Finite Group Databasebeta

← #11802973

Subgroups — #11802973

Order 1152.

1293 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63878C211yesmaximal, characteristic
2C2×#63877C211yesmaximal, characteristic
3C2×D3×Dic3⋊C4C211yesmaximal, characteristic
4#10592674C211yesmaximal, characteristic, complemented
5C3×#4989C211yesmaximal, characteristic
6C3×#4976C211yesmaximal, characteristic, complemented
7#10591379C211yesmaximal, characteristic
8#10591372C211yesmaximal, characteristic
9#10591360C211yesmaximal, characteristic, complemented
10#10591330C211yesmaximal, characteristic, complemented
11#10591278C211yesmaximal, characteristic
12#10591268C211yesmaximal, characteristic, complemented
13#10591247C211yesmaximal, characteristic, complemented
14#10591244C211yesmaximal, characteristic, complemented
15#10591234C211yesmaximal, characteristic, complemented
16#75968—31nomaximal
17#74382—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45#63878C418yescomplemented
46#63877—24no—
47D3×Dic3⋊C4—24no—
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C22×Dic3⋊C4—31no—
57C2×#892—31no—
58C2×D3×C4⋊C4—31no—
59C2×#877—31no—
60C2×#877—31no—
61C2×#872—31no—
62C3×#389—31no—
63C3×#385—31no—
64#5210—31no—
65#4989—31no—
66#4989D311yescharacteristic
67#4984—31no—
68#4976—31no—
69#4976D311yescharacteristic, complemented
70#4975—31no—
71#4975—31no—
72#4975—31no—
73#4975—31no—
74#4975—61no—
75#4972—31no—
76#4950—31no—
77#4946—31no—
78#4928—31no—
79#4668—31no—
80#4668—31no—
81#4650—31no—
82#4650—31no—
83#4650—31no—
84#4650—31no—
85#4647—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
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—41no—
104C2×C3×C4×D3—41no—
105C2×D3×Dic3—22no—
106C2×D3×Dic3—41no—
107C2×D3×Dic3—41no—
108C2×D3×Dic3C2×C414yes—
109C2×D3×Dic3D414yes—
110C2×D3×Dic3Q814yes—
111C32×C4⋊C4—41no—
112C4⋊(C3⋊Dic3)—41no—
113#3750—22no—
114#3750—22no—
115#3750—41no—
116#3750—41no—
117C4×C3⋊Dic3C2×C414yescomplemented
118C3×(C2×D3)⋊C4—22no—
119C3×(C2×D3)⋊C4C2×C414yes—
120C3×Dic3⋊C4—22no—
121C3×Dic3⋊C4—41no—
122C3×Dic3⋊C4—41no—
123C3×Dic3⋊C4C2×C414yescomplemented
124C3×C4×Dic3—22no—
125#3724—22no—
126#3724—22no—
127Dic3⋊Dic3—22no—
128Dic3⋊Dic3—41no—
129Dic3⋊Dic3—41no—
130Dic3⋊Dic3C2×C414yescomplemented
131(C2×D3)⋊Dic3—22no—
132(C2×D3)⋊Dic3C2×C414yes—
133Dic32—22no—
134Dic32C2×C414yescomplemented
135#2317—91noSylow
136C23×C3×C4—31no—
137C23×Dic3—31no—
138C23×Dic3—31no—
139C22×C4×D3—31no—
140C22×C4×D3—31no—
141C22×C4×D3C2×D311yescharacteristic
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4C2×D311yescharacteristic
148C2×C3×C4⋊C4C2×D311yescharacteristic
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—31no—
151C2×C3×C42—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4C2×D311yescharacteristic
157C2×(C2×D3)⋊C4C2×D311yescharacteristic
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⋊C4—31no—
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—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—61no—
182C2×Dic3⋊C4—61no—
183C2×Dic3⋊C4—61no—
184C2×Dic3⋊C4—61no—
185C2×Dic3⋊C4—64no—
186C2×Dic3⋊C4C2×D311yescharacteristic
187C2×Dic3⋊C4C2×D311yescharacteristic
188C2×Dic3⋊C4C2×D311yescharacteristic
189C2×Dic3⋊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—
197C2×C4×Dic3C2×D311yescharacteristic
198#892—38no—
199D3×C4⋊C4—64no—
200#877—38no—
201#877—64no—
202#872—64no—
203C3×#95—31no—
204C3×#95—31no—
205C3×#95—31no—
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⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
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×C4—21no—
235C2×C32×C4C22×C412yes—
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⋊Dic3—21no—
244C2×C3⋊Dic3C22×C412yes—
245C2×C3⋊Dic3C22×C412yes—
246C2×C3⋊Dic3C2×D412yes—
247C2×C3⋊Dic3C2×Q812yes—
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×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C22×C412yes—
265C2×C3×Dic3C22×C412yes—
266C2×C3×Dic3C22×C412yes—
267C2×C3×Dic3C2×D412yes—
268C2×C3×Dic3C2×Q812yes—
269C3×C4×D3—44no—
270D3×Dic3—44no—
271D3×Dic3C4⋊C4116yescomplemented
272C2×#117—91no—
273C2×#117—91no—
274C22×C4⋊C4—91no—
275#389—31no—
276#389—91no—
277#389—91no—
278#389—91no—
279#385—31no—
280#385—91no—
281#385—91no—
282#385—91no—
283#384—91no—
284#384—91no—
285#382—91no—
286#382—91no—
287C24×C3—31no—
288C23×D3C22×D311yescharacteristic
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
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×C4—31no—
299C22×C3×C4—62no—
300C22×C3×C4—121no—
301C22×C3×C4—121no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—34no—
311C22×Dic3—34no—
312C22×Dic3—34no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—62no—
324C22×Dic3—121no—
325C22×Dic3—121no—
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C2×C4×D3—22no—
334C2×C4×D3—34no—
335C2×C4×D3—34no—
336C2×C4×D3—34no—
337C2×C4×D3—41no—
338C2×C4×D3—41no—
339C2×C4×D3—62no—
340C2×C4×D3—121no—
341C2×C4×D3—121no—
342C3×C4⋊C4—34no—
343C3×C4⋊C4—41no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4—42no—
346C3×C4⋊C4—62no—
347C3×C4⋊C4—121no—
348C3×C4⋊C4—121no—
349C3×C22⋊C4—34no—
350C3×C22⋊C4—62no—
351C3×C42—62no—
352#217—34no—
353#217—62no—
354(C2×D3)⋊C4—22no—
355(C2×D3)⋊C4—34no—
356(C2×D3)⋊C4—62no—
357(C2×D3)⋊C4C4×D314yes—
358C4⋊Dic3—34no—
359C4⋊Dic3—62no—
360C4⋊Dic3—121no—
361C4⋊Dic3—121no—
362C4⋊Dic3—121no—
363C4⋊Dic3—121no—
364C4⋊Dic3—122no—
365Dic3⋊C4—22no—
366Dic3⋊C4—34no—
367Dic3⋊C4—41no—
368Dic3⋊C4—41no—
369Dic3⋊C4—62no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4—62no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375Dic3⋊C4—62no—
376Dic3⋊C4—62no—
377Dic3⋊C4—62no—
378Dic3⋊C4—122no—
379Dic3⋊C4—122no—
380Dic3⋊C4—121no—
381Dic3⋊C4—121no—
382Dic3⋊C4—121no—
383Dic3⋊C4—121no—
384Dic3⋊C4—121no—
385Dic3⋊C4—121no—
386Dic3⋊C4—122no—
387Dic3⋊C4—122no—
388Dic3⋊C4C4×D314yescomplemented
389C4×Dic3—22no—
390C4×Dic3—34no—
391C4×Dic3—34no—
392C4×Dic3—34no—
393C4×Dic3—34no—
394C4×Dic3—64no—
395C4×Dic3—62no—
396C4×Dic3—62no—
397C22×C32C23×C411yescharacteristic
398C22×C32C22×D411yescharacteristic
399C22×C32C22×Q811yescharacteristic
400C22×C32H(5,𝔽2)11yescharacteristic
401C22×C32H(5,𝔽2)11yescharacteristic
402C22×C322−1+411yescharacteristic
403C22×C322−1+411yescharacteristic
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—41no—
413C32×C4—41no—
414C3⋊Dic3—22no—
415C3⋊Dic3—41no—
416C3⋊Dic3—41no—
417C3⋊Dic3C2×C4⋊C414yes—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3C2×C4⋊C414yes—
425C23×C4—31no—
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—91no—
435C2×C4⋊C4—91no—
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×C4⋊C4—91no—
443C2×C4⋊C4—91no—
444C2×C4⋊C4—91no—
445C2×C4⋊C4—184no—
446C2×C4⋊C4D3211yescharacteristic
447C2×C22⋊C4—31no—
448C2×C22⋊C4—31no—
449C2×C22⋊C4—91no—
450C2×C22⋊C4—91no—
451C2×C42—31no—
452C2×C42—91no—
453C2×C42—91no—
454C2×C42—91no—
455#95—31no—
456#95—31no—
457#95—31no—
458#95—31no—
459#95—91no—
460#95—91no—
461#95—91no—
462#95—91no—
463C23×C3—21no—
464C23×C3—32no—
465C23×C3—32no—
466C23×C3—32no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3C23×D311yescharacteristic
472C23×C3C23×D311yescharacteristic
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3C2×C4×D312yes—
478C22×D3D3×D412yes—
479C22×D3D3×Q812yes—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
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—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—22no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—32no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
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×C4—61no—
526C2×C3×C4—124no—
527C2×C3×C4C2×C4×D312yes—
528C2×C3×C4C2×C4×D312yes—
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—32no—
546C2×Dic3—32no—
547C2×Dic3—32no—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—32no—
551C2×Dic3—316no—
552C2×Dic3—32no—
553C2×Dic3—32no—
554C2×Dic3—62no—
555C2×Dic3—62no—
556C2×Dic3—62no—
557C2×Dic3—62no—
558C2×Dic3—62no—
559C2×Dic3—62no—
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—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—121no—
577C2×Dic3—121no—
578C2×Dic3—121no—
579C2×Dic3—121no—
580C2×Dic3—121no—
581C2×Dic3—121no—
582C2×Dic3—124no—
583C2×Dic3C2×C4×D312yes—
584C2×Dic3C2×C4×D312yes—
585C2×Dic3C2×C4×D312yes—
586C2×Dic3D3×D412yes—
587C2×Dic3D3×Q812yes—
588C4×D3—316no—
589C4×D3—44no—
590C4×D3—124no—
591C2×C32C22×C4⋊C411yescharacteristic
592C2×C32#52011yescharacteristic
593C2×C32#52011yescharacteristic
594C2×C32#53511yescharacteristic
595C2×C32#53611yescharacteristic
596C2×C32#54411yescharacteristic
597C2×C32#54411yescharacteristic
598C3×D3—24no—
599C24—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—62no—
608C22×C4—94no—
609C22×C4—94no—
610C22×C4—94no—
611C22×C4—91no—
612C22×C4—91no—
613C22×C4—91no—
614C22×C4—91no—
615C22×C4—121no—
616C22×C4—121no—
617C22×C4—182no—
618C22×C4—361no—
619C22×C4—361no—
620C22×C4C2×D3211yescharacteristic
621C22×C4C2×D3211yescharacteristic
622C22×C4C2×D3211yescharacteristic
623C4⋊C4—34no—
624C4⋊C4—41no—
625C4⋊C4—62no—
626C4⋊C4—94no—
627C4⋊C4—121no—
628C4⋊C4—121no—
629C4⋊C4—182no—
630C4⋊C4—182no—
631C4⋊C4—182no—
632C4⋊C4—182no—
633C4⋊C4—182no—
634C4⋊C4—361no—
635C4⋊C4—361no—
636C4⋊C4—361no—
637C4⋊C4—361no—
638C4⋊C4—361no—
639C22⋊C4—34no—
640C22⋊C4—62no—
641C22⋊C4—94no—
642C22⋊C4—182no—
643C42—62no—
644C42—94no—
645C42—94no—
646C42—182no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—34no—
655C22×C3—62no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—62no—
659C22×C3—62no—
660C22×C3—62no—
661C22×C3C22×C4×D311yescharacteristic
662C22×C3C22×C4×D311yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C2×D3×D411yescharacteristic
665C22×C3#100411yescharacteristic
666C22×C3#100411yescharacteristic
667C22×C3#100411yescharacteristic
668C22×C3C2×D3×Q811yescharacteristic
669C22×C3C2×D3×Q811yescharacteristic
670C22×C3#100711yescharacteristic
671C22×C3#100911yescharacteristic
672C22×C3#101011yescharacteristic
673C22×C3#101011yescharacteristic
674C22×C3#101011yescharacteristic
675C2×D3—22no—
676C2×D3—22no—
677C2×D3—22no—
678C2×D3—22no—
679C2×D3—22no—
680C2×D3—22no—
681C2×D3D3×C4⋊C414yes—
682C3×C4—24no—
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—34no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—62no—
691C3×C4—62no—
692C3×C4—81no—
693C3×C4—81no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698Dic3—22no—
699Dic3—22no—
700Dic3—34no—
701Dic3—34no—
702Dic3—41no—
703Dic3—41no—
704Dic3—41no—
705Dic3—41no—
706Dic3—64no—
707Dic3—64no—
708Dic3—62no—
709Dic3—62no—
710Dic3—121no—
711Dic3—121no—
712Dic3—121no—
713Dic3—121no—
714Dic3—241no—
715Dic3—241no—
716Dic3D3×C4⋊C414yes—
717C32#231711yescharacteristic, complemented, Sylow
718C23—32no—
719C23—32no—
720C23—32no—
721C23—61no—
722C23—61no—
723C23—61no—
724C23—61no—
725C23C22×D3211yescharacteristic
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—32no—
738C2×C4—32no—
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—916no—
756C2×C4—92no—
757C2×C4—92no—
758C2×C4—92no—
759C2×C4—92no—
760C2×C4—124no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4—181no—
764C2×C4—181no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4—181no—
768C2×C4—181no—
769C2×C4—364no—
770C2×C4C4×D3212yes—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—64no—
779C2×C3C2×D3×C4⋊C411yescharacteristic
780C2×C3C2×D3×C4⋊C411yescharacteristic
781C2×C3#554611yescharacteristic
782C2×C3#554611yescharacteristic
783C2×C3#554611yescharacteristic
784C2×C3#557411yescharacteristic
785C2×C3#559211yescharacteristic
786C2×C3#560711yescharacteristic
787C2×C3#562311yescharacteristic
788C2×C3#562311yescharacteristic
789C2×C3#562811yescharacteristic
790C2×C3#564811yescharacteristic
791C2×C3#568911yescharacteristic
792C2×C3#572911yescharacteristic
793D3—24no—
794C22—34no—
795C22—62no—
796C22—62no—
797C22—62no—
798C22—62no—
799C22—62no—
800C22—62no—
801C22#6429811yescharacteristic
802C22C2×C4×D3211yescharacteristic
803C22D32×D411yescharacteristic
804C22#6431411yescharacteristic
805C22#6431511yescharacteristic
806C22D32×Q811yescharacteristic
807C22#6433011yescharacteristic
808C4—22no—
809C4—34no—
810C4—41no—
811C4—41no—
812C4—62no—
813C4—62no—
814C4—94no—
815C4—121no—
816C4—121no—
817C4—121no—
818C4—121no—
819C4—182no—
820C4—361no—
821C4—361no—
822C3—21no—
823C3#7438211yescharacteristic, complemented
824C3#7596811yescharacteristic, complemented
825C2—64no—
826C2#1059436111yescharacteristic
827C2#1059436511yescharacteristic
828C2#1059439011yescharacteristic
829C2D32×C4⋊C411yescharacteristic
830C2#1059487611yescharacteristic
831C2#1059528511yescharacteristic
832C2#1059536911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2317
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10592674C2semidirect
6. C3×#4976C2semidirect
9. #10591360C2semidirect
10. #10591330C2semidirect
12. #10591268C2semidirect
13. #10591247C2semidirect
14. #10591244C2semidirect
15. #10591234C2semidirect
45. #63878C4semidirect
69. #4976D3semidirect
117. C4×C3⋊Dic3C2×C4semidirect
123. C3×Dic3⋊C4C2×C4semidirect
130. Dic3⋊Dic3C2×C4semidirect
134. Dic32C2×C4semidirect
271. D3×Dic3C4⋊C4semidirect
388. Dic3⋊C4C4×D3semidirect
717. C32#2317semidirect
823. C3#74382semidirect
824. C3#75968semidirect

Maximal subgroups

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

subgroupindex
C2×#638782
C2×#638772
C2×D3×Dic3⋊C42
#105926742
C3×#49892
C3×#49762
#105913792
#105913722
#105913602
#105913302
#105912782
#105912682
#105912472
#105912442
#105912342
#759683
#743823