Finite Group Databasebeta

← #11805196

Subgroups — #11805196

Order 1152.

1373 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×#63883C211yesmaximal, characteristic
3C2×#63836C211yesmaximal, characteristic
4C3×#4978C211yesmaximal, characteristic, complemented
5C3×#4976C211yesmaximal, characteristic, complemented
6#10591371C211yesmaximal, characteristic
7#10591367C211yesmaximal, characteristic
8#10591335C211yesmaximal, characteristic, complemented
9#10591334C211yesmaximal, characteristic, complemented
10C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
11#10591272C211yesmaximal, characteristic, complemented
12#10591268C211yesmaximal, characteristic, complemented
13#10591241C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic
15#10591219C211yesmaximal, characteristic
16#76200—31nomaximal
17#74961—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27#64101—24no—
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42#63883C418yescomplemented
43#63836—24no—
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#892—31no—
57C2×#892—31no—
58C2×#892—31no—
59C2×#892—61no—
60C2×D3×C4⋊C4—31no—
61C2×D3×C4⋊C4—31no—
62C2×#872—31no—
63C3×#389—31no—
64C3×#387—31no—
65#4987—31no—
66#4984—31no—
67#4980—31no—
68#4978—31no—
69#4978D311yescharacteristic, complemented
70#4976D311yescharacteristic, complemented
71Dic3×C4⋊C4—31no—
72C4×(C2×D3)⋊C4—31no—
73C4×C4⋊Dic3—31no—
74C4×Dic3⋊C4—31no—
75#4667—31no—
76#4666—31no—
77#4664—31no—
78#4664—31no—
79#4664—31no—
80#4664—31no—
81#4655—31no—
82#4655—31no—
83#4654—31no—
84#4653—31no—
85#4649—31no—
86#4647—31no—
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⋊D3C2×C414yes—
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×#624—22no—
109C2×#624C2×C414yes—
110C2×#624C2×C414yes—
111C32×C4⋊C4—22no—
112#3752—22no—
113#3752D414yes—
114C4⋊(C3⋊Dic3)—22no—
115C4×C3⋊Dic3—22no—
116C4×C3⋊Dic3—22no—
117C3×Dic3⋊C4—22no—
118C3×Dic3⋊C4—22no—
119C3×Dic3⋊C4C2×C414yes—
120C3×Dic3⋊C4C2×C414yes—
121C3×C4×Dic3—22no—
122C3×C4×Dic3—22no—
123Dic3⋊Dic3—22no—
124Dic3⋊Dic3—22no—
125Dic3⋊Dic3C2×C414yes—
126Dic3⋊Dic3C2×C414yes—
127#3722—22no—
128#3722—22no—
129Dic32—22no—
130Dic32—22no—
131#2344—91noSylow
132C22×C4×D3—31no—
133C22×C4×D3—31no—
134C22×C4×D3—31no—
135C22×C4×D3—31no—
136C22×C4×D3—31no—
137C22×C4×D3—31no—
138C22×C4×D3—61no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4C2×D311yescharacteristic
145C2×C3×C4⋊C4C2×D311yescharacteristic
146C2×C3×C42—31no—
147C2×C3×C42—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—61no—
157C2×(C2×D3)⋊C4—61no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—31no—
164C2×C4⋊Dic3—61no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4C2×D311yescharacteristic
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×Dic3⋊C4C2×D311yescharacteristic
172C2×Dic3⋊C4C2×D311yescharacteristic
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—61no—
182C2×C4×Dic3—61no—
183C2×C4×Dic3C2×D311yescharacteristic
184C2×C4×Dic3C2×D311yescharacteristic
185#892—64no—
186#892—64no—
187#892—64no—
188#892—68no—
189D3×C4⋊C4—38no—
190D3×C4⋊C4—38no—
191#872—64no—
192C3×#95—31no—
193C3×#95—31no—
194C3×#95—31no—
195C3×#95—31no—
196C3×#95—31no—
197C3×#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C3⋊#95C2×D311yescharacteristic
215C3⋊#95C2×D311yescharacteristic
216C23×C32C2411yescharacteristic
217C22×C3⋊D3—21no—
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3—21no—
221C22×C3⋊D3C22×C412yes—
222C22×C3⋊D3C2×D412yes—
223C22×C3⋊D3#4112yes—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4C22×C412yes—
232C2×C32×C4C2×D412yes—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C22×C412yes—
241C2×C3⋊Dic3C2×D412yes—
242C4×C3⋊D3—28no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
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×Dic3—21no—
261C2×C3×Dic3C22×C412yes—
262C2×C3×Dic3C22×C412yes—
263C2×C3×Dic3C22×C412yes—
264C2×C3×Dic3C22×C412yes—
265C2×C3×Dic3#4112yes—
266C2×C3×Dic3#4112yes—
267#624—28no—
268#624—28no—
269C2×#117—91no—
270C2×#117—91no—
271C22×C4⋊C4—91no—
272#389—31no—
273#389—91no—
274#387—31no—
275#387—91no—
276#387—91no—
277#387—91no—
278#381—91no—
279#381—91no—
280#380—91no—
281C4×C4⋊C4—91no—
282C4×C4⋊C4—91no—
283C4×C22⋊C4—91no—
284C23×D3—31no—
285C23×D3—31no—
286C23×D3—61no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C2×C4×D3—34no—
322C2×C4×D3—34no—
323C2×C4×D3—34no—
324C2×C4×D3—34no—
325C2×C4×D3—34no—
326C2×C4×D3—34no—
327C2×C4×D3—64no—
328C2×C4×D3—62no—
329C2×C4×D3—62no—
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—64no—
339C2×C4×D3—64no—
340C2×C4×D3—62no—
341C2×C4×D3—62no—
342C3×C4⋊C4—24no—
343C3×C4⋊C4—22no—
344C3×C4⋊C4—22no—
345C3×C4⋊C4—34no—
346C3×C4⋊C4—34no—
347C3×C4⋊C4—62no—
348C3×C4⋊C4—62no—
349C3×C42—62no—
350C3×C42—62no—
351(C2×D3)⋊C4—34no—
352(C2×D3)⋊C4—34no—
353(C2×D3)⋊C4—64no—
354(C2×D3)⋊C4—62no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4—62no—
357(C2×D3)⋊C4—62no—
358(C2×D3)⋊C4—62no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—64no—
361C4⋊Dic3—34no—
362C4⋊Dic3—34no—
363C4⋊Dic3—62no—
364C4⋊Dic3—62no—
365C4⋊Dic3—62no—
366C4⋊Dic3—62no—
367C4⋊Dic3—64no—
368Dic3⋊C4—22no—
369Dic3⋊C4—22no—
370Dic3⋊C4—34no—
371Dic3⋊C4—34no—
372Dic3⋊C4—62no—
373Dic3⋊C4—62no—
374Dic3⋊C4C4×D314yes—
375Dic3⋊C4C4×D314yes—
376C4×Dic3—22no—
377C4×Dic3—22no—
378C4×Dic3—62no—
379C4×Dic3—62no—
380C4×Dic3—62no—
381C4×Dic3—62no—
382C4×Dic3—62no—
383C4×Dic3—64no—
384C4×Dic3—64no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C22×C32C23×C411yescharacteristic
389C22×C32C22×D411yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32C2×#4111yescharacteristic
393C22×C322−1+411yescharacteristic
394C22×C322−1+411yescharacteristic
395C2×C3⋊D3—22no—
396C2×C3⋊D3—22no—
397C2×C3⋊D3—22no—
398C2×C3⋊D3—22no—
399C2×C3⋊D3—22no—
400C2×C3⋊D3—22no—
401C2×C3⋊D3C4×D414yes—
402C32×C4—22no—
403C32×C4—22no—
404C32×C4—41no—
405C3⋊Dic3—22no—
406C3⋊Dic3—22no—
407C3⋊Dic3—41no—
408C3×Dic3—22no—
409C3×Dic3—22no—
410C3×Dic3—22no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C3×Dic3#11714yescomplemented
416C23×C4—91no—
417C23×C4—91no—
418C23×C4—91no—
419#117—184no—
420#117—184no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—98no—
426C2×C4⋊C4—91no—
427C2×C4⋊C4—91no—
428C2×C4⋊C4—91no—
429C2×C4⋊C4—91no—
430C2×C4⋊C4—91no—
431C2×C4⋊C4D3211yescharacteristic
432C2×C22⋊C4—91no—
433C2×C22⋊C4—91no—
434C2×C22⋊C4—91no—
435C2×C22⋊C4—91no—
436C2×C42—31no—
437C2×C42—31no—
438C2×C42—91no—
439C2×C42—91no—
440C2×C42—91no—
441C2×C42—91no—
442#95—31no—
443#95—31no—
444#95—31no—
445#95—31no—
446#95—31no—
447#95—31no—
448#95—91no—
449#95—91no—
450#95—91no—
451#95—91no—
452#95—91no—
453#95—91no—
454C23×C3—21no—
455C23×C3C23×D311yescharacteristic
456C23×C3C23×D311yescharacteristic
457C22×D3—32no—
458C22×D3—32no—
459C22×D3—32no—
460C22×D3—32no—
461C22×D3—32no—
462C22×D3—32no—
463C22×D3—62no—
464C22×D3—62no—
465C22×D3—62no—
466C22×D3—61no—
467C22×D3—61no—
468C22×D3—61no—
469C22×D3—61no—
470C22×D3—61no—
471C22×D3—61no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—121no—
475C22×D3—121no—
476C22×D3—121no—
477C22×D3—121no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—22no—
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—22no—
496C2×C3×C4—22no—
497C2×C3×C4—32no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4C2×C4×D312yes—
526C2×C3×C4C2×C4×D312yes—
527C2×C3×C4D3×D412yes—
528C2×C3×C4D3×D412yes—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
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—32no—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—32no—
551C2×Dic3—62no—
552C2×Dic3—62no—
553C2×Dic3—62no—
554C2×Dic3—62no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—62no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—121no—
571C2×Dic3—121no—
572C2×Dic3—121no—
573C2×Dic3—121no—
574C2×Dic3C2×C4×D312yes—
575C2×Dic3C2×C4×D312yes—
576C2×Dic3C2×C4×D312yes—
577C2×Dic3C2×C4×D312yes—
578C2×Dic3#23712yes—
579C2×Dic3#23912yes—
580C4×D3—68no—
581C4×D3—68no—
582C4×D3—68no—
583C4×D3—68no—
584C4×D3—68no—
585C4×D3—616no—
586C4×D3—68no—
587C2×C32C2×#11711yescharacteristic
588C2×C32C2×C4×D411yescharacteristic
589C2×C32#51911yescharacteristic
590C2×C32#54711yescharacteristic
591C2×C32#54711yescharacteristic
592C2×C32#55211yescharacteristic
593C2×C32#55211yescharacteristic
594C3⋊D3—24no—
595C24—91no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—94no—
605C22×C4—94no—
606C22×C4—91no—
607C22×C4—91no—
608C22×C4—94no—
609C22×C4—91no—
610C22×C4—182no—
611C22×C4—182no—
612C22×C4—182no—
613C22×C4—182no—
614C22×C4—182no—
615C22×C4—182no—
616C22×C4C2×D3211yescharacteristic
617C22×C4C2×D3211yescharacteristic
618C22×C4C2×D3211yescharacteristic
619C4⋊C4—22no—
620C4⋊C4—34no—
621C4⋊C4—34no—
622C4⋊C4—62no—
623C4⋊C4—62no—
624C4⋊C4—94no—
625C4⋊C4—94no—
626C4⋊C4—182no—
627C4⋊C4—182no—
628C4⋊C4—182no—
629C22⋊C4—94no—
630C22⋊C4—182no—
631C22⋊C4—182no—
632C22⋊C4—182no—
633C42—62no—
634C42—62no—
635C42—182no—
636C42—182no—
637C42—182no—
638C42—182no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3C22×C4×D311yescharacteristic
647C22×C3C22×C4×D311yescharacteristic
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C2×#23711yescharacteristic
651C22×C3C2×#23911yescharacteristic
652C22×C3#100711yescharacteristic
653C22×C3#100711yescharacteristic
654C22×C3D3×#4111yescharacteristic
655C22×C3D3×#4111yescharacteristic
656C22×C3D3×#4111yescharacteristic
657C22×C3D3×#4111yescharacteristic
658C22×C3#101011yescharacteristic
659C22×C3#101011yescharacteristic
660C2×D3—34no—
661C2×D3—34no—
662C2×D3—64no—
663C2×D3—62no—
664C2×D3—62no—
665C2×D3—62no—
666C2×D3—62no—
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—62no—
672C2×D3—62no—
673C2×D3—62no—
674C2×D3—62no—
675C2×D3—122no—
676C2×D3—122no—
677C2×D3—122no—
678C2×D3—122no—
679C2×D3—122no—
680C2×D3—122no—
681C3×C4—24no—
682C3×C4—22no—
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—22no—
686C3×C4—34no—
687C3×C4—42no—
688C3×C4—42no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—62no—
692C3×C4—62no—
693C3×C4—62no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698Dic3—22no—
699Dic3—22no—
700Dic3—22no—
701Dic3—41no—
702Dic3—41no—
703Dic3—41no—
704Dic3—41no—
705Dic3—64no—
706Dic3—62no—
707Dic3—62no—
708Dic3—62no—
709Dic3—62no—
710Dic3—122no—
711Dic3—122no—
712Dic3—121no—
713Dic3—121no—
714Dic3#89214yescomplemented
715C32#234411yescharacteristic, complemented, Sylow
716C23—92no—
717C23—92no—
718C23—92no—
719C23—181no—
720C23—181no—
721C23—181no—
722C23—181no—
723C23C22×D3211yescharacteristic
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—92no—
756C2×C4—92no—
757C2×C4—188no—
758C2×C4—188no—
759C2×C4—188no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4—181no—
764C2×C4—181no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4C4×D3212yes—
768C2×C4#381112yes—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3C2×#89211yescharacteristic
777C2×C3D3×#11711yescharacteristic
778C2×C3C4×D3×D411yescharacteristic
779C2×C3C4×D3×D411yescharacteristic
780C2×C3#557211yescharacteristic
781C2×C3#557211yescharacteristic
782C2×C3#561111yescharacteristic
783C2×C3#563111yescharacteristic
784C2×C3#563911yescharacteristic
785C2×C3#565511yescharacteristic
786C2×C3#569311yescharacteristic
787C2×C3#569411yescharacteristic
788C2×C3#570811yescharacteristic
789C2×C3#572611yescharacteristic
790D3—64no—
791D3—64no—
792D3—124no—
793C22—94no—
794C22—182no—
795C22—182no—
796C22—182no—
797C22—182no—
798C22—182no—
799C22—182no—
800C22C2×C4×D3211yescharacteristic
801C22#6430611yescharacteristic
802C22#6430911yescharacteristic
803C22D3×#23711yescharacteristic
804C22#6431611yescharacteristic
805C22D3×#23911yescharacteristic
806C22C2×#381111yescharacteristic
807C4—22no—
808C4—22no—
809C4—34no—
810C4—41no—
811C4—62no—
812C4—62no—
813C4—62no—
814C4—121no—
815C4—121no—
816C4—121no—
817C4—121no—
818C4—182no—
819C4—182no—
820C4—361no—
821C3—21no—
822C3#7496111yescharacteristic, complemented
823C3#7620011yescharacteristic, complemented
824C2—184no—
825C2#1059433411yescharacteristic
826C2#1059434711yescharacteristic
827C2#1059446211yescharacteristic
828C2D3×#89211yescharacteristic
829C2C4×#381111yescharacteristic
830C2#1059516211yescharacteristic
831C2#1059534111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2344
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4978C2semidirect
5. C3×#4976C2semidirect
8. #10591335C2semidirect
9. #10591334C2semidirect
10. C4×Dic3⋊Dic3C2semidirect
11. #10591272C2semidirect
12. #10591268C2semidirect
13. #10591241C2semidirect
42. #63883C4semidirect
69. #4978D3semidirect
70. #4976D3semidirect
415. C3×Dic3#117semidirect
714. Dic3#892semidirect
715. C32#2344semidirect
822. C3#74961semidirect
823. C3#76200semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#638832
C2×#638362
C3×#49782
C3×#49762
#105913712
#105913672
#105913352
#105913342
C4×Dic3⋊Dic32
#105912722
#105912682
#105912412
#105912332
#105912192
#762003
#749613