Finite Group Databasebeta

← #11803280

Subgroups — #11803280

Order 1152.

1947 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64091C211yesmaximal, characteristic
2C2×#63974C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4C3×#4951C211yesmaximal, characteristic, complemented
5C3×#4951C211yesmaximal, characteristic, complemented
6#10591722C211yesmaximal, characteristic, complemented
7#10591714C211yesmaximal, characteristic, complemented
8#10591704C211yesmaximal, characteristic, complemented
9#10591380C211yesmaximal, characteristic, complemented
10#10591380C211yesmaximal, characteristic, complemented
11#10591378C211yesmaximal, characteristic, complemented
12#10591320C211yesmaximal, characteristic, complemented
13#10591266C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591202C211yesmaximal, characteristic, complemented
16#75827—31nomaximal
17#75826—31nomaximal
18C24×C3⋊D3C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28#64091C418yescomplemented
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
34C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
35C2×C3×C4×Dic3C2211yescharacteristic, complemented
36C2×C3×C4×Dic3C2211yescharacteristic, complemented
37#63974—24no—
38C2×#3724C2211yescharacteristic, complemented
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic, complemented
46C2×#3722C2211yescharacteristic, complemented
47C2×#3722C2211yescharacteristic, complemented
48C2×Dic32C2211yescharacteristic, complemented
49#63894—24no—
50C3×C3⋊#95C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×#893—31no—
57C2×#882—31no—
58C2×#882—31no—
59C2×#882—61no—
60C2×D3×C22⋊C4—31no—
61C2×D3×C22⋊C4—31no—
62C2×C4×D12—31no—
63C3×#388—31no—
64C3×#388—31no—
65#4990—31no—
66#4989—31no—
67#4988—31no—
68#4957—31no—
69#4957—31no—
70#4956—31no—
71#4956—31no—
72#4955—31no—
73#4955—31no—
74#4951D311yescharacteristic, complemented
75#4951D311yescharacteristic, complemented
76#4940—31no—
77#4939—31no—
78C4×(C2×D3)⋊C4—31no—
79#4670—31no—
80#4669—31no—
81#4668—31no—
82#4666—31no—
83#4665—31no—
84#4665—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
100C2×#638—41no—
101C2×#638—41no—
102C2×#638C2×C414yescomplemented
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C4⋊(C3⋊D3)—22no—
105C2×C4⋊(C3⋊D3)—22no—
106C2×C4⋊(C3⋊D3)—41no—
107C2×C4⋊(C3⋊D3)—41no—
108C2×C4⋊(C3⋊D3)C2×C414yes—
109C2×C4⋊(C3⋊D3)C2×C414yescomplemented
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C2×#624—22no—
119C2×#624—22no—
120C2×#624—41no—
121C2×#624—41no—
122C2×#624—41no—
123C2×#624—41no—
124C2×#624—41no—
125C2×#624—41no—
126C2×#624D414yescomplemented
127C32×C22⋊C4C2×C414yescomplemented
128#3752C2×C414yescomplemented
129#3752C2×C414yescomplemented
130C3×#217—22no—
131C3×#217—22no—
132C3×#217—41no—
133C3×#217—41no—
134C3×C4⋊Dic3—22no—
135C3×C4⋊Dic3—41no—
136C3×C4×Dic3—22no—
137C3×C4×Dic3—41no—
138#3724—41no—
139#3722—22no—
140#3722—22no—
141#3722—22no—
142#3722—22no—
143#3722—22no—
144#3722—41no—
145#3722—41no—
146#3722—41no—
147#3722—41no—
148Dic32—41no—
149#2321—91noSylow
150C24×D3—31no—
151C24×D3—31no—
152C24×D3—61no—
153C22×#67—31no—
154C22×#67—31no—
155C22×#67—61no—
156C22×D12—31no—
157C22×D12—31no—
158C22×D12—31no—
159C22×D12—31no—
160C22×D12—61no—
161C22×D12—61no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—31no—
167C22×C4×D3—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C22⋊C4—21no—
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×#217C2×D311yescharacteristic
180C2×#217C2×D311yescharacteristic
181C2×#217C2×D311yescharacteristic
182C2×#217C2×D311yescharacteristic
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—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—31no—
205C2×(C2×D3)⋊C4—61no—
206C2×(C2×D3)⋊C4—61no—
207C2×C4⋊Dic3C2×D311yescharacteristic, complemented
208C2×C4⋊Dic3C2×D311yescharacteristic, complemented
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3C2×D311yescharacteristic, complemented
214C2×C4×Dic3C2×D311yescharacteristic, complemented
215#893—64no—
216#882—38no—
217#882—38no—
218#882—68no—
219D3×C22⋊C4—64no—
220D3×C22⋊C4—64no—
221C4×D12—64no—
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⋊#95C2×D311yescharacteristic, complemented
231C3⋊#95C2×D311yescharacteristic, complemented
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—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⋊D3C22×C412yes—
268C22×C3⋊D3C2×D412yes—
269C22×C3⋊D3#4112yes—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4C22×C412yes—
275C2×C32×C4C22×C412yes—
276#638—44no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3C22×C412yes—
280C4⋊(C3⋊D3)—28no—
281C4⋊(C3⋊D3)—44no—
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×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×Dic3—21no—
304C2×C3×Dic3C2×D412yes—
305C2×C3×Dic3C2×D412yes—
306#624—44no—
307#624—44no—
308#624—44no—
309C2×#120—91no—
310C2×C4×D4—91no—
311C22×C22⋊C4—91no—
312#390—91no—
313#390—91no—
314#388—31no—
315#388—31no—
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×C3C22×D311yescharacteristic
326C24×C3C22×D311yescharacteristic
327C23×D3—31no—
328C23×D3—31no—
329C23×D3—31no—
330C23×D3—31no—
331C23×D3—31no—
332C23×D3—31no—
333C23×D3—34no—
334C23×D3—34no—
335C23×D3—61no—
336C23×D3—61no—
337C23×D3—64no—
338C23×D3—61no—
339C23×D3—62no—
340C23×D3—62no—
341C23×D3—62no—
342C23×D3—62no—
343C23×D3—122no—
344C23×D3—122no—
345C23×D3—121no—
346C23×D3—121no—
347C23×D3—121no—
348C23×D3—121no—
349C23×D3—121no—
350C23×D3—121no—
351C23×D3—121no—
352C23×D3—121no—
353C23×D3—122no—
354C23×D3—122no—
355C23×D3—122no—
356C23×D3—122no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
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×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C2×#67—34no—
372C2×#67—34no—
373C2×#67—64no—
374C2×#67—121no—
375C2×#67—121no—
376C2×#67—121no—
377C2×#67—121no—
378C2×#67—122no—
379C2×#67—122no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—61no—
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C2×D12—34no—
392C2×D12—34no—
393C2×D12—34no—
394C2×D12—34no—
395C2×D12—64no—
396C2×D12—64no—
397C2×D12—62no—
398C2×D12—62no—
399C2×D12—62no—
400C2×D12—62no—
401C2×D12—122no—
402C2×D12—122no—
403C2×D12—121no—
404C2×D12—121no—
405C2×D12—121no—
406C2×D12—121no—
407C2×D12—122no—
408C2×D12—122no—
409C2×C4×D3—34no—
410C2×C4×D3—34no—
411C2×C4×D3—62no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3—121no—
416C2×C4×D3—121no—
417C2×C4×D3—121no—
418C2×C4×D3—121no—
419C2×C4×D3—121no—
420C2×C4×D3—121no—
421C2×C4×D3—121no—
422C2×C4×D3—121no—
423C2×C4×D3—121no—
424C2×C4×D3—121no—
425C2×C4×D3—121no—
426C2×C4×D3—121no—
427C3×C4⋊C4—62no—
428C3×C4⋊C4—121no—
429C3×C22⋊C4—24no—
430C3×C22⋊C4—62no—
431C3×C22⋊C4—62no—
432C3×C22⋊C4—121no—
433C3×C22⋊C4—121no—
434C3×C22⋊C4C4×D314yescomplemented
435C3×C22⋊C4C4×D314yescomplemented
436C3×C42—62no—
437C3×C42—121no—
438#217—22no—
439#217—22no—
440#217—41no—
441#217—41no—
442(C2×D3)⋊C4—34no—
443(C2×D3)⋊C4—34no—
444(C2×D3)⋊C4—34no—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—64no—
447(C2×D3)⋊C4—64no—
448(C2×D3)⋊C4—62no—
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—62no—
456(C2×D3)⋊C4—62no—
457(C2×D3)⋊C4—62no—
458(C2×D3)⋊C4—121no—
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—
464(C2×D3)⋊C4—121no—
465(C2×D3)⋊C4—121no—
466C4⋊Dic3—22no—
467C4⋊Dic3—41no—
468Dic3⋊C4—121no—
469Dic3⋊C4—121no—
470C4×Dic3—22no—
471C4×Dic3—41no—
472C4×Dic3—121no—
473C4×Dic3—121no—
474C22×C32—22no—
475C22×C32—22no—
476C22×C32—22no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32—41no—
481C22×C32C23×C411yescharacteristic
482C22×C32C22×D411yescharacteristic
483C22×C32C2×#4111yescharacteristic
484C22×C32H(5,𝔽2)11yescharacteristic
485C22×C32H(5,𝔽2)11yescharacteristic
486C22×C32H(5,𝔽2)11yescharacteristic
487C22×C32H(5,𝔽2)11yescharacteristic
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—22no—
496C2×C3⋊D3—22no—
497C2×C3⋊D3—22no—
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—416no—
501C2×C3⋊D3—41no—
502C2×C3⋊D3—41no—
503C2×C3⋊D3—41no—
504C2×C3⋊D3—41no—
505C2×C3⋊D3—41no—
506C2×C3⋊D3—41no—
507C2×C3⋊D3—41no—
508C2×C3⋊D3—41no—
509C2×C3⋊D3C4×D414yes—
510C32×C4—22no—
511C32×C4—22no—
512C3⋊Dic3—22no—
513C3×Dic3—22no—
514C3×Dic3—22no—
515C3×Dic3—41no—
516C3×Dic3—41no—
517C3×Dic3—41no—
518C3×Dic3—41no—
519C3×Dic3—41no—
520C3×Dic3—41no—
521C25—91no—
522C22×D4—91no—
523C22×D4—91no—
524C22×D4—91no—
525C23×C4—91no—
526C23×C4—91no—
527C23×C4—91no—
528#120—98no—
529C4×D4—184no—
530C2×C4⋊C4—31no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—91no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
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—91no—
547C2×C22⋊C4—91no—
548C2×C22⋊C4—184no—
549C2×C22⋊C4D3211yescharacteristic
550C2×C42—31no—
551C2×C42—31no—
552C2×C42—91no—
553#95—31no—
554#95—31no—
555#95—31no—
556#95—31no—
557#95—91no—
558#95—91no—
559C23×C3—22no—
560C23×C3—22no—
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—21no—
573C23×C3—21no—
574C23×C3—22no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3C2×C4×D312yes—
580C23×C3C2×C4×D312yes—
581C23×C3C23×D311yescharacteristic
582C23×C3C23×D311yescharacteristic
583C22×D3—32no—
584C22×D3—32no—
585C22×D3—32no—
586C22×D3—32no—
587C22×D3—32no—
588C22×D3—32no—
589C22×D3—32no—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—32no—
593C22×D3—62no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—68no—
599C22×D3—68no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—62no—
609C22×D3—62no—
610C22×D3—61no—
611C22×D3—61no—
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—61no—
621C22×D3—61no—
622C22×D3—61no—
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—128no—
635C22×D3—121no—
636C22×D3—121no—
637C22×D3—121no—
638C22×D3—121no—
639C22×D3—121no—
640C22×D3—121no—
641C22×D3—121no—
642C22×D3—121no—
643C22×D3—121no—
644C22×D3—121no—
645C22×D3—121no—
646C22×D3—121no—
647C22×D3—121no—
648C22×D3—121no—
649C22×D3—124no—
650C22×D3—124no—
651C22×D3—124no—
652C22×D3—124no—
653C22×D3—128no—
654C22×D3—124no—
655C22×D3—124no—
656C22×D3—124no—
657C22×D3—124no—
658C22×D3—124no—
659C22×D3—124no—
660C22×D3—124no—
661C22×D3—124no—
662C22×D3—128no—
663C22×D3—128no—
664C22×D3—128no—
665C22×D3—128no—
666C22×D3—128no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—32no—
678C2×C3×C4—32no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
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×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4C2×C4×D312yes—
706C2×C3×C4C2×C4×D312yes—
707C2×C3×C4C2×C4×D312yes—
708C2×C3×C4C2×C4×D312yes—
709#67—124no—
710#67—124no—
711#67—128no—
712C2×Dic3—21no—
713C2×Dic3—21no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—21no—
721C2×Dic3—21no—
722C2×Dic3—21no—
723C2×Dic3—21no—
724C2×Dic3—21no—
725C2×Dic3—21no—
726C2×Dic3—21no—
727C2×Dic3—21no—
728C2×Dic3—21no—
729C2×Dic3—21no—
730C2×Dic3—21no—
731C2×Dic3—21no—
732C2×Dic3—21no—
733C2×Dic3—21no—
734C2×Dic3—32no—
735C2×Dic3—32no—
736C2×Dic3—62no—
737C2×Dic3—61no—
738C2×Dic3—61no—
739C2×Dic3—61no—
740C2×Dic3—61no—
741C2×Dic3—121no—
742C2×Dic3—121no—
743C2×Dic3D3×D412yes—
744C2×Dic3D3×D412yes—
745D12—68no—
746D12—68no—
747D12—128no—
748D12—124no—
749D12—124no—
750D12—128no—
751C4×D3—124no—
752C4×D3—124no—
753C4×D3—124no—
754C4×D3—124no—
755C4×D3—124no—
756C4×D3—124no—
757C2×C32—42no—
758C2×C32C2×C4×D411yescharacteristic
759C2×C32#51811yescharacteristic
760C2×C32#51811yescharacteristic
761C2×C32#53411yescharacteristic
762C2×C32#53511yescharacteristic
763C2×C32#53811yescharacteristic
764C2×C32#53811yescharacteristic
765C3⋊D3—24no—
766C3⋊D3—42no—
767C3⋊D3—42no—
768C24—91no—
769C24—91no—
770C24—91no—
771C24—94no—
772C24—182no—
773C24—182no—
774C24—361no—
775C24—361no—
776C24—361no—
777C24—361no—
778C24C2×D3211yescharacteristic
779C2×D4—94no—
780C2×D4—94no—
781C2×D4—94no—
782C2×D4—182no—
783C2×D4—182no—
784C2×D4—361no—
785C2×D4—361no—
786C2×D4—361no—
787C2×D4—361no—
788C22×C4—31no—
789C22×C4—31no—
790C22×C4—31no—
791C22×C4—31no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—94no—
797C22×C4—91no—
798C22×C4—182no—
799C22×C4—182no—
800C22×C4—361no—
801C22×C4—361no—
802C22×C4—361no—
803C22×C4—361no—
804C22×C4—361no—
805C22×C4—361no—
806C22×C4C2×D3211yescharacteristic
807C22×C4C2×D3211yescharacteristic
808C4⋊C4—62no—
809C4⋊C4—121no—
810C4⋊C4—361no—
811C22⋊C4—62no—
812C22⋊C4—62no—
813C22⋊C4—94no—
814C22⋊C4—94no—
815C22⋊C4—121no—
816C22⋊C4—121no—
817C22⋊C4—182no—
818C22⋊C4—182no—
819C22⋊C4—182no—
820C22⋊C4—182no—
821C22⋊C4—182no—
822C22⋊C4—361no—
823C22⋊C4—361no—
824C22⋊C4—361no—
825C22⋊C4—361no—
826C22⋊C4#62414yescomplemented
827C42—62no—
828C42—121no—
829C42—361no—
830C22×C3—24no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—41no—
854C22×C3—41no—
855C22×C3—41no—
856C22×C3—41no—
857C22×C3—41no—
858C22×C3C22×C4×D311yescharacteristic
859C22×C3C22×C4×D311yescharacteristic
860C22×C3C2×D3×D411yescharacteristic
861C22×C3C2×D3×D411yescharacteristic
862C22×C3#100411yescharacteristic
863C22×C3#100411yescharacteristic
864C22×C3D3×#4111yescharacteristic
865C22×C3D3×#4111yescharacteristic
866C22×C3#100911yescharacteristic
867C22×C3#100911yescharacteristic
868C22×C3#100911yescharacteristic
869C22×C3#100911yescharacteristic
870C22×C3#100911yescharacteristic
871C22×C3#100911yescharacteristic
872C2×D3—34no—
873C2×D3—34no—
874C2×D3—64no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—62no—
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—122no—
901C2×D3—122no—
902C2×D3—122no—
903C2×D3—122no—
904C2×D3—122no—
905C2×D3—122no—
906C2×D3—122no—
907C2×D3—122no—
908C2×D3—122no—
909C2×D3—122no—
910C2×D3—122no—
911C2×D3—1216no—
912C2×D3—1216no—
913C2×D3—122no—
914C2×D3—122no—
915C2×D3—122no—
916C2×D3—122no—
917C2×D3—1232no—
918C2×D3—121no—
919C2×D3—121no—
920C2×D3—121no—
921C2×D3—121no—
922C2×D3—121no—
923C2×D3—121no—
924C2×D3—121no—
925C2×D3—121no—
926C2×D3—121no—
927C2×D3—121no—
928C2×D3—121no—
929C2×D3—121no—
930C2×D3—121no—
931C2×D3—121no—
932C2×D3—121no—
933C2×D3—121no—
934C2×D3—241no—
935C2×D3—241no—
936C2×D3—241no—
937C2×D3—241no—
938C3×C4—22no—
939C3×C4—22no—
940C3×C4—22no—
941C3×C4—22no—
942C3×C4—42no—
943C3×C4—42no—
944C3×C4—62no—
945C3×C4—62no—
946C3×C4—121no—
947C3×C4—121no—
948C3×C4—121no—
949C3×C4—121no—
950C3×C4—121no—
951C3×C4—121no—
952Dic3—22no—
953Dic3—22no—
954Dic3—41no—
955Dic3—41no—
956Dic3—41no—
957Dic3—41no—
958Dic3—41no—
959Dic3—41no—
960Dic3—62no—
961Dic3—62no—
962Dic3—122no—
963C32#232111yescharacteristic, complemented, Sylow
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—92no—
971C23—92no—
972C23—92no—
973C23—92no—
974C23—92no—
975C23—188no—
976C23—181no—
977C23—181no—
978C23—181no—
979C23—181no—
980C23—181no—
981C23—181no—
982C23—181no—
983C23—181no—
984C23—181no—
985C23—181no—
986C23—181no—
987C23—181no—
988C23—181no—
989C23—181no—
990C23—181no—
991C23—181no—
992C23—364no—
993C23—364no—
994C23—364no—
995C23—364no—
996C23—364no—
997C23—364no—
998C23C2×#62412yes—
999C23C22×D3211yescharacteristic
1000D4—188no—
1001D4—364no—
1002D4—364no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—32no—
1008C2×C4—32no—
1009C2×C4—61no—
1010C2×C4—61no—
1011C2×C4—61no—
1012C2×C4—61no—
1013C2×C4—61no—
1014C2×C4—61no—
1015C2×C4—61no—
1016C2×C4—61no—
1017C2×C4—61no—
1018C2×C4—61no—
1019C2×C4—61no—
1020C2×C4—61no—
1021C2×C4—61no—
1022C2×C4—61no—
1023C2×C4—61no—
1024C2×C4—61no—
1025C2×C4—61no—
1026C2×C4—61no—
1027C2×C4—61no—
1028C2×C4—61no—
1029C2×C4—61no—
1030C2×C4—61no—
1031C2×C4—92no—
1032C2×C4—181no—
1033C2×C4—181no—
1034C2×C4—364no—
1035C2×C4—364no—
1036C2×C4—364no—
1037C2×C4C2×#62412yes—
1038C2×C4C2×#62412yes—
1039C2×C3—21no—
1040C2×C3—21no—
1041C2×C3—21no—
1042C2×C3—21no—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—44no—
1047C2×C3—42no—
1048C2×C3—42no—
1049C2×C3#552111yescharacteristic
1050C2×C3#552111yescharacteristic
1051C2×C3C4×D3×D411yescharacteristic
1052C2×C3C4×D3×D411yescharacteristic
1053C2×C3#554511yescharacteristic
1054C2×C3#554511yescharacteristic
1055C2×C3#560511yescharacteristic
1056C2×C3#560711yescharacteristic
1057C2×C3#565311yescharacteristic
1058C2×C3#565711yescharacteristic
1059C2×C3#567411yescharacteristic
1060C2×C3#567811yescharacteristic
1061C2×C3#570411yescharacteristic
1062C2×C3#570411yescharacteristic
1063D3—64no—
1064D3—64no—
1065D3—124no—
1066D3—124no—
1067D3—122no—
1068D3—122no—
1069D3—122no—
1070D3—122no—
1071D3—242no—
1072C22—22no—
1073C22—22no—
1074C22—22no—
1075C22—41no—
1076C22—41no—
1077C22—41no—
1078C22—41no—
1079C22—94no—
1080C22—182no—
1081C22—182no—
1082C22—182no—
1083C22—182no—
1084C22—182no—
1085C22—182no—
1086C22—182no—
1087C22—182no—
1088C22—182no—
1089C22—182no—
1090C22—182no—
1091C22—182no—
1092C22—3616no—
1093C22—361no—
1094C22—361no—
1095C22—361no—
1096C22—361no—
1097C22—361no—
1098C22—361no—
1099C22—361no—
1100C22—361no—
1101C22#6430811yescharacteristic
1102C22#6430811yescharacteristic
1103C22D32×D411yescharacteristic
1104C22#6431211yescharacteristic
1105C22#6431411yescharacteristic
1106C22#6431411yescharacteristic
1107C22C22×#62411yescharacteristic
1108C4—22no—
1109C4—22no—
1110C4—62no—
1111C4—62no—
1112C4—121no—
1113C4—121no—
1114C4—121no—
1115C4—121no—
1116C4—121no—
1117C4—121no—
1118C4—182no—
1119C3—21no—
1120C3#7582611yescharacteristic, complemented
1121C3#7582711yescharacteristic, complemented
1122C2—42no—
1123C2—184no—
1124C2—362no—
1125C2—362no—
1126C2#1059416211yescharacteristic
1127C2#1059423211yescharacteristic
1128C2#1059426411yescharacteristic
1129C2#1059428711yescharacteristic
1130C2#1059499611yescharacteristic
1131C2D4×#62411yescharacteristic
1132C2#1059522311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#64091C2
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×#63974C2semidirect
3. C2×#63894C2semidirect
4. C3×#4951C2semidirect
5. C3×#4951C2semidirect
6. #10591722C2semidirect
7. #10591714C2semidirect
8. #10591704C2semidirect
9. #10591380C2semidirect
10. #10591380C2semidirect
11. #10591378C2semidirect
12. #10591320C2semidirect
13. #10591266C2semidirect
14. #10591233C2semidirect
15. #10591202C2semidirect
24. C22×#624C22semidirect
28. #64091C4semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C2×C3×C4⋊Dic3C22semidirect
35. C2×C3×C4×Dic3C22semidirect
36. C2×C3×C4×Dic3C22semidirect
38. C2×#3724C22semidirect
45. C2×#3722C22semidirect
46. C2×#3722C22semidirect
47. C2×#3722C22semidirect
48. C2×Dic32C22semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
74. #4951D3semidirect
75. #4951D3semidirect
94. C23×C3⋊D3C2×C4semidirect
102. C2×#638C2×C4semidirect
109. C2×C4⋊(C3⋊D3)C2×C4semidirect
126. C2×#624D4semidirect
127. C32×C22⋊C4C2×C4semidirect
128. #3752C2×C4semidirect
129. #3752C2×C4semidirect
207. C2×C4⋊Dic3C2×D3semidirect
208. C2×C4⋊Dic3C2×D3semidirect
213. C2×C4×Dic3C2×D3semidirect
214. C2×C4×Dic3C2×D3semidirect
230. C3⋊#95C2×D3semidirect
231. C3⋊#95C2×D3semidirect
232. C3⋊#95C2×D3semidirect
233. C3⋊#95C2×D3semidirect
434. C3×C22⋊C4C4×D3semidirect
435. C3×C22⋊C4C4×D3semidirect
826. C22⋊C4#624semidirect
963. C32#2321semidirect
1120. C3#75826semidirect
1121. C3#75827semidirect

Maximal subgroups

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

subgroupindex
C2×#640912
C2×#639742
C2×#638942
C3×#49512
#105917222
#105917142
#105917042
#105913802
#105913782
#105913202
#105912662
#105912332
#105912022
#758273
#758263