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—124no—
646C2×Dic3C2×C4×D312yes—
647C2×Dic3C2×C4×D312yes—
648C2×Dic3C2×C4×D312yes—
649C2×Dic3D3×D412yes—
650C2×Dic3D3×D412yes—
651C2×Dic3D3×D412yes—
652C2×Dic3D3×Q812yes—
653D12—316no—
654C4×D3—44no—
655C4×D3—68no—
656C4×D3—68no—
657C4×D3—68no—
658C4×D3—128no—
659C4×D3—124no—
660C4×D3—124no—
661C4×D3—124no—
662C4×D3—124no—
663C4×D3—124no—
664C2×C32C22×C4⋊C411yescharacteristic
665C2×C32C2×C4×D411yescharacteristic
666C2×C32#52011yescharacteristic
667C2×C32D4211yescharacteristic
668C2×C32#54711yescharacteristic
669C2×C32D4×Q811yescharacteristic
670C2×C32#55411yescharacteristic
671C3⋊D3—24no—
672C3×D3—24no—
673C24—31no—
674C24—91no—
675C2×D4—94no—
676C2×D4—94no—
677C2×D4—94no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—94no—
688C22×C4—91no—
689C22×C4—94no—
690C22×C4—91no—
691C22×C4—91no—
692C22×C4—121no—
693C22×C4—182no—
694C22×C4—182no—
695C22×C4—182no—
696C22×C4—182no—
697C22×C4—182no—
698C22×C4—182no—
699C22×C4—182no—
700C22×C4—182no—
701C22×C4—182no—
702C22×C4—182no—
703C22×C4—361no—
704C22×C4—361no—
705C22×C4—361no—
706C22×C4C2×D3211yescharacteristic
707C22×C4C2×D3211yescharacteristic
708C22×C4C2×D3211yescharacteristic
709C4⋊C4—34no—
710C4⋊C4—62no—
711C4⋊C4—62no—
712C4⋊C4—62no—
713C4⋊C4—62no—
714C4⋊C4—94no—
715C4⋊C4—121no—
716C4⋊C4—182no—
717C4⋊C4—182no—
718C4⋊C4—182no—
719C4⋊C4—182no—
720C4⋊C4—182no—
721C4⋊C4—361no—
722C22⋊C4—34no—
723C22⋊C4—62no—
724C22⋊C4—94no—
725C22⋊C4—182no—
726C22⋊C4—182no—
727C22⋊C4—182no—
728C42—62no—
729C42—94no—
730C42—182no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—34no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—62no—
744C22×C3—62no—
745C22×C3C22×C4×D311yescharacteristic
746C22×C3C22×C4×D311yescharacteristic
747C22×C3C2×D3×D411yescharacteristic
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C22×C3C2×D3×D411yescharacteristic
751C22×C3#100411yescharacteristic
752C22×C3C2×D3×Q811yescharacteristic
753C22×C3C2×D3×Q811yescharacteristic
754C22×C3#100711yescharacteristic
755C22×C3D3×#4111yescharacteristic
756C22×C3D3×#4111yescharacteristic
757C22×C3#100911yescharacteristic
758C22×C3#101011yescharacteristic
759C2×D3—22no—
760C2×D3—22no—
761C2×D3—22no—
762C2×D3—22no—
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—34no—
766C2×D3—34no—
767C2×D3—64no—
768C2×D3—62no—
769C2×D3—62no—
770C2×D3—62no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—62no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—62no—
778C2×D3—62no—
779C2×D3—62no—
780C2×D3—122no—
781C2×D3—122no—
782C2×D3—122no—
783C2×D3—122no—
784C2×D3—122no—
785C2×D3—122no—
786C2×D3D3×C4⋊C414yescomplemented
787C3×C4—22no—
788C3×C4—22no—
789C3×C4—34no—
790C3×C4—42no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4—41no—
795C3×C4—62no—
796C3×C4—62no—
797C3×C4—62no—
798C3×C4—62no—
799C3×C4—81no—
800C3×C4—81no—
801C3×C4—121no—
802C3×C4—121no—
803Dic3—22no—
804Dic3—22no—
805Dic3—22no—
806Dic3—22no—
807Dic3—34no—
808Dic3—34no—
809Dic3—41no—
810Dic3—41no—
811Dic3—64no—
812Dic3—121no—
813Dic3—121no—
814Dic3—121no—
815Dic3—121no—
816Dic3—241no—
817Dic3—241no—
818Dic3D3×C4⋊C414yescomplemented
819C32D4×C4⋊C411yescharacteristic, complemented, Sylow
820C23—32no—
821C23—32no—
822C23—32no—
823C23—61no—
824C23—61no—
825C23—61no—
826C23—61no—
827C23—92no—
828C23—92no—
829C23—92no—
830C23—181no—
831C23—181no—
832C23—181no—
833C23—181no—
834C23C22×D3211yescharacteristic
835D4—916no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—32no—
845C2×C4—32no—
846C2×C4—32no—
847C2×C4—32no—
848C2×C4—32no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—92no—
866C2×C4—92no—
867C2×C4—92no—
868C2×C4—124no—
869C2×C4—188no—
870C2×C4—188no—
871C2×C4—181no—
872C2×C4—181no—
873C2×C4—181no—
874C2×C4—181no—
875C2×C4—181no—
876C2×C4—181no—
877C2×C4—364no—
878C2×C4—364no—
879C2×C4—364no—
880C2×C4C4×D3212yes—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—64no—
889C2×C3C2×D3×C4⋊C411yescharacteristic
890C2×C3C2×D3×C4⋊C411yescharacteristic
891C2×C3C4×D3×D411yescharacteristic
892C2×C3C4×D3×D411yescharacteristic
893C2×C3#554611yescharacteristic
894C2×C3#557411yescharacteristic
895C2×C3#559011yescharacteristic
896C2×C3#560911yescharacteristic
897C2×C3#563111yescharacteristic
898C2×C3#563211yescharacteristic
899C2×C3#563611yescharacteristic
900C2×C3#565511yescharacteristic
901C2×C3#569011yescharacteristic
902C2×C3#572711yescharacteristic
903D3—24no—
904D3—64no—
905D3—64no—
906D3—124no—
907C22—34no—
908C22—62no—
909C22—62no—
910C22—62no—
911C22—62no—
912C22—62no—
913C22—62no—
914C22—94no—
915C22—182no—
916C22—182no—
917C22—182no—
918C22—182no—
919C22—182no—
920C22—182no—
921C22#6429711yescharacteristic
922C22C2×C4×D3211yescharacteristic
923C22#6430711yescharacteristic
924C22D32×D411yescharacteristic
925C22D32×D411yescharacteristic
926C22#6431211yescharacteristic
927C22D32×Q811yescharacteristic
928C4—22no—
929C4—34no—
930C4—41no—
931C4—41no—
932C4—62no—
933C4—62no—
934C4—62no—
935C4—62no—
936C4—94no—
937C4—121no—
938C4—121no—
939C4—361no—
940C4—361no—
941C3—21no—
942C3#7439311yescharacteristic, complemented
943C3#7620211yescharacteristic, complemented
944C2—64no—
945C2—184no—
946C2#1059388911yescharacteristic
947C2#1059406411yescharacteristic
948C2#1059425511yescharacteristic
949C2#1059427511yescharacteristic
950C2#1059437811yescharacteristic
951C2#1059439511yescharacteristic
952C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32D4×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63900C2semidirect
5. C2×D3×Dic3⋊C4C2semidirect
6. #10592366C2semidirect
7. C3×#4668C2semidirect
8. C3×#4647C2semidirect
9. #10591377C2semidirect
10. #10591375C2semidirect
11. #10591374C2semidirect
12. #10591369C2semidirect
13. #10591265C2semidirect
14. #10591244C2semidirect
15. #10591243C2semidirect
49. #63881C4semidirect
82. #4668D3semidirect
88. #4647D3semidirect
99. C2×C4×C3⋊D3C2×C4semidirect
124. C2×D3×Dic3C2×C4semidirect
130. C3×(C2×D3)⋊C4C2×C4semidirect
136. C3×Dic3⋊C4C2×C4semidirect
139. #3724D4semidirect
143. #3722C2×C4semidirect
146. Dic32C2×C4semidirect
291. #626C4⋊C4semidirect
413. (C2×D3)⋊C4C4×D3semidirect
435. Dic3⋊C4C4×D3semidirect
454. C2×C3⋊D3C2×C4⋊C4semidirect
461. C2×C3×D3C2×C4⋊C4semidirect
467. C3⋊Dic3C4×D4semidirect
474. C3×Dic3C2×C4⋊C4semidirect
786. C2×D3D3×C4⋊C4semidirect
818. Dic3D3×C4⋊C4semidirect
819. C32D4×C4⋊C4semidirect
942. C3#74393semidirect
943. C3#76202semidirect

Maximal subgroups

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

subgroupindex
C2×#639042
C2×#639002
C2×#638812
C2×#638802
C2×D3×Dic3⋊C42
#105923662
C3×#46682
C3×#46472
#105913772
#105913752
#105913742
#105913692
#105912652
#105912442
#105912432
#762023
#743933