Finite Group Databasebeta

← #11859534

Subgroups — #11859534

Order 1152.

1030 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5548C211yesmaximal, characteristic
2C2×#63815C211yesmaximal, characteristic, complemented
3C2×#63814C211yesmaximal, characteristic, complemented
4#10592710C211yesmaximal, characteristic, complemented
5C3×#5011C211yesmaximal, characteristic, complemented
6#10591158C211yesmaximal, characteristic, complemented
7#10591155C211yesmaximal, characteristic, complemented
8#10591151C211yesmaximal, characteristic, complemented
9#10591147C211yesmaximal, characteristic, complemented
10#10591145C211yesmaximal, characteristic, complemented
11#10591145C211yesmaximal, characteristic, complemented
12#10590336C211yesmaximal, characteristic, complemented
13#10590330C211yesmaximal, characteristic, complemented
14#10590326C211yesmaximal, characteristic, complemented
15D3×#803C211yesmaximal, characteristic, complemented
16#83276—31nomaximal
17#79480—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#940C411yescharacteristic
24C3×#938C411yescharacteristic
25C3×C4×#67C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29C3×#895C411yescharacteristic
30C3×#888C411yescharacteristic
31C3×#885C411yescharacteristic
32C3×#885C411yescharacteristic
33C3×#884C411yescharacteristic
34C3×#884C411yescharacteristic
35C3×C4×D12C2211yescharacteristic
36C3×C42×D3C2211yescharacteristic
37C2×#3711C2211yescharacteristic
38C2×#3711C2211yescharacteristic
39C2×#3711C2211yescharacteristic
40C2×#3711C2211yescharacteristic
41#63815—24no—
42#63814—24no—
43C2×D3×C3⋊C8C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46C2×D3×C3⋊C8C2211yescharacteristic
47#63657C2211yescharacteristic
48#63657C2211yescharacteristic
49C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
50#63630C2211yescharacteristic
51C3×#830C2211yescharacteristic
52C3×#830C2211yescharacteristic
53C3×C4⋊(C3⋊C8)C2211yescharacteristic
54C3×#803C2211yescharacteristic
55Dic3⋊(C3⋊C8)C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#63554C2211yescharacteristic
62#63554C2211yescharacteristic
63C3×#532—31no—
64C2×#948—31no—
65C2×#948—31no—
66C2×#907—31no—
67C2×#901—31no—
68#5548D311yescharacteristic
69C3×#435—31no—
70#5234—31no—
71#5234—31no—
72#5127—31no—
73#5111—31no—
74#5011—31no—
75#5011—31no—
76#5011—31no—
77#5011—31no—
78#5011—31no—
79#5011—31no—
80#5011—31no—
81#5011—31no—
82#5011—61no—
83#5011D311yescharacteristic, complemented
84#4924—31no—
85C2×#803—31no—
86#4837—31no—
87#4836—31no—
88#4730—31no—
89#4728—31no—
90#4727—31no—
91#4727—31no—
92#4706—31no—
93D3×#97—31no—
94C2×C32×D4C2×C411yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C3×#67C2×C411yescharacteristic
98C2×C3×#67C2×C411yescharacteristic
99C2×C3×#67C2×C411yescharacteristic
100C2×C3×#67C2×C411yescharacteristic
101C2×C3×#67C2×C411yescharacteristic
102C2×C3×#67C2×C411yescharacteristic
103C3×#235—22no—
104C3×#235—22no—
105C3×#235—22no—
106C3×#235—22no—
107C2×C3×D12C2×C411yescharacteristic
108C2×C3×D12C2×C411yescharacteristic
109C2×C3×D12C2×C411yescharacteristic
110C2×C3×C4×D3C2×C411yescharacteristic
111C2×C3×C4×D3C2×C411yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2×C411yescharacteristic
116C2×C3×Dic6C2×C411yescharacteristic
117C32×C4⋊C4C2×C411yescharacteristic
118C32×C22⋊C4C2×C411yescharacteristic
119C32×C22⋊C4C2×C411yescharacteristic
120C32×C42C2311yescharacteristic
121#3748—22no—
122C2×C3⋊(C3⋊C8)—22no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#217C2×C411yescharacteristic
128C3×#217C2×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×C4×Dic3C2×C411yescharacteristic
137C3×C4×Dic3C2×C411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C3×#208—22no—
140C2×C3×C3⋊C8—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—
149D3×C3⋊C8—22no—
150D3×C3⋊C8—22no—
151D3×C3⋊C8—22no—
152D3×C3⋊C8D414yescomplemented
153#2932—91noSylow
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C2×#235C2×D311yescharacteristic
157C2×#235C2×D311yescharacteristic
158C2×C3×M16—31no—
159C22×C3×C8—31no—
160C3×C4⋊Q8—31no—
161C3×#127—31no—
162C3×#124—31no—
163C3×#124—31no—
164C3×#121—31no—
165C3×#121—31no—
166C3×#121—31no—
167C3×#121—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
174C2×C3×C42—31no—
175#948—64no—
176#948—64no—
177#940Dic311yescharacteristic
178#938Dic311yescharacteristic
179C4×#67C2×D311yescharacteristic
180C4×#67C2×D311yescharacteristic
181C2×#208—31no—
182C2×#208—31no—
183C2×#208—31no—
184C2×#208—31no—
185C2×#208—31no—
186C2×#208—31no—
187C2×#208—61no—
188C2×#208C2×D311yescharacteristic
189C22×C3⋊C8—31no—
190C22×C3⋊C8—31no—
191C22×C3⋊C8—31no—
192C22×C3⋊C8—31no—
193C22×C3⋊C8—31no—
194C22×C3⋊C8—31no—
195C22×C3⋊C8—61no—
196C22×C3⋊C8C2×D311yescharacteristic
197#907—64no—
198#901—64no—
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×D3×C8—31no—
204C2×D3×C8—31no—
205C2×D3×C8—31no—
206C2×D3×C8—31no—
207#895Dic311yescharacteristic
208#888Dic311yescharacteristic
209#885Dic311yescharacteristic
210#885Dic311yescharacteristic
211#884Dic311yescharacteristic
212#884Dic311yescharacteristic
213C4×D12C2×D311yescharacteristic
214C42×D3C2×D311yescharacteristic
215C3×C4⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×#97—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
231(C2×D3)⋊C8—31no—
232(C2×D3)⋊C8—31no—
233(C2×D3)⋊C8—31no—
234(C2×D3)⋊C8—31no—
235#815—31no—
236#815—31no—
237Dic3⋊C8—31no—
238Dic3⋊C8—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
245#803—31no—
246#803—31no—
247#803—31no—
248#803—31no—
249#803—61no—
250#803C2×D311yescharacteristic
251C23×C32C22×C411yescharacteristic
252C23×C32C22×C411yescharacteristic
253C22×C3×D3C22×C411yescharacteristic
254C22×C3×D3C22×C411yescharacteristic
255C22×C3×D3C22×C411yescharacteristic
256C32×D4—41no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C22×C411yescharacteristic
262C2×C32×C4C22×C411yescharacteristic
263C2×C32×C4C22×C411yescharacteristic
264C2×C32×C4C22×C411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C3×#67—22no—
267C3×#67—22no—
268C3×#67—22no—
269C3×#67—22no—
270C3×#67—41no—
271C3×#67—41no—
272C2×C3×Dic3C22×C411yescharacteristic
273C2×C3×Dic3C22×C411yescharacteristic
274C2×C3×Dic3C22×C411yescharacteristic
275C2×C3×Dic3C22×C411yescharacteristic
276C2×C3×Dic3C22×C411yescharacteristic
277C3×D12—22no—
278C3×D12—22no—
279C3×D12—41no—
280C3×C4×D3—21no—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—41no—
285C3×C4×D3—41no—
286C3×C4×D3C2×D412yes—
287C3×C4×D3#4112yes—
288C3×Dic6—22no—
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—
299C2×#131—91no—
300#532—31no—
301#435—31no—
302#435—91no—
303#435—91no—
304#435—91no—
305#435—91no—
306#435—91no—
307#435—91no—
308#435—91no—
309#423—91no—
310#408—91no—
311#408—91no—
312C2×#97—91no—
313C3×#41—62no—
314C3×#41—62no—
315C3×#41—62no—
316C3×#41—62no—
317C2×C3×Q8—31no—
318C2×C3×Q8—31no—
319C2×C3×D4—21no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4C4×D311yescharacteristic
330C2×C3×D4C2×Dic311yescharacteristic
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C2×#67C2×Dic311yescharacteristic
343C2×#67C2×Dic311yescharacteristic
344C2×#67C2×Dic311yescharacteristic
345C2×#67C2×Dic311yescharacteristic
346C2×#67C2×Dic311yescharacteristic
347C2×#67C2×Dic311yescharacteristic
348#235—22no—
349#235—22no—
350#235—22no—
351#235—22no—
352C2×D12C2×Dic311yescharacteristic
353C2×D12C2×Dic311yescharacteristic
354C2×D12C2×Dic311yescharacteristic
355C2×C4×D3C2×Dic311yescharacteristic
356C2×C4×D3C2×Dic311yescharacteristic
357C2×C4×D3C22×D311yescharacteristic
358C2×C4×D3C22×D311yescharacteristic
359C2×C4×D3C22×D311yescharacteristic
360C2×Dic6C2×Dic311yescharacteristic
361C2×Dic6C2×Dic311yescharacteristic
362C3×M16—62no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C2×C3×C8—31no—
366C2×C3×C8—31no—
367C2×C3×C8—62no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4C4×D311yescharacteristic
373C3×C4⋊C4C2×Dic311yescharacteristic
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
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×C42—31no—
389C3×C42—31no—
390C3×C42C22×D311yescharacteristic
391C3×C42C22×D311yescharacteristic
392#217C2×Dic311yescharacteristic
393#217C2×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
401C4×Dic3C2×Dic311yescharacteristic
402C4×Dic3C2×Dic311yescharacteristic
403C4×Dic3C22×D311yescharacteristic
404#208—22no—
405#208—62no—
406#208—62no—
407#208—62no—
408#208—62no—
409#208—62no—
410#208—62no—
411#208—122no—
412C2×C3⋊C8—22no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—34no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—31no—
421C2×C3⋊C8—31no—
422C2×C3⋊C8—61no—
423C2×C3⋊C8—61no—
424C2×C3⋊C8—61no—
425C2×C3⋊C8—61no—
426C2×C3⋊C8—62no—
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—
440D3×C8—34no—
441D3×C8—62no—
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×D3C4×D412yes—
460C32×C4—21no—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4—21no—
464C32×C4C22×D411yescharacteristic
465C32×C4C2×#4111yescharacteristic
466C3×Dic3—21no—
467C3×Dic3—21no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3C4×D412yes—
471C2×#41—31no—
472C2×#41—31no—
473#131—184no—
474#131—184no—
475C2×M16—31no—
476C2×M16—91no—
477C2×M16—91no—
478C2×M16—91no—
479C2×M16—91no—
480C2×M16—91no—
481C22×C8—31no—
482C22×C8—91no—
483C22×C8—91no—
484C22×C8—91no—
485C22×C8—91no—
486C22×C8—91no—
487C4⋊Q8—31no—
488#127—31no—
489#124—31no—
490#124—31no—
491#121—31no—
492#121—31no—
493#121—31no—
494#121—31no—
495C4×D4—31no—
496C4×D4—31no—
497C4×D4—31no—
498C4×D4D3211yescharacteristic
499C2×C42—31no—
500C4⋊C8—31no—
501C4⋊C8—91no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C22⋊C8—31no—
505C22⋊C8—31no—
506C22⋊C8—91no—
507C22⋊C8—91no—
508C22⋊C8—91no—
509C22⋊C8—91no—
510C22⋊C8—91no—
511C22⋊C8—91no—
512#97—31no—
513#97—91no—
514#97—91no—
515#97—91no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—31no—
519C23×C3—31no—
520C23×C3—31no—
521C23×C3C2×C4×D311yescharacteristic
522C23×C3C2×C4×D311yescharacteristic
523C23×C3C22×Dic311yescharacteristic
524C23×C3C22×Dic311yescharacteristic
525C22×D3C22×Dic311yescharacteristic
526C22×D3C22×Dic311yescharacteristic
527C22×D3C22×Dic311yescharacteristic
528C3×Q8—62no—
529C3×Q8—62no—
530C3×D4—41no—
531C3×D4—41no—
532C3×D4—42no—
533C3×D4—62no—
534C3×D4—62no—
535C3×D4—62no—
536C3×D4—62no—
537C3×D4—62no—
538C3×D4—62no—
539C3×D4—121no—
540C3×D4—121no—
541C3×D4—121no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
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—31no—
556C2×C3×C4—32no—
557C2×C3×C4—32no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—121no—
571C2×C3×C4—121no—
572C2×C3×C4C2×C4×D311yescharacteristic
573C2×C3×C4C2×C4×D311yescharacteristic
574C2×C3×C4C2×C4×D311yescharacteristic
575C2×C3×C4C2×C4×D311yescharacteristic
576C2×C3×C4C22×Dic311yescharacteristic
577C2×C3×C4C22×Dic311yescharacteristic
578C2×C3×C4C22×Dic311yescharacteristic
579C2×C3×C4C22×Dic311yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D311yescharacteristic
582#67—22no—
583#67—22no—
584#67—22no—
585#67—22no—
586#67—41no—
587#67—41no—
588C2×Dic3C22×Dic311yescharacteristic
589C2×Dic3C22×Dic311yescharacteristic
590C2×Dic3C22×Dic311yescharacteristic
591C2×Dic3C22×Dic311yescharacteristic
592C2×Dic3C22×Dic311yescharacteristic
593D12—22no—
594D12—22no—
595D12—41no—
596C4×D3—21no—
597C4×D3—21no—
598C4×D3—21no—
599C4×D3—21no—
600C4×D3—41no—
601C4×D3—41no—
602C4×D3D3×D412yes—
603C4×D3#23712yes—
604Dic6—22no—
605Dic6—22no—
606C3×C8—32no—
607C3×C8—61no—
608C3×C8—61no—
609C3×C8—61no—
610C3⋊C8—21no—
611C3⋊C8—21no—
612C3⋊C8—21no—
613C3⋊C8—32no—
614C3⋊C8—32no—
615C3⋊C8—62no—
616C3⋊C8—61no—
617C3⋊C8—61no—
618C3⋊C8—61no—
619C3⋊C8—61no—
620C3⋊C8—61no—
621C3⋊C8—61no—
622C3⋊C8—121no—
623C3⋊C8—121no—
624C3⋊C8—121no—
625C3⋊C8D3×D412yes—
626C2×C32—41no—
627C2×C32—41no—
628C2×C32C2×C4×D411yescharacteristic
629C2×C32#56811yescharacteristic
630C2×C32#56811yescharacteristic
631C3×D3—22no—
632C3×D3—41no—
633C3×D3—41no—
634#41—62no—
635#41—62no—
636#41—62no—
637#41—62no—
638C2×Q8—31no—
639C2×Q8—31no—
640C2×D4—31no—
641C2×D4—31no—
642C2×D4—31no—
643C2×D4—31no—
644C2×D4—31no—
645C2×D4—31no—
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—31no—
649C2×D4D3×Dic311yescharacteristic
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4C2×D3211yescharacteristic
656C22×C4C2×D3211yescharacteristic
657M16—62no—
658M16—182no—
659M16—182no—
660M16—182no—
661M16—182no—
662M16—182no—
663C2×C8—31no—
664C2×C8—31no—
665C2×C8—31no—
666C2×C8—31no—
667C2×C8—62no—
668C2×C8—94no—
669C2×C8—91no—
670C2×C8—91no—
671C2×C8—91no—
672C2×C8—91no—
673C2×C8—182no—
674C2×C8—182no—
675C2×C8—182no—
676C2×C8—182no—
677C4⋊C4—31no—
678C4⋊C4—31no—
679C4⋊C4—31no—
680C4⋊C4D3×Dic311yescharacteristic
681C22⋊C4—31no—
682C22⋊C4—31no—
683C22⋊C4—31no—
684C22⋊C4—31no—
685C22⋊C4—31no—
686C22⋊C4—31no—
687C22⋊C4D3×Dic311yescharacteristic
688C22⋊C4D3×Dic311yescharacteristic
689C42—31no—
690C42—31no—
691C42—31no—
692C42C2×D3211yescharacteristic
693C22×C3—22no—
694C22×C3—21no—
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—32no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3C22×C4×D311yescharacteristic
722C22×C3C23×Dic311yescharacteristic
723C2×D3—21no—
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3D4×Dic312yes—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—32no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—61no—
748C3×C4—61no—
749C3×C4—61no—
750C3×C4—61no—
751C3×C4C2×D3×D411yescharacteristic
752C3×C4C2×D3×D411yescharacteristic
753C3×C4C2×#23711yescharacteristic
754C3×C4D3×#4111yescharacteristic
755Dic3—21no—
756Dic3—21no—
757Dic3—21no—
758Dic3—21no—
759Dic3D4×Dic312yes—
760C32#293211yescharacteristic, complemented, Sylow
761C23—31no—
762C23—31no—
763C23—31no—
764C23C2×D3×Dic311yescharacteristic
765C23C2×D3×Dic311yescharacteristic
766Q8—62no—
767Q8—62no—
768D4—41no—
769D4—62no—
770D4—62no—
771D4—62no—
772D4—62no—
773D4—62no—
774D4—62no—
775D4—121no—
776D4—121no—
777D4—121no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—31no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—31no—
786C2×C4—31no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4C2×D3×Dic311yescharacteristic
796C2×C4C2×D3×Dic311yescharacteristic
797C2×C4C2×D3×Dic311yescharacteristic
798C2×C4C2×D3×Dic311yescharacteristic
799C2×C4C22×D3211yescharacteristic
800C8—32no—
801C8—61no—
802C8—61no—
803C8—61no—
804C8—92no—
805C8—181no—
806C8—181no—
807C8—181no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—42no—
812C2×C3—41no—
813C2×C3—41no—
814C2×C3—41no—
815C2×C3—41no—
816C2×C3—62no—
817C2×C3—81no—
818C2×C3—121no—
819C2×C3—121no—
820C2×C3C4×D3×D411yescharacteristic
821C2×C3#574511yescharacteristic
822C2×C3#575011yescharacteristic
823C2×C3C2×D4×Dic311yescharacteristic
824C2×C3#581911yescharacteristic
825C2×C3#581911yescharacteristic
826D3—22no—
827D3—41no—
828D3—41no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—32no—
836C22—61no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—61no—
844C22C22×D3×Dic311yescharacteristic
845C4—21no—
846C4—21no—
847C4—21no—
848C4—21no—
849C4—32no—
850C4—61no—
851C4—61no—
852C4—61no—
853C4—61no—
854C4D32×D411yescharacteristic
855C4D3×#23711yescharacteristic
856C3—21no—
857C3#7948011yescharacteristic, complemented
858C3#8327611yescharacteristic, complemented
859C2—41no—
860C2—41no—
861C2—62no—
862C2—121no—
863C2—121no—
864C2#1059477611yescharacteristic
865C2D3×D4×Dic311yescharacteristic
866C2#1059544111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×D4C22
prime radicalC3×#5548C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2932
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×#63814C2semidirect
4. #10592710C2semidirect
5. C3×#5011C2semidirect
6. #10591158C2semidirect
7. #10591155C2semidirect
8. #10591151C2semidirect
9. #10591147C2semidirect
10. #10591145C2semidirect
11. #10591145C2semidirect
12. #10590336C2semidirect
13. #10590330C2semidirect
14. #10590326C2semidirect
15. D3×#803C2semidirect
83. #5011D3semidirect
152. D3×C3⋊C8D4semidirect
760. C32#2932semidirect
857. C3#79480semidirect
858. C3#83276semidirect

Maximal subgroups

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

subgroupindex
C3×#55482
C2×#638152
C2×#638142
#105927102
C3×#50112
#105911582
#105911552
#105911512
#105911472
#105911452
#105903362
#105903302
#105903262
D3×#8032
#832763
#794803