Finite Group Databasebeta

← #11801539

Subgroups — #11801539

Order 1152.

1535 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63894C211yesmaximal, characteristic
2C2×C4×#624C211yesmaximal, characteristic, complemented
3C2×#63836C211yesmaximal, characteristic, complemented
4#10592364C211yesmaximal, characteristic
5C3×#4654C211yesmaximal, characteristic, complemented
6C3×#4649C211yesmaximal, characteristic, complemented
7#10591380C211yesmaximal, characteristic
8#10591374C211yesmaximal, characteristic, complemented
9#10591290C211yesmaximal, characteristic, complemented
10#10591289C211yesmaximal, characteristic, complemented
11#10591270C211yesmaximal, characteristic, complemented
12#10591258C211yesmaximal, characteristic, complemented
13#10591239C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591233C211yesmaximal, characteristic, complemented
16#74937—31nomaximal
17#73754—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63894C418yescomplemented
44C4×#624—24no—
45#63836—24no—
46C32×#95C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#893—31no—
57C2×#892—31no—
58C2×C4×D12—31no—
59C2×#872—31no—
60C2×C42×D3—31no—
61C2×C42×D3—31no—
62C3×#387—31no—
63C3×C4×C4⋊C4—31no—
64#4990—31no—
65#4990—31no—
66#4989—31no—
67#4989—31no—
68#4989—31no—
69#4980—31no—
70#4940—31no—
71C4×(C2×D3)⋊C4—31no—
72C4×(C2×D3)⋊C4—31no—
73#4932—31no—
74#4669—31no—
75#4668—31no—
76#4666—31no—
77#4666—31no—
78#4665—31no—
79#4665—31no—
80#4665—31no—
81#4665—31no—
82#4665—61no—
83#4654—31no—
84#4654D311yescharacteristic, complemented
85#4649D311yescharacteristic, complemented
86#4648—31no—
87C23×C3⋊D3C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—22no—
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)C2×C414yes—
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—22no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C2×#624—22no—
109C2×#624—22no—
110C2×#624—22no—
111C2×#624—22no—
112C2×#624—22no—
113C2×#624—22no—
114C2×#624—22no—
115C2×#624C2×C414yes—
116C2×#624C2×C414yescomplemented
117#3752—22no—
118#3752—22no—
119#3752—22no—
120C3×C4⋊Dic3C2×C414yescomplemented
121C3×Dic3⋊C4—22no—
122C3×Dic3⋊C4—22no—
123C3×Dic3⋊C4—22no—
124C3×C4×Dic3—22no—
125C3×C4×Dic3—22no—
126C3×C4×Dic3—22no—
127C3×C4×Dic3C2×C414yescomplemented
128Dic3⋊Dic3—22no—
129#3722—22no—
130#3722—22no—
131#3722—22no—
132#3722C2×C414yes—
133#3722C2×C414yescomplemented
134Dic32—22no—
135Dic32—22no—
136Dic32D414yescomplemented
137#2290—91noSylow
138C22×D12—31no—
139C22×D12—31no—
140C22×D12—61no—
141C22×C4×D3—31no—
142C22×C4×D3—31no—
143C22×C4×D3—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—61no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C42—31no—
155C2×C3×C42—31no—
156C2×C3×C42—31no—
157C2×C3×C42—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—61no—
175C2×(C2×D3)⋊C4—61no—
176C2×(C2×D3)⋊C4—61no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3C2×D311yescharacteristic
179C2×Dic3⋊C4—31no—
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×Dic3C2×D311yescharacteristic
190C2×C4×Dic3C2×D311yescharacteristic
191C2×C4×Dic3C2×D311yescharacteristic
192C2×C4×Dic3C2×D311yescharacteristic
193#893—38no—
194#892—64no—
195C4×D12—38no—
196#872—64no—
197C42×D3—64no—
198C42×D3—64no—
199C3×#95—21no—
200C3×#95—31no—
201C3×#95—31no—
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
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C23×C32C2411yescharacteristic
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3C22×C412yes—
233C22×C3⋊D3C22×C412yes—
234C22×C3⋊D3#4112yes—
235C22×C3⋊D3#4112yes—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C22×C412yes—
244C2×C32×C4#4112yes—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C2×D412yes—
251C4⋊(C3⋊D3)—28no—
252C4×C3⋊D3—28no—
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×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C22×C412yes—
270C2×C3×Dic3C22×C412yes—
271C2×C3×Dic3C22×C412yes—
272C2×C3×Dic3C22×C412yes—
273C2×C3×Dic3C2×D412yes—
274C2×C3×Dic3C2×D412yes—
275C2×C3×Dic3#4112yes—
276C2×C3×Dic3#4112yes—
277#624—28no—
278#624—28no—
279#624—28no—
280C2×C4×D4—91no—
281C2×#117—91no—
282C22×C42—91no—
283#388—91no—
284#388—91no—
285#387—31no—
286#387—91no—
287#386—91no—
288#386—91no—
289#385—91no—
290#385—91no—
291C4×C4⋊C4—31no—
292C4×C22⋊C4—91no—
293C4×C22⋊C4—91no—
294#376—91no—
295C23×D3—31no—
296C23×D3—31no—
297C23×D3—31no—
298C23×D3—31no—
299C23×D3—61no—
300C23×D3—61no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C2×D12—34no—
333C2×D12—34no—
334C2×D12—64no—
335C2×D12—62no—
336C2×D12—62no—
337C2×D12—62no—
338C2×D12—62no—
339C2×D12—122no—
340C2×D12—122no—
341C2×C4×D3—34no—
342C2×C4×D3—34no—
343C2×C4×D3—34no—
344C2×C4×D3—34no—
345C2×C4×D3—62no—
346C2×C4×D3—62no—
347C2×C4×D3—62no—
348C2×C4×D3—62no—
349C2×C4×D3—62no—
350C2×C4×D3—62no—
351C2×C4×D3—62no—
352C2×C4×D3—62no—
353C2×C4×D3—62no—
354C2×C4×D3—62no—
355C2×C4×D3—62no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3—62no—
362C2×C4×D3—62no—
363C2×C4×D3—62no—
364C2×C4×D3—62no—
365C2×C4×D3—122no—
366C2×C4×D3—122no—
367C2×C4×D3—122no—
368C3×C4⋊C4—34no—
369C3×C4⋊C4—62no—
370C3×C4⋊C4—62no—
371C3×C4⋊C4—62no—
372C3×C42—34no—
373C3×C42—62no—
374C3×C42—62no—
375C3×C42—62no—
376(C2×D3)⋊C4—34no—
377(C2×D3)⋊C4—34no—
378(C2×D3)⋊C4—34no—
379(C2×D3)⋊C4—34no—
380(C2×D3)⋊C4—62no—
381(C2×D3)⋊C4—62no—
382(C2×D3)⋊C4—62no—
383(C2×D3)⋊C4—62no—
384(C2×D3)⋊C4—62no—
385(C2×D3)⋊C4—62no—
386(C2×D3)⋊C4—62no—
387(C2×D3)⋊C4—62no—
388(C2×D3)⋊C4—62no—
389(C2×D3)⋊C4—62no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—62no—
392(C2×D3)⋊C4—122no—
393(C2×D3)⋊C4—122no—
394(C2×D3)⋊C4—122no—
395C4⋊Dic3—62no—
396C4⋊Dic3C4×D314yescomplemented
397Dic3⋊C4—22no—
398Dic3⋊C4—22no—
399Dic3⋊C4—22no—
400Dic3⋊C4—62no—
401C4×Dic3—22no—
402C4×Dic3—22no—
403C4×Dic3—22no—
404C4×Dic3—34no—
405C4×Dic3—34no—
406C4×Dic3—62no—
407C4×Dic3—62no—
408C4×Dic3—62no—
409C4×Dic3—62no—
410C4×Dic3C4×D314yescomplemented
411C22×C32C23×C411yescharacteristic
412C22×C32C22×D411yescharacteristic
413C22×C32C2×#4111yescharacteristic
414C22×C32C2×#4111yescharacteristic
415C22×C32C2×#4111yescharacteristic
416C22×C32C2×#4111yescharacteristic
417C22×C32C2×#4111yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—22no—
420C2×C3⋊D3—22no—
421C2×C3⋊D3—22no—
422C2×C3⋊D3—22no—
423C2×C3⋊D3—22no—
424C2×C3⋊D3—22no—
425C2×C3⋊D3—22no—
426C2×C3⋊D3—22no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3#11714yescomplemented
432C32×C4—22no—
433C32×C4—22no—
434C32×C4—41no—
435C3⋊Dic3—22no—
436C3⋊Dic3—41no—
437C3×Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—22no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C3×Dic3C4×D414yes—
445C22×D4—91no—
446C23×C4—91no—
447C23×C4—91no—
448C23×C4—91no—
449C23×C4—91no—
450C4×D4—98no—
451#117—184no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4—91no—
457C2×C22⋊C4—91no—
458C2×C22⋊C4—91no—
459C2×C22⋊C4—91no—
460C2×C22⋊C4—91no—
461C2×C22⋊C4—91no—
462C2×C22⋊C4—91no—
463C2×C22⋊C4—91no—
464C2×C22⋊C4—91no—
465C2×C42—31no—
466C2×C42—31no—
467C2×C42—31no—
468C2×C42—31no—
469C2×C42—91no—
470C2×C42—91no—
471C2×C42—91no—
472C2×C42—184no—
473#95—31no—
474#95—31no—
475#95—31no—
476#95—31no—
477#95—91no—
478#95—91no—
479#95—91no—
480#95—91no—
481#95—91no—
482#95D3211yescharacteristic
483C23×C3—21no—
484C23×C3C23×D311yescharacteristic
485C23×C3C23×D311yescharacteristic
486C22×D3—32no—
487C22×D3—32no—
488C22×D3—32no—
489C22×D3—32no—
490C22×D3—32no—
491C22×D3—32no—
492C22×D3—32no—
493C22×D3—32no—
494C22×D3—62no—
495C22×D3—62no—
496C22×D3—62no—
497C22×D3—62no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—61no—
506C22×D3—61no—
507C22×D3—61no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—61no—
511C22×D3—61no—
512C22×D3—61no—
513C22×D3—61no—
514C22×D3—61no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—121no—
519C22×D3—121no—
520C22×D3—121no—
521C22×D3—121no—
522C22×D3—121no—
523C22×D3—121no—
524C22×D3—121no—
525C22×D3—121no—
526C22×D3—121no—
527C22×D3—121no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—32no—
545C2×C3×C4—32no—
546C2×C3×C4—32no—
547C2×C3×C4—32no—
548C2×C3×C4—32no—
549C2×C3×C4—32no—
550C2×C3×C4—32no—
551C2×C3×C4—32no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4C2×C4×D312yes—
576C2×C3×C4C2×C4×D312yes—
577C2×C3×C4#23512yes—
578C2×C3×C4#23912yes—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—62no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—121no—
609C2×Dic3—121no—
610C2×Dic3—121no—
611C2×Dic3—121no—
612C2×Dic3—121no—
613C2×Dic3C2×C4×D312yes—
614C2×Dic3C2×C4×D312yes—
615C2×Dic3C2×C4×D312yes—
616C2×Dic3C2×C4×D312yes—
617C2×Dic3#23512yes—
618C2×Dic3D3×D412yes—
619C2×Dic3D3×D412yes—
620C2×Dic3#23912yes—
621D12—68no—
622D12—68no—
623D12—128no—
624C4×D3—68no—
625C4×D3—68no—
626C4×D3—68no—
627C4×D3—68no—
628C4×D3—68no—
629C4×D3—68no—
630C4×D3—68no—
631C4×D3—68no—
632C4×D3—128no—
633C2×C32C2×#11711yescharacteristic
634C2×C32C2×C4×D411yescharacteristic
635C2×C32C4×#4111yescharacteristic
636C2×C32#52511yescharacteristic
637C2×C32#52511yescharacteristic
638C2×C32#52911yescharacteristic
639C2×C32#52911yescharacteristic
640C3⋊D3—24no—
641C3⋊D3—42no—
642C24—91no—
643C24—91no—
644C2×D4—94no—
645C2×D4—182no—
646C2×D4—182no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—94no—
656C22×C4—94no—
657C22×C4—91no—
658C22×C4—91no—
659C22×C4—182no—
660C22×C4—182no—
661C22×C4—182no—
662C22×C4—182no—
663C22×C4—182no—
664C22×C4—182no—
665C22×C4—182no—
666C22×C4—182no—
667C22×C4—182no—
668C22×C4—182no—
669C22×C4C2×D3211yescharacteristic
670C22×C4C2×D3211yescharacteristic
671C22×C4C2×D3211yescharacteristic
672C4⋊C4—34no—
673C4⋊C4—62no—
674C4⋊C4—62no—
675C4⋊C4—62no—
676C4⋊C4—182no—
677C22⋊C4—94no—
678C22⋊C4—94no—
679C22⋊C4—182no—
680C22⋊C4—182no—
681C22⋊C4—182no—
682C22⋊C4—182no—
683C22⋊C4—182no—
684C22⋊C4—182no—
685C42—34no—
686C42—62no—
687C42—62no—
688C42—62no—
689C42—94no—
690C42—182no—
691C42—182no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3C22×C4×D311yescharacteristic
700C22×C3C22×C4×D311yescharacteristic
701C22×C3C2×#23511yescharacteristic
702C22×C3C2×#23511yescharacteristic
703C22×C3C2×D3×D411yescharacteristic
704C22×C3C2×D3×D411yescharacteristic
705C22×C3C2×#23911yescharacteristic
706C22×C3C2×#23911yescharacteristic
707C22×C3D3×#4111yescharacteristic
708C22×C3D3×#4111yescharacteristic
709C22×C3D3×#4111yescharacteristic
710C22×C3D3×#4111yescharacteristic
711C22×C3D3×#4111yescharacteristic
712C22×C3D3×#4111yescharacteristic
713C2×D3—34no—
714C2×D3—34no—
715C2×D3—64no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—62no—
723C2×D3—62no—
724C2×D3—62no—
725C2×D3—62no—
726C2×D3—62no—
727C2×D3—62no—
728C2×D3—62no—
729C2×D3—62no—
730C2×D3—62no—
731C2×D3—62no—
732C2×D3—62no—
733C2×D3—62no—
734C2×D3—122no—
735C2×D3—122no—
736C2×D3—122no—
737C2×D3—122no—
738C2×D3—122no—
739C2×D3—122no—
740C2×D3—122no—
741C2×D3—122no—
742C2×D3—122no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—241no—
752C2×D3—241no—
753C2×D3—241no—
754C2×D3—241no—
755C3×C4—22no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—34no—
760C3×C4—42no—
761C3×C4—42no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4—62no—
765C3×C4—62no—
766C3×C4—62no—
767C3×C4—62no—
768C3×C4—62no—
769C3×C4—81no—
770C3×C4—121no—
771C3×C4—121no—
772Dic3—22no—
773Dic3—22no—
774Dic3—22no—
775Dic3—22no—
776Dic3—22no—
777Dic3—41no—
778Dic3—41no—
779Dic3—62no—
780Dic3—62no—
781Dic3—122no—
782Dic3—121no—
783Dic3—121no—
784Dic3—241no—
785Dic3#89314yes—
786C32#229011yescharacteristic, complemented, Sylow
787C23—92no—
788C23—92no—
789C23—92no—
790C23—92no—
791C23—181no—
792C23—181no—
793C23—181no—
794C23—181no—
795C23—181no—
796C23—181no—
797C23—181no—
798C23—181no—
799C23—181no—
800C23—181no—
801C23C22×D3211yescharacteristic
802D4—188no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—32no—
817C2×C4—32no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—92no—
835C2×C4—188no—
836C2×C4—188no—
837C2×C4—188no—
838C2×C4—188no—
839C2×C4—181no—
840C2×C4—181no—
841C2×C4—181no—
842C2×C4—181no—
843C2×C4—181no—
844C2×C4#379912yes—
845C2×C4C4×D3212yes—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3C4×#23511yescharacteristic
854C2×C3C2×#89311yescharacteristic
855C2×C3D3×#11711yescharacteristic
856C2×C3D3×#11711yescharacteristic
857C2×C3C4×D3×D411yescharacteristic
858C2×C3#554711yescharacteristic
859C2×C3#554711yescharacteristic
860C2×C3C4×#23911yescharacteristic
861C2×C3#558011yescharacteristic
862C2×C3#558011yescharacteristic
863C2×C3#562711yescharacteristic
864C2×C3#565611yescharacteristic
865C2×C3#569111yescharacteristic
866C2×C3#570611yescharacteristic
867D3—64no—
868D3—64no—
869D3—124no—
870D3—122no—
871D3—122no—
872D3—242no—
873C22—94no—
874C22—182no—
875C22—182no—
876C22—182no—
877C22—182no—
878C22—182no—
879C22—182no—
880C22—182no—
881C22—182no—
882C22—182no—
883C22—361no—
884C22—361no—
885C22—361no—
886C22—361no—
887C22C2×#379911yescharacteristic
888C22C2×C4×D3211yescharacteristic
889C22D3×#23511yescharacteristic
890C22D32×D411yescharacteristic
891C22#6431211yescharacteristic
892C22#6431211yescharacteristic
893C22D3×#23911yescharacteristic
894C4—22no—
895C4—22no—
896C4—34no—
897C4—41no—
898C4—62no—
899C4—62no—
900C4—62no—
901C4—62no—
902C4—62no—
903C4—121no—
904C4—121no—
905C4—182no—
906C4—361no—
907C3—21no—
908C3#7375411yescharacteristic, complemented
909C3#7493711yescharacteristic, complemented
910C2—184no—
911C2—362no—
912C2C4×#379911yescharacteristic
913C2#1059405211yescharacteristic
914C2#1059406611yescharacteristic
915C2#1059426611yescharacteristic
916C2#1059442311yescharacteristic
917C2#1059446411yescharacteristic
918C2D3×#89311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#95D32
hypocenterC32#2290
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×C4×#624C2semidirect
3. C2×#63836C2semidirect
5. C3×#4654C2semidirect
6. C3×#4649C2semidirect
8. #10591374C2semidirect
9. #10591290C2semidirect
10. #10591289C2semidirect
11. #10591270C2semidirect
12. #10591258C2semidirect
13. #10591239C2semidirect
14. #10591233C2semidirect
15. #10591233C2semidirect
43. #63894C4semidirect
84. #4654D3semidirect
85. #4649D3semidirect
116. C2×#624C2×C4semidirect
120. C3×C4⋊Dic3C2×C4semidirect
127. C3×C4×Dic3C2×C4semidirect
133. #3722C2×C4semidirect
136. Dic32D4semidirect
396. C4⋊Dic3C4×D3semidirect
410. C4×Dic3C4×D3semidirect
431. C2×C3⋊D3#117semidirect
786. C32#2290semidirect
908. C3#73754semidirect
909. C3#74937semidirect

Maximal subgroups

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

subgroupindex
C2×#638942
C2×C4×#6242
C2×#638362
#105923642
C3×#46542
C3×#46492
#105913802
#105913742
#105912902
#105912892
#105912702
#105912582
#105912392
#105912332
#749373
#737543