Finite Group Databasebeta

← #11859383

Subgroups — #11859383

Order 1152.

1476 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64116C211yesmaximal, characteristic, complemented
2C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596018C211yesmaximal, characteristic
4C32×#436C211yesmaximal, characteristic, complemented
5#10592827C211yesmaximal, characteristic, complemented
6#10592827C211yesmaximal, characteristic, complemented
7#10592710C211yesmaximal, characteristic, complemented
8#10592538C211yesmaximal, characteristic, complemented
9#10592535C211yesmaximal, characteristic, complemented
10#10592429C211yesmaximal, characteristic, complemented
11#10592427C211yesmaximal, characteristic, complemented
12#10592426C211yesmaximal, characteristic, complemented
13#10592425C211yesmaximal, characteristic, complemented
14#10592388C211yesmaximal, characteristic, complemented
15#10592387C211yesmaximal, characteristic, complemented
16#79537—34nomaximal
17C2×#3828C2211yescharacteristic
18C22×C4×C3⋊D3C2211yescharacteristic
19C2×C32×M16C2211yescharacteristic
20C2×C32×M16C2211yescharacteristic, complemented
21C32×C4×D4C2211yescharacteristic
22#64148C411yescharacteristic
23#64146C411yescharacteristic
24C4×#638C2211yescharacteristic
25C4×#638C2211yescharacteristic
26C2×#3748C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
28#64116—24no—
29M16×C3⋊D3—24no—
30C2×#3743C2211yescharacteristic
31C2×#3743C2211yescharacteristic
32C2×#3743C2211yescharacteristic
33C2×#3743C2211yescharacteristic
34C2×#3743C2211yescharacteristic, complemented
35C2×C8×C3⋊D3C2211yescharacteristic
36C2×C8×C3⋊D3C2211yescharacteristic
37C2×C8×C3⋊D3C2211yescharacteristic, complemented
38#64105C411yescharacteristic
39#64103C411yescharacteristic
40#64093C411yescharacteristic
41#64092C411yescharacteristic
42#64091C411yescharacteristic
43#64087C411yescharacteristic
44C4×C4⋊(C3⋊D3)C2211yescharacteristic
45#64081C2211yescharacteristic
46C32×C4⋊C8C2211yescharacteristic, complemented
47C32×C22⋊C8C2211yescharacteristic
48C32×C22⋊C8C2211yescharacteristic, complemented
49C32×C4×C8C2211yescharacteristic, complemented
50#63657C2211yescharacteristic
51#63657C2211yescharacteristic, complemented
52#63647C2211yescharacteristic
53#63647C2211yescharacteristic
54#63647C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56#63642C2211yescharacteristic, complemented
57#63641C2211yescharacteristic, complemented
58#63641C2211yescharacteristic, complemented
59C8×C3⋊Dic3C2211yescharacteristic, complemented
60C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
61#63630C2211yescharacteristic, complemented
62C2×#907—34no—
63C2×D3×M16—34no—
64#5547—34no—
65C3×#436D314yescomplemented
66#5128—34no—
67#5128—34no—
68#5011—34no—
69#4839—34no—
70#4836—34no—
71#4730—34no—
72#4728—34no—
73#4727—34no—
74#4726—34no—
75#4689—34no—
76#4688—34no—
77C23×C3⋊D3C2×C411yescharacteristic
78C2×C32×D4C2×C411yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C2×#638C2×C411yescharacteristic
82C2×#638C2×C411yescharacteristic
83C2×#638C2×C411yescharacteristic
84C2×#638C2×C411yescharacteristic
85C22×C3⋊Dic3C2×C411yescharacteristic
86#3828—22no—
87#3828—22no—
88C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
89C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
90C2×C4×C3⋊D3—22no—
91C2×C4×C3⋊D3—22no—
92C2×C4×C3⋊D3C2×C411yescharacteristic
93C2×C4×C3⋊D3C2×C411yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634C2×C411yescharacteristic
98C32×M16—22no—
99C32×M16—22no—
100C2×C32×C8C2311yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C4⋊C4C2×C411yescharacteristic
105C32×C22⋊C4C2×C411yescharacteristic
106C32×C22⋊C4C2×C411yescharacteristic
107C32×C42C2311yescharacteristic
108#3757C2×C411yescharacteristic
109#3757C2×C411yescharacteristic
110#3752C2×C411yescharacteristic
111#3752C2×C411yescharacteristic
112#3752C2×C411yescharacteristic
113#3752C2×C411yescharacteristic
114#3752C2×C411yescharacteristic
115#3752C2×C411yescharacteristic
116C4⋊(C3⋊Dic3)C2×C411yescharacteristic
117#3750C2×C411yescharacteristic
118#3750C2×C411yescharacteristic
119#3750C2×C411yescharacteristic
120#3750C2×C411yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122#3748—22no—
123C2×C3⋊(C3⋊C8)—22no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128#3743—22no—
129#3743—22no—
130#3743—22no—
131#3743—22no—
132#3743—22no—
133C8×C3⋊D3—22no—
134C8×C3⋊D3—22no—
135C8×C3⋊D3D414yescomplemented
136#2930—91noSylow
137C2×#235—34no—
138C22×C4×D3—34no—
139C2×C3×M16C2×D314yes—
140C2×C3×M16C2×D314yescomplemented
141C3×C4×D4C2×D314yes—
142#939—34no—
143#937—34no—
144C4×#67—34no—
145C4×#67—34no—
146C2×#208—34no—
147C22×C3⋊C8—34no—
148#907—616no—
149D3×M16—616no—
150C2×ΓL(1,𝔽25)—34no—
151C2×ΓL(1,𝔽25)—34no—
152C2×ΓL(1,𝔽25)—34no—
153C2×ΓL(1,𝔽25)—34no—
154C2×ΓL(1,𝔽25)—34no—
155C2×D3×C8—34no—
156C2×D3×C8—34no—
157C2×D3×C8—34no—
158#896—34no—
159#894—34no—
160#884—34no—
161#883—34no—
162#882—34no—
163#878—34no—
164C4×D12—34no—
165#872—34no—
166C3×C4⋊C8C2×D314yescomplemented
167C3×C22⋊C8C2×D314yes—
168C3×C22⋊C8C2×D314yescomplemented
169C3×C4×C8C2×D314yescomplemented
170#830—34no—
171#830—34no—
172(C2×D3)⋊C8—34no—
173(C2×D3)⋊C8—34no—
174(C2×D3)⋊C8—34no—
175(C2×D3)⋊C8—34no—
176#815—34no—
177Dic3⋊C8—34no—
178Dic3⋊C8—34no—
179C8×Dic3—34no—
180C4⋊(C3⋊C8)—34no—
181#803—34no—
182C23×C32C22×C411yescharacteristic
183C23×C32C22×C411yescharacteristic
184C22×C3⋊D3—22no—
185C22×C3⋊D3—41no—
186C22×C3⋊D3—41no—
187C22×C3⋊D3C22×C411yescharacteristic
188C22×C3⋊D3C22×C411yescharacteristic
189C22×C3⋊D3C22×C411yescharacteristic
190C32×D4—41no—
191C2×C32×C4—21no—
192C2×C32×C4—21no—
193C2×C32×C4—21no—
194C2×C32×C4—21no—
195C2×C32×C4C22×C411yescharacteristic
196C2×C32×C4C22×C411yescharacteristic
197C2×C32×C4C22×C411yescharacteristic
198C2×C32×C4C22×C411yescharacteristic
199C2×C32×C4C2411yescharacteristic
200#638—22no—
201#638—22no—
202#638—41no—
203#638—41no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3C22×C411yescharacteristic
206C2×C3⋊Dic3C22×C411yescharacteristic
207C2×C3⋊Dic3C22×C411yescharacteristic
208C2×C3⋊Dic3C22×C411yescharacteristic
209C2×C3⋊Dic3C22×C411yescharacteristic
210C4⋊(C3⋊D3)—22no—
211C4⋊(C3⋊D3)—41no—
212C4×C3⋊D3—22no—
213C4×C3⋊D3—21no—
214C4×C3⋊D3—21no—
215C4×C3⋊D3—21no—
216C4×C3⋊D3—21no—
217C4×C3⋊D3—22no—
218C4×C3⋊D3C2×D412yes—
219C4×C3⋊D3#4112yes—
220#634—22no—
221C32×C8—21no—
222C32×C8—21no—
223C32×C8—21no—
224C32×C8C2×D412yes—
225C3⋊(C3⋊C8)—21no—
226C3⋊(C3⋊C8)—21no—
227C3⋊(C3⋊C8)—21no—
228C3⋊(C3⋊C8)C2×D412yes—
229C2×#131—91no—
230C22×M16—91no—
231#525—91no—
232#436—91no—
233#436—91no—
234#436—91no—
235#436C3⋊D311yescharacteristic, complemented
236#435—91no—
237#435—91no—
238#435—91no—
239#435—91no—
240#424—91no—
241#408—91no—
242#407—91no—
243#405—91no—
244C23×D3—34no—
245C2×C3×D4C4×D314yes—
246C22×C3×C4C22×D314yes—
247C22×C3×C4C22×D314yes—
248C2×#67—34no—
249C2×#67—34no—
250C2×#67—34no—
251C2×#67—34no—
252C22×Dic3—34no—
253#235—68no—
254#235—68no—
255C2×D12—34no—
256C2×D12—34no—
257C2×C4×D3—34no—
258C2×C4×D3—34no—
259C2×C4×D3—34no—
260C2×C4×D3—34no—
261C2×C4×D3—34no—
262C2×C4×D3—68no—
263C2×C4×D3—68no—
264C2×Dic6—34no—
265C3×M16—28no—
266C3×M16—28no—
267C2×C3×C8C22×D314yes—
268C2×C3×C8C22×D314yes—
269C2×C3×C8C22×D314yes—
270C2×C3×C8C22×D314yes—
271C3×C4⋊C4C4×D314yes—
272C3×C22⋊C4C4×D314yes—
273C3×C22⋊C4C4×D314yes—
274C3×C42C22×D314yes—
275#217—34no—
276#217—34no—
277(C2×D3)⋊C4—34no—
278(C2×D3)⋊C4—34no—
279(C2×D3)⋊C4—34no—
280(C2×D3)⋊C4—34no—
281(C2×D3)⋊C4—34no—
282(C2×D3)⋊C4—34no—
283C4⋊Dic3—34no—
284Dic3⋊C4—34no—
285Dic3⋊C4—34no—
286Dic3⋊C4—34no—
287Dic3⋊C4—34no—
288C4×Dic3—34no—
289#208—68no—
290C2×C3⋊C8—34no—
291C2×C3⋊C8—34no—
292C2×C3⋊C8—34no—
293C2×C3⋊C8—34no—
294C2×C3⋊C8—68no—
295ΓL(1,𝔽25)—68no—
296ΓL(1,𝔽25)—68no—
297ΓL(1,𝔽25)—68no—
298ΓL(1,𝔽25)—68no—
299ΓL(1,𝔽25)—68no—
300D3×C8—316no—
301D3×C8—68no—
302D3×C8—68no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32C23×C411yescharacteristic
310C2×C3⋊D3—21no—
311C2×C3⋊D3—21no—
312C2×C3⋊D3—21no—
313C2×C3⋊D3—21no—
314C2×C3⋊D3—21no—
315C2×C3⋊D3—21no—
316C2×C3⋊D3—21no—
317C2×C3⋊D3—21no—
318C2×C3⋊D3—44no—
319C2×C3⋊D3C4×D412yes—
320C32×C4—21no—
321C32×C4—21no—
322C32×C4—21no—
323C32×C4—21no—
324C32×C4C22×D411yescharacteristic
325C32×C4C2×#4111yescharacteristic
326C3⋊Dic3—21no—
327C3⋊Dic3—21no—
328C3⋊Dic3—21no—
329C3⋊Dic3—21no—
330C3⋊Dic3C4×D412yes—
331C2×#41—91no—
332C23×C4—91no—
333#131—184no—
334C2×M16—91no—
335C2×M16—91no—
336C2×M16—91no—
337C2×M16—91no—
338C2×M16—91no—
339C2×M16—91no—
340C2×M16—184no—
341C2×M16C2×C3⋊D311yescharacteristic
342C2×M16C2×C3⋊D311yescharacteristic, complemented
343C22×C8—91no—
344C22×C8—91no—
345C22×C8—91no—
346C22×C8—91no—
347#123—91no—
348#123—91no—
349C22⋊Q8—91no—
350C22⋊Q8—91no—
351#121—91no—
352#121—91no—
353#120—91no—
354#120—91no—
355C4×D4—91no—
356C4×D4—91no—
357C4×D4—91no—
358C4×D4C2×C3⋊D311yescharacteristic
359#117—91no—
360C4⋊C8—91no—
361C4⋊C8—91no—
362C4⋊C8—91no—
363C4⋊C8C2×C3⋊D311yescharacteristic, complemented
364C22⋊C8—91no—
365C22⋊C8—91no—
366C22⋊C8—91no—
367C22⋊C8—91no—
368C22⋊C8—91no—
369C22⋊C8—91no—
370C22⋊C8C2×C3⋊D311yescharacteristic
371C22⋊C8C2×C3⋊D311yescharacteristic, complemented
372#97—91no—
373#97—91no—
374C4×C8—91no—
375C4×C8C2×C3⋊D311yescharacteristic, complemented
376C23×C3C2×C4×D314yes—
377C23×C3C2×C4×D314yes—
378C22×D3—34no—
379C22×D3—34no—
380C22×D3—34no—
381C22×D3—68no—
382C22×D3—124no—
383C22×D3—124no—
384C3×D4—44no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4C2×C4×D314yes—
390C2×C3×C4C2×C4×D314yes—
391C2×C3×C4C2×C4×D314yes—
392C2×C3×C4C2×C4×D314yes—
393C2×C3×C4C23×D314yes—
394#67—68no—
395#67—68no—
396#67—124no—
397#67—124no—
398C2×Dic3—34no—
399C2×Dic3—34no—
400C2×Dic3—34no—
401C2×Dic3—34no—
402C2×Dic3—34no—
403C2×Dic3—68no—
404D12—68no—
405D12—124no—
406C4×D3—38no—
407C4×D3—38no—
408C4×D3—68no—
409C4×D3—68no—
410C4×D3—64no—
411C4×D3—64no—
412C4×D3—64no—
413C4×D3—64no—
414Dic6—68no—
415C3×C8—24no—
416C3×C8—24no—
417C3×C8—24no—
418C3×C8D3×D418yes—
419C3⋊C8—38no—
420C3⋊C8—64no—
421C3⋊C8—64no—
422C3⋊C8—64no—
423C2×C32—41no—
424C2×C32—41no—
425C2×C32C2×C4×D411yescharacteristic
426C2×C32#56811yescharacteristic
427C2×C32#56811yescharacteristic
428C3⋊D3—22no—
429C3⋊D3—41no—
430C3⋊D3—41no—
431C24—91no—
432#41—182no—
433#41—182no—
434C2×Q8—91no—
435C2×D4—91no—
436C2×D4—91no—
437C2×D4—91no—
438C2×D4—91no—
439C2×D4—91no—
440C2×D4—91no—
441C2×D4C4×C3⋊D311yescharacteristic
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—91no—
445C22×C4—91no—
446C22×C4—91no—
447C22×C4—91no—
448C22×C4—182no—
449C22×C4—182no—
450C22×C4C22×C3⋊D311yescharacteristic
451C22×C4C22×C3⋊D311yescharacteristic
452M16—22no—
453M16—22no—
454M16—182no—
455M16—182no—
456M16—182no—
457M16—182no—
458M16—182no—
459M16—182no—
460C2×C8—91no—
461C2×C8—94no—
462C2×C8—91no—
463C2×C8—91no—
464C2×C8—91no—
465C2×C8—182no—
466C2×C8—182no—
467C2×C8—182no—
468C2×C8C22×C3⋊D311yescharacteristic
469C2×C8C22×C3⋊D311yescharacteristic
470C2×C8C22×C3⋊D311yescharacteristic
471C2×C8C22×C3⋊D311yescharacteristic
472C4⋊C4—91no—
473C4⋊C4—91no—
474C4⋊C4—91no—
475C4⋊C4—91no—
476C4⋊C4—91no—
477C4⋊C4C4×C3⋊D311yescharacteristic
478C22⋊C4—91no—
479C22⋊C4—91no—
480C22⋊C4—91no—
481C22⋊C4—91no—
482C22⋊C4—91no—
483C22⋊C4—91no—
484C22⋊C4—91no—
485C22⋊C4—91no—
486C22⋊C4C4×C3⋊D311yescharacteristic
487C22⋊C4C4×C3⋊D311yescharacteristic
488C42—91no—
489C42C22×C3⋊D311yescharacteristic
490C22×C3—24no—
491C22×C3—24no—
492C22×C3—24no—
493C22×C3—24no—
494C22×C3—24no—
495C22×C3—24no—
496C22×C3C22×C4×D314yes—
497C2×D3—38no—
498C2×D3—64no—
499C2×D3—64no—
500C2×D3—64no—
501C2×D3—64no—
502C2×D3—64no—
503C2×D3—64no—
504C2×D3—64no—
505C2×D3—64no—
506C2×D3—1216no—
507C3×C4—24no—
508C3×C4—24no—
509C3×C4—24no—
510C3×C4—24no—
511C3×C4C2×D3×D414yes—
512C3×C4D3×#4114yes—
513Dic3—38no—
514Dic3—64no—
515Dic3—64no—
516Dic3—64no—
517Dic3—64no—
518C32#293011yescharacteristic, complemented, Sylow
519C23—91no—
520C23—91no—
521C23—91no—
522C23—182no—
523C23—361no—
524C23—361no—
525C23C2×C4×C3⋊D311yescharacteristic
526C23C2×C4×C3⋊D311yescharacteristic
527Q8—182no—
528D4—41no—
529D4—182no—
530D4—182no—
531D4—182no—
532D4—361no—
533D4—361no—
534D4—361no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—91no—
540C2×C4—92no—
541C2×C4—92no—
542C2×C4—91no—
543C2×C4—91no—
544C2×C4—91no—
545C2×C4—91no—
546C2×C4—182no—
547C2×C4—182no—
548C2×C4—182no—
549C2×C4—181no—
550C2×C4—181no—
551C2×C4—181no—
552C2×C4—181no—
553C2×C4C2×C4×C3⋊D311yescharacteristic
554C2×C4C2×C4×C3⋊D311yescharacteristic
555C2×C4C2×C4×C3⋊D311yescharacteristic
556C2×C4C2×C4×C3⋊D311yescharacteristic
557C2×C4C23×C3⋊D311yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—92no—
562C8—181no—
563C8—181no—
564C8—181no—
565C8D4×C3⋊D312yes—
566C2×C3—44no—
567C2×C3—44no—
568C2×C3C4×D3×D414yes—
569C2×C3#574514yes—
570C2×C3#575014yes—
571D3—68no—
572D3—124no—
573D3—124no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—92no—
581C22—181no—
582C22—181no—
583C22—181no—
584C22—181no—
585C22—181no—
586C22—181no—
587C22—181no—
588C22—181no—
589C22—364no—
590C22C22×C4×C3⋊D311yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—92no—
596C4—181no—
597C4—181no—
598C4—181no—
599C4—181no—
600C4C2×D4×C3⋊D311yescharacteristic
601C4#41×C3⋊D311yescharacteristic
602C3#7953714yescomplemented
603C2—41no—
604C2—41no—
605C2—182no—
606C2—361no—
607C2—361no—
608C2C4×D4×C3⋊D311yescharacteristic
609C2#1059621611yescharacteristic
610C2#1059622111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×C3⋊D3
commutator, socleC22×C32C23×C4
FittingC32×#436C2
prime radical#10596018C2
cosocleC2×C32×C4C24
hypercenter#436C3⋊D3
hypocenterC32#2930
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#64116C2semidirect
2. C2×M16×C3⋊D3C2semidirect
4. C32×#436C2semidirect
5. #10592827C2semidirect
6. #10592827C2semidirect
7. #10592710C2semidirect
8. #10592538C2semidirect
9. #10592535C2semidirect
10. #10592429C2semidirect
11. #10592427C2semidirect
12. #10592426C2semidirect
13. #10592425C2semidirect
14. #10592388C2semidirect
15. #10592387C2semidirect
20. C2×C32×M16C22semidirect
27. C22×C3⋊(C3⋊C8)C22semidirect
34. C2×#3743C22semidirect
37. C2×C8×C3⋊D3C22semidirect
46. C32×C4⋊C8C22semidirect
48. C32×C22⋊C8C22semidirect
49. C32×C4×C8C22semidirect
51. #63657C22semidirect
54. #63647C22semidirect
55. #63647C22semidirect
56. #63642C22semidirect
57. #63641C22semidirect
58. #63641C22semidirect
59. C8×C3⋊Dic3C22semidirect
60. C4⋊(C3⋊(C3⋊C8))C22semidirect
61. #63630C22semidirect
65. C3×#436D3semidirect
135. C8×C3⋊D3D4semidirect
140. C2×C3×M16C2×D3semidirect
166. C3×C4⋊C8C2×D3semidirect
168. C3×C22⋊C8C2×D3semidirect
169. C3×C4×C8C2×D3semidirect
235. #436C3⋊D3semidirect
342. C2×M16C2×C3⋊D3semidirect
363. C4⋊C8C2×C3⋊D3semidirect
371. C22⋊C8C2×C3⋊D3semidirect
375. C4×C8C2×C3⋊D3semidirect
518. C32#2930semidirect
602. C3#79537semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
C2×M16×C3⋊D32
#105960182
C32×#4362
#105928272
#105927102
#105925382
#105925352
#105924292
#105924272
#105924262
#105924252
#105923882
#105923872
#795373