Finite Group Databasebeta

← #11805433

Subgroups — #11805433

Order 1152.

1761 conjugacy classes of subgroups.

The subgroup lattice has 963 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C2×#67⋊Dic3C211yesmaximal, characteristic
4C2×#67⋊Dic3C211yesmaximal, characteristic
5C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C3×#5210C211yesmaximal, characteristic, complemented
7#10591720C211yesmaximal, characteristic, complemented
8#10591719C211yesmaximal, characteristic, complemented
9#10591372C211yesmaximal, characteristic, complemented
10#10591369C211yesmaximal, characteristic, complemented
11#10591330C211yesmaximal, characteristic, complemented
12#10591278C211yesmaximal, characteristic, complemented
13#10591244C211yesmaximal, characteristic, complemented
14#10591243C211yesmaximal, characteristic, complemented
15#10591234C211yesmaximal, characteristic, complemented
16D4×Dic3⋊C4—31nomaximal
17#74393—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3750—24no—
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C3×C4×#67—24no—
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39#67⋊Dic3—24no—
40#67⋊Dic3C418yescomplemented
41C2×#3724C2211yescharacteristic
42C2×#3724C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×Dic32C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51D3×Dic3⋊C4—24no—
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58C2×C3×C4×D4—31no—
59C2×D4×Dic3—31no—
60C2×D4×Dic3—31no—
61C2×C4×#67D311yescharacteristic
62C22×Dic3⋊C4—31no—
63C22×Dic3⋊C4—31no—
64C22×Dic3⋊C4—31no—
65C22×Dic3⋊C4—61no—
66C2×D3×C4⋊C4—31no—
67C2×#67⋊C4—31no—
68C2×#67⋊C4—31no—
69C3×#385—31no—
70#5210—31no—
71#5210D311yescharacteristic, complemented
72#4989—31no—
73#4976—31no—
74#4975—31no—
75#4975—31no—
76#4972—31no—
77#4950—31no—
78#4946—31no—
79#4946—31no—
80#4942—31no—
81#4942—31no—
82#4942—31no—
83C4×Dic3⋊C4—31no—
84#4928—31no—
85#4668—31no—
86#4667—31no—
87#4649—31no—
88#4647—31no—
89C24×C32C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4—22no—
92C22×C32×C4—22no—
93C22×C32×C4—41no—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3⋊Dic3—22no—
97C22×C3⋊Dic3—22no—
98C22×C3⋊Dic3—22no—
99C22×C3⋊Dic3—22no—
100C22×C3⋊Dic3—41no—
101C22×C3⋊Dic3C2×C414yescomplemented
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C2×C3×#67C2×C414yes—
107C2×C3×#67D414yes—
108C2×C3×#67Q814yes—
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3—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#3750—22no—
126#3750—22no—
127#3750—22no—
128#3750D414yescomplemented
129C3×#217—22no—
130C3×#217—22no—
131C3×#217C2×C414yescomplemented
132C3×(C2×D3)⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4—22no—
135C3×Dic3⋊C4—41no—
136C3×C4×Dic3—22no—
137#3724—22no—
138#3724—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3—41no—
142Dic3⋊Dic3C2×C414yescomplemented
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3C2×C414yescomplemented
145Dic32—22no—
146Dic32C2×C414yescomplemented
147D4×C4⋊C4—91noSylow
148C22×C3×D4—31no—
149C23×C3×C4—21no—
150C23×C3×C4—31no—
151C23×C3×C4C2×D311yescharacteristic
152C23×C3×C4C2×D311yescharacteristic
153C22×#67C2×D311yescharacteristic
154C23×Dic3—31no—
155C23×Dic3—31no—
156C23×Dic3—31no—
157C23×Dic3—31no—
158C23×Dic3—31no—
159C23×Dic3—31no—
160C23×Dic3—61no—
161C23×Dic3—61no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3C2×D311yescharacteristic
165C3×C4×D4—64no—
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×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C42—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217C2×D311yescharacteristic
177C2×#217C2×D311yescharacteristic
178C2×#217C2×D311yescharacteristic
179D4×Dic3—38no—
180D4×Dic3—64no—
181C4×#67—24no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4C2×D311yescharacteristic
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—31no—
187C2×C4⋊Dic3—31no—
188C2×C4⋊Dic3—31no—
189C2×Dic3⋊C4—31no—
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—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—61no—
206C2×Dic3⋊C4—61no—
207C2×Dic3⋊C4—61no—
208C2×Dic3⋊C4—61no—
209C2×Dic3⋊C4—64no—
210C2×Dic3⋊C4—64no—
211C2×Dic3⋊C4—64no—
212C2×Dic3⋊C4—68no—
213C2×Dic3⋊C4C2×D311yescharacteristic
214C2×Dic3⋊C4C2×D311yescharacteristic
215C2×Dic3⋊C4C2×D311yescharacteristic
216C2×C4×Dic3—31no—
217C2×C4×Dic3—31no—
218C2×C4×Dic3—31no—
219C2×C4×Dic3—31no—
220C2×C4×Dic3C2×D311yescharacteristic
221D3×C4⋊C4—64no—
222#67⋊C4—38no—
223#67⋊C4—64no—
224C3×#95—31no—
225C3×#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95C2×D311yescharacteristic
235C3⋊#95C2×D311yescharacteristic
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32C22×C412yes—
241C23×C32C2×D412yes—
242C23×C32C2×Q812yes—
243C23×C32C2411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3C22×C412yes—
249C22×C3×D3C2×D412yes—
250C22×C3×D3C2×Q812yes—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—44no—
257C2×C32×C4C2×D412yes—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—28no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—44no—
267C2×C3⋊Dic3C22×C412yes—
268C2×C3⋊Dic3C22×C412yes—
269C2×C3⋊Dic3C2×D412yes—
270C2×C3⋊Dic3C2×D412yes—
271C2×C3⋊Dic3#4112yes—
272C3×#67C4⋊C4116yescomplemented
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×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3C22×C412yes—
290C2×C3×Dic3C22×C412yes—
291C2×C3×Dic3C22×C412yes—
292C2×C3×Dic3C2×D412yes—
293C2×C3×Dic3C2×Q812yes—
294C3×C4×D3—44no—
295D3×Dic3—28no—
296D3×Dic3—44no—
297C2×C4×D4—31no—
298C2×C4×D4—91no—
299C2×C4×D4—91no—
300C22×C4⋊C4—91no—
301C22×C4⋊C4—91no—
302#389—91no—
303#389—91no—
304#385—31no—
305#385—91no—
306#385—91no—
307#385—91no—
308#384—91no—
309#380—91no—
310#380—91no—
311C4×C4⋊C4—91no—
312C24×C3—21no—
313C24×C3—31no—
314C24×C3C22×D311yescharacteristic
315C24×C3C22×D311yescharacteristic
316C23×D3C22×D311yescharacteristic
317C2×C3×D4—34no—
318C2×C3×D4—34no—
319C2×C3×D4—34no—
320C22×C3×C4—24no—
321C22×C3×C4—22no—
322C22×C3×C4—22no—
323C22×C3×C4—22no—
324C22×C3×C4—22no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—42no—
335C22×C3×C4—41no—
336C22×C3×C4—41no—
337C22×C3×C4—42no—
338C22×C3×C4—62no—
339C22×C3×C4—62no—
340C22×C3×C4—121no—
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C2×#67Dic614yes—
346C2×#67C4×D314yes—
347C2×#67#6714yes—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—34no—
351C22×Dic3—34no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—34no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—64no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364C22×Dic3—62no—
365C22×Dic3—62no—
366C22×Dic3—62no—
367C22×Dic3—62no—
368C22×Dic3—62no—
369C22×Dic3—62no—
370C22×Dic3—62no—
371C22×Dic3—62no—
372C22×Dic3—62no—
373C22×Dic3—62no—
374C22×Dic3—64no—
375C22×Dic3—64no—
376C22×Dic3—64no—
377C22×Dic3—62no—
378C22×Dic3—62no—
379C22×Dic3—122no—
380C22×Dic3—121no—
381C22×Dic3—121no—
382C22×Dic3—121no—
383C22×Dic3—122no—
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C2×C4×D3—22no—
392C2×C4×D3—22no—
393C2×C4×D3—34no—
394C2×C4×D3—41no—
395C2×C4×D3—62no—
396C2×C4×D3—62no—
397C2×C4×D3—62no—
398C2×C4×D3—62no—
399C2×C4×D3—121no—
400C3×C4⋊C4—62no—
401C3×C4⋊C4—62no—
402C3×C4⋊C4—121no—
403C3×C22⋊C4—34no—
404C3×C22⋊C4—62no—
405C3×C22⋊C4—62no—
406C3×C22⋊C4—62no—
407C3×C42—62no—
408#217—22no—
409#217—22no—
410#217—34no—
411#217—62no—
412#217C4×D314yescomplemented
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—62no—
416C4⋊Dic3—34no—
417C4⋊Dic3—62no—
418C4⋊Dic3—62no—
419C4⋊Dic3—121no—
420Dic3⋊C4—22no—
421Dic3⋊C4—22no—
422Dic3⋊C4—34no—
423Dic3⋊C4—34no—
424Dic3⋊C4—34no—
425Dic3⋊C4—41no—
426Dic3⋊C4—64no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—62no—
434Dic3⋊C4—62no—
435Dic3⋊C4—62no—
436Dic3⋊C4—64no—
437Dic3⋊C4—64no—
438Dic3⋊C4—64no—
439Dic3⋊C4—62no—
440Dic3⋊C4—62no—
441Dic3⋊C4—62no—
442Dic3⋊C4—121no—
443C4×Dic3—22no—
444C4×Dic3—34no—
445C4×Dic3—34no—
446C4×Dic3—62no—
447C4×Dic3—62no—
448C22×C32—22no—
449C22×C32—22no—
450C22×C32—22no—
451C22×C32—22no—
452C22×C32—22no—
453C22×C32—22no—
454C22×C32C2×C4⋊C414yescomplemented
455C22×C32C23×C411yescharacteristic
456C22×C32C22×D411yescharacteristic
457C22×C32C22×D411yescharacteristic
458C22×C32C22×Q811yescharacteristic
459C22×C32C2×#4111yescharacteristic
460C22×C32H(5,𝔽2)11yescharacteristic
461C22×C322−1+411yescharacteristic
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3C2×C4⋊C414yescomplemented
469C32×C4—22no—
470C32×C4—41no—
471C3⋊Dic3—22no—
472C3⋊Dic3—22no—
473C3⋊Dic3—41no—
474C3⋊Dic3C4×D414yescomplemented
475C3×Dic3—22no—
476C3×Dic3—22no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3C2×C4⋊C414yescomplemented
482C22×D4—31no—
483C23×C4—31no—
484C23×C4—91no—
485C23×C4—91no—
486C23×C4—91no—
487C23×C4—91no—
488C23×C4D3211yescharacteristic
489C4×D4—64no—
490C4×D4—98no—
491C4×D4—184no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—91no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4—91no—
502C2×C4⋊C4—91no—
503C2×C4⋊C4—91no—
504C2×C4⋊C4—91no—
505C2×C4⋊C4—184no—
506C2×C4⋊C4—184no—
507C2×C22⋊C4—31no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—91no—
512C2×C22⋊C4—91no—
513C2×C42—31no—
514C2×C42—91no—
515C2×C42—91no—
516#95—31no—
517#95—31no—
518#95—91no—
519#95—91no—
520#95—91no—
521#95—91no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—32no—
539C23×C3—32no—
540C23×C3—32no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3C2×Dic612yes—
546C23×C3C2×C4×D312yes—
547C23×C3C2×C4×D312yes—
548C23×C3D3×D412yes—
549C23×C3D3×Q812yes—
550C23×C3C2×#6712yes—
551C23×C3C23×D311yescharacteristic
552C23×C3C23×D311yescharacteristic
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3C2×Dic612yes—
558C22×D3C2×C4×D312yes—
559C22×D3C2×#6712yes—
560C3×D4—316no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—22no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—22no—
573C2×C3×C4—32no—
574C2×C3×C4—32no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—44no—
583C2×C3×C4—44no—
584C2×C3×C4—48no—
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—61no—
600C2×C3×C4—61no—
601C2×C3×C4—124no—
602C2×C3×C4D3×D412yes—
603C2×C3×C4D3×D412yes—
604#67Dic3⋊C4116yescomplemented
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—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—32no—
624C2×Dic3—32no—
625C2×Dic3—32no—
626C2×Dic3—32no—
627C2×Dic3—32no—
628C2×Dic3—32no—
629C2×Dic3—32no—
630C2×Dic3—32no—
631C2×Dic3—62no—
632C2×Dic3—62no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—62no—
636C2×Dic3—68no—
637C2×Dic3—68no—
638C2×Dic3—68no—
639C2×Dic3—62no—
640C2×Dic3—616no—
641C2×Dic3—62no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—62no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—121no—
658C2×Dic3—121no—
659C2×Dic3—121no—
660C2×Dic3—121no—
661C2×Dic3—124no—
662C2×Dic3—124no—
663C2×Dic3—124no—
664C2×Dic3—128no—
665C2×Dic3C2×Dic612yes—
666C2×Dic3C2×C4×D312yes—
667C2×Dic3C2×C4×D312yes—
668C2×Dic3C2×C4×D312yes—
669C2×Dic3C2×#6712yes—
670C4×D3—44no—
671C4×D3—68no—
672C4×D3—124no—
673C2×C32—24no—
674C2×C32C22×C4⋊C411yescharacteristic
675C2×C32C2×C4×D411yescharacteristic
676C2×C32#52011yescharacteristic
677C2×C32D4211yescharacteristic
678C2×C32#54711yescharacteristic
679C2×C32D4×Q811yescharacteristic
680C2×C32#55411yescharacteristic
681C3×D3—24no—
682C24—31no—
683C24C2×D3211yescharacteristic
684C2×D4—34no—
685C2×D4—34no—
686C2×D4—34no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—41no—
697C22×C4—62no—
698C22×C4—62no—
699C22×C4—94no—
700C22×C4—91no—
701C22×C4—91no—
702C22×C4—91no—
703C22×C4—94no—
704C22×C4—91no—
705C22×C4—121no—
706C22×C4—182no—
707C22×C4—182no—
708C22×C4—182no—
709C22×C4—182no—
710C22×C4—182no—
711C22×C4—182no—
712C22×C4—182no—
713C22×C4—182no—
714C22×C4—361no—
715C22×C4—361no—
716C22×C4C2×D3211yescharacteristic
717C22×C4C2×D3211yescharacteristic
718C4⋊C4—62no—
719C4⋊C4—62no—
720C4⋊C4—94no—
721C4⋊C4—94no—
722C4⋊C4—121no—
723C4⋊C4—182no—
724C4⋊C4—182no—
725C4⋊C4—182no—
726C4⋊C4—182no—
727C4⋊C4—182no—
728C4⋊C4—182no—
729C4⋊C4—182no—
730C4⋊C4—361no—
731C22⋊C4—34no—
732C22⋊C4—62no—
733C22⋊C4—62no—
734C22⋊C4—62no—
735C22⋊C4—94no—
736C22⋊C4—182no—
737C42—62no—
738C42—94no—
739C42—182no—
740C22×C3—24no—
741C22×C3—24no—
742C22×C3—24no—
743C22×C3—24no—
744C22×C3—24no—
745C22×C3—24no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—24no—
766C22×C3—34no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3D3×C4⋊C414yescomplemented
774C22×C3C2×Dic3⋊C414yescomplemented
775C22×C3C22×Dic611yescharacteristic
776C22×C3C22×C4×D311yescharacteristic
777C22×C3C22×C4×D311yescharacteristic
778C22×C3C2×D3×D411yescharacteristic
779C22×C3C2×D3×D411yescharacteristic
780C22×C3C2×D3×D411yescharacteristic
781C22×C3#100411yescharacteristic
782C22×C3#100411yescharacteristic
783C22×C3C2×D3×Q811yescharacteristic
784C22×C3D3×#4111yescharacteristic
785C22×C3D3×#4111yescharacteristic
786C22×C3#101011yescharacteristic
787C22×C3#101011yescharacteristic
788C22×C3C22×#6711yescharacteristic
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3C2×Dic3⋊C414yescomplemented
796C3×C4—22no—
797C3×C4—22no—
798C3×C4—34no—
799C3×C4—42no—
800C3×C4—42no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—62no—
804C3×C4—62no—
805C3×C4—121no—
806C3×C4—121no—
807C3×C4—121no—
808C3×C4—121no—
809Dic3—22no—
810Dic3—22no—
811Dic3—34no—
812Dic3—34no—
813Dic3—41no—
814Dic3—41no—
815Dic3—41no—
816Dic3—41no—
817Dic3—64no—
818Dic3—64no—
819Dic3—62no—
820Dic3—62no—
821Dic3—62no—
822Dic3—62no—
823Dic3—122no—
824Dic3—122no—
825Dic3—121no—
826Dic3—121no—
827Dic3C2×Dic3⋊C414yescomplemented
828C32D4×C4⋊C411yescharacteristic, complemented, Sylow
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—32no—
834C23—32no—
835C23—32no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23D3×Dic612yes—
841C23C4×D3212yes—
842C23D3×#6712yes—
843C23C22×D3211yescharacteristic
844D4—316no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—44no—
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—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—92no—
873C2×C4—92no—
874C2×C4—92no—
875C2×C4—92no—
876C2×C4—92no—
877C2×C4—124no—
878C2×C4—188no—
879C2×C4—188no—
880C2×C4—181no—
881C2×C4—181no—
882C2×C4—181no—
883C2×C4—181no—
884C2×C4—181no—
885C2×C4—181no—
886C2×C4—181no—
887C2×C4—364no—
888C2×C4—364no—
889C2×C4#381112yes—
890C2×C3—28no—
891C2×C3—24no—
892C2×C3—24no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—64no—
901C2×C3C2×D3×C4⋊C411yescharacteristic
902C2×C3D4×Dic611yescharacteristic
903C2×C3#553911yescharacteristic
904C2×C3C4×D3×D411yescharacteristic
905C2×C3C4×D3×D411yescharacteristic
906C2×C3#554611yescharacteristic
907C2×C3#554611yescharacteristic
908C2×C3#559011yescharacteristic
909C2×C3#563211yescharacteristic
910C2×C3#563611yescharacteristic
911C2×C3#565511yescharacteristic
912C2×C3C22×Dic3⋊C411yescharacteristic
913C2×C3D4×#6711yescharacteristic
914C2×C3#582411yescharacteristic
915D3—24no—
916C22—22no—
917C22—22no—
918C22—22no—
919C22—22no—
920C22—22no—
921C22—22no—
922C22—34no—
923C22—62no—
924C22—62no—
925C22—62no—
926C22—62no—
927C22—62no—
928C22—62no—
929C22D3×Dic3⋊C414yescomplemented
930C22C2×D3×Dic611yescharacteristic
931C22#6429811yescharacteristic
932C22C2×C4×D3211yescharacteristic
933C22#6430611yescharacteristic
934C22C2×D3×#6711yescharacteristic
935C22C2×#381111yescharacteristic
936C22#6433011yescharacteristic
937C4—22no—
938C4—34no—
939C4—41no—
940C4—62no—
941C4—62no—
942C4—94no—
943C4—121no—
944C4—121no—
945C4—121no—
946C4—121no—
947C4—182no—
948C4—182no—
949C4—361no—
950C3—21no—
951C3#7439311yescharacteristic, complemented
952C3D4×Dic3⋊C411yescharacteristic, complemented
953C2—24no—
954C2—64no—
955C2C2×D3×Dic3⋊C411yescharacteristic
956C2#1059487611yescharacteristic
957C2#1059488811yescharacteristic
958C2#1059491511yescharacteristic
959C2#1059495911yescharacteristic
960C2C4×#381111yescharacteristic
961C2#1059552611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32D4×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3750C2semidirect
5. C2×D3×Dic3⋊C4C2semidirect
6. C3×#5210C2semidirect
7. #10591720C2semidirect
8. #10591719C2semidirect
9. #10591372C2semidirect
10. #10591369C2semidirect
11. #10591330C2semidirect
12. #10591278C2semidirect
13. #10591244C2semidirect
14. #10591243C2semidirect
15. #10591234C2semidirect
40. #67⋊Dic3C4semidirect
71. #5210D3semidirect
101. C22×C3⋊Dic3C2×C4semidirect
124. C2×D3×Dic3C2×C4semidirect
128. #3750D4semidirect
131. C3×#217C2×C4semidirect
142. Dic3⋊Dic3C2×C4semidirect
144. (C2×D3)⋊Dic3C2×C4semidirect
146. Dic32C2×C4semidirect
272. C3×#67C4⋊C4semidirect
412. #217C4×D3semidirect
454. C22×C32C2×C4⋊C4semidirect
468. C2×C3×D3C2×C4⋊C4semidirect
474. C3⋊Dic3C4×D4semidirect
481. C3×Dic3C2×C4⋊C4semidirect
604. #67Dic3⋊C4semidirect
773. C22×C3D3×C4⋊C4semidirect
774. C22×C3C2×Dic3⋊C4semidirect
795. C2×D3C2×Dic3⋊C4semidirect
827. Dic3C2×Dic3⋊C4semidirect
828. C32D4×C4⋊C4semidirect
929. C22D3×Dic3⋊C4semidirect
951. C3#74393semidirect
952. C3D4×Dic3⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C2×C3×C4×#672
C2×#67⋊Dic32
C2×D3×Dic3⋊C42
C3×#52102
#105917202
#105917192
#105913722
#105913692
#105913302
#105912782
#105912442
#105912432
#105912342
D4×Dic3⋊C43
#743933