Finite Group Databasebeta

← #11803282

Subgroups — #11803282

Order 1152.

1745 conjugacy classes of subgroups.

The subgroup lattice has 1091 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63977C211yesmaximal, characteristic
2C2×D3×#217C211yesmaximal, characteristic, complemented
3C2×#63880C211yesmaximal, characteristic, complemented
4#10592656C211yesmaximal, characteristic, complemented
5C3×#4955C211yesmaximal, characteristic, complemented
6C3×#4945C211yesmaximal, characteristic, complemented
7#10591722C211yesmaximal, characteristic, complemented
8#10591701C211yesmaximal, characteristic, complemented
9#10591384C211yesmaximal, characteristic, complemented
10#10591372C211yesmaximal, characteristic, complemented
11#10591368C211yesmaximal, characteristic, complemented
12#10591364C211yesmaximal, characteristic, complemented
13#10591287C211yesmaximal, characteristic, complemented
14#10591280C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16#75827—31nomaximal
17#73821—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#624C2211yescharacteristic, complemented
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic, complemented
28C2×#3752C2211yescharacteristic, complemented
29C2×#3750C2211yescharacteristic, complemented
30C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
39C2×C3×C4×Dic3C2211yescharacteristic, complemented
40#63977C418yescomplemented
41D3×#217—24no—
42C2×Dic3⋊Dic3C2211yescharacteristic, complemented
43C2×#3722C2211yescharacteristic, complemented
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×Dic32C2211yescharacteristic, complemented
49#63880—24no—
50C3×C3⋊#95C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×#953—31no—
57C22×#217—31no—
58C2×#882—31no—
59C2×#67⋊C4—31no—
60C2×D3×C22⋊C4—31no—
61C2×C4×D12—31no—
62C3×#388—31no—
63C3×#379—31no—
64#4989—31no—
65#4988—31no—
66#4958—31no—
67#4957—31no—
68#4957—31no—
69#4957—31no—
70#4957—61no—
71#4956—31no—
72#4956—31no—
73#4956—31no—
74#4955D311yescharacteristic, complemented
75#4951—31no—
76#4946—31no—
77#4945—31no—
78#4945D311yescharacteristic, complemented
79#4944—31no—
80#4944—31no—
81Dic3×C22⋊C4—31no—
82#4940—31no—
83#4670—31no—
84#4666—31no—
85#4665—31no—
86#4665—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3—22no—
90C23×C3×D3—22no—
91C23×C3×D3—41no—
92C23×C3×D3—41no—
93C23×C3×D3—41no—
94C23×C3×D3—41no—
95C23×C3×D3C2×C414yescomplemented
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×#638—41no—
101C2×#638—41no—
102C2×#638C2×C414yescomplemented
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×#626—22no—
113C2×#626—22no—
114C2×#626—41no—
115C2×#626—41no—
116C2×#626C2×C414yes—
117C2×#626C2×C414yescomplemented
118C2×#624—22no—
119C2×#624—41no—
120C2×#624—41no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—41no—
123C2×D3×Dic3—41no—
124C2×D3×Dic3—41no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3D414yescomplemented
127C32×C22⋊C4—41no—
128#3757—22no—
129#3752—22no—
130#3752—41no—
131#3750—41no—
132C4×C3⋊Dic3—41no—
133C3×#217—22no—
134C3×#217—41no—
135C3×#217C2×C414yescomplemented
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—41no—
139C3×(C2×D3)⋊C4—41no—
140C3×Dic3⋊C4—41no—
141C3×C4×Dic3—22no—
142Dic3⋊Dic3—22no—
143#3722—41no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3C2×C414yescomplemented
147(C2×D3)⋊Dic3C2×C414yescomplemented
148Dic32—41no—
149#2321—91noSylow
150C25×C3—31no—
151C24×D3C2×D311yescharacteristic
152C22×#67—31no—
153C22×#67—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—61no—
157C23×Dic3—31no—
158C23×Dic3—31no—
159C22×D12—31no—
160C22×D12—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C22⋊C4—21no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4C2×D311yescharacteristic
175C2×C3×C22⋊C4C2×D311yescharacteristic
176C2×C3×C42—31no—
177#953—38no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—61no—
185C2×#217—64no—
186C2×#217C2×D311yescharacteristic
187C2×#217C2×D311yescharacteristic
188C2×#217C2×D311yescharacteristic
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—61no—
200C2×(C2×D3)⋊C4—61no—
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×C4⋊Dic3—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—61no—
210C2×Dic3⋊C4C2×D311yescharacteristic, complemented
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3—31no—
214C2×C4×Dic3—31no—
215C2×C4×Dic3—61no—
216C2×C4×Dic3C2×D311yescharacteristic, complemented
217#882—38no—
218#67⋊C4—64no—
219D3×C22⋊C4—64no—
220C4×D12—64no—
221C3×#95—31no—
222C3×#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95C2×D311yescharacteristic, complemented
232C3⋊#95C2×D311yescharacteristic, complemented
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32C22×C412yes—
240C23×C32C2411yescharacteristic
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3C22×C412yes—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—28no—
259C22×C3×D3—44no—
260C22×C3×D3—44no—
261C22×C3×D3—44no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3C22×C412yes—
266C22×C3×D3C22×C412yes—
267C22×C3×D3C2×D412yes—
268C22×C3×D3#4112yes—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275#638—44no—
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⋊Dic3C22×C412yes—
284C2×C3⋊Dic3C2×D412yes—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3C22×C412yes—
301C2×C3×Dic3C22×C412yes—
302C2×C3×Dic3C2×D412yes—
303#626—28no—
304#626—44no—
305#624—44no—
306D3×Dic3—44no—
307D3×Dic3—44no—
308C2×#120—91no—
309C2×C4×D4—91no—
310C22×C22⋊C4—91no—
311#390—91no—
312#390—91no—
313#388—31no—
314#388—91no—
315#388—91no—
316#388—91no—
317#386—91no—
318#386—91no—
319#386—91no—
320#385—91no—
321#379—31no—
322C4×C22⋊C4—91no—
323C24×C3—21no—
324C24×C3—31no—
325C24×C3—31no—
326C24×C3—34no—
327C24×C3—62no—
328C24×C3—62no—
329C24×C3—121no—
330C24×C3—121no—
331C24×C3—121no—
332C24×C3—121no—
333C24×C3C22×D311yescharacteristic
334C24×C3C22×D311yescharacteristic
335C23×D3—22no—
336C23×D3—22no—
337C23×D3—31no—
338C23×D3—31no—
339C23×D3—41no—
340C23×D3—41no—
341C23×D3—41no—
342C23×D3—41no—
343C23×D3—61no—
344C23×D3C4×D314yescomplemented
345C23×D3C22×D311yescharacteristic
346C23×D3C22×D311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C2×#67—34no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—34no—
363C2×#67—64no—
364C2×#67—62no—
365C2×#67—62no—
366C2×#67—121no—
367C2×#67—121no—
368C2×#67—121no—
369C2×#67—121no—
370C2×#67—121no—
371C2×#67—121no—
372C2×#67—122no—
373C2×#67—122no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—34no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—62no—
385C22×Dic3—121no—
386C22×Dic3—121no—
387C22×Dic3—121no—
388C22×Dic3—121no—
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C2×D12—34no—
396C2×D12—34no—
397C2×D12—62no—
398C2×D12—62no—
399C2×D12—121no—
400C2×D12—121no—
401C2×C4×D3—34no—
402C2×C4×D3—62no—
403C2×C4×D3—62no—
404C2×C4×D3—62no—
405C2×C4×D3—121no—
406C2×C4×D3—121no—
407C2×C4×D3—121no—
408C2×C4×D3—121no—
409C2×C4×D3—121no—
410C2×C4×D3—121no—
411C2×C4×D3—121no—
412C2×C4×D3—121no—
413C3×C4⋊C4—121no—
414C3×C22⋊C4—34no—
415C3×C22⋊C4—41no—
416C3×C22⋊C4—41no—
417C3×C22⋊C4—42no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—62no—
421C3×C22⋊C4—121no—
422C3×C22⋊C4—121no—
423C3×C22⋊C4—121no—
424C3×C42—62no—
425#217—22no—
426#217—34no—
427#217—34no—
428#217—41no—
429#217—62no—
430#217—62no—
431#217—62no—
432#217—62no—
433#217—122no—
434#217C4×D314yescomplemented
435(C2×D3)⋊C4—22no—
436(C2×D3)⋊C4—22no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—41no—
440(C2×D3)⋊C4—41no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—122no—
446(C2×D3)⋊C4—121no—
447(C2×D3)⋊C4—121no—
448(C2×D3)⋊C4—121no—
449(C2×D3)⋊C4—121no—
450(C2×D3)⋊C4—122no—
451C4⋊Dic3—62no—
452Dic3⋊C4—41no—
453Dic3⋊C4—62no—
454Dic3⋊C4—121no—
455Dic3⋊C4—121no—
456Dic3⋊C4—122no—
457C4×Dic3—22no—
458C4×Dic3—121no—
459C4×Dic3—121no—
460C4×Dic3—121no—
461C4×Dic3—121no—
462C4×Dic3—122no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32C23×C411yescharacteristic
471C22×C32C22×D411yescharacteristic
472C22×C32C2×#4111yescharacteristic
473C22×C32H(5,𝔽2)11yescharacteristic
474C22×C32H(5,𝔽2)11yescharacteristic
475C22×C32H(5,𝔽2)11yescharacteristic
476C22×C32H(5,𝔽2)11yescharacteristic
477C2×C3⋊D3—22no—
478C2×C3⋊D3—22no—
479C2×C3⋊D3—22no—
480C2×C3⋊D3—41no—
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—416no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3C4×D414yes—
499C32×C4—41no—
500C32×C4—41no—
501C3⋊Dic3—22no—
502C3⋊Dic3—22no—
503C3⋊Dic3—41no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C3×Dic3—41no—
510C25—31no—
511C22×D4—91no—
512C22×D4—91no—
513C22×D4—91no—
514C23×C4—91no—
515C23×C4—91no—
516C23×C4—91no—
517#120—98no—
518C4×D4—184no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—184no—
538C2×C22⋊C4D3211yescharacteristic
539C2×C42—31no—
540C2×C42—91no—
541C2×C42—91no—
542#95—31no—
543#95—31no—
544#95—91no—
545#95—91no—
546#95—91no—
547#95—91no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—22no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—32no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—68no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—124no—
584C23×C3—124no—
585C23×C3—124no—
586C23×C3—124no—
587C23×C3—124no—
588C23×C3—124no—
589C23×C3C2×C4×D312yes—
590C23×C3C2×C4×D312yes—
591C23×C3C23×D311yescharacteristic
592C23×C3C23×D311yescharacteristic
593C22×D3—21no—
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—28no—
604C22×D3—32no—
605C22×D3—32no—
606C22×D3—44no—
607C22×D3—44no—
608C22×D3—44no—
609C22×D3—44no—
610C22×D3—44no—
611C22×D3—44no—
612C22×D3—62no—
613C22×D3—61no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—121no—
626C22×D3—121no—
627C22×D3—121no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3—121no—
631C22×D3C2×C4×D312yes—
632C22×D3C2×C4×D312yes—
633C22×D3D3×D412yes—
634C22×D3#23712yes—
635C2×C3×C4—22no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671#67—68no—
672#67—124no—
673#67—124no—
674#67—124no—
675#67—128no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—32no—
692C2×Dic3—32no—
693C2×Dic3—32no—
694C2×Dic3—32no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—62no—
698C2×Dic3—62no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—121no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—121no—
717C2×Dic3—121no—
718C2×Dic3—124no—
719C2×Dic3—124no—
720C2×Dic3C2×C4×D312yes—
721C2×Dic3C2×C4×D312yes—
722C2×Dic3D3×D412yes—
723D12—68no—
724D12—124no—
725C4×D3—124no—
726C4×D3—124no—
727C4×D3—124no—
728C4×D3—124no—
729C2×C32—42no—
730C2×C32C2×C4×D411yescharacteristic
731C2×C32#51811yescharacteristic
732C2×C32#51811yescharacteristic
733C2×C32#53411yescharacteristic
734C2×C32#53511yescharacteristic
735C2×C32#53811yescharacteristic
736C2×C32#53811yescharacteristic
737C3⋊D3—42no—
738C3×D3—24no—
739C3×D3—42no—
740C24—31no—
741C24—31no—
742C24—34no—
743C24—62no—
744C24—62no—
745C24—91no—
746C24—121no—
747C24—121no—
748C24—121no—
749C24—121no—
750C24C2×D3211yescharacteristic
751C2×D4—94no—
752C2×D4—94no—
753C2×D4—94no—
754C2×D4—182no—
755C2×D4—182no—
756C2×D4—361no—
757C2×D4—361no—
758C2×D4—361no—
759C2×D4—361no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—94no—
767C22×C4—91no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—182no—
771C22×C4—182no—
772C22×C4—361no—
773C22×C4—361no—
774C22×C4—361no—
775C22×C4—361no—
776C22×C4—361no—
777C22×C4—361no—
778C22×C4C2×D3211yescharacteristic
779C22×C4C2×D3211yescharacteristic
780C4⋊C4—121no—
781C4⋊C4—182no—
782C4⋊C4—361no—
783C22⋊C4—34no—
784C22⋊C4—41no—
785C22⋊C4—62no—
786C22⋊C4—62no—
787C22⋊C4—62no—
788C22⋊C4—94no—
789C22⋊C4—94no—
790C22⋊C4—121no—
791C22⋊C4—121no—
792C22⋊C4—121no—
793C22⋊C4—182no—
794C22⋊C4—182no—
795C22⋊C4—182no—
796C22⋊C4—182no—
797C22⋊C4—361no—
798C22⋊C4—361no—
799C42—62no—
800C42—361no—
801C42—361no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—34no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—62no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3—1216no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3C22×C4×D311yescharacteristic
846C22×C3C22×C4×D311yescharacteristic
847C22×C3C2×D3×D411yescharacteristic
848C22×C3C2×D3×D411yescharacteristic
849C22×C3C2×#23711yescharacteristic
850C22×C3#100411yescharacteristic
851C22×C3#100411yescharacteristic
852C22×C3#100411yescharacteristic
853C22×C3#100411yescharacteristic
854C22×C3#100411yescharacteristic
855C22×C3D3×#4111yescharacteristic
856C22×C3#100911yescharacteristic
857C22×C3#100911yescharacteristic
858C22×C3#100911yescharacteristic
859C2×D3—22no—
860C2×D3—22no—
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—416no—
869C2×D3—41no—
870C2×D3—41no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—62no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—122no—
880C2×D3—122no—
881C2×D3—122no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—241no—
891C2×D3—241no—
892C2×D3—241no—
893C2×D3—241no—
894C2×D3#67⋊C414yes—
895C3×C4—42no—
896C3×C4—41no—
897C3×C4—41no—
898C3×C4—41no—
899C3×C4—41no—
900C3×C4—62no—
901C3×C4—62no—
902C3×C4—62no—
903C3×C4—81no—
904C3×C4—121no—
905C3×C4—121no—
906C3×C4—121no—
907Dic3—22no—
908Dic3—22no—
909Dic3—22no—
910Dic3—41no—
911Dic3—41no—
912Dic3—41no—
913Dic3—64no—
914Dic3—62no—
915Dic3—62no—
916Dic3—62no—
917Dic3—62no—
918Dic3—122no—
919Dic3—121no—
920Dic3—121no—
921Dic3—241no—
922C32#232111yescharacteristic, complemented, Sylow
923C23—21no—
924C23—21no—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—32no—
930C23—32no—
931C23—32no—
932C23—32no—
933C23—68no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—61no—
942C23—61no—
943C23—61no—
944C23—92no—
945C23—124no—
946C23—124no—
947C23—124no—
948C23—124no—
949C23—124no—
950C23—124no—
951C23—181no—
952C23—181no—
953C23—181no—
954C23—181no—
955C23—181no—
956C23—181no—
957C23C4×D3212yes—
958C23C22×D3211yescharacteristic
959D4—188no—
960D4—364no—
961D4—364no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—32no—
969C2×C4—32no—
970C2×C4—32no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—92no—
987C2×C4—92no—
988C2×C4—181no—
989C2×C4—181no—
990C2×C4—181no—
991C2×C4—181no—
992C2×C4—181no—
993C2×C4—181no—
994C2×C4—181no—
995C2×C4—364no—
996C2×C4—364no—
997C2×C4—364no—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—42no—
1006C2×C3—42no—
1007C2×C3—64no—
1008C2×C3—82no—
1009C2×C3—122no—
1010C2×C3C2×#67⋊C411yescharacteristic
1011C2×C3#548611yescharacteristic
1012C2×C3#548611yescharacteristic
1013C2×C3#552111yescharacteristic
1014C2×C3C4×D3×D411yescharacteristic
1015C2×C3#554511yescharacteristic
1016C2×C3#558911yescharacteristic
1017C2×C3#559211yescharacteristic
1018C2×C3#559311yescharacteristic
1019C2×C3#559311yescharacteristic
1020C2×C3#560711yescharacteristic
1021C2×C3#565311yescharacteristic
1022C2×C3#567811yescharacteristic
1023C2×C3#570411yescharacteristic
1024D3—24no—
1025D3—42no—
1026D3—122no—
1027D3—122no—
1028D3—242no—
1029C22—22no—
1030C22—22no—
1031C22—22no—
1032C22—34no—
1033C22—41no—
1034C22—41no—
1035C22—41no—
1036C22—41no—
1037C22—62no—
1038C22—62no—
1039C22—62no—
1040C22—62no—
1041C22—62no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—1216no—
1047C22—121no—
1048C22—121no—
1049C22—121no—
1050C22—121no—
1051C22—182no—
1052C22—182no—
1053C22—182no—
1054C22—361no—
1055C22—361no—
1056C22—361no—
1057C22—361no—
1058C22C2×C4×D3211yescharacteristic
1059C22#6430711yescharacteristic
1060C22D32×D411yescharacteristic
1061C22D3×#23711yescharacteristic
1062C22#6431411yescharacteristic
1063C22#6431411yescharacteristic
1064C22#6433011yescharacteristic
1065C4—41no—
1066C4—41no—
1067C4—62no—
1068C4—62no—
1069C4—62no—
1070C4—121no—
1071C4—121no—
1072C4—121no—
1073C4—182no—
1074C4—182no—
1075C4—361no—
1076C3—21no—
1077C3#7382111yescharacteristic, complemented
1078C3#7582711yescharacteristic, complemented
1079C2—42no—
1080C2—64no—
1081C2—122no—
1082C2—362no—
1083C2#1059412611yescharacteristic
1084C2#1059418211yescharacteristic
1085C2D3×#67⋊C411yescharacteristic
1086C2#1059426211yescharacteristic
1087C2#1059505611yescharacteristic
1088C2#1059518411yescharacteristic
1089C2#1059528511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63977C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×#217C2semidirect
3. C2×#63880C2semidirect
4. #10592656C2semidirect
5. C3×#4955C2semidirect
6. C3×#4945C2semidirect
7. #10591722C2semidirect
8. #10591701C2semidirect
9. #10591384C2semidirect
10. #10591372C2semidirect
11. #10591368C2semidirect
12. #10591364C2semidirect
13. #10591287C2semidirect
14. #10591280C2semidirect
15. #10591275C2semidirect
22. C22×#624C22semidirect
27. C2×#3752C22semidirect
28. C2×#3752C22semidirect
29. C2×#3750C22semidirect
30. C2×C4×C3⋊Dic3C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. #63977C4semidirect
42. C2×Dic3⋊Dic3C22semidirect
43. C2×#3722C22semidirect
48. C2×Dic32C22semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
74. #4955D3semidirect
78. #4945D3semidirect
95. C23×C3×D3C2×C4semidirect
102. C2×#638C2×C4semidirect
117. C2×#626C2×C4semidirect
126. C2×D3×Dic3D4semidirect
135. C3×#217C2×C4semidirect
146. (C2×D3)⋊Dic3C2×C4semidirect
147. (C2×D3)⋊Dic3C2×C4semidirect
210. C2×Dic3⋊C4C2×D3semidirect
216. C2×C4×Dic3C2×D3semidirect
231. C3⋊#95C2×D3semidirect
232. C3⋊#95C2×D3semidirect
344. C23×D3C4×D3semidirect
434. #217C4×D3semidirect
922. C32#2321semidirect
1077. C3#73821semidirect
1078. C3#75827semidirect

Maximal subgroups

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

subgroupindex
C2×#639772
C2×D3×#2172
C2×#638802
#105926562
C3×#49552
C3×#49452
#105917222
#105917012
#105913842
#105913722
#105913682
#105913642
#105912872
#105912802
#105912752
#758273
#738213