Finite Group Databasebeta

← #11824508

Subgroups — #11824508

Order 1152.

1513 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64105C211yesmaximal, characteristic, complemented
2C2×#63899C211yesmaximal, characteristic, complemented
3C2×#63896C211yesmaximal, characteristic, complemented
4C2×#63881C211yesmaximal, characteristic
5C2×#63865C211yesmaximal, characteristic, complemented
6C2×#63840C211yesmaximal, characteristic, complemented
7C3×#4993C211yesmaximal, characteristic, complemented
8C3×#4975C211yesmaximal, characteristic, complemented
9#10591384C211yesmaximal, characteristic
10#10591383C211yesmaximal, characteristic
11#10591350C211yesmaximal, characteristic, complemented
12#10591303C211yesmaximal, characteristic, complemented
13#10591244C211yesmaximal, characteristic, complemented
14#10591243C211yesmaximal, characteristic, complemented
15#10591203C211yesmaximal, characteristic, complemented
16#78037—31nomaximal
17#74334—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28#64105—24no—
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×#3724C2211yescharacteristic
41C2×#3724C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×#3722C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51C2×Dic32C2211yescharacteristic
52#63899—24no—
53#63896—24no—
54#63881—24no—
55#63865—24no—
56#63840—24no—
57C3×C3⋊#95C2211yescharacteristic
58#63579C2211yescharacteristic
59C2×#896—31no—
60C2×#896—31no—
61C2×#896—31no—
62C2×#896—31no—
63C2×#896—31no—
64C2×#896—31no—
65C2×#896—61no—
66C2×#893—31no—
67C2×#888—31no—
68C2×#888—31no—
69C2×#67⋊C4—31no—
70C2×#878—31no—
71C2×#878—31no—
72C3×#399—31no—
73C3×#384—31no—
74#4993—31no—
75#4993—31no—
76#4993—31no—
77#4993—31no—
78#4993D311yescharacteristic, complemented
79#4988—31no—
80#4975—31no—
81#4975—31no—
82#4975D311yescharacteristic, complemented
83#4957—31no—
84#4957—31no—
85#4949—31no—
86#4939—31no—
87C4×Dic3⋊C4—31no—
88#4677—31no—
89#4649—31no—
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—22no—
100C2×C4×C3⋊D3—22no—
101C2×#634—22no—
102C2×#634—22no—
103C2×#634—22no—
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C2×#627—22no—
112C2×#627—22no—
113C2×#627—22no—
114C2×#626—22no—
115C2×#626—22no—
116C2×#626Q814yescomplemented
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C32×C4⋊C4—22no—
121#3752—22no—
122#3752—22no—
123#3750—22no—
124#3750D414yescomplemented
125C3×(C2×D3)⋊C4—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×C4⋊Dic3—22no—
129C3×Dic3⋊C4—22no—
130C3×Dic3⋊C4—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4—22no—
135C3×C4×Dic3—22no—
136#3724—22no—
137#3724D414yescomplemented
138Dic3⋊Dic3—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—22no—
141#3722—22no—
142#3722—22no—
143#3722—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146Dic32—22no—
147Dic32D414yes—
148#2542—91noSylow
149C22×#67—31no—
150C23×Dic3—31no—
151C22×D12—31no—
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—61no—
156C22×Dic6—31no—
157C22×Dic6—31no—
158C22×Dic6—31no—
159C22×Dic6—31no—
160C22×Dic6—61no—
161C2×C3×C4⋊C4—21no—
162C2×C3×C4⋊C4—31no—
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×C4⋊C4C2×D311yescharacteristic
170C2×C3×C4⋊C4C2×D311yescharacteristic
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C42—31no—
175C2×#217—31no—
176C2×#217—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—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—61no—
190C2×(C2×D3)⋊C4—61no—
191C2×(C2×D3)⋊C4C2×D311yescharacteristic
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×(C2×D3)⋊C4C2×D311yescharacteristic
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3C2×D311yescharacteristic
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—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—61no—
210C2×Dic3⋊C4—61no—
211C2×Dic3⋊C4C2×D311yescharacteristic
212C2×Dic3⋊C4C2×D311yescharacteristic
213C2×Dic3⋊C4C2×D311yescharacteristic
214C2×Dic3⋊C4C2×D311yescharacteristic
215C2×Dic3⋊C4C2×D311yescharacteristic
216C2×Dic3⋊C4C2×D311yescharacteristic
217C2×C4×Dic3—31no—
218C2×C4×Dic3—31no—
219C2×C4×Dic3—31no—
220C2×C4×Dic3—31no—
221C2×C4×Dic3C2×D311yescharacteristic
222#896—64no—
223#896—64no—
224#896—64no—
225#896—64no—
226#896—64no—
227#896—64no—
228#896—68no—
229#893—64no—
230#888—64no—
231#888—64no—
232#67⋊C4—64no—
233#878—64no—
234#878—64no—
235C3×#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95C2×D311yescharacteristic
239C23×C32C2411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3C2×Q812yes—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3C2×Q812yes—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4C2×D412yes—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3C2×D412yes—
269C2×C3⋊Dic3C2×D412yes—
270C2×C3⋊Dic3C2×D412yes—
271C2×C3⋊Dic3C2×D412yes—
272C4×C3⋊D3—44no—
273#634—44no—
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×Dic3C2×D412yes—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3C2×D412yes—
292C2×C3×Dic3C2×D412yes—
293C2×C3×Dic3C2×Q812yes—
294C2×C3×Dic3#4112yes—
295#627—44no—
296#626—28no—
297D3×Dic3—44no—
298C2×C4⋊Q8—91no—
299C2×C22⋊Q8—91no—
300C2×C22⋊Q8—91no—
301C2×C22⋊Q8—91no—
302C2×C22⋊Q8—91no—
303C2×C4×D4—91no—
304#399—31no—
305#399—91no—
306#399—91no—
307#399—91no—
308#390—91no—
309#390—91no—
310#384—31no—
311#384—91no—
312C4×C4⋊C4—91no—
313C24×C3—31no—
314C23×D3—31no—
315C23×D3—31no—
316C23×D3—61no—
317C23×D3C22×D311yescharacteristic
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C2×#67—34no—
335C2×#67—62no—
336C2×#67—62no—
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346C22×Dic3—62no—
347C22×Dic3—62no—
348C22×Dic3—62no—
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C2×D12—34no—
357C2×D12—62no—
358C2×D12—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—62no—
368C2×C4×D3—64no—
369C2×C4×D3—122no—
370C2×C4×D3—122no—
371C2×Dic6—62no—
372C2×Dic6—62no—
373C2×Dic6—62no—
374C2×Dic6—62no—
375C2×Dic6—62no—
376C2×Dic6—62no—
377C2×Dic6—62no—
378C2×Dic6—62no—
379C2×Dic6—62no—
380C2×Dic6—62no—
381C2×Dic6—62no—
382C2×Dic6—62no—
383C2×Dic6—64no—
384C2×Dic6—122no—
385C2×Dic6—122no—
386C3×C4⋊C4—24no—
387C3×C4⋊C4—22no—
388C3×C4⋊C4—22no—
389C3×C4⋊C4—62no—
390C3×C4⋊C4—62no—
391C3×C4⋊C4—62no—
392C3×C4⋊C4—62no—
393C3×C4⋊C4—62no—
394C3×C4⋊C4—62no—
395C3×C4⋊C4—62no—
396C3×C22⋊C4—62no—
397C3×C22⋊C4—62no—
398C3×C22⋊C4—62no—
399C3×C42—62no—
400#217—62no—
401#217—62no—
402(C2×D3)⋊C4—22no—
403(C2×D3)⋊C4—22no—
404(C2×D3)⋊C4—22no—
405(C2×D3)⋊C4—62no—
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—64no—
412(C2×D3)⋊C4—64no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—62no—
416(C2×D3)⋊C4—62no—
417(C2×D3)⋊C4—62no—
418(C2×D3)⋊C4—62no—
419C4⋊Dic3—22no—
420C4⋊Dic3—62no—
421C4⋊Dic3—62no—
422C4⋊Dic3—62no—
423Dic3⋊C4—22no—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4—22no—
427Dic3⋊C4—22no—
428Dic3⋊C4—22no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4—64no—
434Dic3⋊C4—62no—
435Dic3⋊C4—62no—
436Dic3⋊C4—62no—
437Dic3⋊C4—62no—
438Dic3⋊C4—64no—
439Dic3⋊C4—62no—
440Dic3⋊C4—62no—
441Dic3⋊C4—62no—
442C4×Dic3—22no—
443C4×Dic3—34no—
444C4×Dic3—34no—
445C4×Dic3—62no—
446C4×Dic3—62no—
447C22×C32C22×D411yescharacteristic
448C22×C32C22×D411yescharacteristic
449C22×C32C22×D411yescharacteristic
450C22×C32C22×Q811yescharacteristic
451C22×C32C2×#4111yescharacteristic
452C22×C322−1+411yescharacteristic
453C22×C322−1+411yescharacteristic
454C2×C3⋊D3—22no—
455C2×C3⋊D3—22no—
456C2×C3⋊D3—22no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C32×C4—22no—
469C32×C4—41no—
470C32×C4—41no—
471C3⋊Dic3—22no—
472C3⋊Dic3—41no—
473C3⋊Dic3#12714yes—
474C3×Dic3—22no—
475C3×Dic3—22no—
476C3×Dic3—22no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3C22⋊Q814yescomplemented
481C22×Q8—91no—
482C22×Q8—91no—
483C22×D4—91no—
484C23×C4—91no—
485C23×C4—91no—
486C4⋊Q8—184no—
487C22⋊Q8—184no—
488C22⋊Q8—184no—
489C22⋊Q8—184no—
490C22⋊Q8—184no—
491C4×D4—184no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
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—91no—
506C2×C4⋊C4D3211yescharacteristic
507C2×C22⋊C4—31no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—91no—
511C2×C22⋊C4—91no—
512C2×C22⋊C4—91no—
513C2×C22⋊C4—91no—
514C2×C22⋊C4—91no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4—91no—
517C2×C42—31no—
518C2×C42—91no—
519C2×C42—91no—
520#95—31no—
521#95—91no—
522C23×C3—21no—
523C23×C3—32no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3C23×D311yescharacteristic
531C23×C3C23×D311yescharacteristic
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—32no—
539C22×D3—32no—
540C22×D3—62no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—121no—
556C22×D3—121no—
557C22×D3—121no—
558C22×D3—121no—
559C22×D3D3×Q812yes—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—22no—
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—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—22no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
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—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4D3×D412yes—
607C2×C3×C4D3×D412yes—
608#67—68no—
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—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—32no—
625C2×Dic3—32no—
626C2×Dic3—32no—
627C2×Dic3—32no—
628C2×Dic3—32no—
629C2×Dic3—32no—
630C2×Dic3—32no—
631C2×Dic3—32no—
632C2×Dic3—62no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—62no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—62no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—121no—
650C2×Dic3—121no—
651C2×Dic3—124no—
652C2×Dic3#23512yes—
653C2×Dic3D3×D412yes—
654C2×Dic3D3×D412yes—
655C2×Dic3D3×D412yes—
656C2×Dic3D3×D412yes—
657C2×Dic3D3×Q812yes—
658D12—68no—
659C4×D3—124no—
660C4×D3—124no—
661C4×D3—124no—
662C4×D3—128no—
663Dic6—124no—
664Dic6—124no—
665Dic6—124no—
666Dic6—124no—
667Dic6—128no—
668C2×C32C2×C22⋊Q811yescharacteristic
669C2×C32C2×#12711yescharacteristic
670C2×C32#53611yescharacteristic
671C2×C32#54711yescharacteristic
672C2×C32#54711yescharacteristic
673C2×C32D4×Q811yescharacteristic
674C2×C32D4×Q811yescharacteristic
675C3⋊D3—42no—
676C3×D3—42no—
677C24—31no—
678C24—91no—
679C2×Q8—182no—
680C2×Q8—182no—
681C2×Q8—182no—
682C2×Q8—182no—
683C2×Q8—182no—
684C2×Q8—182no—
685C2×D4—94no—
686C2×D4—182no—
687C2×D4—182no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—91no—
696C22×C4—91no—
697C22×C4—91no—
698C22×C4—182no—
699C22×C4—182no—
700C22×C4—182no—
701C22×C4—182no—
702C22×C4—182no—
703C22×C4—182no—
704C22×C4C2×D3211yescharacteristic
705C22×C4C2×D3211yescharacteristic
706C22×C4C2×D3211yescharacteristic
707C4⋊C4—22no—
708C4⋊C4—62no—
709C4⋊C4—62no—
710C4⋊C4—62no—
711C4⋊C4—62no—
712C4⋊C4—62no—
713C4⋊C4—62no—
714C4⋊C4—62no—
715C4⋊C4—94no—
716C4⋊C4—94no—
717C4⋊C4—182no—
718C4⋊C4—182no—
719C4⋊C4—182no—
720C4⋊C4—182no—
721C4⋊C4—182no—
722C22⋊C4—62no—
723C22⋊C4—62no—
724C22⋊C4—62no—
725C22⋊C4—182no—
726C22⋊C4—182no—
727C22⋊C4—182no—
728C22⋊C4—182no—
729C22⋊C4—182no—
730C22⋊C4—182no—
731C22⋊C4—182no—
732C42—62no—
733C42—94no—
734C42—182no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—62no—
743C22×C3—62no—
744C22×C3—62no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3C2×#23511yescharacteristic
750C22×C3C2×D3×D411yescharacteristic
751C22×C3C2×D3×D411yescharacteristic
752C22×C3C2×D3×D411yescharacteristic
753C22×C3C2×D3×D411yescharacteristic
754C22×C3C2×D3×D411yescharacteristic
755C22×C3C2×D3×D411yescharacteristic
756C22×C3C2×D3×Q811yescharacteristic
757C22×C3C2×D3×Q811yescharacteristic
758C22×C3#100711yescharacteristic
759C22×C3#100711yescharacteristic
760C22×C3D3×#4111yescharacteristic
761C22×C3#101011yescharacteristic
762C22×C3#101011yescharacteristic
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—22no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—64no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—62no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—122no—
778C2×D3—122no—
779C2×D3—122no—
780C2×D3—122no—
781C2×D3—122no—
782C2×D3—122no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—121no—
790C2×D3—121no—
791C3×C4—22no—
792C3×C4—22no—
793C3×C4—34no—
794C3×C4—42no—
795C3×C4—42no—
796C3×C4—42no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—41no—
800C3×C4—41no—
801C3×C4—62no—
802C3×C4—62no—
803C3×C4—62no—
804C3×C4—121no—
805C3×C4—121no—
806C3×C4—121no—
807Dic3—22no—
808Dic3—22no—
809Dic3—22no—
810Dic3—34no—
811Dic3—34no—
812Dic3—41no—
813Dic3—41no—
814Dic3—41no—
815Dic3—64no—
816Dic3—62no—
817Dic3—62no—
818Dic3—122no—
819Dic3—122no—
820Dic3—121no—
821Dic3—121no—
822Dic3#89614yescomplemented
823C32#254211yescharacteristic, complemented, Sylow
824C23—32no—
825C23—61no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—92no—
832C23—181no—
833C23—181no—
834C23—181no—
835C23—181no—
836C23—181no—
837C23—181no—
838C23C22×D3211yescharacteristic
839Q8—364no—
840Q8—364no—
841D4—188no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
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—32no—
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—92no—
872C2×C4—92no—
873C2×C4—92no—
874C2×C4—92no—
875C2×C4—181no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—181no—
879C2×C4—181no—
880C2×C4—364no—
881C2×C4—364no—
882C2×C4#381112yes—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—122no—
891C2×C3#550711yescharacteristic
892C2×C3#550711yescharacteristic
893C2×C3C2×#89611yescharacteristic
894C2×C3D3×C22⋊Q811yescharacteristic
895C2×C3#563211yescharacteristic
896C2×C3#563211yescharacteristic
897C2×C3#564811yescharacteristic
898C2×C3#565511yescharacteristic
899C2×C3#565511yescharacteristic
900C2×C3D3×#12711yescharacteristic
901C2×C3D3×#12711yescharacteristic
902C2×C3#572411yescharacteristic
903C2×C3#572711yescharacteristic
904C2×C3#572711yescharacteristic
905D3—42no—
906D3—124no—
907D3—122no—
908D3—122no—
909C22—62no—
910C22—62no—
911C22—62no—
912C22—121no—
913C22—121no—
914C22—121no—
915C22—121no—
916C22—182no—
917C22—182no—
918C22—182no—
919C22—361no—
920C22—361no—
921C22—361no—
922C22—361no—
923C22#6429711yescharacteristic
924C22D3×#23511yescharacteristic
925C22D32×D411yescharacteristic
926C22D32×D411yescharacteristic
927C22#6431511yescharacteristic
928C22D32×Q811yescharacteristic
929C22C2×#381111yescharacteristic
930C4—22no—
931C4—34no—
932C4—41no—
933C4—41no—
934C4—62no—
935C4—62no—
936C4—62no—
937C4—94no—
938C4—121no—
939C4—121no—
940C4—121no—
941C4—182no—
942C4—361no—
943C3—21no—
944C3#7433411yescharacteristic, complemented
945C3#7803711yescharacteristic, complemented
946C2—122no—
947C2—362no—
948C2#1059436611yescharacteristic
949C2#1059437811yescharacteristic
950C2#1059451311yescharacteristic
951C2D3×#89611yescharacteristic
952C2#1059491711yescharacteristic
953C2#1059530011yescharacteristic
954C2#1059536111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64105C2semidirect
2. C2×#63899C2semidirect
3. C2×#63896C2semidirect
5. C2×#63865C2semidirect
6. C2×#63840C2semidirect
7. C3×#4993C2semidirect
8. C3×#4975C2semidirect
11. #10591350C2semidirect
12. #10591303C2semidirect
13. #10591244C2semidirect
14. #10591243C2semidirect
15. #10591203C2semidirect
78. #4993D3semidirect
82. #4975D3semidirect
116. C2×#626Q8semidirect
124. #3750D4semidirect
137. #3724D4semidirect
480. C3×Dic3C22⋊Q8semidirect
822. Dic3#896semidirect
823. C32#2542semidirect
944. C3#74334semidirect
945. C3#78037semidirect

Maximal subgroups

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

subgroupindex
C2×#641052
C2×#638992
C2×#638962
C2×#638812
C2×#638652
C2×#638402
C3×#49932
C3×#49752
#105913842
#105913832
#105913502
#105913032
#105912442
#105912432
#105912032
#780373
#743343