Finite Group Databasebeta

← #11801830

Subgroups — #11801830

Order 1152.

1429 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#624C211yesmaximal, characteristic
2C2×#63836C211yesmaximal, characteristic
3C2×#63836C211yesmaximal, characteristic
4#10592367C211yesmaximal, characteristic
5C3×#4649C211yesmaximal, characteristic, complemented
6C3×#4647C211yesmaximal, characteristic, complemented
7#10591378C211yesmaximal, characteristic
8#10591374C211yesmaximal, characteristic
9#10591330C211yesmaximal, characteristic, complemented
10#10591290C211yesmaximal, characteristic
11#10591268C211yesmaximal, characteristic, complemented
12Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
13#10591246C211yesmaximal, characteristic, complemented
14#10591243C211yesmaximal, characteristic, complemented
15Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#75963—31nomaximal
17#73755—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45C4×#624—24no—
46#63836—24no—
47#63836C418yescomplemented
48C32×#95C2211yescharacteristic
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#892—31no—
57C2×#892—31no—
58C2×#872—31no—
59C2×#872—31no—
60C2×C42×D3—31no—
61C2×C42×D3—31no—
62C3×#389—31no—
63C3×C4×C4⋊C4—31no—
64#4989—31no—
65#4989—31no—
66#4989—31no—
67#4989—31no—
68#4984—31no—
69#4976—31no—
70#4976—31no—
71Dic3×C4⋊C4—31no—
72Dic3×C4⋊C4—31no—
73#4972—31no—
74C4×C4⋊Dic3—31no—
75C4×Dic3⋊C4—31no—
76C4×Dic3⋊C4—31no—
77#4928—31no—
78#4668—31no—
79#4668—31no—
80#4668—31no—
81#4668—31no—
82#4668—61no—
83#4649—31no—
84#4649D311yescharacteristic, complemented
85#4647—31no—
86#4647D311yescharacteristic, complemented
87C23×C3⋊D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C4×C3⋊D3—22no—
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
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×#624—22no—
106C2×#624—22no—
107C2×#624—22no—
108C2×#624C2×C414yes—
109C2×#624D414yes—
110C2×#624Q814yes—
111#3752—22no—
112#3752C2×C414yes—
113C4⋊(C3⋊Dic3)—22no—
114#3750—22no—
115C3×C4⋊Dic3—22no—
116C3×Dic3⋊C4—22no—
117C3×Dic3⋊C4—22no—
118C3×Dic3⋊C4—22no—
119C3×Dic3⋊C4—22no—
120C3×Dic3⋊C4C2×C414yescomplemented
121C3×C4×Dic3—22no—
122C3×C4×Dic3—22no—
123C3×C4×Dic3—22no—
124C3×C4×Dic3C2×C414yescomplemented
125#3724—22no—
126Dic3⋊Dic3—22no—
127Dic3⋊Dic3—22no—
128Dic3⋊Dic3C2×C414yescomplemented
129#3722—22no—
130#3722C2×C414yes—
131Dic32—22no—
132Dic32—22no—
133Dic32—22no—
134Dic32C2×C414yescomplemented
135#2296—91noSylow
136C22×C4×D3—31no—
137C22×C4×D3—31no—
138C22×C4×D3—31no—
139C22×C4×D3—31no—
140C22×C4×D3—31no—
141C22×C4×D3—31no—
142C22×C4×D3—61no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—31no—
148C2×C3×C4⋊C4—31no—
149C2×C3×C42—31no—
150C2×C3×C42—31no—
151C2×C3×C42—31no—
152C2×C3×C42—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—61no—
162C2×(C2×D3)⋊C4—61no—
163C2×C4⋊Dic3—31no—
164C2×C4⋊Dic3—31no—
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—61no—
169C2×C4⋊Dic3C2×D311yescharacteristic
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—61no—
178C2×Dic3⋊C4C2×D311yescharacteristic
179C2×Dic3⋊C4C2×D311yescharacteristic
180C2×Dic3⋊C4C2×D311yescharacteristic
181C2×Dic3⋊C4C2×D311yescharacteristic
182C2×Dic3⋊C4C2×D311yescharacteristic
183C2×C4×Dic3—31no—
184C2×C4×Dic3—31no—
185C2×C4×Dic3—31no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3C2×D311yescharacteristic
192C2×C4×Dic3C2×D311yescharacteristic
193C2×C4×Dic3C2×D311yescharacteristic
194C2×C4×Dic3C2×D311yescharacteristic
195#892—38no—
196#892—64no—
197#872—38no—
198#872—64no—
199C42×D3—64no—
200C42×D3—64no—
201C3×#95—21no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95C2×D311yescharacteristic
205C3×#95C2×D311yescharacteristic
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—61no—
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C23×C32C2411yescharacteristic
220C22×C3⋊D3—21no—
221C22×C3⋊D3—21no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3C22×C412yes—
225C22×C3⋊D3C2×D412yes—
226C22×C3⋊D3C2×Q812yes—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4C22×C412yes—
235C2×C32×C4#4112yes—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3C22×C412yes—
244C2×C3⋊Dic3#4112yes—
245C4×C3⋊D3—28no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C22×C412yes—
261C2×C3×Dic3C22×C412yes—
262C2×C3×Dic3C22×C412yes—
263C2×C3×Dic3C22×C412yes—
264C2×C3×Dic3C2×D412yes—
265C2×C3×Dic3C2×D412yes—
266C2×C3×Dic3C2×Q812yes—
267C2×C3×Dic3C2×Q812yes—
268C2×C3×Dic3#4112yes—
269C2×C3×Dic3#4112yes—
270#624—28no—
271#624C4⋊C4116yescomplemented
272C2×#117—91no—
273C2×#117—91no—
274C22×C42—91no—
275#389—31no—
276#389—91no—
277#389—91no—
278#389—91no—
279#385—91no—
280#385—91no—
281#385—91no—
282#385—91no—
283C4×C4⋊C4—31no—
284C4×C4⋊C4—91no—
285C4×C4⋊C4—91no—
286C4×C4⋊C4—91no—
287C23×D3—31no—
288C23×D3—31no—
289C23×D3—61no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C2×C4×D3—34no—
325C2×C4×D3—34no—
326C2×C4×D3—34no—
327C2×C4×D3—34no—
328C2×C4×D3—34no—
329C2×C4×D3—34no—
330C2×C4×D3—62no—
331C2×C4×D3—62no—
332C2×C4×D3—62no—
333C2×C4×D3—62no—
334C2×C4×D3—62no—
335C2×C4×D3—62no—
336C2×C4×D3—62no—
337C2×C4×D3—62no—
338C2×C4×D3—62no—
339C2×C4×D3—62no—
340C2×C4×D3—62no—
341C2×C4×D3—62no—
342C2×C4×D3—122no—
343C2×C4×D3—122no—
344C2×C4×D3—122no—
345C3×C4⋊C4—34no—
346C3×C4⋊C4—62no—
347C3×C4⋊C4—62no—
348C3×C4⋊C4—62no—
349C3×C4⋊C4—62no—
350C3×C4⋊C4—62no—
351C3×C42—34no—
352C3×C42—62no—
353C3×C42—62no—
354C3×C42—62no—
355(C2×D3)⋊C4—34no—
356(C2×D3)⋊C4—34no—
357(C2×D3)⋊C4—34no—
358(C2×D3)⋊C4—34no—
359(C2×D3)⋊C4—64no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—122no—
365C4⋊Dic3—22no—
366C4⋊Dic3—34no—
367C4⋊Dic3—62no—
368C4⋊Dic3—62no—
369C4⋊Dic3—62no—
370C4⋊Dic3—62no—
371C4⋊Dic3—122no—
372Dic3⋊C4—22no—
373Dic3⋊C4—22no—
374Dic3⋊C4—22no—
375Dic3⋊C4—22no—
376Dic3⋊C4—34no—
377Dic3⋊C4—62no—
378Dic3⋊C4—62no—
379Dic3⋊C4—62no—
380Dic3⋊C4—62no—
381Dic3⋊C4—62no—
382Dic3⋊C4—62no—
383Dic3⋊C4—122no—
384Dic3⋊C4C4×D314yescomplemented
385C4×Dic3—22no—
386C4×Dic3—22no—
387C4×Dic3—22no—
388C4×Dic3—34no—
389C4×Dic3—34no—
390C4×Dic3—62no—
391C4×Dic3—62no—
392C4×Dic3—62no—
393C4×Dic3—62no—
394C4×Dic3—62no—
395C4×Dic3—62no—
396C4×Dic3C4×D314yescomplemented
397C22×C32C23×C411yescharacteristic
398C22×C32C22×D411yescharacteristic
399C22×C32C22×Q811yescharacteristic
400C22×C32C2×#4111yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32C2×#4111yescharacteristic
404C2×C3⋊D3—22no—
405C2×C3⋊D3—22no—
406C2×C3⋊D3—22no—
407C2×C3⋊D3—22no—
408C2×C3⋊D3—22no—
409C2×C3⋊D3—22no—
410C2×C3⋊D3C2×C4⋊C414yes—
411C32×C4—22no—
412C32×C4—22no—
413C32×C4—41no—
414C3⋊Dic3—22no—
415C3⋊Dic3—22no—
416C3⋊Dic3—41no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3C2×C4⋊C414yes—
424C3×Dic3C2×C4⋊C414yes—
425C23×C4—91no—
426C23×C4—91no—
427C23×C4—91no—
428#117—98no—
429#117—184no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—91no—
437C2×C4⋊C4—91no—
438C2×C4⋊C4—91no—
439C2×C4⋊C4—91no—
440C2×C4⋊C4—91no—
441C2×C4⋊C4—91no—
442C2×C22⋊C4—91no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C42—31no—
447C2×C42—31no—
448C2×C42—31no—
449C2×C42—31no—
450C2×C42—91no—
451C2×C42—91no—
452C2×C42—91no—
453C2×C42—91no—
454C2×C42—184no—
455#95—31no—
456#95—31no—
457#95—91no—
458#95—91no—
459#95—91no—
460#95—91no—
461#95—91no—
462#95D3211yescharacteristic
463C23×C3—21no—
464C23×C3C23×D311yescharacteristic
465C23×C3C23×D311yescharacteristic
466C22×D3—32no—
467C22×D3—32no—
468C22×D3—32no—
469C22×D3—32no—
470C22×D3—32no—
471C22×D3—32no—
472C22×D3—62no—
473C22×D3—62no—
474C22×D3—62no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—121no—
484C22×D3—121no—
485C22×D3—121no—
486C22×D3—121no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—32no—
504C2×C3×C4—32no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4C2×C4×D312yes—
535C2×C3×C4C2×C4×D312yes—
536C2×C3×C4#23512yes—
537C2×C3×C4#23912yes—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—32no—
553C2×Dic3—32no—
554C2×Dic3—32no—
555C2×Dic3—32no—
556C2×Dic3—62no—
557C2×Dic3—62no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—121no—
573C2×Dic3—121no—
574C2×Dic3—121no—
575C2×Dic3—121no—
576C2×Dic3—121no—
577C2×Dic3—121no—
578C2×Dic3—121no—
579C2×Dic3C2×C4×D312yes—
580C2×Dic3C2×C4×D312yes—
581C2×Dic3C2×C4×D312yes—
582C2×Dic3C2×C4×D312yes—
583C2×Dic3#23512yes—
584C2×Dic3D3×D412yes—
585C2×Dic3D3×D412yes—
586C2×Dic3#23712yes—
587C2×Dic3D3×Q812yes—
588C2×Dic3D3×Q812yes—
589C4×D3—316no—
590C4×D3—316no—
591C4×D3—68no—
592C4×D3—68no—
593C4×D3—68no—
594C4×D3—68no—
595C4×D3—128no—
596C2×C32C22×C4⋊C411yescharacteristic
597C2×C32C4×#4111yescharacteristic
598C2×C32C4×#4111yescharacteristic
599C2×C32#52511yescharacteristic
600C2×C32#52511yescharacteristic
601C2×C32#53311yescharacteristic
602C2×C32#53311yescharacteristic
603C3⋊D3—24no—
604C24—91no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—94no—
614C22×C4—94no—
615C22×C4—94no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—182no—
620C22×C4—182no—
621C22×C4—182no—
622C22×C4—182no—
623C22×C4—182no—
624C22×C4—182no—
625C22×C4C2×D3211yescharacteristic
626C22×C4C2×D3211yescharacteristic
627C22×C4C2×D3211yescharacteristic
628C4⋊C4—34no—
629C4⋊C4—62no—
630C4⋊C4—62no—
631C4⋊C4—62no—
632C4⋊C4—62no—
633C4⋊C4—62no—
634C4⋊C4—94no—
635C4⋊C4—182no—
636C4⋊C4—182no—
637C4⋊C4—182no—
638C4⋊C4—182no—
639C4⋊C4—182no—
640C22⋊C4—94no—
641C22⋊C4—94no—
642C22⋊C4—182no—
643C22⋊C4—182no—
644C42—34no—
645C42—62no—
646C42—62no—
647C42—62no—
648C42—94no—
649C42—182no—
650C42—182no—
651C42—182no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3C22×C4×D311yescharacteristic
660C22×C3C22×C4×D311yescharacteristic
661C22×C3C2×#23511yescharacteristic
662C22×C3C2×#23511yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C2×#23711yescharacteristic
666C22×C3C2×D3×Q811yescharacteristic
667C22×C3C2×D3×Q811yescharacteristic
668C22×C3C2×#23911yescharacteristic
669C22×C3D3×#4111yescharacteristic
670C22×C3D3×#4111yescharacteristic
671C22×C3D3×#4111yescharacteristic
672C22×C3D3×#4111yescharacteristic
673C2×D3—34no—
674C2×D3—34no—
675C2×D3—64no—
676C2×D3—62no—
677C2×D3—62no—
678C2×D3—62no—
679C2×D3—62no—
680C2×D3—62no—
681C2×D3—62no—
682C2×D3—62no—
683C2×D3—62no—
684C2×D3—62no—
685C2×D3—62no—
686C2×D3—62no—
687C2×D3—62no—
688C2×D3—122no—
689C2×D3—122no—
690C2×D3—122no—
691C2×D3—122no—
692C2×D3—122no—
693C2×D3—122no—
694C3×C4—22no—
695C3×C4—22no—
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—34no—
699C3×C4—34no—
700C3×C4—42no—
701C3×C4—42no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—62no—
705C3×C4—62no—
706C3×C4—62no—
707C3×C4—62no—
708C3×C4—81no—
709C3×C4—121no—
710C3×C4—121no—
711Dic3—22no—
712Dic3—22no—
713Dic3—22no—
714Dic3—22no—
715Dic3—41no—
716Dic3—41no—
717Dic3—62no—
718Dic3—62no—
719Dic3—62no—
720Dic3—62no—
721Dic3—122no—
722Dic3—122no—
723Dic3—121no—
724Dic3—121no—
725Dic3—241no—
726Dic3D3×C4⋊C414yes—
727Dic3D3×C4⋊C414yes—
728C32#229611yescharacteristic, complemented, Sylow
729C23—92no—
730C23—92no—
731C23—92no—
732C23—181no—
733C23—181no—
734C23—181no—
735C23—181no—
736C23C22×D3211yescharacteristic
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—32no—
745C2×C4—32no—
746C2×C4—32no—
747C2×C4—32no—
748C2×C4—32no—
749C2×C4—32no—
750C2×C4—32no—
751C2×C4—32no—
752C2×C4—32no—
753C2×C4—32no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—916no—
769C2×C4—92no—
770C2×C4—92no—
771C2×C4—188no—
772C2×C4—188no—
773C2×C4—181no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4#379912yes—
781C2×C4C4×D3212yes—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3C4×#23511yescharacteristic
790C2×C3C2×D3×C4⋊C411yescharacteristic
791C2×C3C2×D3×C4⋊C411yescharacteristic
792C2×C3#552211yescharacteristic
793C2×C3C4×#23711yescharacteristic
794C2×C3#554711yescharacteristic
795C2×C3#554711yescharacteristic
796C2×C3C4×#23911yescharacteristic
797C2×C3#557811yescharacteristic
798C2×C3#557811yescharacteristic
799C2×C3#560611yescharacteristic
800C2×C3#562711yescharacteristic
801C2×C3#568811yescharacteristic
802C2×C3#572811yescharacteristic
803D3—64no—
804D3—64no—
805D3—124no—
806C22—94no—
807C22—182no—
808C22—182no—
809C22—182no—
810C22—182no—
811C22—182no—
812C22—182no—
813C22C2×#379911yescharacteristic
814C22C2×C4×D3211yescharacteristic
815C22D3×#23511yescharacteristic
816C22D32×D411yescharacteristic
817C22D3×#23711yescharacteristic
818C22#6431211yescharacteristic
819C22D32×Q811yescharacteristic
820C4—22no—
821C4—22no—
822C4—34no—
823C4—34no—
824C4—41no—
825C4—62no—
826C4—62no—
827C4—62no—
828C4—62no—
829C4—121no—
830C4—121no—
831C4—182no—
832C4—182no—
833C4—361no—
834C3—21no—
835C3#7375511yescharacteristic, complemented
836C3#7596311yescharacteristic, complemented
837C2—184no—
838C2C4×#379911yescharacteristic
839C2#1059404811yescharacteristic
840C2#1059406611yescharacteristic
841C2#1059428611yescharacteristic
842C2#1059439711yescharacteristic
843C2#1059439811yescharacteristic
844C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2296
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
5. C3×#4649C2semidirect
6. C3×#4647C2semidirect
9. #10591330C2semidirect
11. #10591268C2semidirect
12. Dic3×C4⋊Dic3C2semidirect
13. #10591246C2semidirect
14. #10591243C2semidirect
15. Dic3×Dic3⋊C4C2semidirect
47. #63836C4semidirect
84. #4649D3semidirect
86. #4647D3semidirect
120. C3×Dic3⋊C4C2×C4semidirect
124. C3×C4×Dic3C2×C4semidirect
128. Dic3⋊Dic3C2×C4semidirect
134. Dic32C2×C4semidirect
271. #624C4⋊C4semidirect
384. Dic3⋊C4C4×D3semidirect
396. C4×Dic3C4×D3semidirect
728. C32#2296semidirect
835. C3#73755semidirect
836. C3#75963semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6242
C2×#638362
#105923672
C3×#46492
C3×#46472
#105913782
#105913742
#105913302
#105912902
#105912682
Dic3×C4⋊Dic32
#105912462
#105912432
Dic3×Dic3⋊C42
#759633
#737553