Finite Group Databasebeta

← #11803277

Subgroups — #11803277

Order 1152.

1953 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63981C211yesmaximal, characteristic
3C2×#63881C211yesmaximal, characteristic, complemented
4C3×#4957C211yesmaximal, characteristic, complemented
5C3×#4945C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic, complemented
7#10591714C211yesmaximal, characteristic, complemented
8#10591702C211yesmaximal, characteristic, complemented
9#10591387C211yesmaximal, characteristic, complemented
10#10591383C211yesmaximal, characteristic, complemented
11#10591364C211yesmaximal, characteristic, complemented
12#10591290C211yesmaximal, characteristic, complemented
13#10591289C211yesmaximal, characteristic, complemented
14C4×#3722C211yesmaximal, characteristic, complemented
15#10591258C211yesmaximal, characteristic, complemented
16#76429—31nomaximal
17#75826—31nomaximal
18C24×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C22⋊C4×C3⋊D3—24no—
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C3×C4×Dic3C2211yescharacteristic, complemented
38C2×C3×C4×Dic3C2211yescharacteristic, complemented
39#63981C418yescomplemented
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
48C2×Dic32C2211yescharacteristic, complemented
49#63881—24no—
50C3×C3⋊#95C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×#937—31no—
57C2×#893—31no—
58C2×#882—31no—
59C2×#67⋊C4—31no—
60C2×D3×C22⋊C4—31no—
61C2×D3×C22⋊C4—31no—
62C2×D3×C22⋊C4—61no—
63C3×#390—31no—
64C3×#388—31no—
65#5220—31no—
66#4990—31no—
67#4990—31no—
68#4989—31no—
69#4958—31no—
70#4957—31no—
71#4957D311yescharacteristic, complemented
72#4956—31no—
73#4956—31no—
74#4955—31no—
75#4955—31no—
76#4951—31no—
77#4945—31no—
78#4945D311yescharacteristic, complemented
79#4940—31no—
80#4939—31no—
81C4×(C2×D3)⋊C4—31no—
82C4×(C2×D3)⋊C4—31no—
83#4669—31no—
84#4668—31no—
85#4665—31no—
86#4665—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3—22no—
89C23×C3⋊D3—22no—
90C23×C3⋊D3—41no—
91C23×C3⋊D3—41no—
92C23×C3⋊D3—41no—
93C23×C3⋊D3—41no—
94C23×C3⋊D3C2×C414yescomplemented
95C23×C3⋊D3C2311yescharacteristic
96C23×C3⋊D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C4×C3⋊D3—22no—
103C2×C4×C3⋊D3—41no—
104C2×C4×C3⋊D3—41no—
105C2×C4×C3⋊D3—41no—
106C2×C4×C3⋊D3—41no—
107C2×C4×C3⋊D3D414yescomplemented
108C2×C3×#67—41no—
109C2×C3×#67—41no—
110C2×C3×#67C2×C414yescomplemented
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C2×#626—22no—
119C2×#626—22no—
120C2×#626—41no—
121C2×#626—41no—
122C2×#626C2×C414yes—
123C2×#626C2×C414yescomplemented
124C2×D3×Dic3—22no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3—41no—
127C32×C22⋊C4—22no—
128#3757—22no—
129#3752—22no—
130#3752—22no—
131C3×#217—41no—
132C3×#217—41no—
133C3×#217C2×C414yescomplemented
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—41no—
136C3×Dic3⋊C4—22no—
137C3×Dic3⋊C4—41no—
138C3×C4×Dic3—41no—
139C3×C4×Dic3—41no—
140Dic3⋊Dic3—41no—
141#3722—22no—
142#3722—22no—
143#3722—41no—
144#3722—41no—
145#3722C2×C414yescomplemented
146#3722C2×C414yescomplemented
147(C2×D3)⋊Dic3—41no—
148Dic32—22no—
149#2321—91noSylow
150C24×D3—31no—
151C24×D3—31no—
152C24×D3—61no—
153C22×C3×D4—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67C2×D311yescharacteristic
157C23×Dic3—31no—
158C22×D12—31no—
159C22×D12—31no—
160C22×C4×D3—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—61no—
166C22×C4×D3—61no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C22⋊C4—21no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4C2×D311yescharacteristic
176C2×C3×C22⋊C4C2×D311yescharacteristic
177C2×C3×C42—31no—
178C2×C3×C42—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—61no—
183C2×#217C2×D311yescharacteristic
184C2×#217C2×D311yescharacteristic
185C2×#217C2×D311yescharacteristic
186#937—38no—
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—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4—61no—
206C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
207C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
208C2×C4⋊Dic3—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4C2×D311yescharacteristic, complemented
211C2×Dic3⋊C4C2×D311yescharacteristic, complemented
212C2×C4×Dic3—31no—
213C2×C4×Dic3—31no—
214C2×C4×Dic3C2×D311yescharacteristic, complemented
215C2×C4×Dic3C2×D311yescharacteristic, complemented
216#893—64no—
217#882—38no—
218#67⋊C4—64no—
219D3×C22⋊C4—64no—
220D3×C22⋊C4—64no—
221D3×C22⋊C4—68no—
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⋊#95—31no—
232C3⋊#95C2×D311yescharacteristic, complemented
233C3⋊#95C2×D311yescharacteristic, complemented
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32C22×C412yes—
241C23×C32C2411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—28no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—44no—
254C22×C3⋊D3—44no—
255C22×C3⋊D3—44no—
256C22×C3⋊D3—44no—
257C22×C3⋊D3—44no—
258C22×C3⋊D3—44no—
259C22×C3⋊D3C22×C412yes—
260C22×C3⋊D3C22×C412yes—
261C22×C3⋊D3C2×D412yes—
262C22×C3⋊D3#4112yes—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3C22×C412yes—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4C2×D412yes—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3C2×D412yes—
282C4×C3⋊D3—44no—
283C4×C3⋊D3—44no—
284C3×#67—44no—
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×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3C22×C412yes—
304C2×C3×Dic3C22×C412yes—
305C2×C3×Dic3C22×C412yes—
306#626—28no—
307#626—44no—
308D3×Dic3—44no—
309C2×#120—91no—
310C2×C4×D4—91no—
311C22×C22⋊C4—91no—
312#390—31no—
313#390—91no—
314#388—31no—
315#388—91no—
316#388—91no—
317#388—91no—
318#386—91no—
319#386—91no—
320#386—91no—
321#385—91no—
322#379—91no—
323C4×C22⋊C4—91no—
324C24×C3—21no—
325C24×C3—31no—
326C24×C3C22×D311yescharacteristic
327C24×C3C22×D311yescharacteristic
328C23×D3—31no—
329C23×D3—31no—
330C23×D3—31no—
331C23×D3—31no—
332C23×D3—34no—
333C23×D3—34no—
334C23×D3—61no—
335C23×D3—64no—
336C23×D3—61no—
337C23×D3—62no—
338C23×D3—62no—
339C23×D3—62no—
340C23×D3—62no—
341C23×D3—64no—
342C23×D3—64no—
343C23×D3—121no—
344C23×D3—121no—
345C23×D3—121no—
346C23×D3—121no—
347C23×D3—121no—
348C23×D3—121no—
349C23×D3—121no—
350C23×D3—121no—
351C23×D3—122no—
352C23×D3—122no—
353C23×D3—122no—
354C23×D3—122no—
355C23×D3C22×D311yescharacteristic
356C2×C3×D4—34no—
357C2×C3×D4—121no—
358C2×C3×D4—121no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C2×#67—34no—
373C2×#67—34no—
374C2×#67—41no—
375C2×#67—41no—
376C2×#67—62no—
377C2×#67—62no—
378C2×#67—121no—
379C2×#67—121no—
380C2×#67C4×D314yescomplemented
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—62no—
388C22×Dic3—121no—
389C22×Dic3—121no—
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C2×D12—34no—
398C2×D12—34no—
399C2×D12—62no—
400C2×D12—62no—
401C2×D12—121no—
402C2×D12—121no—
403C2×C4×D3—34no—
404C2×C4×D3—34no—
405C2×C4×D3—64no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—64no—
410C2×C4×D3—121no—
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—121no—
420C2×C4×D3—122no—
421C2×C4×D3—122no—
422C2×C4×D3—122no—
423C2×C4×D3—122no—
424C3×C4⋊C4—62no—
425C3×C4⋊C4—121no—
426C3×C22⋊C4—24no—
427C3×C22⋊C4—22no—
428C3×C22⋊C4—22no—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—62no—
431C3×C22⋊C4—121no—
432C3×C22⋊C4—121no—
433C3×C22⋊C4—121no—
434C3×C42—121no—
435C3×C42—121no—
436#217—41no—
437#217—41no—
438#217—62no—
439#217—62no—
440#217—64no—
441#217—121no—
442#217C4×D314yescomplemented
443(C2×D3)⋊C4—22no—
444(C2×D3)⋊C4—34no—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—41no—
449(C2×D3)⋊C4—62no—
450(C2×D3)⋊C4—62no—
451(C2×D3)⋊C4—62no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—62no—
455(C2×D3)⋊C4—64no—
456(C2×D3)⋊C4—64no—
457(C2×D3)⋊C4—62no—
458(C2×D3)⋊C4—62no—
459(C2×D3)⋊C4—121no—
460(C2×D3)⋊C4—121no—
461(C2×D3)⋊C4—121no—
462(C2×D3)⋊C4—121no—
463(C2×D3)⋊C4—121no—
464C4⋊Dic3—121no—
465Dic3⋊C4—22no—
466Dic3⋊C4—41no—
467Dic3⋊C4—121no—
468C4×Dic3—41no—
469C4×Dic3—41no—
470C4×Dic3—62no—
471C4×Dic3—62no—
472C22×C32—22no—
473C22×C32—22no—
474C22×C32—22no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32C23×C411yescharacteristic
480C22×C32C22×D411yescharacteristic
481C22×C32C2×#4111yescharacteristic
482C22×C32H(5,𝔽2)11yescharacteristic
483C22×C32H(5,𝔽2)11yescharacteristic
484C22×C32H(5,𝔽2)11yescharacteristic
485C22×C32H(5,𝔽2)11yescharacteristic
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—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—416no—
496C2×C3⋊D3—41no—
497C2×C3⋊D3—41no—
498C2×C3⋊D3—41no—
499C2×C3⋊D3—41no—
500C2×C3⋊D3C4×D414yes—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—41no—
505C2×C3×D3—41no—
506C2×C3×D3—41no—
507C2×C3×D3—41no—
508C32×C4—22no—
509C32×C4—41no—
510C3⋊Dic3—22no—
511C3⋊Dic3—41no—
512C3×Dic3—22no—
513C3×Dic3—22no—
514C3×Dic3—22no—
515C3×Dic3—41no—
516C3×Dic3—41no—
517C3×Dic3—41no—
518C3×Dic3—41no—
519C25—91no—
520C22×D4—31no—
521C22×D4—91no—
522C22×D4—91no—
523C23×C4—91no—
524C23×C4—91no—
525C23×C4—91no—
526#120—98no—
527C4×D4—184no—
528C2×C4⋊C4—31no—
529C2×C4⋊C4—31no—
530C2×C4⋊C4—91no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4—91no—
543C2×C22⋊C4—91no—
544C2×C22⋊C4—91no—
545C2×C22⋊C4—91no—
546C2×C22⋊C4—184no—
547C2×C22⋊C4D3211yescharacteristic
548C2×C42—31no—
549C2×C42—31no—
550C2×C42—91no—
551#95—31no—
552#95—31no—
553#95—91no—
554#95—91no—
555#95—91no—
556#95—91no—
557C23×C3—22no—
558C23×C3—22no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—22no—
573C23×C3—32no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3C2×C4×D312yes—
585C23×C3C2×C4×D312yes—
586C23×C3C23×D311yescharacteristic
587C23×C3C23×D311yescharacteristic
588C22×D3—21no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—32no—
595C22×D3—32no—
596C22×D3—32no—
597C22×D3—32no—
598C22×D3—32no—
599C22×D3—32no—
600C22×D3—32no—
601C22×D3—32no—
602C22×D3—62no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—62no—
606C22×D3—68no—
607C22×D3—68no—
608C22×D3—62no—
609C22×D3—62no—
610C22×D3—62no—
611C22×D3—62no—
612C22×D3—61no—
613C22×D3—61no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—62no—
621C22×D3—616no—
622C22×D3—62no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—61no—
627C22×D3—61no—
628C22×D3—61no—
629C22×D3—61no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—61no—
633C22×D3—61no—
634C22×D3—61no—
635C22×D3—121no—
636C22×D3—121no—
637C22×D3—121no—
638C22×D3—121no—
639C22×D3—124no—
640C22×D3—124no—
641C22×D3—124no—
642C22×D3—124no—
643C22×D3—128no—
644C22×D3—128no—
645C22×D3—128no—
646C22×D3—128no—
647C22×D3—128no—
648C22×D3—128no—
649C22×D3—124no—
650C22×D3—124no—
651C22×D3—124no—
652C22×D3—124no—
653C22×D3—124no—
654C22×D3—124no—
655C22×D3—124no—
656C22×D3—124no—
657C22×D3C2×C4×D312yes—
658C3×D4—124no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—22no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—22no—
671C2×C3×C4—32no—
672C2×C3×C4—32no—
673C2×C3×C4—32no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4D3×D412yes—
697C2×C3×C4D3×D412yes—
698#67—44no—
699#67—68no—
700#67—124no—
701C2×Dic3—21no—
702C2×Dic3—21no—
703C2×Dic3—21no—
704C2×Dic3—21no—
705C2×Dic3—21no—
706C2×Dic3—21no—
707C2×Dic3—21no—
708C2×Dic3—21no—
709C2×Dic3—21no—
710C2×Dic3—21no—
711C2×Dic3—21no—
712C2×Dic3—21no—
713C2×Dic3—21no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—32no—
720C2×Dic3—32no—
721C2×Dic3—62no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—62no—
727C2×Dic3—61no—
728C2×Dic3—61no—
729C2×Dic3—61no—
730C2×Dic3—61no—
731C2×Dic3—61no—
732C2×Dic3—61no—
733C2×Dic3—121no—
734C2×Dic3—121no—
735C2×Dic3—121no—
736C2×Dic3—121no—
737C2×Dic3—124no—
738C2×Dic3C2×C4×D312yes—
739C2×Dic3C2×C4×D312yes—
740C2×Dic3C2×C4×D312yes—
741D12—68no—
742D12—124no—
743C4×D3—124no—
744C4×D3—124no—
745C4×D3—124no—
746C4×D3—128no—
747C4×D3—128no—
748C4×D3—124no—
749C4×D3—124no—
750C2×C32—42no—
751C2×C32C2×C4×D411yescharacteristic
752C2×C32#51811yescharacteristic
753C2×C32#51811yescharacteristic
754C2×C32#53411yescharacteristic
755C2×C32#53511yescharacteristic
756C2×C32#53811yescharacteristic
757C2×C32#53811yescharacteristic
758C3⋊D3—24no—
759C3⋊D3—42no—
760C3×D3—42no—
761C24—31no—
762C24—91no—
763C24—91no—
764C24—94no—
765C24—182no—
766C24—182no—
767C24—361no—
768C24—361no—
769C24—361no—
770C24—361no—
771C24C2×D3211yescharacteristic
772C2×D4—34no—
773C2×D4—94no—
774C2×D4—94no—
775C2×D4—121no—
776C2×D4—121no—
777C2×D4—182no—
778C2×D4—182no—
779C2×D4—361no—
780C2×D4—361no—
781C22×C4—31no—
782C22×C4—31no—
783C22×C4—31no—
784C22×C4—31no—
785C22×C4—31no—
786C22×C4—31no—
787C22×C4—31no—
788C22×C4—91no—
789C22×C4—94no—
790C22×C4—91no—
791C22×C4—182no—
792C22×C4—182no—
793C22×C4—361no—
794C22×C4—361no—
795C22×C4—361no—
796C22×C4—361no—
797C22×C4—361no—
798C22×C4—361no—
799C22×C4C2×D3211yescharacteristic
800C22×C4C2×D3211yescharacteristic
801C4⋊C4—62no—
802C4⋊C4—121no—
803C4⋊C4—361no—
804C22⋊C4—22no—
805C22⋊C4—34no—
806C22⋊C4—62no—
807C22⋊C4—94no—
808C22⋊C4—94no—
809C22⋊C4—121no—
810C22⋊C4—121no—
811C22⋊C4—121no—
812C22⋊C4—182no—
813C22⋊C4—182no—
814C22⋊C4—182no—
815C22⋊C4—182no—
816C22⋊C4—182no—
817C22⋊C4—361no—
818C22⋊C4—361no—
819C22⋊C4—361no—
820C42—121no—
821C42—121no—
822C42—182no—
823C22×C3—24no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3—121no—
857C22×C3—121no—
858C22×C3C22×C4×D311yescharacteristic
859C22×C3C22×C4×D311yescharacteristic
860C22×C3C2×D3×D411yescharacteristic
861C22×C3C2×D3×D411yescharacteristic
862C22×C3#100411yescharacteristic
863C22×C3#100411yescharacteristic
864C22×C3#100411yescharacteristic
865C22×C3#100411yescharacteristic
866C22×C3D3×#4111yescharacteristic
867C22×C3D3×#4111yescharacteristic
868C22×C3#100911yescharacteristic
869C22×C3#100911yescharacteristic
870C22×C3#100911yescharacteristic
871C22×C3#100911yescharacteristic
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—34no—
876C2×D3—34no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—64no—
882C2×D3—64no—
883C2×D3—64no—
884C2×D3—64no—
885C2×D3—64no—
886C2×D3—64no—
887C2×D3—64no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—62no—
893C2×D3—62no—
894C2×D3—62no—
895C2×D3—62no—
896C2×D3—62no—
897C2×D3—62no—
898C2×D3—62no—
899C2×D3—62no—
900C2×D3—64no—
901C2×D3—62no—
902C2×D3—62no—
903C2×D3—62no—
904C2×D3—62no—
905C2×D3—62no—
906C2×D3—62no—
907C2×D3—122no—
908C2×D3—122no—
909C2×D3—1232no—
910C2×D3—1216no—
911C2×D3—1216no—
912C2×D3—122no—
913C2×D3—122no—
914C2×D3—122no—
915C2×D3—122no—
916C2×D3—121no—
917C2×D3—121no—
918C2×D3—121no—
919C2×D3—121no—
920C2×D3—121no—
921C2×D3—121no—
922C2×D3—121no—
923C2×D3—121no—
924C3×C4—22no—
925C3×C4—22no—
926C3×C4—42no—
927C3×C4—42no—
928C3×C4—41no—
929C3×C4—41no—
930C3×C4—62no—
931C3×C4—62no—
932C3×C4—62no—
933C3×C4—121no—
934C3×C4—121no—
935C3×C4—121no—
936C3×C4—121no—
937Dic3—22no—
938Dic3—22no—
939Dic3—22no—
940Dic3—41no—
941Dic3—41no—
942Dic3—41no—
943Dic3—41no—
944Dic3—62no—
945Dic3—62no—
946Dic3—122no—
947Dic3—122no—
948Dic3—121no—
949Dic3—121no—
950C32#232111yescharacteristic, complemented, Sylow
951C23—21no—
952C23—21no—
953C23—21no—
954C23—21no—
955C23—21no—
956C23—21no—
957C23—32no—
958C23—61no—
959C23—61no—
960C23—61no—
961C23—61no—
962C23—61no—
963C23—61no—
964C23—92no—
965C23—92no—
966C23—92no—
967C23—92no—
968C23—188no—
969C23—181no—
970C23—181no—
971C23—181no—
972C23—181no—
973C23—181no—
974C23—181no—
975C23—181no—
976C23—181no—
977C23—181no—
978C23—181no—
979C23—364no—
980C23—364no—
981C23—364no—
982C23—364no—
983C23—364no—
984C23—364no—
985C23C4×D3212yes—
986C23C22×D3211yescharacteristic
987D4—124no—
988D4—188no—
989D4—364no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—32no—
996C2×C4—32no—
997C2×C4—32no—
998C2×C4—61no—
999C2×C4—61no—
1000C2×C4—61no—
1001C2×C4—61no—
1002C2×C4—61no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
1006C2×C4—61no—
1007C2×C4—61no—
1008C2×C4—61no—
1009C2×C4—61no—
1010C2×C4—61no—
1011C2×C4—61no—
1012C2×C4—61no—
1013C2×C4—61no—
1014C2×C4—61no—
1015C2×C4—61no—
1016C2×C4—92no—
1017C2×C4—181no—
1018C2×C4—181no—
1019C2×C4—181no—
1020C2×C4—181no—
1021C2×C4—181no—
1022C2×C4—364no—
1023C2×C4—364no—
1024C2×C4—364no—
1025C2×C4#381112yes—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—44no—
1034C2×C3—42no—
1035C2×C3—42no—
1036C2×C3—122no—
1037C2×C3#548611yescharacteristic
1038C2×C3#552111yescharacteristic
1039C2×C3C4×D3×D411yescharacteristic
1040C2×C3C4×D3×D411yescharacteristic
1041C2×C3#554511yescharacteristic
1042C2×C3#554511yescharacteristic
1043C2×C3#560511yescharacteristic
1044C2×C3#560511yescharacteristic
1045C2×C3#561311yescharacteristic
1046C2×C3#565711yescharacteristic
1047C2×C3#567411yescharacteristic
1048C2×C3#567811yescharacteristic
1049C2×C3#570411yescharacteristic
1050C2×C3#571511yescharacteristic
1051D3—42no—
1052D3—68no—
1053D3—64no—
1054D3—64no—
1055D3—124no—
1056D3—122no—
1057D3—122no—
1058C22—22no—
1059C22—22no—
1060C22—22no—
1061C22—41no—
1062C22—41no—
1063C22—41no—
1064C22—41no—
1065C22—62no—
1066C22—62no—
1067C22—62no—
1068C22—94no—
1069C22—121no—
1070C22—121no—
1071C22—121no—
1072C22—121no—
1073C22—182no—
1074C22—182no—
1075C22—182no—
1076C22—182no—
1077C22—182no—
1078C22—182no—
1079C22—182no—
1080C22—182no—
1081C22—182no—
1082C22—3616no—
1083C22—361no—
1084C22—361no—
1085C22—361no—
1086C22—361no—
1087C22C2×C4×D3211yescharacteristic
1088C22#6430611yescharacteristic
1089C22#6431411yescharacteristic
1090C22#6431411yescharacteristic
1091C22#6431411yescharacteristic
1092C22#6431411yescharacteristic
1093C22C2×#381111yescharacteristic
1094C4—22no—
1095C4—41no—
1096C4—62no—
1097C4—62no—
1098C4—62no—
1099C4—121no—
1100C4—121no—
1101C4—121no—
1102C4—121no—
1103C4—182no—
1104C4—361no—
1105C3—21no—
1106C3#7582611yescharacteristic, complemented
1107C3#7642911yescharacteristic, complemented
1108C2—42no—
1109C2—122no—
1110C2—184no—
1111C2—362no—
1112C2#1059418211yescharacteristic
1113C2#1059422511yescharacteristic
1114C2#1059422611yescharacteristic
1115C2#1059425611yescharacteristic
1116C2C4×#381111yescharacteristic
1117C2#1059516811yescharacteristic
1118C2#1059530811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63981C2
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
1. C2×C22⋊C4×C3⋊D3C2semidirect
3. C2×#63881C2semidirect
4. C3×#4957C2semidirect
5. C3×#4945C2semidirect
6. #10591721C2semidirect
7. #10591714C2semidirect
8. #10591702C2semidirect
9. #10591387C2semidirect
10. #10591383C2semidirect
11. #10591364C2semidirect
12. #10591290C2semidirect
13. #10591289C2semidirect
14. C4×#3722C2semidirect
15. #10591258C2semidirect
24. C22×D3×Dic3C22semidirect
33. C2×C3×(C2×D3)⋊C4C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×C4×Dic3C22semidirect
38. C2×C3×C4×Dic3C22semidirect
39. #63981C4semidirect
40. C2×Dic3⋊Dic3C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
48. C2×Dic32C22semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
71. #4957D3semidirect
78. #4945D3semidirect
94. C23×C3⋊D3C2×C4semidirect
107. C2×C4×C3⋊D3D4semidirect
110. C2×C3×#67C2×C4semidirect
123. C2×#626C2×C4semidirect
133. C3×#217C2×C4semidirect
145. #3722C2×C4semidirect
146. #3722C2×C4semidirect
206. C2×(C2×D3)⋊C4C2×D3semidirect
207. C2×(C2×D3)⋊C4C2×D3semidirect
210. C2×Dic3⋊C4C2×D3semidirect
211. C2×Dic3⋊C4C2×D3semidirect
214. C2×C4×Dic3C2×D3semidirect
215. C2×C4×Dic3C2×D3semidirect
232. C3⋊#95C2×D3semidirect
233. C3⋊#95C2×D3semidirect
380. C2×#67C4×D3semidirect
442. #217C4×D3semidirect
950. C32#2321semidirect
1106. C3#75826semidirect
1107. C3#76429semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
C2×#639812
C2×#638812
C3×#49572
C3×#49452
#105917212
#105917142
#105917022
#105913872
#105913832
#105913642
#105912902
#105912892
C4×#37222
#105912582
#764293
#758263