Finite Group Databasebeta

← #11824493

Subgroups — #11824493

Order 1152.

1481 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
1C2×C3×#878C211yesmaximal, characteristic, complemented
2C2×#63964C211yesmaximal, characteristic, complemented
3C2×#63952C211yesmaximal, characteristic
4C2×#63895C211yesmaximal, characteristic, complemented
5C2×#63888C211yesmaximal, characteristic, complemented
6C2×#63839C211yesmaximal, characteristic, complemented
7#10592656C211yesmaximal, characteristic
8C3×#4949C211yesmaximal, characteristic, complemented
9#10591715C211yesmaximal, characteristic, complemented
10#10591704C211yesmaximal, characteristic
11#10591359C211yesmaximal, characteristic, complemented
12#10591350C211yesmaximal, characteristic, complemented
13#10591244C211yesmaximal, characteristic, complemented
14#10591241C211yesmaximal, characteristic, complemented
15#10591203C211yesmaximal, characteristic, complemented
16#82780—31nomaximal
17#78037—31nomaximal
18C22×#638C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C3×#878—24no—
39C2×#3724C2211yescharacteristic
40C2×#3724C2211yescharacteristic
41C2×#3724C2211yescharacteristic
42C2×#3724C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47#63964—24no—
48C2×#3722C2211yescharacteristic
49C2×#3722C2211yescharacteristic
50C2×#3722C2211yescharacteristic
51C2×Dic32C2211yescharacteristic
52C2×Dic32C2211yescharacteristic
53#63952—24no—
54#63895—24no—
55#63888—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×#896—31no—
67C2×#888—31no—
68C2×#67⋊C4—31no—
69C2×#878—31no—
70C2×#878D311yescharacteristic, complemented
71C3×#399—31no—
72#4993—31no—
73#4993—31no—
74#4993—31no—
75#4975—31no—
76#4975—31no—
77#4975—31no—
78#4975—31no—
79Dic3×C4⋊C4—31no—
80#4957—31no—
81#4957—31no—
82#4957—31no—
83#4957—31no—
84#4957—61no—
85#4949—31no—
86#4949—31no—
87#4949D311yescharacteristic, complemented
88#4677—31no—
89#4649—31no—
90C24×C32C2311yescharacteristic
91C23×C3⋊D3C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—22no—
95C2×#638—22no—
96C2×#638Q814yescomplemented
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3×Dic3—22no—
101C22×C3×Dic3—22no—
102C22×C3×Dic3—22no—
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C2×C3×Dic6—22no—
112C2×C3×Dic6—22no—
113C2×C3×Dic6—22no—
114C2×#627—22no—
115C2×#627—22no—
116C2×#627—22no—
117C2×#624—22no—
118C2×#624—22no—
119C2×#624—22no—
120C32×C22⋊C4—22no—
121#3757—22no—
122#3752—22no—
123#3752—22no—
124#3750—22no—
125C4×C3⋊Dic3—22no—
126C3×#217—22no—
127C3×#217—22no—
128C3×#217—22no—
129C3×C4⋊Dic3—22no—
130C3×C4⋊Dic3—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4D414yescomplemented
135#3724—22no—
136#3724—22no—
137#3724—22no—
138#3724—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3—22no—
142Dic3⋊Dic3D414yescomplemented
143#3722—22no—
144#3722—22no—
145#3722—22no—
146Dic32—22no—
147Dic32D414yes—
148#2542—91noSylow
149C22×C3×Q8—31no—
150C23×C3×C4—31no—
151C22×#67—31no—
152C22×#67—31no—
153C22×#67—61no—
154C23×Dic3C2×D311yescharacteristic
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×Dic6—31no—
158C22×Dic6—31no—
159C22×Dic6C2×D311yescharacteristic
160C3×C22⋊Q8—64no—
161C2×C3×C4⋊C4—31no—
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×C22⋊C4—21no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4C2×D311yescharacteristic
172C2×C3×C22⋊C4C2×D311yescharacteristic
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—61no—
176C2×#217C2×D311yescharacteristic
177C2×#217C2×D311yescharacteristic
178C2×#217C2×D311yescharacteristic
179#946—64no—
180#944—64no—
181C4×#67—64no—
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—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—61no—
193C2×(C2×D3)⋊C4—61no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3C2×D311yescharacteristic
199C2×C4⋊Dic3C2×D311yescharacteristic
200#924—64no—
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—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
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—64no—
229#896—64no—
230#888—64no—
231#67⋊C4—64no—
232#878—24no—
233#878—64no—
234C3×#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95C2×D311yescharacteristic
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32C2×Q812yes—
245C23×C32C2411yescharacteristic
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—21no—
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×C4C2×D412yes—
259#638—28no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3C2×D412yes—
266C2×C3⋊Dic3C2×D412yes—
267C2×C3⋊Dic3C2×Q812yes—
268C2×C3⋊Dic3#4112yes—
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×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—44no—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3C2×D412yes—
292C2×C3×Dic3C2×D412yes—
293C2×C3×Dic3C2×D412yes—
294C3×Dic6—44no—
295#627—44no—
296#624—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—21no—
313C24×C3C22×D311yescharacteristic
314C24×C3C22×D311yescharacteristic
315C23×D3—31no—
316C23×D3—31no—
317C23×D3—61no—
318C2×C3×Q8—62no—
319C2×C3×Q8—62no—
320C2×C3×Q8—62no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C2×#67—34no—
339C2×#67—34no—
340C2×#67—64no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—122no—
346C2×#67—122no—
347C22×Dic3—22no—
348C22×Dic3—22no—
349C22×Dic3—22no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—61no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C2×C4×D3—62no—
368C2×C4×D3—62no—
369C2×C4×D3—62no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×Dic6—22no—
374C2×Dic6—22no—
375C2×Dic6—22no—
376C2×Dic6—62no—
377C2×Dic6—62no—
378C2×Dic6—62no—
379C2×Dic6—62no—
380C2×Dic6—62no—
381C2×Dic6—62no—
382C3×C4⋊C4—34no—
383C3×C4⋊C4—62no—
384C3×C4⋊C4—62no—
385C3×C4⋊C4—62no—
386C3×C4⋊C4—62no—
387C3×C4⋊C4—62no—
388C3×C22⋊C4—22no—
389C3×C22⋊C4—22no—
390C3×C22⋊C4—42no—
391C3×C22⋊C4—62no—
392C3×C22⋊C4—62no—
393C3×C22⋊C4—62no—
394#217—22no—
395#217—22no—
396#217—22no—
397#217—62no—
398#217—62no—
399#217—122no—
400(C2×D3)⋊C4—62no—
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—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—122no—
411(C2×D3)⋊C4—122no—
412C4⋊Dic3—22no—
413C4⋊Dic3—22no—
414C4⋊Dic3—34no—
415C4⋊Dic3—62no—
416C4⋊Dic3—62no—
417C4⋊Dic3—62no—
418Dic3⋊C4—22no—
419Dic3⋊C4—22no—
420Dic3⋊C4—22no—
421Dic3⋊C4—34no—
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—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—62no—
434Dic3⋊C4—62no—
435Dic3⋊C4—122no—
436Dic3⋊C4#6714yescomplemented
437C4×Dic3—34no—
438C4×Dic3—34no—
439C4×Dic3—62no—
440C4×Dic3—62no—
441C4×Dic3—62no—
442C4×Dic3—62no—
443C4×Dic3—122no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32C22×D411yescharacteristic
452C22×C32C22×D411yescharacteristic
453C22×C32C22×D411yescharacteristic
454C22×C32C22×Q811yescharacteristic
455C22×C32C2×#4111yescharacteristic
456C22×C322−1+411yescharacteristic
457C22×C322−1+411yescharacteristic
458C2×C3⋊D3—22no—
459C2×C3⋊D3—22no—
460C2×C3⋊D3—22no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3⋊D3—41no—
465C32×C4—22no—
466C32×C4—41no—
467C3⋊Dic3—22no—
468C3⋊Dic3—41no—
469C3⋊Dic3C22⋊Q814yescomplemented
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—41no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3#12714yes—
478C22×Q8—31no—
479C22×Q8—91no—
480C22×D4—91no—
481C23×C4—31no—
482C23×C4—91no—
483C4⋊Q8—184no—
484C22⋊Q8—64no—
485C22⋊Q8—184no—
486C22⋊Q8—184no—
487C22⋊Q8—184no—
488C4×D4—184no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—31no—
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×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×C22⋊C4—91no—
513C2×C22⋊C4D3211yescharacteristic
514C2×C42—91no—
515C2×C42—91no—
516C2×C42—91no—
517#95—31no—
518#95—91no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—22no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3D3×Q812yes—
540C23×C3D3×Q812yes—
541C23×C3C23×D311yescharacteristic
542C23×C3C23×D311yescharacteristic
543C22×D3—32no—
544C22×D3—32no—
545C22×D3—62no—
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—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—121no—
559C22×D3—121no—
560C22×D3—121no—
561C22×D3—121no—
562C22×D3—121no—
563C22×D3—121no—
564C3×Q8—124no—
565C2×C3×C4—21no—
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—22no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
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—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—124no—
606C2×C3×C4D3×D412yes—
607C2×C3×C4C2×#6712yes—
608#67—68no—
609#67—68no—
610#67—128no—
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—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—32no—
630C2×Dic3—32no—
631C2×Dic3—32no—
632C2×Dic3—32no—
633C2×Dic3—32no—
634C2×Dic3—32no—
635C2×Dic3—32no—
636C2×Dic3—32no—
637C2×Dic3—44no—
638C2×Dic3—62no—
639C2×Dic3—62no—
640C2×Dic3—62no—
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—61no—
651C2×Dic3—61no—
652C2×Dic3—121no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655C2×Dic3—121no—
656C2×Dic3—121no—
657C2×Dic3D3×D412yes—
658C2×Dic3D3×D412yes—
659C2×Dic3D3×D412yes—
660C2×Dic3D3×D412yes—
661C2×Dic3C2×#6712yes—
662C2×Dic3C2×#6712yes—
663C4×D3—124no—
664C4×D3—124no—
665Dic6—44no—
666Dic6—124no—
667Dic6—124no—
668C2×C32—42no—
669C2×C32C2×C22⋊Q811yescharacteristic
670C2×C32C2×#12711yescharacteristic
671C2×C32#53611yescharacteristic
672C2×C32#54711yescharacteristic
673C2×C32#54711yescharacteristic
674C2×C32D4×Q811yescharacteristic
675C2×C32D4×Q811yescharacteristic
676C3⋊D3—42no—
677C24—91no—
678C24C2×D3211yescharacteristic
679C2×Q8—62no—
680C2×Q8—62no—
681C2×Q8—62no—
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—31no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—62no—
699C22×C4—91no—
700C22×C4—91no—
701C22×C4—91no—
702C22×C4—182no—
703C22×C4—182no—
704C22×C4—182no—
705C22×C4C2×D3211yescharacteristic
706C22×C4C2×D3211yescharacteristic
707C4⋊C4—34no—
708C4⋊C4—62no—
709C4⋊C4—62no—
710C4⋊C4—62no—
711C4⋊C4—62no—
712C4⋊C4—62no—
713C4⋊C4—94no—
714C4⋊C4—182no—
715C4⋊C4—182no—
716C4⋊C4—182no—
717C4⋊C4—182no—
718C4⋊C4—182no—
719C4⋊C4—182no—
720C4⋊C4—182no—
721C4⋊C4—182no—
722C22⋊C4—22no—
723C22⋊C4—62no—
724C22⋊C4—62no—
725C22⋊C4—62no—
726C22⋊C4—182no—
727C22⋊C4—182no—
728C22⋊C4—182no—
729C22⋊C4—182no—
730C22⋊C4—182no—
731C22⋊C4—182no—
732C42—94no—
733C42—182no—
734C42—182no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—81no—
760C22×C3—81no—
761C22×C3—81no—
762C22×C3—81no—
763C22×C3C2×D3×D411yescharacteristic
764C22×C3C2×D3×D411yescharacteristic
765C22×C3C2×D3×D411yescharacteristic
766C22×C3C2×D3×D411yescharacteristic
767C22×C3C2×D3×D411yescharacteristic
768C22×C3C2×D3×Q811yescharacteristic
769C22×C3C2×D3×Q811yescharacteristic
770C22×C3#100711yescharacteristic
771C22×C3D3×#4111yescharacteristic
772C22×C3D3×#4111yescharacteristic
773C22×C3#101011yescharacteristic
774C22×C3#101011yescharacteristic
775C22×C3#101011yescharacteristic
776C22×C3C22×#6711yescharacteristic
777C2×D3—62no—
778C2×D3—62no—
779C2×D3—62no—
780C2×D3—62no—
781C2×D3—62no—
782C2×D3—62no—
783C2×D3—122no—
784C2×D3—122no—
785C2×D3—122no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—121no—
790C2×D3—121no—
791C2×D3—121no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—241no—
795C2×D3—241no—
796C2×D3—241no—
797C2×D3—241no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—34no—
801C3×C4—42no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4—62no—
807C3×C4—81no—
808C3×C4—121no—
809C3×C4—121no—
810C3×C4—121no—
811C3×C4—121no—
812Dic3—22no—
813Dic3—22no—
814Dic3—22no—
815Dic3—34no—
816Dic3—34no—
817Dic3—41no—
818Dic3—41no—
819Dic3—41no—
820Dic3—41no—
821Dic3—64no—
822Dic3—62no—
823Dic3—62no—
824Dic3—122no—
825Dic3—121no—
826Dic3—121no—
827Dic3—241no—
828Dic3#94014yes—
829C32#254211yescharacteristic, complemented, Sylow
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—92no—
837C23—181no—
838C23—181no—
839C23—181no—
840C23—181no—
841C23—181no—
842C23—181no—
843C23#379712yes—
844C23C22×D3211yescharacteristic
845Q8—124no—
846Q8—364no—
847D4—188no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—32no—
858C2×C4—32no—
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—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—92no—
878C2×C4—92no—
879C2×C4—92no—
880C2×C4—92no—
881C2×C4—124no—
882C2×C4—181no—
883C2×C4—181no—
884C2×C4—181no—
885C2×C4—181no—
886C2×C4—181no—
887C2×C4—364no—
888C2×C4D3×#6712yes—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—42no—
897C2×C3—42no—
898C2×C3—82no—
899C2×C3D3×C22⋊Q811yescharacteristic
900C2×C3D3×C22⋊Q811yescharacteristic
901C2×C3#562811yescharacteristic
902C2×C3#563111yescharacteristic
903C2×C3#563211yescharacteristic
904C2×C3#563211yescharacteristic
905C2×C3#563211yescharacteristic
906C2×C3#564811yescharacteristic
907C2×C3#565511yescharacteristic
908C2×C3#565511yescharacteristic
909C2×C3D3×#12711yescharacteristic
910C2×C3C2×#94011yescharacteristic
911C2×C3Q8×#6711yescharacteristic
912C2×C3#582411yescharacteristic
913D3—122no—
914D3—122no—
915D3—242no—
916C22—22no—
917C22—22no—
918C22—22no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—182no—
924C22—182no—
925C22—182no—
926C22—361no—
927C22—361no—
928C22—361no—
929C22—361no—
930C22#6429711yescharacteristic
931C22C2×#379711yescharacteristic
932C22#6430911yescharacteristic
933C22D32×D411yescharacteristic
934C22D32×D411yescharacteristic
935C22#6431211yescharacteristic
936C22C2×D3×#6711yescharacteristic
937C4—22no—
938C4—34no—
939C4—41no—
940C4—62no—
941C4—62no—
942C4—62no—
943C4—94no—
944C4—121no—
945C4—121no—
946C4—121no—
947C4—121no—
948C4—182no—
949C4—361no—
950C3—21no—
951C3#7803711yescharacteristic, complemented
952C3#8278011yescharacteristic, complemented
953C2—42no—
954C2—362no—
955C2#1059405611yescharacteristic
956C2#1059406411yescharacteristic
957C2#1059406711yescharacteristic
958C2#1059407211yescharacteristic
959C2#1059480311yescharacteristic
960C2#1059514911yescharacteristic
961C2D3×#94011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#878C2semidirect
2. C2×#63964C2semidirect
4. C2×#63895C2semidirect
5. C2×#63888C2semidirect
6. C2×#63839C2semidirect
8. C3×#4949C2semidirect
9. #10591715C2semidirect
11. #10591359C2semidirect
12. #10591350C2semidirect
13. #10591244C2semidirect
14. #10591241C2semidirect
15. #10591203C2semidirect
70. C2×#878D3semidirect
87. #4949D3semidirect
96. C2×#638Q8semidirect
134. C3×Dic3⋊C4D4semidirect
142. Dic3⋊Dic3D4semidirect
436. Dic3⋊C4#67semidirect
469. C3⋊Dic3C22⋊Q8semidirect
829. C32#2542semidirect
951. C3#78037semidirect
952. C3#82780semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8782
C2×#639642
C2×#639522
C2×#638952
C2×#638882
C2×#638392
#105926562
C3×#49492
#105917152
#105917042
#105913592
#105913502
#105912442
#105912412
#105912032
#827803
#780373