Finite Group Databasebeta

← #11805458

Subgroups — #11805458

Order 1152.

1637 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C4×#625C211yesmaximal, characteristic
3C2×#63879C211yesmaximal, characteristic
4C2×#63879C211yesmaximal, characteristic
5C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
6#10592675C211yesmaximal, characteristic, complemented
7C3×#4989C211yesmaximal, characteristic, complemented
8#10591377C211yesmaximal, characteristic, complemented
9#10591366C211yesmaximal, characteristic, complemented
10#10591295C211yesmaximal, characteristic, complemented
11#10591278C211yesmaximal, characteristic, complemented
12#10591277C211yesmaximal, characteristic, complemented
13#10591264C211yesmaximal, characteristic, complemented
14#10591244C211yesmaximal, characteristic, complemented
15#10591241C211yesmaximal, characteristic, complemented
16C4⋊C4×#67—31nomaximal
17#74393—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C3×D3×C4⋊C4—24no—
37C2×#3724C2211yescharacteristic
38C2×#3724C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48C4×#625—24no—
49#63879—24no—
50#63879C418yescomplemented
51D3×Dic3⋊C4—24no—
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58C22×C3×C4⋊C4—31no—
59C2×C4×#67—31no—
60C2×C4×#67—31no—
61C2×C4×#67—31no—
62C2×C4×#67—31no—
63C22×Dic3⋊C4—31no—
64C2×D3×C4⋊C4—31no—
65C2×D3×C4⋊C4D311yescharacteristic, complemented
66C2×#67⋊C4—31no—
67C2×#67⋊C4—31no—
68C3×#385—31no—
69#5212—31no—
70#5210—31no—
71#5210—31no—
72#4989—31no—
73#4989—31no—
74#4989D311yescharacteristic, complemented
75#4987—31no—
76#4976—31no—
77#4976—31no—
78#4976—31no—
79#4976—61no—
80#4975—31no—
81#4975—31no—
82Dic3×C4⋊C4—31no—
83#4950—31no—
84#4942—31no—
85#4668—31no—
86#4667—31no—
87#4649—31no—
88#4647—31no—
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×C3×C4×D3—22no—
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×D3—41no—
113C2×C3×C4×D3—41no—
114C2×C3×C4×D3—41no—
115C2×C3×C4×D3C2×C414yescomplemented
116C2×#625C2×C414yes—
117C2×#625D414yes—
118C2×#625Q814yes—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—41no—
124C2×D3×Dic3C2×C414yescomplemented
125C32×C4⋊C4—22no—
126#3750—22no—
127#3750—22no—
128#3750C2×C414yescomplemented
129C4×C3⋊Dic3—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4C2×C414yescomplemented
132C3×C4⋊Dic3—22no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4—41no—
135C3×Dic3⋊C4D414yescomplemented
136#3724—22no—
137#3724—22no—
138Dic3⋊Dic3—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—41no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3C2×C414yescomplemented
145Dic32—22no—
146Dic32C2×C414yescomplemented
147D4×C4⋊C4—91noSylow
148C23×C3×C4—31no—
149C23×C3×C4—31no—
150C23×C3×C4—31no—
151C23×C3×C4—31no—
152C22×#67—31no—
153C22×#67—31no—
154C23×Dic3—31no—
155C23×Dic3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3C2×D311yescharacteristic
159C22×C4×D3C2×D311yescharacteristic
160C22×C4×D3C2×D311yescharacteristic
161C22×C4×D3C2×D311yescharacteristic
162C2×C3×C4⋊C4—21no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—64no—
168C2×C3×C4⋊C4C2×D311yescharacteristic
169C2×C3×C4⋊C4C2×D311yescharacteristic
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C4×#67—38no—
177C4×#67—64no—
178C4×#67—64no—
179C4×#67—64no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4C2×D311yescharacteristic
185C2×(C2×D3)⋊C4C2×D311yescharacteristic
186C2×C4⋊Dic3—31no—
187C2×C4⋊Dic3—31no—
188C2×C4⋊Dic3—31no—
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—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—61no—
204C2×Dic3⋊C4—61no—
205C2×Dic3⋊C4—61no—
206C2×Dic3⋊C4—64no—
207C2×Dic3⋊C4C2×D311yescharacteristic
208C2×Dic3⋊C4C2×D311yescharacteristic
209C2×Dic3⋊C4C2×D311yescharacteristic
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3—31no—
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3—61no—
217D3×C4⋊C4—24no—
218D3×C4⋊C4—64no—
219#67⋊C4—38no—
220#67⋊C4—64no—
221C3×#95—31no—
222C3×#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—61no—
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×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C22×C412yes—
245C22×C3×D3C22×C412yes—
246C22×C3×D3C2×D412yes—
247C22×C3×D3C2×D412yes—
248C22×C3×D3C2×Q812yes—
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×C4C22×C412yes—
258C2×C32×C4C2×D412yes—
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⋊Dic3C22×C412yes—
268C2×C3⋊Dic3C22×C412yes—
269C2×C3⋊Dic3C2×D412yes—
270C2×C3⋊Dic3C2×Q812yes—
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×Dic3—21no—
284C2×C3×Dic3C22×C412yes—
285C2×C3×Dic3C22×C412yes—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3#4112yes—
289C3×C4×D3—28no—
290C3×C4×D3—44no—
291C3×C4×D3—44no—
292C3×C4×D3—44no—
293#625C4⋊C4116yescomplemented
294D3×Dic3—28no—
295D3×Dic3—44no—
296C2×C4×D4—91no—
297C2×C4×D4—91no—
298C2×C4×D4—91no—
299C22×C4⋊C4—31no—
300C22×C4⋊C4—91no—
301#389—91no—
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—
312C24×C3—31no—
313C23×D3C22×D311yescharacteristic
314C23×D3C22×D311yescharacteristic
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—34no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—62no—
326C22×C3×C4—62no—
327C22×C3×C4—62no—
328C22×C3×C4—62no—
329C22×C3×C4—62no—
330C22×C3×C4—62no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4—121no—
334C22×C3×C4—121no—
335C22×C3×C4—121no—
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C2×#67—34no—
343C2×#67—34no—
344C2×#67—34no—
345C2×#67—34no—
346C2×#67—34no—
347C2×#67—34no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—34no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—62no—
362C22×Dic3—62no—
363C22×Dic3—62no—
364C22×Dic3—62no—
365C22×Dic3—121no—
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C2×C4×D3—22no—
373C2×C4×D3—22no—
374C2×C4×D3—22no—
375C2×C4×D3—22no—
376C2×C4×D3—22no—
377C2×C4×D3—22no—
378C2×C4×D3—22no—
379C2×C4×D3—22no—
380C2×C4×D3—34no—
381C2×C4×D3—41no—
382C2×C4×D3—41no—
383C2×C4×D3—41no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—121no—
389C2×C4×D3C4×D314yescomplemented
390C3×C4⋊C4—22no—
391C3×C4⋊C4—22no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—42no—
394C3×C4⋊C4—62no—
395C3×C4⋊C4—62no—
396C3×C4⋊C4—121no—
397C3×C22⋊C4—34no—
398C3×C22⋊C4—62no—
399#217—34no—
400#217—62no—
401#217—62no—
402#217—62no—
403(C2×D3)⋊C4—22no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4C4×D314yescomplemented
409C4⋊Dic3—22no—
410C4⋊Dic3—62no—
411C4⋊Dic3—62no—
412C4⋊Dic3—121no—
413Dic3⋊C4—22no—
414Dic3⋊C4—34no—
415Dic3⋊C4—34no—
416Dic3⋊C4—41no—
417Dic3⋊C4—64no—
418Dic3⋊C4—62no—
419Dic3⋊C4—62no—
420Dic3⋊C4—62no—
421Dic3⋊C4—62no—
422Dic3⋊C4—62no—
423Dic3⋊C4—62no—
424Dic3⋊C4—62no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—122no—
429Dic3⋊C4—122no—
430Dic3⋊C4—121no—
431Dic3⋊C4#6714yescomplemented
432C4×Dic3—34no—
433C4×Dic3—34no—
434C4×Dic3—62no—
435C4×Dic3—62no—
436C4×Dic3—62no—
437C4×Dic3—62no—
438C4×Dic3—122no—
439C22×C32C23×C411yescharacteristic
440C22×C32C22×D411yescharacteristic
441C22×C32C22×D411yescharacteristic
442C22×C32C22×Q811yescharacteristic
443C22×C32C2×#4111yescharacteristic
444C22×C32H(5,𝔽2)11yescharacteristic
445C22×C322−1+411yescharacteristic
446C2×C3×D3—22no—
447C2×C3×D3—22no—
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×D3—22no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3C2×C4⋊C414yescomplemented
459C2×C3×D3C2×C4⋊C414yescomplemented
460C32×C4—22no—
461C32×C4—22no—
462C32×C4—41no—
463C3⋊Dic3—22no—
464C3⋊Dic3—41no—
465C3⋊Dic3—41no—
466C3⋊Dic3C2×C4⋊C414yescomplemented
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—41no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C3×Dic3C4×D414yescomplemented
473C22×D4—91no—
474C23×C4—31no—
475C23×C4—31no—
476C23×C4—31no—
477C23×C4—31no—
478C23×C4—91no—
479C23×C4—91no—
480C4×D4—98no—
481C4×D4—184no—
482C4×D4—184no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—64no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—184no—
497C2×C4⋊C4D3211yescharacteristic
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C42—91no—
505C2×C42—91no—
506C2×C42—91no—
507#95—31no—
508#95—31no—
509#95—91no—
510#95—91no—
511#95—91no—
512#95—91no—
513C23×C3—21no—
514C23×C3—32no—
515C23×C3—32no—
516C23×C3—32no—
517C23×C3—32no—
518C23×C3—32no—
519C23×C3—32no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3C23×D311yescharacteristic
529C23×C3C23×D311yescharacteristic
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3C2×C4×D312yes—
539C22×D3C2×C4×D312yes—
540C22×D3D3×D412yes—
541C22×D3D3×D412yes—
542C22×D3D3×Q812yes—
543C22×D3D3×Q812yes—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—32no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—32no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—68no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—124no—
587C2×C3×C4—124no—
588C2×C3×C4—124no—
589C2×C3×C4C2×C4×D312yes—
590C2×C3×C4C2×C4×D312yes—
591C2×C3×C4D3×D412yes—
592C2×C3×C4C2×#6712yes—
593#67—316no—
594#67—316no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—32no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—32no—
613C2×Dic3—32no—
614C2×Dic3—32no—
615C2×Dic3—32no—
616C2×Dic3—62no—
617C2×Dic3—62no—
618C2×Dic3—62no—
619C2×Dic3—62no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—68no—
625C2×Dic3—62no—
626C2×Dic3—61no—
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—121no—
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×Dic3#23512yes—
649C2×Dic3C2×#6712yes—
650C2×Dic3C2×#6712yes—
651C4×D3—28no—
652C4×D3—44no—
653C4×D3—44no—
654C4×D3—44no—
655C4×D3—68no—
656C4×D3—124no—
657C2×C32C22×C4⋊C411yescharacteristic
658C2×C32C2×C4×D411yescharacteristic
659C2×C32#52011yescharacteristic
660C2×C32D4211yescharacteristic
661C2×C32#54711yescharacteristic
662C2×C32D4×Q811yescharacteristic
663C2×C32#55411yescharacteristic
664C3×D3—24no—
665C3×D3—24no—
666C24—31no—
667C24—31no—
668C2×D4—94no—
669C2×D4—94no—
670C2×D4—94no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—34no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—94no—
687C22×C4—91no—
688C22×C4—91no—
689C22×C4—91no—
690C22×C4—91no—
691C22×C4—121no—
692C22×C4—121no—
693C22×C4—121no—
694C22×C4—182no—
695C22×C4—182no—
696C22×C4—182no—
697C22×C4—182no—
698C22×C4—361no—
699C22×C4C2×D3211yescharacteristic
700C22×C4C2×D3211yescharacteristic
701C22×C4C2×D3211yescharacteristic
702C4⋊C4—22no—
703C4⋊C4—34no—
704C4⋊C4—62no—
705C4⋊C4—62no—
706C4⋊C4—94no—
707C4⋊C4—121no—
708C4⋊C4—182no—
709C4⋊C4—182no—
710C4⋊C4—182no—
711C4⋊C4—182no—
712C4⋊C4—182no—
713C4⋊C4—182no—
714C4⋊C4—361no—
715C22⋊C4—34no—
716C22⋊C4—62no—
717C22⋊C4—94no—
718C22⋊C4—182no—
719C22⋊C4—182no—
720C22⋊C4—182no—
721C42—94no—
722C42—182no—
723C42—182no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—34no—
732C22×C3—34no—
733C22×C3—62no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—62no—
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×#23511yescharacteristic
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C22×C3C2×D3×D411yescharacteristic
751C22×C3#100411yescharacteristic
752C22×C3#100411yescharacteristic
753C22×C3C2×D3×Q811yescharacteristic
754C22×C3C2×D3×Q811yescharacteristic
755C22×C3#100711yescharacteristic
756C22×C3D3×#4111yescharacteristic
757C22×C3#101011yescharacteristic
758C22×C3C22×#6711yescharacteristic
759C2×D3—22no—
760C2×D3—22no—
761C2×D3—22no—
762C2×D3—22no—
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—22no—
766C2×D3—22no—
767C2×D3—22no—
768C2×D3—22no—
769C2×D3—22no—
770C2×D3—22no—
771C2×D3D3×C4⋊C414yescomplemented
772C2×D3D3×C4⋊C414yescomplemented
773C3×C4—22no—
774C3×C4—22no—
775C3×C4—22no—
776C3×C4—22no—
777C3×C4—34no—
778C3×C4—42no—
779C3×C4—42no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—62no—
783C3×C4—62no—
784C3×C4—81no—
785C3×C4—121no—
786C3×C4—121no—
787C3×C4—121no—
788Dic3—22no—
789Dic3—22no—
790Dic3—34no—
791Dic3—34no—
792Dic3—41no—
793Dic3—41no—
794Dic3—41no—
795Dic3—64no—
796Dic3—62no—
797Dic3—62no—
798Dic3—122no—
799Dic3—122no—
800Dic3—121no—
801Dic3—121no—
802Dic3—121no—
803Dic3—121no—
804Dic3—241no—
805Dic3C4×#6714yescomplemented
806C32D4×C4⋊C411yescharacteristic, complemented, Sylow
807C23—32no—
808C23—32no—
809C23—32no—
810C23—32no—
811C23—32no—
812C23—32no—
813C23—61no—
814C23—61no—
815C23—61no—
816C23—61no—
817C23—61no—
818C23—61no—
819C23—61no—
820C23—61no—
821C23C22×D3211yescharacteristic
822D4—916no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—32no—
831C2×C4—32no—
832C2×C4—32no—
833C2×C4—32no—
834C2×C4—32no—
835C2×C4—68no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—92no—
850C2×C4—92no—
851C2×C4—92no—
852C2×C4—92no—
853C2×C4—124no—
854C2×C4—124no—
855C2×C4—124no—
856C2×C4—188no—
857C2×C4—181no—
858C2×C4—181no—
859C2×C4—181no—
860C2×C4—181no—
861C2×C4—181no—
862C2×C4—181no—
863C2×C4—181no—
864C2×C4—181no—
865C2×C4—364no—
866C2×C4C4×D3212yes—
867C2×C4D3×#6712yes—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—64no—
876C2×C3—64no—
877C2×C3C2×D3×C4⋊C411yescharacteristic
878C2×C3C2×D3×C4⋊C411yescharacteristic
879C2×C3#550411yescharacteristic
880C2×C3#550711yescharacteristic
881C2×C3#551111yescharacteristic
882C2×C3C4×D3×D411yescharacteristic
883C2×C3#554611yescharacteristic
884C2×C3#559011yescharacteristic
885C2×C3#563211yescharacteristic
886C2×C3#563611yescharacteristic
887C2×C3#565511yescharacteristic
888C2×C3C2×C4×#6711yescharacteristic
889C2×C3D4×#6711yescharacteristic
890C2×C3Q8×#6711yescharacteristic
891D3—24no—
892D3—24no—
893C22—34no—
894C22—34no—
895C22—62no—
896C22—62no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—62no—
904C22—62no—
905C22—62no—
906C22—62no—
907C22C2×C4×D3211yescharacteristic
908C22D3×#23511yescharacteristic
909C22D32×D411yescharacteristic
910C22#6431311yescharacteristic
911C22#6431511yescharacteristic
912C22D32×Q811yescharacteristic
913C22C2×D3×#6711yescharacteristic
914C4—22no—
915C4—22no—
916C4—34no—
917C4—41no—
918C4—62no—
919C4—62no—
920C4—94no—
921C4—121no—
922C4—121no—
923C4—121no—
924C4—182no—
925C4—361no—
926C4—361no—
927C3—21no—
928C3#7439311yescharacteristic, complemented
929C3C4⋊C4×#6711yescharacteristic, complemented
930C2—64no—
931C2—64no—
932C2#1059435911yescharacteristic
933C2#1059451311yescharacteristic
934C2#1059453311yescharacteristic
935C2D32×C4⋊C411yescharacteristic
936C2C4×D3×#6711yescharacteristic
937C2#1059528711yescharacteristic
938C2#1059540011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenterC2×C4⋊C4D32
hypocenterC32D4×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×C4⋊C4C2semidirect
5. C2×D3×Dic3⋊C4C2semidirect
6. #10592675C2semidirect
7. C3×#4989C2semidirect
8. #10591377C2semidirect
9. #10591366C2semidirect
10. #10591295C2semidirect
11. #10591278C2semidirect
12. #10591277C2semidirect
13. #10591264C2semidirect
14. #10591244C2semidirect
15. #10591241C2semidirect
50. #63879C4semidirect
65. C2×D3×C4⋊C4D3semidirect
74. #4989D3semidirect
115. C2×C3×C4×D3C2×C4semidirect
124. C2×D3×Dic3C2×C4semidirect
128. #3750C2×C4semidirect
131. C3×(C2×D3)⋊C4C2×C4semidirect
135. C3×Dic3⋊C4D4semidirect
144. (C2×D3)⋊Dic3C2×C4semidirect
146. Dic32C2×C4semidirect
293. #625C4⋊C4semidirect
389. C2×C4×D3C4×D3semidirect
408. (C2×D3)⋊C4C4×D3semidirect
431. Dic3⋊C4#67semidirect
458. C2×C3×D3C2×C4⋊C4semidirect
459. C2×C3×D3C2×C4⋊C4semidirect
466. C3⋊Dic3C2×C4⋊C4semidirect
472. C3×Dic3C4×D4semidirect
771. C2×D3D3×C4⋊C4semidirect
772. C2×D3D3×C4⋊C4semidirect
805. Dic3C4×#67semidirect
806. C32D4×C4⋊C4semidirect
928. C3#74393semidirect
929. C3C4⋊C4×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×C4×#6252
C2×#638792
C2×D3×Dic3⋊C42
#105926752
C3×#49892
#105913772
#105913662
#105912952
#105912782
#105912772
#105912642
#105912442
#105912412
C4⋊C4×#673
#743933