Finite Group Databasebeta

← #11824509

Subgroups — #11824509

Order 1152.

1445 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#896C211yesmaximal, characteristic, complemented
2C2×#63893C211yesmaximal, characteristic, complemented
3C2×#63887C211yesmaximal, characteristic, complemented
4C2×#63879C211yesmaximal, characteristic
5C2×#63851C211yesmaximal, characteristic, complemented
6C2×#63839C211yesmaximal, characteristic, complemented
7#10592674C211yesmaximal, characteristic, complemented
8C3×#4993C211yesmaximal, characteristic, complemented
9#10591386C211yesmaximal, characteristic
10#10591385C211yesmaximal, characteristic
11#10591317C211yesmaximal, characteristic, complemented
12#10591303C211yesmaximal, characteristic, complemented
13#10591303C211yesmaximal, characteristic, complemented
14#10591244C211yesmaximal, characteristic, complemented
15#10591241C211yesmaximal, characteristic, complemented
16#82780—31nomaximal
17#78037—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#625C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C3×#896—24no—
40C2×#3724C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51C2×Dic32C2211yescharacteristic
52#63893—24no—
53#63887—24no—
54#63879—24no—
55#63851—24no—
56#63839—24no—
57C3×C3⋊#95C2211yescharacteristic
58#63579C2211yescharacteristic
59C2×C3×C22⋊Q8—31no—
60C2×#946—31no—
61C2×#944—31no—
62C2×C4×#67—31no—
63C2×#924—31no—
64C2×#897—31no—
65C2×#896—31no—
66C2×#896D311yescharacteristic, complemented
67C2×#888—31no—
68C2×#67⋊C4—31no—
69C2×#878—31no—
70C2×#878—31no—
71C3×#399—31no—
72#4993—31no—
73#4993—31no—
74#4993D311yescharacteristic, complemented
75#4975—31no—
76#4975—31no—
77#4975—31no—
78#4975—31no—
79#4975—61no—
80Dic3×C4⋊C4—31no—
81#4957—31no—
82#4957—31no—
83#4957—31no—
84#4957—31no—
85#4949—31no—
86#4949—31no—
87#4949—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
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—22no—
108C2×C3×Dic6—22no—
109C2×C3×Dic6—22no—
110C2×C3×Dic6—22no—
111C2×#627—22no—
112C2×#627—22no—
113C2×#627—22no—
114C2×#625—22no—
115C2×#625—22no—
116C2×#625Q814yescomplemented
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C32×C4⋊C4—22no—
121C4⋊(C3⋊Dic3)—22no—
122#3750—22no—
123#3750—22no—
124#3750—22no—
125#3750—22no—
126C4×C3⋊Dic3—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4—22no—
135C3×Dic3⋊C4D414yescomplemented
136#3724—22no—
137Dic3⋊Dic3—22no—
138Dic3⋊Dic3—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3D414yescomplemented
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146Dic32—22no—
147Dic32D414yes—
148#2542—91noSylow
149C22×C3×Q8—31no—
150C23×C3×C4—31no—
151C22×#67—31no—
152C22×#67—31no—
153C23×Dic3—31no—
154C22×C4×D3—31no—
155C22×C4×D3C2×D311yescharacteristic
156C22×Dic6—31no—
157C22×Dic6—31no—
158C22×Dic6C2×D311yescharacteristic
159C3×C22⋊Q8—64no—
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4C2×D311yescharacteristic
166C2×C3×C4⋊C4C2×D311yescharacteristic
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177#946—64no—
178#944—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)⋊C4—31no—
185C2×(C2×D3)⋊C4C2×D311yescharacteristic
186C2×(C2×D3)⋊C4C2×D311yescharacteristic
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×(C2×D3)⋊C4C2×D311yescharacteristic
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—61no—
197#924—64no—
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—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—61no—
213C2×Dic3⋊C4—61no—
214C2×Dic3⋊C4—61no—
215C2×Dic3⋊C4—61no—
216C2×Dic3⋊C4C2×D311yescharacteristic
217C2×Dic3⋊C4C2×D311yescharacteristic
218C2×Dic3⋊C4C2×D311yescharacteristic
219C2×Dic3⋊C4C2×D311yescharacteristic
220C2×C4×Dic3—31no—
221C2×C4×Dic3—31no—
222C2×C4×Dic3—31no—
223C2×C4×Dic3—31no—
224C2×C4×Dic3—31no—
225C2×C4×Dic3—31no—
226C2×C4×Dic3—61no—
227#897—64no—
228#896—24no—
229#896—64no—
230#888—64no—
231#67⋊C4—64no—
232#878—64no—
233#878—64no—
234C3×#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95C2×D311yescharacteristic
238C23×C32C2411yescharacteristic
239C22×C3×D3—21no—
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×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3C2×Q812yes—
252C22×C3×D3C2×Q812yes—
253C2×C32×C4—21no—
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×C4C2×D412yes—
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⋊Dic3C2×D412yes—
271C2×C3⋊Dic3C2×D412yes—
272C2×C3⋊Dic3C2×Q812yes—
273C2×C3⋊Dic3#4112yes—
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×Dic3C2×D412yes—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3C2×D412yes—
292C3×C4×D3—44no—
293C3×Dic6—44no—
294#627—44no—
295#625—28no—
296D3×Dic3—44no—
297C2×C4⋊Q8—91no—
298C2×C22⋊Q8—31no—
299C2×C22⋊Q8—91no—
300C2×C22⋊Q8—91no—
301C2×C22⋊Q8—91no—
302C2×C4×D4—91no—
303#399—31no—
304#399—91no—
305#399—91no—
306#399—91no—
307#390—91no—
308#390—91no—
309#384—91no—
310#384—91no—
311C4×C4⋊C4—91no—
312C24×C3—31no—
313C24×C3—31no—
314C23×D3C22×D311yescharacteristic
315C23×D3C22×D311yescharacteristic
316C2×C3×Q8—62no—
317C2×C3×Q8—62no—
318C2×C3×Q8—62no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
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×C4—62no—
329C22×C3×C4—62no—
330C22×C3×C4—62no—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C2×#67—34no—
338C2×#67—34no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C2×#67—62no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—62no—
356C22×Dic3—62no—
357C22×Dic3—62no—
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C2×C4×D3—22no—
365C2×C4×D3—22no—
366C2×C4×D3—22no—
367C2×C4×D3—62no—
368C2×C4×D3—62no—
369C2×C4×D3—62no—
370C2×Dic6—22no—
371C2×Dic6—22no—
372C2×Dic6—22no—
373C2×Dic6—62no—
374C2×Dic6—62no—
375C2×Dic6—62no—
376C2×Dic6—62no—
377C2×Dic6—62no—
378C2×Dic6—62no—
379C3×C4⋊C4—22no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—34no—
382C3×C4⋊C4—42no—
383C3×C4⋊C4—62no—
384C3×C4⋊C4—62no—
385C3×C4⋊C4—62no—
386C3×C22⋊C4—62no—
387C3×C22⋊C4—62no—
388C3×C22⋊C4—62no—
389C3×C22⋊C4—62no—
390C3×C22⋊C4—62no—
391#217—62no—
392#217—62no—
393#217—62no—
394#217—62no—
395#217—62no—
396(C2×D3)⋊C4—22no—
397(C2×D3)⋊C4—22no—
398(C2×D3)⋊C4—22no—
399(C2×D3)⋊C4—22no—
400(C2×D3)⋊C4—22no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406C4⋊Dic3—34no—
407C4⋊Dic3—62no—
408C4⋊Dic3—62no—
409C4⋊Dic3—62no—
410C4⋊Dic3—62no—
411C4⋊Dic3—62no—
412C4⋊Dic3—122no—
413Dic3⋊C4—22no—
414Dic3⋊C4—22no—
415Dic3⋊C4—22no—
416Dic3⋊C4—34no—
417Dic3⋊C4—62no—
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—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—122no—
431Dic3⋊C4—122no—
432Dic3⋊C4—122no—
433Dic3⋊C4—122no—
434Dic3⋊C4#6714yescomplemented
435C4×Dic3—34no—
436C4×Dic3—34no—
437C4×Dic3—62no—
438C4×Dic3—62no—
439C4×Dic3—62no—
440C4×Dic3—62no—
441C4×Dic3—64no—
442C22×C32C22×D411yescharacteristic
443C22×C32C22×D411yescharacteristic
444C22×C32C22×D411yescharacteristic
445C22×C32C22×Q811yescharacteristic
446C22×C32C2×#4111yescharacteristic
447C22×C322−1+411yescharacteristic
448C22×C322−1+411yescharacteristic
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—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C32×C4—22no—
464C32×C4—41no—
465C32×C4—41no—
466C3⋊Dic3—22no—
467C3⋊Dic3—41no—
468C3⋊Dic3—41no—
469C3⋊Dic3C22⋊Q814yescomplemented
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—41no—
474C3×Dic3—41no—
475C3×Dic3#12714yes—
476C22×Q8—31no—
477C22×Q8—91no—
478C22×D4—91no—
479C23×C4—31no—
480C23×C4—91no—
481C4⋊Q8—184no—
482C22⋊Q8—64no—
483C22⋊Q8—184no—
484C22⋊Q8—184no—
485C22⋊Q8—184no—
486C4×D4—184no—
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—91no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4D3211yescharacteristic
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—31no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C22⋊C4—91no—
512C2×C42—91no—
513C2×C42—91no—
514C2×C42—91no—
515#95—31no—
516#95—91no—
517C23×C3—21no—
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×C3—61no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3C23×D311yescharacteristic
533C23×C3C23×D311yescharacteristic
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3D3×Q812yes—
547C22×D3D3×Q812yes—
548C3×Q8—124no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
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—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—22no—
568C2×C3×C4—32no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
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—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—124no—
593C2×C3×C4D3×D412yes—
594C2×C3×C4C2×#6712yes—
595#67—68no—
596#67—68no—
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—21no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—32no—
613C2×Dic3—32no—
614C2×Dic3—32no—
615C2×Dic3—32no—
616C2×Dic3—32no—
617C2×Dic3—62no—
618C2×Dic3—62no—
619C2×Dic3—62no—
620C2×Dic3—62no—
621C2×Dic3—62no—
622C2×Dic3—62no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
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—61no—
639C2×Dic3—121no—
640C2×Dic3—121no—
641C2×Dic3—121no—
642C2×Dic3—121no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—124no—
646C2×Dic3D3×D412yes—
647C2×Dic3D3×D412yes—
648C2×Dic3D3×D412yes—
649C2×Dic3D3×D412yes—
650C2×Dic3C2×#6712yes—
651C2×Dic3C2×#6712yes—
652C4×D3—44no—
653C4×D3—124no—
654Dic6—44no—
655Dic6—124no—
656Dic6—124no—
657C2×C32C2×C22⋊Q811yescharacteristic
658C2×C32C2×#12711yescharacteristic
659C2×C32#53611yescharacteristic
660C2×C32#54711yescharacteristic
661C2×C32#54711yescharacteristic
662C2×C32D4×Q811yescharacteristic
663C2×C32D4×Q811yescharacteristic
664C3×D3—42no—
665C3×D3—42no—
666C24—31no—
667C24—31no—
668C2×Q8—62no—
669C2×Q8—62no—
670C2×Q8—62no—
671C2×Q8—182no—
672C2×Q8—182no—
673C2×Q8—182no—
674C2×D4—94no—
675C2×D4—182no—
676C2×D4—182no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—91no—
687C22×C4—91no—
688C22×C4—91no—
689C22×C4—91no—
690C22×C4—182no—
691C22×C4—182no—
692C22×C4—182no—
693C22×C4C2×D3211yescharacteristic
694C22×C4C2×D3211yescharacteristic
695C22×C4C2×D3211yescharacteristic
696C4⋊C4—22no—
697C4⋊C4—34no—
698C4⋊C4—62no—
699C4⋊C4—62no—
700C4⋊C4—62no—
701C4⋊C4—94no—
702C4⋊C4—182no—
703C4⋊C4—182no—
704C4⋊C4—182no—
705C4⋊C4—182no—
706C4⋊C4—182no—
707C4⋊C4—182no—
708C4⋊C4—182no—
709C4⋊C4—182no—
710C4⋊C4—182no—
711C22⋊C4—62no—
712C22⋊C4—62no—
713C22⋊C4—62no—
714C22⋊C4—62no—
715C22⋊C4—62no—
716C22⋊C4—182no—
717C22⋊C4—182no—
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—62no—
732C22×C3—62no—
733C22×C3—62no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3C2×D3×D411yescharacteristic
746C22×C3C2×D3×D411yescharacteristic
747C22×C3C2×D3×D411yescharacteristic
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C22×C3C2×D3×Q811yescharacteristic
751C22×C3C2×D3×Q811yescharacteristic
752C22×C3#100711yescharacteristic
753C22×C3D3×#4111yescharacteristic
754C22×C3D3×#4111yescharacteristic
755C22×C3#101011yescharacteristic
756C22×C3#101011yescharacteristic
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—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C3×C4—24no—
774C3×C4—22no—
775C3×C4—22no—
776C3×C4—34no—
777C3×C4—41no—
778C3×C4—41no—
779C3×C4—41no—
780C3×C4—41no—
781C3×C4—62no—
782C3×C4—62no—
783C3×C4—62no—
784C3×C4—81no—
785C3×C4—81no—
786C3×C4—121no—
787C3×C4—121no—
788Dic3—22no—
789Dic3—22no—
790Dic3—22no—
791Dic3—34no—
792Dic3—34no—
793Dic3—41no—
794Dic3—41no—
795Dic3—64no—
796Dic3—64no—
797Dic3—62no—
798Dic3—62no—
799Dic3—121no—
800Dic3—121no—
801Dic3—121no—
802Dic3—121no—
803Dic3—241no—
804Dic3—241no—
805Dic3#94014yes—
806C32#254211yescharacteristic, complemented, Sylow
807C23—32no—
808C23—32no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—61no—
816C23—61no—
817C23—61no—
818C23—61no—
819C23—61no—
820C23—61no—
821C23C22×D3211yescharacteristic
822Q8—124no—
823Q8—364no—
824D4—188no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—32no—
834C2×C4—32no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—32no—
838C2×C4—32no—
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—61no—
850C2×C4—61no—
851C2×C4—92no—
852C2×C4—92no—
853C2×C4—92no—
854C2×C4—92no—
855C2×C4—124no—
856C2×C4—181no—
857C2×C4—181no—
858C2×C4—181no—
859C2×C4—181no—
860C2×C4—181no—
861C2×C4—181no—
862C2×C4—181no—
863C2×C4—181no—
864C2×C4—364no—
865C2×C4D3×#6712yes—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—122no—
874C2×C3—122no—
875C2×C3D3×C22⋊Q811yescharacteristic
876C2×C3D3×C22⋊Q811yescharacteristic
877C2×C3#562811yescharacteristic
878C2×C3#563111yescharacteristic
879C2×C3#563211yescharacteristic
880C2×C3#563211yescharacteristic
881C2×C3#563211yescharacteristic
882C2×C3#564811yescharacteristic
883C2×C3#565511yescharacteristic
884C2×C3#565511yescharacteristic
885C2×C3D3×#12711yescharacteristic
886C2×C3C2×#94011yescharacteristic
887C2×C3Q8×#6711yescharacteristic
888C2×C3#582411yescharacteristic
889D3—42no—
890D3—42no—
891C22—62no—
892C22—62no—
893C22—62no—
894C22—62no—
895C22—62no—
896C22—62no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22#6429811yescharacteristic
906C22#6430611yescharacteristic
907C22D32×D411yescharacteristic
908C22D32×D411yescharacteristic
909C22#6431511yescharacteristic
910C22D32×Q811yescharacteristic
911C22C2×D3×#6711yescharacteristic
912C4—22no—
913C4—34no—
914C4—41no—
915C4—41no—
916C4—62no—
917C4—62no—
918C4—62no—
919C4—94no—
920C4—121no—
921C4—121no—
922C4—182no—
923C4—361no—
924C4—361no—
925C3—21no—
926C3#7803711yescharacteristic, complemented
927C3#8278011yescharacteristic, complemented
928C2—122no—
929C2—122no—
930C2#1059436511yescharacteristic
931C2#1059437111yescharacteristic
932C2#1059437711yescharacteristic
933C2#1059462411yescharacteristic
934C2#1059488811yescharacteristic
935C2D3×#94011yescharacteristic
936C2#1059540011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×#625C22
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×C3×#896C2semidirect
2. C2×#63893C2semidirect
3. C2×#63887C2semidirect
5. C2×#63851C2semidirect
6. C2×#63839C2semidirect
7. #10592674C2semidirect
8. C3×#4993C2semidirect
11. #10591317C2semidirect
12. #10591303C2semidirect
13. #10591303C2semidirect
14. #10591244C2semidirect
15. #10591241C2semidirect
66. C2×#896D3semidirect
74. #4993D3semidirect
116. C2×#625Q8semidirect
135. C3×Dic3⋊C4D4semidirect
140. Dic3⋊Dic3D4semidirect
434. Dic3⋊C4#67semidirect
469. C3⋊Dic3C22⋊Q8semidirect
806. C32#2542semidirect
926. C3#78037semidirect
927. C3#82780semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8962
C2×#638932
C2×#638872
C2×#638792
C2×#638512
C2×#638392
#105926742
C3×#49932
#105913862
#105913852
#105913172
#105913032
#105912442
#105912412
#827803
#780373