Finite Group Databasebeta

← #11859410

Subgroups — #11859410

Order 1152.

1046 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5547C211yesmaximal, characteristic
2C2×#63815C211yesmaximal, characteristic, complemented
3C2×D3×#208C211yesmaximal, characteristic, complemented
4#10592710C211yesmaximal, characteristic, complemented
5C3×#5012C211yesmaximal, characteristic, complemented
6#10591158C211yesmaximal, characteristic, complemented
7#10591156C211yesmaximal, characteristic, complemented
8#10591156C211yesmaximal, characteristic, complemented
9#10591154C211yesmaximal, characteristic, complemented
10#10591151C211yesmaximal, characteristic, complemented
11#10591145C211yesmaximal, characteristic, complemented
12#10590337C211yesmaximal, characteristic, complemented
13#10590330C211yesmaximal, characteristic, complemented
14#10590324C211yesmaximal, characteristic, complemented
15#10590318C211yesmaximal, characteristic, complemented
16#82917—31nomaximal
17#79537—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×#939C411yescharacteristic
24C3×#937C411yescharacteristic
25C3×C4×#67C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic, complemented
29C3×#896C411yescharacteristic
30C3×#894C411yescharacteristic
31C3×#884C411yescharacteristic
32C3×#883C411yescharacteristic
33C3×#882C411yescharacteristic
34C3×#878C411yescharacteristic
35C3×C4×D12C2211yescharacteristic
36C3×#872C2211yescharacteristic
37C2×#3711C2211yescharacteristic
38C2×#3711C2211yescharacteristic
39C2×#3711C2211yescharacteristic
40C2×#3711C2211yescharacteristic
41C2×#3711C2211yescharacteristic, complemented
42#63815—24no—
43D3×#208—24no—
44C2×D3×C3⋊C8C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46C2×D3×C3⋊C8C2211yescharacteristic, complemented
47#63657C2211yescharacteristic
48#63657C2211yescharacteristic, complemented
49C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
50#63630C2211yescharacteristic, complemented
51C3×#830C2211yescharacteristic
52C3×#830C2211yescharacteristic, complemented
53C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
54C3×C4×C3⋊C8C2211yescharacteristic, complemented
55Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63554C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C3×#525—31no—
64C2×#948—31no—
65C22×#208—31no—
66C2×#907—31no—
67C2×D3×M16—31no—
68#5547D311yescharacteristic
69C3×#436—31no—
70#5234—31no—
71#5207—31no—
72#5128—31no—
73#5128—31no—
74#5012—31no—
75#5012—31no—
76#5012—31no—
77#5012D311yescharacteristic, complemented
78#5011—31no—
79#5011—31no—
80#5011—31no—
81#5011—31no—
82#5011—31no—
83#5011—61no—
84#4999—31no—
85#4997—31no—
86#4839—31no—
87#4836—31no—
88#4730—31no—
89#4728—31no—
90#4727—31no—
91#4726—31no—
92#4689—31no—
93#4688—31no—
94C23×C3×D3C2×C411yescharacteristic
95C2×C32×D4C2×C411yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×C3×#67C2×C411yescharacteristic
99C2×C3×#67C2×C411yescharacteristic
100C2×C3×#67C2×C411yescharacteristic
101C2×C3×#67C2×C411yescharacteristic
102C22×C3×Dic3C2×C411yescharacteristic
103C3×#235—22no—
104C3×#235—22no—
105C2×C3×D12C2×C411yescharacteristic
106C2×C3×D12C2×C411yescharacteristic
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3C2×C411yescharacteristic
110C2×C3×C4×D3C2×C411yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6C2×C411yescharacteristic
115C32×C4⋊C4C2×C411yescharacteristic
116C32×C22⋊C4C2×C411yescharacteristic
117C32×C22⋊C4C2×C411yescharacteristic
118C32×C42C2311yescharacteristic
119#3748—22no—
120C2×C3⋊(C3⋊C8)—22no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217C2×C411yescharacteristic
126C3×#217C2×C411yescharacteristic
127C3×(C2×D3)⋊C4C2×C411yescharacteristic
128C3×(C2×D3)⋊C4C2×C411yescharacteristic
129C3×(C2×D3)⋊C4C2×C411yescharacteristic
130C3×(C2×D3)⋊C4C2×C411yescharacteristic
131C3×(C2×D3)⋊C4C2×C411yescharacteristic
132C3×(C2×D3)⋊C4C2×C411yescharacteristic
133C3×C4⋊Dic3C2×C411yescharacteristic
134C3×Dic3⋊C4C2×C411yescharacteristic
135C3×Dic3⋊C4C2×C411yescharacteristic
136C3×Dic3⋊C4C2×C411yescharacteristic
137C3×Dic3⋊C4C2×C411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C3×#208—22no—
140C3×#208—22no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145#3711—22no—
146#3711—22no—
147#3711—22no—
148#3711—22no—
149#3711—22no—
150D3×C3⋊C8—22no—
151D3×C3⋊C8—22no—
152D3×C3⋊C8D414yescomplemented
153#2930—91noSylow
154C2×C3×#41—31no—
155C23×C3×C4—31no—
156C2×#235C2×D311yescharacteristic
157C22×C4×D3C2×D311yescharacteristic
158C2×C3×M16—31no—
159C2×C3×M16—31no—
160C3×#123—31no—
161C3×#123—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×#121—31no—
165C3×#121—31no—
166C3×#120—31no—
167C3×#120—31no—
168C3×C4×D4—21no—
169C3×C4×D4—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172C3×C4×D4C2×D311yescharacteristic
173C3×C4×D4C2×D311yescharacteristic
174C3×#117—31no—
175#948—64no—
176#939Dic311yescharacteristic
177#937Dic311yescharacteristic
178C4×#67C2×D311yescharacteristic
179C4×#67C2×D311yescharacteristic
180C2×#208—31no—
181C2×#208—31no—
182C2×#208—31no—
183C2×#208—31no—
184C2×#208—31no—
185C2×#208—31no—
186C2×#208—31no—
187C2×#208—61no—
188C2×#208—64no—
189C2×#208C2×D311yescharacteristic
190C2×#208C2×D311yescharacteristic, complemented
191C22×C3⋊C8—31no—
192C22×C3⋊C8—31no—
193C22×C3⋊C8—31no—
194C22×C3⋊C8—31no—
195C22×C3⋊C8—31no—
196C22×C3⋊C8—61no—
197#907—64no—
198D3×M16—64no—
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×D3×C8—31no—
205C2×D3×C8—31no—
206C2×D3×C8—31no—
207#896Dic311yescharacteristic
208#894Dic311yescharacteristic
209#884Dic311yescharacteristic
210#883Dic311yescharacteristic
211#882Dic311yescharacteristic
212#878Dic311yescharacteristic
213C4×D12C2×D311yescharacteristic
214#872C2×D311yescharacteristic
215C3×C4⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×C4×C8—31no—
219#830—31no—
220#830—31no—
221#830—31no—
222#830—31no—
223#830—31no—
224#830—31no—
225#830—31no—
226#830—31no—
227#830—61no—
228#830—61no—
229#830C2×D311yescharacteristic
230#830C2×D311yescharacteristic, complemented
231(C2×D3)⋊C8—31no—
232(C2×D3)⋊C8—31no—
233(C2×D3)⋊C8—31no—
234(C2×D3)⋊C8—31no—
235#815—31no—
236Dic3⋊C8—31no—
237Dic3⋊C8—31no—
238C8×Dic3—31no—
239C4⋊(C3⋊C8)—31no—
240C4⋊(C3⋊C8)—31no—
241C4⋊(C3⋊C8)—31no—
242C4⋊(C3⋊C8)—31no—
243C4⋊(C3⋊C8)—61no—
244C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
245#803—31no—
246#803—31no—
247#803—31no—
248#803—61no—
249C4×C3⋊C8—31no—
250C4×C3⋊C8C2×D311yescharacteristic, complemented
251C23×C32C22×C411yescharacteristic
252C23×C32C22×C411yescharacteristic
253C22×C3×D3—22no—
254C22×C3×D3—41no—
255C22×C3×D3—41no—
256C22×C3×D3C22×C411yescharacteristic
257C22×C3×D3C22×C411yescharacteristic
258C22×C3×D3C22×C411yescharacteristic
259C32×D4—41no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C22×C411yescharacteristic
265C2×C32×C4C22×C411yescharacteristic
266C2×C32×C4C22×C411yescharacteristic
267C2×C32×C4C22×C411yescharacteristic
268C2×C32×C4C2411yescharacteristic
269C3×#67—22no—
270C3×#67—22no—
271C3×#67—41no—
272C3×#67—41no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3C22×C411yescharacteristic
275C2×C3×Dic3C22×C411yescharacteristic
276C2×C3×Dic3C22×C411yescharacteristic
277C2×C3×Dic3C22×C411yescharacteristic
278C2×C3×Dic3C22×C411yescharacteristic
279C3×D12—22no—
280C3×D12—41no—
281C3×C4×D3—22no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—22no—
287C3×C4×D3C2×D412yes—
288C3×C4×D3#4112yes—
289C3×Dic6—22no—
290C3⋊(C3⋊C8)—21no—
291C3⋊(C3⋊C8)—21no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)C2×D412yes—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C3×C3⋊C8—21no—
297C3×C3⋊C8C2×D412yes—
298C2×#131—91no—
299C22×M16—91no—
300#525—31no—
301#436—31no—
302#436—91no—
303#436—91no—
304#436—91no—
305#435—91no—
306#435—91no—
307#435—91no—
308#435—91no—
309#424—91no—
310#408—91no—
311#407—91no—
312#405—91no—
313C24×C3—31no—
314C23×D3C2×Dic311yescharacteristic
315C3×#41—62no—
316C3×#41—62no—
317C2×C3×Q8—31no—
318C2×C3×D4—21no—
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4C4×D311yescharacteristic
326C2×C3×D4C2×Dic311yescharacteristic
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—62no—
336C22×C3×C4—62no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C2×#67C2×Dic311yescharacteristic
342C2×#67C2×Dic311yescharacteristic
343C2×#67C2×Dic311yescharacteristic
344C2×#67C2×Dic311yescharacteristic
345C22×Dic3C2×Dic311yescharacteristic
346#235—22no—
347#235—22no—
348C2×D12C2×Dic311yescharacteristic
349C2×D12C2×Dic311yescharacteristic
350C2×C4×D3—22no—
351C2×C4×D3—22no—
352C2×C4×D3C2×Dic311yescharacteristic
353C2×C4×D3C2×Dic311yescharacteristic
354C2×C4×D3C22×D311yescharacteristic
355C2×C4×D3C22×D311yescharacteristic
356C2×C4×D3C22×D311yescharacteristic
357C2×Dic6C2×Dic311yescharacteristic
358C3×M16—62no—
359C3×M16—62no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4C4×D311yescharacteristic
371C3×C4⋊C4C2×Dic311yescharacteristic
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—31no—
382C3×C22⋊C4C4×D311yescharacteristic
383C3×C22⋊C4C4×D311yescharacteristic
384C3×C22⋊C4C2×Dic311yescharacteristic
385C3×C22⋊C4C2×Dic311yescharacteristic
386C3×C42—21no—
387C3×C42—31no—
388C3×C42C22×D311yescharacteristic
389C3×C42C22×D311yescharacteristic
390#217C2×Dic311yescharacteristic
391#217C2×Dic311yescharacteristic
392(C2×D3)⋊C4C2×Dic311yescharacteristic
393(C2×D3)⋊C4C2×Dic311yescharacteristic
394(C2×D3)⋊C4C2×Dic311yescharacteristic
395(C2×D3)⋊C4C2×Dic311yescharacteristic
396(C2×D3)⋊C4C2×Dic311yescharacteristic
397(C2×D3)⋊C4C2×Dic311yescharacteristic
398C4⋊Dic3C2×Dic311yescharacteristic
399Dic3⋊C4C2×Dic311yescharacteristic
400Dic3⋊C4C2×Dic311yescharacteristic
401Dic3⋊C4C2×Dic311yescharacteristic
402Dic3⋊C4C2×Dic311yescharacteristic
403C4×Dic3C22×D311yescharacteristic
404#208—22no—
405#208—22no—
406#208—62no—
407#208—62no—
408#208—62no—
409#208—62no—
410#208—62no—
411#208—62no—
412#208—62no—
413#208—122no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—34no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—31no—
421C2×C3⋊C8—31no—
422C2×C3⋊C8—31no—
423C2×C3⋊C8—61no—
424C2×C3⋊C8—61no—
425C2×C3⋊C8—61no—
426C2×C3⋊C8—61no—
427C2×C3⋊C8—62no—
428C2×C3⋊C8—62no—
429C2×C3⋊C8—62no—
430C2×C3⋊C8—62no—
431C2×C3⋊C8—122no—
432C2×C3⋊C8C22×D311yescharacteristic
433C2×C3⋊C8C22×D311yescharacteristic
434C2×C3⋊C8C22×D311yescharacteristic
435C2×C3⋊C8C22×D311yescharacteristic
436ΓL(1,𝔽25)—62no—
437ΓL(1,𝔽25)—62no—
438ΓL(1,𝔽25)—62no—
439ΓL(1,𝔽25)—62no—
440ΓL(1,𝔽25)—62no—
441D3×C8—34no—
442D3×C8—62no—
443D3×C8—62no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32C23×C411yescharacteristic
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—44no—
460C2×C3×D3C4×D412yes—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4—21no—
464C32×C4—21no—
465C32×C4C22×D411yescharacteristic
466C32×C4C2×#4111yescharacteristic
467C3×Dic3—21no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3C4×D412yes—
472C2×#41—31no—
473C23×C4—31no—
474#131—184no—
475C2×M16—31no—
476C2×M16—31no—
477C2×M16—91no—
478C2×M16—91no—
479C2×M16—91no—
480C2×M16—91no—
481C2×M16—91no—
482C2×M16—91no—
483C2×M16—184no—
484C22×C8—91no—
485C22×C8—91no—
486C22×C8—91no—
487C22×C8—91no—
488#123—31no—
489#123—31no—
490C22⋊Q8—31no—
491C22⋊Q8—31no—
492#121—31no—
493#121—31no—
494#120—31no—
495#120—31no—
496C4×D4—31no—
497C4×D4—31no—
498C4×D4—31no—
499C4×D4D3211yescharacteristic
500#117—31no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505C22⋊C8—31no—
506C22⋊C8—31no—
507C22⋊C8—91no—
508C22⋊C8—91no—
509C22⋊C8—91no—
510C22⋊C8—91no—
511C22⋊C8—91no—
512C22⋊C8—91no—
513#97—91no—
514#97—91no—
515C4×C8—31no—
516C4×C8—91no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—31no—
520C23×C3—31no—
521C23×C3—31no—
522C23×C3—62no—
523C23×C3—121no—
524C23×C3—121no—
525C23×C3C2×C4×D311yescharacteristic
526C23×C3C2×C4×D311yescharacteristic
527C23×C3C22×Dic311yescharacteristic
528C23×C3C22×Dic311yescharacteristic
529C22×D3—22no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3C22×Dic311yescharacteristic
533C22×D3C22×Dic311yescharacteristic
534C22×D3C22×Dic311yescharacteristic
535C3×Q8—62no—
536C3×D4—41no—
537C3×D4—41no—
538C3×D4—42no—
539C3×D4—62no—
540C3×D4—62no—
541C3×D4—62no—
542C3×D4—121no—
543C3×D4—121no—
544C3×D4—121no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—31no—
559C2×C3×C4—32no—
560C2×C3×C4—32no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—62no—
570C2×C3×C4—62no—
571C2×C3×C4—62no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4C2×C4×D311yescharacteristic
577C2×C3×C4C2×C4×D311yescharacteristic
578C2×C3×C4C2×C4×D311yescharacteristic
579C2×C3×C4C2×C4×D311yescharacteristic
580C2×C3×C4C22×Dic311yescharacteristic
581C2×C3×C4C22×Dic311yescharacteristic
582C2×C3×C4C22×Dic311yescharacteristic
583C2×C3×C4C22×Dic311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586#67—22no—
587#67—22no—
588#67—41no—
589#67—41no—
590C2×Dic3—22no—
591C2×Dic3C22×Dic311yescharacteristic
592C2×Dic3C22×Dic311yescharacteristic
593C2×Dic3C22×Dic311yescharacteristic
594C2×Dic3C22×Dic311yescharacteristic
595C2×Dic3C22×Dic311yescharacteristic
596D12—22no—
597D12—41no—
598C4×D3—22no—
599C4×D3—21no—
600C4×D3—21no—
601C4×D3—21no—
602C4×D3—21no—
603C4×D3—22no—
604C4×D3D3×D412yes—
605C4×D3#23712yes—
606Dic6—22no—
607C3×C8—32no—
608C3×C8—61no—
609C3×C8—61no—
610C3×C8—61no—
611C3⋊C8—21no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—32no—
615C3⋊C8—32no—
616C3⋊C8—62no—
617C3⋊C8—61no—
618C3⋊C8—61no—
619C3⋊C8—61no—
620C3⋊C8—61no—
621C3⋊C8—61no—
622C3⋊C8—61no—
623C3⋊C8—121no—
624C3⋊C8—121no—
625C3⋊C8—121no—
626C3⋊C8D3×D412yes—
627C2×C32—41no—
628C2×C32—41no—
629C2×C32C2×C4×D411yescharacteristic
630C2×C32#56811yescharacteristic
631C2×C32#56811yescharacteristic
632C3×D3—22no—
633C3×D3—41no—
634C3×D3—41no—
635C24—31no—
636#41—62no—
637#41—62no—
638C2×Q8—31no—
639C2×D4—31no—
640C2×D4—31no—
641C2×D4—31no—
642C2×D4—31no—
643C2×D4—31no—
644C2×D4—31no—
645C2×D4D3×Dic311yescharacteristic
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4C2×D3211yescharacteristic
655C22×C4C2×D3211yescharacteristic
656M16—62no—
657M16—62no—
658M16—182no—
659M16—182no—
660M16—182no—
661M16—182no—
662M16—182no—
663M16—182no—
664C2×C8—31no—
665C2×C8—31no—
666C2×C8—31no—
667C2×C8—31no—
668C2×C8—94no—
669C2×C8—91no—
670C2×C8—91no—
671C2×C8—91no—
672C2×C8—91no—
673C2×C8—182no—
674C2×C8—182no—
675C2×C8—182no—
676C4⋊C4—31no—
677C4⋊C4—31no—
678C4⋊C4—31no—
679C4⋊C4—31no—
680C4⋊C4—31no—
681C4⋊C4D3×Dic311yescharacteristic
682C22⋊C4—31no—
683C22⋊C4—31no—
684C22⋊C4—31no—
685C22⋊C4—31no—
686C22⋊C4—31no—
687C22⋊C4—31no—
688C22⋊C4—31no—
689C22⋊C4—31no—
690C22⋊C4D3×Dic311yescharacteristic
691C22⋊C4D3×Dic311yescharacteristic
692C42—31no—
693C42C2×D3211yescharacteristic
694C22×C3—22no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—32no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—124no—
723C22×C3C22×C4×D311yescharacteristic
724C22×C3C23×Dic311yescharacteristic
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—44no—
734C2×D3D4×Dic312yes—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—32no—
746C3×C4—41no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—61no—
753C3×C4—61no—
754C3×C4C2×D3×D411yescharacteristic
755C3×C4C2×D3×D411yescharacteristic
756C3×C4C2×#23711yescharacteristic
757C3×C4D3×#4111yescharacteristic
758Dic3—21no—
759Dic3—21no—
760Dic3—21no—
761Dic3—21no—
762Dic3D4×Dic312yes—
763C32#293011yescharacteristic, complemented, Sylow
764C23—31no—
765C23—31no—
766C23—31no—
767C23—62no—
768C23—121no—
769C23—121no—
770C23C2×D3×Dic311yescharacteristic
771C23C2×D3×Dic311yescharacteristic
772Q8—62no—
773D4—41no—
774D4—62no—
775D4—62no—
776D4—62no—
777D4—121no—
778D4—121no—
779D4—121no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—31no—
785C2×C4—32no—
786C2×C4—32no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4C2×D3×Dic311yescharacteristic
799C2×C4C2×D3×Dic311yescharacteristic
800C2×C4C2×D3×Dic311yescharacteristic
801C2×C4C2×D3×Dic311yescharacteristic
802C2×C4C22×D3211yescharacteristic
803C8—32no—
804C8—61no—
805C8—61no—
806C8—61no—
807C8—92no—
808C8—181no—
809C8—181no—
810C8—181no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—42no—
815C2×C3—41no—
816C2×C3—41no—
817C2×C3—41no—
818C2×C3—41no—
819C2×C3—62no—
820C2×C3—81no—
821C2×C3—121no—
822C2×C3—121no—
823C2×C3C4×D3×D411yescharacteristic
824C2×C3#574511yescharacteristic
825C2×C3#575011yescharacteristic
826C2×C3C2×D4×Dic311yescharacteristic
827C2×C3#581911yescharacteristic
828C2×C3#581911yescharacteristic
829D3—22no—
830D3—41no—
831D3—41no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—32no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—61no—
844C22—61no—
845C22—61no—
846C22—61no—
847C22—124no—
848C22C22×D3×Dic311yescharacteristic
849C4—21no—
850C4—21no—
851C4—21no—
852C4—21no—
853C4—32no—
854C4—61no—
855C4—61no—
856C4—61no—
857C4—61no—
858C4D32×D411yescharacteristic
859C4D3×#23711yescharacteristic
860C3—21no—
861C3#7953711yescharacteristic, complemented
862C3#8291711yescharacteristic, complemented
863C2—41no—
864C2—41no—
865C2—62no—
866C2—121no—
867C2—121no—
868C2#1059477611yescharacteristic
869C2D3×D4×Dic311yescharacteristic
870C2#1059544111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×D4C22
prime radicalC3×#5547C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2930
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63815C2semidirect
3. C2×D3×#208C2semidirect
4. #10592710C2semidirect
5. C3×#5012C2semidirect
6. #10591158C2semidirect
7. #10591156C2semidirect
8. #10591156C2semidirect
9. #10591154C2semidirect
10. #10591151C2semidirect
11. #10591145C2semidirect
12. #10590337C2semidirect
13. #10590330C2semidirect
14. #10590324C2semidirect
15. #10590318C2semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
28. C2×C3×#208C22semidirect
41. C2×#3711C22semidirect
46. C2×D3×C3⋊C8C22semidirect
48. #63657C22semidirect
49. C4⋊(C3⋊(C3⋊C8))C22semidirect
50. #63630C22semidirect
52. C3×#830C22semidirect
53. C3×C4⋊(C3⋊C8)C22semidirect
54. C3×C4×C3⋊C8C22semidirect
55. Dic3⋊(C3⋊C8)C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
61. #63554C22semidirect
62. Dic3×C3⋊C8C22semidirect
77. #5012D3semidirect
152. D3×C3⋊C8D4semidirect
190. C2×#208C2×D3semidirect
230. #830C2×D3semidirect
244. C4⋊(C3⋊C8)C2×D3semidirect
250. C4×C3⋊C8C2×D3semidirect
763. C32#2930semidirect
861. C3#79537semidirect
862. C3#82917semidirect

Maximal subgroups

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

subgroupindex
C3×#55472
C2×#638152
C2×D3×#2082
#105927102
C3×#50122
#105911582
#105911562
#105911542
#105911512
#105911452
#105903372
#105903302
#105903242
#105903182
#829173
#795373