Finite Group Databasebeta

← #11803863

Subgroups — #11803863

Order 1152.

1623 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63911C211yesmaximal, characteristic
2C2×C4×#626C211yesmaximal, characteristic, complemented
3C2×#63880C211yesmaximal, characteristic, complemented
4#10592364C211yesmaximal, characteristic, complemented
5C3×#4665C211yesmaximal, characteristic, complemented
6C3×#4648C211yesmaximal, characteristic, complemented
7#10591387C211yesmaximal, characteristic, complemented
8#10591383C211yesmaximal, characteristic, complemented
9#10591383C211yesmaximal, characteristic, complemented
10#10591382C211yesmaximal, characteristic, complemented
11#10591380C211yesmaximal, characteristic, complemented
12#10591376C211yesmaximal, characteristic, complemented
13#10591364C211yesmaximal, characteristic, complemented
14#10591275C211yesmaximal, characteristic, complemented
15#10591206C211yesmaximal, characteristic, complemented
16#74667—31nomaximal
17#73389—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45#63911C418yescomplemented
46C4×#626—24no—
47#63880—24no—
48C32×#95C2211yescharacteristic
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#940—31no—
57C2×C4×#67—31no—
58C2×#67⋊C4—31no—
59C2×#874—31no—
60C2×C4×D12—31no—
61C2×C4×D12—31no—
62C3×#386—31no—
63C3×#376—31no—
64#5220—31no—
65#5213—31no—
66#4958—31no—
67#4957—31no—
68#4957—31no—
69#4956—31no—
70#4956—31no—
71#4939—31no—
72#4939—31no—
73#4936—31no—
74#4665—31no—
75#4665—31no—
76#4665—31no—
77#4665—31no—
78#4665—31no—
79#4665—31no—
80#4665—31no—
81#4665—31no—
82#4665—31no—
83#4665—61no—
84#4665D311yescharacteristic, complemented
85#4650—31no—
86#4648D311yescharacteristic, complemented
87C23×C3⋊D3C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—41no—
97C2×C4⋊(C3⋊D3)—41no—
98C2×C4⋊(C3⋊D3)C2×C414yescomplemented
99C2×C4×C3⋊D3—22no—
100C2×C4×C3⋊D3—41no—
101C2×C4×C3⋊D3—41no—
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C2×C3×D12—41no—
109C2×C3×D12—41no—
110C2×C3×D12C2×C414yescomplemented
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—41no—
113C2×C3×C4×D3—41no—
114C2×#626—22no—
115C2×#626—22no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#626—41no—
119C2×#626—41no—
120C2×#626—41no—
121C2×#626—41no—
122C2×#626C2×C414yescomplemented
123C2×#626C2×C414yescomplemented
124C2×#626C2×C414yescomplemented
125C2×#626C2×C414yescomplemented
126C2×#624—22no—
127C2×#624—41no—
128C2×#624—41no—
129C2×D3×Dic3—22no—
130C2×D3×Dic3—41no—
131C2×D3×Dic3—41no—
132#3752—22no—
133#3752—41no—
134#3752—41no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—41no—
137C3×(C2×D3)⋊C4—41no—
138C3×C4×Dic3—22no—
139C3×C4×Dic3C2×C414yescomplemented
140C3×C4×Dic3D414yescomplemented
141Dic3⋊Dic3—22no—
142Dic3⋊Dic3—22no—
143#3722—22no—
144#3722—41no—
145#3722—41no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—41no—
148(C2×D3)⋊Dic3—41no—
149#2328—91noSylow
150C22×C3×D4—31no—
151C23×C3×C4—31no—
152C22×#67—31no—
153C22×#67—31no—
154C22×#67—31no—
155C22×#67—31no—
156C23×Dic3—31no—
157C22×D12—31no—
158C22×D12—31no—
159C22×D12—31no—
160C22×D12—31no—
161C22×D12—31no—
162C22×D12—31no—
163C22×D12—61no—
164C22×D12C2×D311yescharacteristic
165C22×C4×D3—31no—
166C22×C4×D3—31no—
167C22×C4×D3—31no—
168C22×C4×D3—31no—
169C22×C4×D3—31no—
170C22×C4×D3—61no—
171C22×C4×D3C2×D311yescharacteristic
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C42—31no—
176C2×C3×C42—31no—
177C2×C3×C42—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181#940—38no—
182C4×#67—64no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
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—61no—
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×C4⋊Dic3—31no—
205C2×C4⋊Dic3—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×C4×Dic3C2×D311yescharacteristic
209C2×C4×Dic3C2×D311yescharacteristic
210C2×C4×Dic3C2×D311yescharacteristic
211#67⋊C4—64no—
212#874—38no—
213C4×D12—64no—
214C4×D12—64no—
215C3×#95—21no—
216C3×#95—31no—
217C3×#95—31no—
218C3×#95—31no—
219C3×#95—31no—
220C3×#95C2×D311yescharacteristic
221C3×#95C2×D311yescharacteristic
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—61no—
229C3⋊#95C2×D311yescharacteristic
230C3⋊#95C2×D311yescharacteristic
231C3⋊#95C2×D311yescharacteristic
232C3⋊#95C2×D311yescharacteristic
233C23×C32C2411yescharacteristic
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3C22×C412yes—
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—21no—
259C22×C3×D3—21no—
260C22×C3×D3C22×C412yes—
261C22×C3×D3C22×C412yes—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C22×C412yes—
270C2×C32×C4C2×D412yes—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C4⋊(C3⋊D3)—44no—
278C4×C3⋊D3—44no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
293C2×C3×Dic3C22×C412yes—
294C2×C3×Dic3C2×D412yes—
295C2×C3×Dic3C2×D412yes—
296C2×C3×Dic3#4112yes—
297C3×D12—44no—
298C3×C4×D3—44no—
299#626—28no—
300#626—28no—
301#626—44no—
302#626—44no—
303#624—44no—
304D3×Dic3—44no—
305C2×#127—91no—
306C2×C4×D4—91no—
307C2×C4×D4—91no—
308#390—91no—
309#390—91no—
310#386—31no—
311#386—91no—
312#386—91no—
313#386—91no—
314#386—91no—
315#386—91no—
316#386—91no—
317#386—91no—
318#382—91no—
319#376—31no—
320C24×C3—31no—
321C24×C3—31no—
322C23×D3—31no—
323C23×D3—31no—
324C23×D3—31no—
325C23×D3—31no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3C22×D311yescharacteristic
329C23×D3C22×D311yescharacteristic
330C2×C3×D4—34no—
331C2×C3×D4—121no—
332C2×C3×D4—121no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—62no—
343C22×C3×C4—121no—
344C22×C3×C4—121no—
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C2×#67—34no—
352C2×#67—34no—
353C2×#67—34no—
354C2×#67—34no—
355C2×#67—62no—
356C2×#67—62no—
357C2×#67—62no—
358C2×#67—62no—
359C2×#67—121no—
360C2×#67—121no—
361C2×#67—121no—
362C2×#67—121no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—62no—
370C22×Dic3—121no—
371C22×Dic3—121no—
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C2×D12—34no—
379C2×D12—34no—
380C2×D12—34no—
381C2×D12—34no—
382C2×D12—34no—
383C2×D12—34no—
384C2×D12—41no—
385C2×D12—41no—
386C2×D12—64no—
387C2×D12—62no—
388C2×D12—62no—
389C2×D12—62no—
390C2×D12—62no—
391C2×D12—121no—
392C2×D12—121no—
393C2×D12—121no—
394C2×D12—121no—
395C2×D12—122no—
396C2×D12—122no—
397C2×D12—121no—
398C2×D12—121no—
399C2×D12—121no—
400C2×D12—121no—
401C2×D12C4×D314yescomplemented
402C2×C4×D3—22no—
403C2×C4×D3—41no—
404C2×C4×D3—41no—
405C2×C4×D3—62no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—122no—
411C2×C4×D3—121no—
412C2×C4×D3—121no—
413C2×C4×D3—121no—
414C2×C4×D3—121no—
415C2×C4×D3—121no—
416C2×C4×D3—121no—
417C2×C4×D3—121no—
418C2×C4×D3—121no—
419C2×C4×D3—122no—
420C2×C4×D3—121no—
421C2×C4×D3—121no—
422C2×C4×D3—122no—
423C3×C22⋊C4—62no—
424C3×C22⋊C4—121no—
425C3×C22⋊C4—121no—
426C3×C42—34no—
427C3×C42—34no—
428C3×C42—62no—
429#217—62no—
430#217—121no—
431#217—121no—
432(C2×D3)⋊C4—22no—
433(C2×D3)⋊C4—41no—
434(C2×D3)⋊C4—41no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—122no—
441(C2×D3)⋊C4—121no—
442(C2×D3)⋊C4—121no—
443(C2×D3)⋊C4—121no—
444(C2×D3)⋊C4—121no—
445(C2×D3)⋊C4—121no—
446(C2×D3)⋊C4—121no—
447(C2×D3)⋊C4—121no—
448(C2×D3)⋊C4—121no—
449(C2×D3)⋊C4—122no—
450(C2×D3)⋊C4—121no—
451(C2×D3)⋊C4—121no—
452(C2×D3)⋊C4—122no—
453C4⋊Dic3—62no—
454C4⋊Dic3—62no—
455Dic3⋊C4—62no—
456Dic3⋊C4—62no—
457C4×Dic3—22no—
458C4×Dic3C4×D314yescomplemented
459C4×Dic3D1214yescomplemented
460C22×C32C23×C411yescharacteristic
461C22×C32C22×D411yescharacteristic
462C22×C32C2×#4111yescharacteristic
463C22×C32H(5,𝔽2)11yescharacteristic
464C22×C32H(5,𝔽2)11yescharacteristic
465C22×C32H(5,𝔽2)11yescharacteristic
466C22×C32H(5,𝔽2)11yescharacteristic
467C2×C3⋊D3—22no—
468C2×C3⋊D3—22no—
469C2×C3⋊D3—22no—
470C2×C3⋊D3—22no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—41no—
476C2×C3⋊D3—41no—
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—41no—
480C2×C3⋊D3—41no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C32×C4—22no—
496C32×C4—22no—
497C32×C4—41no—
498C3⋊Dic3—41no—
499C3⋊Dic3—41no—
500C3×Dic3—22no—
501C3×Dic3—22no—
502C3×Dic3—41no—
503C3×Dic3—41no—
504C3×Dic3—41no—
505C3×Dic3C4×D414yes—
506C22×D4—31no—
507C22×D4—91no—
508C22×D4—91no—
509C22×D4—91no—
510C22×D4—91no—
511C22×D4—91no—
512C23×C4—31no—
513C23×C4—91no—
514C23×C4—91no—
515C23×C4—91no—
516#127—98no—
517C4×D4—184no—
518C4×D4—184no—
519C2×C4⋊C4—91no—
520C2×C4⋊C4—91no—
521C2×C22⋊C4—31no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—91no—
525C2×C22⋊C4—91no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4—91no—
528C2×C22⋊C4—91no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C42—31no—
534C2×C42—31no—
535C2×C42—31no—
536#95—31no—
537#95—31no—
538#95—31no—
539#95—31no—
540#95—91no—
541#95—91no—
542#95—91no—
543#95D3211yescharacteristic
544C23×C3—21no—
545C23×C3—32no—
546C23×C3—32no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3C23×D311yescharacteristic
560C23×C3C23×D311yescharacteristic
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—32no—
574C22×D3—32no—
575C22×D3—32no—
576C22×D3—32no—
577C22×D3—62no—
578C22×D3—62no—
579C22×D3—62no—
580C22×D3—62no—
581C22×D3—61no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3C2×C4×D312yes—
616C22×D3C2×C4×D312yes—
617C3×D4—124no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—32no—
635C2×C3×C4—32no—
636C2×C3×C4—32no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—124no—
660C2×C3×C4C2×C4×D312yes—
661C2×C3×C4C2×C4×D312yes—
662C2×C3×C4C2×D1212yes—
663C2×C3×C4D3×D412yes—
664#67—68no—
665#67—68no—
666#67—124no—
667#67—124no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—62no—
682C2×Dic3—61no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—121no—
695C2×Dic3—121no—
696C2×Dic3—121no—
697C2×Dic3—121no—
698C2×Dic3—121no—
699C2×Dic3—124no—
700C2×Dic3C2×C4×D312yes—
701C2×Dic3C2×C4×D312yes—
702C2×Dic3C2×D1212yes—
703C2×Dic3C2×D1212yes—
704C2×Dic3#23512yes—
705D12—44no—
706D12—68no—
707D12—68no—
708D12—124no—
709D12—124no—
710D12—128no—
711D12—124no—
712D12—124no—
713C4×D3—44no—
714C4×D3—124no—
715C4×D3—124no—
716C4×D3—124no—
717C4×D3—124no—
718C4×D3—128no—
719C4×D3—124no—
720C2×C32C2×C4×D411yescharacteristic
721C2×C32#51811yescharacteristic
722C2×C32#51811yescharacteristic
723C2×C32#53511yescharacteristic
724C2×C32#53511yescharacteristic
725C2×C32#54011yescharacteristic
726C2×C32#54011yescharacteristic
727C3⋊D3—42no—
728C3⋊D3—42no—
729C3×D3—42no—
730C3×D3—42no—
731C24—31no—
732C24—31no—
733C24—91no—
734C24—91no—
735C2×D4—34no—
736C2×D4—94no—
737C2×D4—94no—
738C2×D4—94no—
739C2×D4—94no—
740C2×D4—94no—
741C2×D4—121no—
742C2×D4—121no—
743C2×D4—182no—
744C2×D4—182no—
745C2×D4—182no—
746C2×D4—182no—
747C2×D4—361no—
748C2×D4—361no—
749C2×D4—361no—
750C2×D4—361no—
751C2×D4—361no—
752C2×D4—361no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—62no—
760C22×C4—91no—
761C22×C4—91no—
762C22×C4—121no—
763C22×C4—121no—
764C22×C4—182no—
765C22×C4—182no—
766C22×C4—182no—
767C22×C4—361no—
768C22×C4—361no—
769C22×C4—361no—
770C22×C4—361no—
771C22×C4—361no—
772C22×C4—361no—
773C22×C4C2×D3211yescharacteristic
774C22×C4C2×D3211yescharacteristic
775C22×C4C2×D3211yescharacteristic
776C4⋊C4—182no—
777C4⋊C4—182no—
778C22⋊C4—62no—
779C22⋊C4—121no—
780C22⋊C4—121no—
781C22⋊C4—182no—
782C22⋊C4—182no—
783C22⋊C4—182no—
784C22⋊C4—361no—
785C22⋊C4—361no—
786C22⋊C4—361no—
787C22⋊C4—361no—
788C22⋊C4—361no—
789C22⋊C4—361no—
790C42—34no—
791C42—34no—
792C42—62no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—62no—
806C22×C3—121no—
807C22×C3—121no—
808C22×C3—121no—
809C22×C3—121no—
810C22×C3—121no—
811C22×C3—121no—
812C22×C3—121no—
813C22×C3—121no—
814C22×C3C22×C4×D311yescharacteristic
815C22×C3C22×C4×D311yescharacteristic
816C22×C3C22×D1211yescharacteristic
817C22×C3C2×#23511yescharacteristic
818C22×C3C2×D3×D411yescharacteristic
819C22×C3#100411yescharacteristic
820C22×C3#100411yescharacteristic
821C22×C3#100411yescharacteristic
822C22×C3D3×#4111yescharacteristic
823C22×C3#100911yescharacteristic
824C22×C3#100911yescharacteristic
825C22×C3#100911yescharacteristic
826C22×C3#100911yescharacteristic
827C22×C3#100911yescharacteristic
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—64no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—62no—
849C2×D3—62no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—122no—
856C2×D3—122no—
857C2×D3—122no—
858C2×D3—122no—
859C2×D3—122no—
860C2×D3—122no—
861C2×D3—122no—
862C2×D3—122no—
863C2×D3—122no—
864C2×D3—121no—
865C2×D3—121no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—241no—
881C2×D3—241no—
882C2×D3—241no—
883C2×D3—241no—
884C3×C4—22no—
885C3×C4—22no—
886C3×C4—22no—
887C3×C4—22no—
888C3×C4—34no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—41no—
892C3×C4—41no—
893C3×C4—62no—
894C3×C4—62no—
895C3×C4—81no—
896C3×C4—121no—
897C3×C4—121no—
898C3×C4—121no—
899Dic3—22no—
900Dic3—22no—
901Dic3—41no—
902Dic3—41no—
903Dic3—41no—
904Dic3—122no—
905Dic3—121no—
906Dic3—121no—
907Dic3—121no—
908Dic3—121no—
909Dic3—241no—
910Dic3C4×D1214yes—
911C32#232811yescharacteristic, complemented, Sylow
912C23—32no—
913C23—32no—
914C23—61no—
915C23—61no—
916C23—61no—
917C23—61no—
918C23—61no—
919C23—61no—
920C23—61no—
921C23—61no—
922C23—61no—
923C23—61no—
924C23—61no—
925C23—61no—
926C23—92no—
927C23—92no—
928C23—181no—
929C23—181no—
930C23—181no—
931C23—181no—
932C23—181no—
933C23—181no—
934C23—181no—
935C23—181no—
936C23—181no—
937C23—181no—
938C23—181no—
939C23—181no—
940C23C22×D3211yescharacteristic
941D4—124no—
942D4—188no—
943D4—188no—
944D4—364no—
945D4—364no—
946D4—364no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—32no—
955C2×C4—32no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—124no—
973C2×C4—181no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—364no—
980C2×C4—364no—
981C2×C4—364no—
982C2×C4C4×D3212yes—
983C2×C4D3×D1212yes—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—122no—
992C2×C3—122no—
993C2×C3C2×C4×D1211yescharacteristic
994C2×C3#548611yescharacteristic
995C2×C3#552111yescharacteristic
996C2×C3#552111yescharacteristic
997C2×C3#552511yescharacteristic
998C2×C3#552511yescharacteristic
999C2×C3#553511yescharacteristic
1000C2×C3#553511yescharacteristic
1001C2×C3C4×D3×D411yescharacteristic
1002C2×C3#554511yescharacteristic
1003C2×C3#559211yescharacteristic
1004C2×C3#560711yescharacteristic
1005C2×C3#561511yescharacteristic
1006C2×C3#566311yescharacteristic
1007D3—42no—
1008D3—42no—
1009D3—124no—
1010D3—122no—
1011D3—122no—
1012D3—122no—
1013D3—122no—
1014D3—242no—
1015C22—62no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—62no—
1020C22—62no—
1021C22—121no—
1022C22—121no—
1023C22—121no—
1024C22—121no—
1025C22—121no—
1026C22—121no—
1027C22—121no—
1028C22—121no—
1029C22—182no—
1030C22—182no—
1031C22—182no—
1032C22—182no—
1033C22—182no—
1034C22—182no—
1035C22—361no—
1036C22—361no—
1037C22—361no—
1038C22—361no—
1039C22—361no—
1040C22—361no—
1041C22—361no—
1042C22—361no—
1043C22C2×C4×D3211yescharacteristic
1044C22C2×D3×D1211yescharacteristic
1045C22D3×#23511yescharacteristic
1046C22#6431411yescharacteristic
1047C22#6431411yescharacteristic
1048C22#6431411yescharacteristic
1049C22#6432011yescharacteristic
1050C4—22no—
1051C4—22no—
1052C4—34no—
1053C4—41no—
1054C4—62no—
1055C4—62no—
1056C4—121no—
1057C4—121no—
1058C4—121no—
1059C4—361no—
1060C4—361no—
1061C3—21no—
1062C3#7338911yescharacteristic, complemented
1063C3#7466711yescharacteristic, complemented
1064C2—122no—
1065C2—122no—
1066C2—362no—
1067C2—362no—
1068C2C4×D3×D1211yescharacteristic
1069C2#1059408011yescharacteristic
1070C2#1059418211yescharacteristic
1071C2#1059420611yescharacteristic
1072C2#1059454611yescharacteristic
1073C2#1059460411yescharacteristic
1074C2#1059462811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63911C2
hypercenter#95D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×C4×#626C2semidirect
3. C2×#63880C2semidirect
4. #10592364C2semidirect
5. C3×#4665C2semidirect
6. C3×#4648C2semidirect
7. #10591387C2semidirect
8. #10591383C2semidirect
9. #10591383C2semidirect
10. #10591382C2semidirect
11. #10591380C2semidirect
12. #10591376C2semidirect
13. #10591364C2semidirect
14. #10591275C2semidirect
15. #10591206C2semidirect
45. #63911C4semidirect
84. #4665D3semidirect
86. #4648D3semidirect
98. C2×C4⋊(C3⋊D3)C2×C4semidirect
110. C2×C3×D12C2×C4semidirect
122. C2×#626C2×C4semidirect
123. C2×#626C2×C4semidirect
124. C2×#626C2×C4semidirect
125. C2×#626C2×C4semidirect
139. C3×C4×Dic3C2×C4semidirect
140. C3×C4×Dic3D4semidirect
401. C2×D12C4×D3semidirect
458. C4×Dic3C4×D3semidirect
459. C4×Dic3D12semidirect
911. C32#2328semidirect
1062. C3#73389semidirect
1063. C3#74667semidirect

Maximal subgroups

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

subgroupindex
C2×#639112
C2×C4×#6262
C2×#638802
#105923642
C3×#46652
C3×#46482
#105913872
#105913832
#105913822
#105913802
#105913762
#105913642
#105912752
#105912062
#746673
#733893