Finite Group Databasebeta

← #11824492

Subgroups — #11824492

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×#64087C211yesmaximal, characteristic, complemented
2C2×#63982C211yesmaximal, characteristic, complemented
3C2×#67⋊Dic3C211yesmaximal, characteristic
4C2×#63899C211yesmaximal, characteristic, complemented
5C2×#63896C211yesmaximal, characteristic, complemented
6C2×#63840C211yesmaximal, characteristic, complemented
7C3×#4957C211yesmaximal, characteristic
8C3×#4949C211yesmaximal, characteristic, complemented
9#10591715C211yesmaximal, characteristic, complemented
10#10591707C211yesmaximal, characteristic
11#10591349C211yesmaximal, characteristic, complemented
12#10591317C211yesmaximal, characteristic, complemented
13#10591303C211yesmaximal, characteristic, complemented
14#10591244C211yesmaximal, characteristic, complemented
15#10591243C211yesmaximal, characteristic, complemented
16#78037—31nomaximal
17#76349—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28#64087—24no—
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39#63982—24no—
40#67⋊Dic3—24no—
41C2×#3724C2211yescharacteristic
42C2×#3724C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×(C2×D3)⋊Dic3C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52C2×Dic32C2211yescharacteristic
53C2×Dic32C2211yescharacteristic
54#63899—24no—
55#63896—24no—
56#63840—24no—
57C3×C3⋊#95C2211yescharacteristic
58#63579C2211yescharacteristic
59C2×D4×Dic3—31no—
60C2×#896—31no—
61C2×#896—31no—
62C2×#888—31no—
63C2×#888—31no—
64C2×#67⋊C4—31no—
65C2×#878—31no—
66C2×#878—31no—
67C2×#878—31no—
68C2×#878—31no—
69C2×#878—31no—
70C2×#878—31no—
71C2×#878—61no—
72C3×#399—31no—
73C3×#390—31no—
74#5221—31no—
75#4993—31no—
76#4975—31no—
77#4975—31no—
78#4975—31no—
79#4957—31no—
80#4957D311yescharacteristic
81#4949—31no—
82#4949—31no—
83#4949—31no—
84#4949—31no—
85#4949D311yescharacteristic, complemented
86#4935—31no—
87C4×Dic3⋊C4—31no—
88#4677—31no—
89#4649—31no—
90C24×C32C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—22no—
95C22×C3⋊Dic3—22no—
96C22×C3⋊Dic3—22no—
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C2×#634—22no—
102C2×#634—22no—
103C2×#634—22no—
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67Q814yescomplemented
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C2×#627—22no—
115C2×#627—22no—
116C2×#627—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C32×C22⋊C4—22no—
121#3757—22no—
122C4⋊(C3⋊Dic3)—22no—
123#3750—22no—
124#3750D414yescomplemented
125C3×#217—22no—
126C3×#217—22no—
127C3×#217—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×C4⋊Dic3—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×C4×Dic3—22no—
135#3724—22no—
136#3724D414yescomplemented
137Dic3⋊Dic3—22no—
138Dic3⋊Dic3—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3—22no—
142Dic3⋊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×D4—31no—
150C22×#67C2×D311yescharacteristic
151C23×Dic3—31no—
152C23×Dic3—31no—
153C23×Dic3—31no—
154C23×Dic3—61no—
155C22×C4×D3—31no—
156C22×Dic6—31no—
157C22×Dic6—31no—
158C22×Dic6—31no—
159C22×Dic6—31no—
160C22×Dic6—61no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C22⋊C4—21no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
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×C3×C42—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—61no—
180C2×#217C2×D311yescharacteristic
181C2×#217C2×D311yescharacteristic
182C2×#217C2×D311yescharacteristic
183D4×Dic3—64no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×C4⋊Dic3—31no—
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—31no—
197C2×C4⋊Dic3—61no—
198C2×C4⋊Dic3C2×D311yescharacteristic
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—31no—
213C2×Dic3⋊C4—61no—
214C2×Dic3⋊C4—61no—
215C2×Dic3⋊C4C2×D311yescharacteristic
216C2×Dic3⋊C4C2×D311yescharacteristic
217C2×Dic3⋊C4C2×D311yescharacteristic
218C2×C4×Dic3—31no—
219C2×C4×Dic3—31no—
220C2×C4×Dic3—31no—
221C2×C4×Dic3—31no—
222C2×C4×Dic3C2×D311yescharacteristic
223#896—64no—
224#896—64no—
225#888—64no—
226#888—64no—
227#67⋊C4—64no—
228#878—64no—
229#878—64no—
230#878—64no—
231#878—64no—
232#878—64no—
233#878—64no—
234#878—68no—
235C3×#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95C2×D311yescharacteristic
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32C2×Q812yes—
246C23×C32C2411yescharacteristic
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×C4C2×D412yes—
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⋊Dic3—21no—
268C2×C3⋊Dic3—44no—
269C2×C3⋊Dic3C2×D412yes—
270C2×C3⋊Dic3C2×D412yes—
271C2×C3⋊Dic3C2×D412yes—
272C2×C3⋊Dic3C2×D412yes—
273#634—44no—
274C3×#67—28no—
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×Dic3—21no—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3C2×D412yes—
292C2×C3×Dic3C2×D412yes—
293C2×C3×Dic3C2×D412yes—
294C2×C3×Dic3C2×Q812yes—
295C2×C3×Dic3#4112yes—
296#627—44no—
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—31no—
309#390—91no—
310#384—91no—
311#384—91no—
312C4×C4⋊C4—91no—
313C24×C3—21no—
314C24×C3—31no—
315C24×C3C22×D311yescharacteristic
316C24×C3C22×D311yescharacteristic
317C23×D3C22×D311yescharacteristic
318C2×C3×D4—34no—
319C2×C3×D4—62no—
320C2×C3×D4—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×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C2×#67—22no—
335C2×#67—22no—
336C2×#67Dic614yescomplemented
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—62no—
350C22×Dic3—62no—
351C22×Dic3—62no—
352C22×Dic3—62no—
353C22×Dic3—62no—
354C22×Dic3—62no—
355C22×Dic3—62no—
356C22×Dic3—62no—
357C22×Dic3—62no—
358C22×Dic3—64no—
359C22×Dic3—122no—
360C22×Dic3—122no—
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C2×C4×D3—62no—
369C2×C4×D3—62no—
370C2×C4×D3—62no—
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—62no—
387C3×C4⋊C4—62no—
388C3×C4⋊C4—62no—
389C3×C4⋊C4—62no—
390C3×C22⋊C4—24no—
391C3×C22⋊C4—22no—
392C3×C22⋊C4—22no—
393C3×C22⋊C4—62no—
394C3×C22⋊C4—62no—
395C3×C22⋊C4—62no—
396C3×C22⋊C4—62no—
397C3×C22⋊C4—62no—
398C3×C42—62no—
399#217—22no—
400#217—22no—
401#217—22no—
402#217—62no—
403#217—62no—
404#217—62no—
405#217—64no—
406#217—62no—
407#217—62no—
408(C2×D3)⋊C4—22no—
409(C2×D3)⋊C4—22no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
413C4⋊Dic3—22no—
414C4⋊Dic3—62no—
415C4⋊Dic3—62no—
416C4⋊Dic3—62no—
417C4⋊Dic3—62no—
418C4⋊Dic3—62no—
419C4⋊Dic3—62no—
420C4⋊Dic3—64no—
421C4⋊Dic3—62no—
422C4⋊Dic3—62no—
423Dic3⋊C4—22no—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—64no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—62no—
434Dic3⋊C4—62no—
435Dic3⋊C4—64no—
436Dic3⋊C4—62no—
437Dic3⋊C4—62no—
438Dic3⋊C4—62no—
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×C32—22no—
448C22×C32—22no—
449C22×C32—22no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32C22×D411yescharacteristic
455C22×C32C22×D411yescharacteristic
456C22×C32C22×D411yescharacteristic
457C22×C32C22×Q811yescharacteristic
458C22×C32C2×#4111yescharacteristic
459C22×C322−1+411yescharacteristic
460C22×C322−1+411yescharacteristic
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—
470C3⋊Dic3—22no—
471C3⋊Dic3—41no—
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—31no—
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—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—91no—
506C2×C4⋊C4—91no—
507C2×C22⋊C4—31no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—31no—
512C2×C22⋊C4—91no—
513C2×C22⋊C4—91no—
514C2×C22⋊C4—91no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4D3211yescharacteristic
517C2×C42—31no—
518C2×C42—91no—
519C2×C42—91no—
520#95—31no—
521#95—91no—
522C23×C3—22no—
523C23×C3—22no—
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—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—22no—
538C23×C3—32no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3C2×Dic612yes—
550C23×C3D3×Q812yes—
551C23×C3C23×D311yescharacteristic
552C23×C3C23×D311yescharacteristic
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3C2×Dic612yes—
560C3×D4—68no—
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—32no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
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—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4D3×D412yes—
599C2×C3×C4D3×D412yes—
600#67—28no—
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—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—32no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—32no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—62no—
627C2×Dic3—62no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—62no—
633C2×Dic3—62no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—121no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—121no—
650C2×Dic3—121no—
651C2×Dic3—121no—
652C2×Dic3—124no—
653C2×Dic3—124no—
654C2×Dic3—124no—
655C2×Dic3—128no—
656C2×Dic3C2×Dic612yes—
657C2×Dic3D3×D412yes—
658C2×Dic3D3×D412yes—
659C2×Dic3D3×D412yes—
660C2×Dic3D3×D412yes—
661C2×Dic3#23712yes—
662C4×D3—124no—
663Dic6—124no—
664Dic6—124no—
665Dic6—124no—
666Dic6—124no—
667Dic6—128no—
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—31no—
678C24C2×D3211yescharacteristic
679C2×Q8—182no—
680C2×Q8—182no—
681C2×Q8—182no—
682C2×Q8—182no—
683C2×Q8—182no—
684C2×Q8—182no—
685C2×D4—34no—
686C2×D4—62no—
687C2×D4—62no—
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—91no—
699C22×C4—182no—
700C22×C4—182no—
701C22×C4—182no—
702C22×C4—182no—
703C22×C4—182no—
704C22×C4—182no—
705C22×C4C2×D3211yescharacteristic
706C22×C4C2×D3211yescharacteristic
707C4⋊C4—62no—
708C4⋊C4—62no—
709C4⋊C4—62no—
710C4⋊C4—62no—
711C4⋊C4—94no—
712C4⋊C4—94no—
713C4⋊C4—182no—
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—62no—
727C22⋊C4—62no—
728C22⋊C4—182no—
729C22⋊C4—182no—
730C22⋊C4—182no—
731C22⋊C4—182no—
732C42—62no—
733C42—94no—
734C42—182no—
735C22×C3—24no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3C22×Dic611yescharacteristic
771C22×C3C2×D3×D411yescharacteristic
772C22×C3C2×D3×D411yescharacteristic
773C22×C3C2×D3×D411yescharacteristic
774C22×C3C2×D3×D411yescharacteristic
775C22×C3C2×D3×D411yescharacteristic
776C22×C3C2×D3×D411yescharacteristic
777C22×C3C2×#23711yescharacteristic
778C22×C3C2×D3×Q811yescharacteristic
779C22×C3D3×#4111yescharacteristic
780C22×C3#101011yescharacteristic
781C22×C3#101011yescharacteristic
782C22×C3#101011yescharacteristic
783C22×C3#101011yescharacteristic
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C3×C4—22no—
792C3×C4—22no—
793C3×C4—34no—
794C3×C4—42no—
795C3×C4—42no—
796C3×C4—41no—
797C3×C4—41no—
798C3×C4—62no—
799C3×C4—62no—
800C3×C4—62no—
801C3×C4—121no—
802C3×C4—121no—
803C3×C4—121no—
804Dic3—22no—
805Dic3—22no—
806Dic3—22no—
807Dic3—34no—
808Dic3—34no—
809Dic3—41no—
810Dic3—41no—
811Dic3—41no—
812Dic3—64no—
813Dic3—62no—
814Dic3—62no—
815Dic3—122no—
816Dic3—122no—
817Dic3—122no—
818Dic3—121no—
819Dic3—121no—
820Dic3—121no—
821Dic3—121no—
822Dic3#87814yescomplemented
823C32#254211yescharacteristic, complemented, Sylow
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—32no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23D3×Dic612yes—
838C23C22×D3211yescharacteristic
839Q8—364no—
840Q8—364no—
841D4—68no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—32no—
848C2×C4—32no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
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—92no—
869C2×C4—92no—
870C2×C4—92no—
871C2×C4—92no—
872C2×C4—181no—
873C2×C4—181no—
874C2×C4—181no—
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—44no—
891C2×C3—42no—
892C2×C3—42no—
893C2×C3—122no—
894C2×C3C2×#87811yescharacteristic
895C2×C3D4×Dic611yescharacteristic
896C2×C3D4×Dic611yescharacteristic
897C2×C3#561111yescharacteristic
898C2×C3#561111yescharacteristic
899C2×C3D3×C22⋊Q811yescharacteristic
900C2×C3#563211yescharacteristic
901C2×C3#563211yescharacteristic
902C2×C3#564811yescharacteristic
903C2×C3#565511yescharacteristic
904C2×C3#565511yescharacteristic
905C2×C3#567511yescharacteristic
906C2×C3D3×#12711yescharacteristic
907C2×C3D3×#12711yescharacteristic
908D3—42no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—62no—
917C22—62no—
918C22—62no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—121no—
923C22C2×D3×Dic611yescharacteristic
924C22#6429811yescharacteristic
925C22#6430911yescharacteristic
926C22D32×D411yescharacteristic
927C22D32×D411yescharacteristic
928C22D3×#23711yescharacteristic
929C22C2×#381111yescharacteristic
930C4—22no—
931C4—34no—
932C4—41no—
933C4—62no—
934C4—62no—
935C4—62no—
936C4—94no—
937C4—121no—
938C4—121no—
939C4—121no—
940C4—182no—
941C4—361no—
942C4—361no—
943C3—21no—
944C3#7634911yescharacteristic, complemented
945C3#7803711yescharacteristic, complemented
946C2—42no—
947C2—122no—
948C2D3×#87811yescharacteristic
949C2#1059405711yescharacteristic
950C2#1059406211yescharacteristic
951C2#1059407111yescharacteristic
952C2#1059491511yescharacteristic
953C2#1059516211yescharacteristic
954C2#1059530011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×C3×#67C22
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×#64087C2semidirect
2. C2×#63982C2semidirect
4. C2×#63899C2semidirect
5. C2×#63896C2semidirect
6. C2×#63840C2semidirect
8. C3×#4949C2semidirect
9. #10591715C2semidirect
11. #10591349C2semidirect
12. #10591317C2semidirect
13. #10591303C2semidirect
14. #10591244C2semidirect
15. #10591243C2semidirect
85. #4949D3semidirect
106. C2×C3×#67Q8semidirect
124. #3750D4semidirect
136. #3724D4semidirect
336. C2×#67Dic6semidirect
480. C3×Dic3C22⋊Q8semidirect
822. Dic3#878semidirect
823. C32#2542semidirect
944. C3#76349semidirect
945. C3#78037semidirect

Maximal subgroups

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

subgroupindex
C2×#640872
C2×#639822
C2×#67⋊Dic32
C2×#638992
C2×#638962
C2×#638402
C3×#49572
C3×#49492
#105917152
#105917072
#105913492
#105913172
#105913032
#105912442
#105912432
#780373
#763493