Finite Group Databasebeta

← #11859382

Subgroups — #11859382

Order 1152.

738 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×#63469C211yesmaximal, characteristic, complemented
2C2×M16×D9C211yesmaximal, characteristic, complemented
3#10589649C211yesmaximal, characteristic
4C9×#436C211yesmaximal, characteristic, complemented
5#10588810C211yesmaximal, characteristic, complemented
6#10588810C211yesmaximal, characteristic, complemented
7#10588688C211yesmaximal, characteristic, complemented
8#10588523C211yesmaximal, characteristic, complemented
9#10588520C211yesmaximal, characteristic, complemented
10#10588412C211yesmaximal, characteristic, complemented
11#10588410C211yesmaximal, characteristic, complemented
12#10588409C211yesmaximal, characteristic, complemented
13#10588408C211yesmaximal, characteristic, complemented
14#10588371C211yesmaximal, characteristic, complemented
15#10588370C211yesmaximal, characteristic, complemented
16#79537—31nomaximal
17C2×#3697C2211yescharacteristic
18C22×C4×D9C2211yescharacteristic
19C2×C9×M16C2211yescharacteristic
20C2×C9×M16C2211yescharacteristic, complemented
21C4×D4×C9C2211yescharacteristic
22#63501C411yescharacteristic
23#63499C411yescharacteristic
24C4×#611C2211yescharacteristic
25C4×#611C2211yescharacteristic
26C2×#3667C2211yescharacteristic
27C22×C9⋊C8C2211yescharacteristic, complemented
28#63469—24no—
29M16×D9—24no—
30C2×#3663C2211yescharacteristic
31C2×#3663C2211yescharacteristic
32C2×#3663C2211yescharacteristic
33C2×#3663C2211yescharacteristic
34C2×#3663C2211yescharacteristic, complemented
35C2×C8×D9C2211yescharacteristic
36C2×C8×D9C2211yescharacteristic
37C2×C8×D9C2211yescharacteristic, complemented
38#63458C411yescharacteristic
39#63456C411yescharacteristic
40#63446C411yescharacteristic
41#63445C411yescharacteristic
42#63444C411yescharacteristic
43#63440C411yescharacteristic
44C4×D36C2211yescharacteristic
45#63434C2211yescharacteristic
46C9×C4⋊C8C2211yescharacteristic, complemented
47C9×C22⋊C8C2211yescharacteristic
48C9×C22⋊C8C2211yescharacteristic, complemented
49C4×C8×C9C2211yescharacteristic, complemented
50#63389C2211yescharacteristic
51#63389C2211yescharacteristic, complemented
52(C2×D9)⋊C8C2211yescharacteristic
53(C2×D9)⋊C8C2211yescharacteristic
54(C2×D9)⋊C8C2211yescharacteristic, complemented
55(C2×D9)⋊C8C2211yescharacteristic, complemented
56#63375C2211yescharacteristic, complemented
57Dic9⋊C8C2211yescharacteristic, complemented
58Dic9⋊C8C2211yescharacteristic, complemented
59C8×Dic9C2211yescharacteristic, complemented
60C4⋊(C9⋊C8)C2211yescharacteristic, complemented
61#63362C2211yescharacteristic, complemented
62C2×#907—31no—
63C2×D3×M16—31no—
64#5547—31no—
65C3×#436D311yescharacteristic
66#5128—31no—
67#5128—31no—
68#5011—31no—
69#4839—31no—
70#4836—31no—
71#4730—31no—
72#4728—31no—
73#4727—31no—
74#4726—31no—
75#4689—31no—
76#4688—31no—
77C23×D9C2×C411yescharacteristic
78C2×D4×C9C2×C411yescharacteristic
79C22×C4×C9C2311yescharacteristic
80C22×C4×C9C2311yescharacteristic
81C2×#611C2×C411yescharacteristic
82C2×#611C2×C411yescharacteristic
83C2×#611C2×C411yescharacteristic
84C2×#611C2×C411yescharacteristic
85C22×Dic9C2×C411yescharacteristic
86#3697—22no—
87#3697—22no—
88C2×D36C2×C411yescharacteristic
89C2×D36C2×C411yescharacteristic
90C2×C4×D9—22no—
91C2×C4×D9—22no—
92C2×C4×D9C2×C411yescharacteristic
93C2×C4×D9C2×C411yescharacteristic
94C2×C4×D9C2311yescharacteristic
95C2×C4×D9C2311yescharacteristic
96C2×C4×D9C2311yescharacteristic
97C2×Dic18C2×C411yescharacteristic
98C9×M16—22no—
99C9×M16—22no—
100C2×C8×C9C2311yescharacteristic
101C2×C8×C9C2311yescharacteristic
102C2×C8×C9C2311yescharacteristic
103C2×C8×C9C2311yescharacteristic
104C9×C4⋊C4C2×C411yescharacteristic
105C9×C22⋊C4C2×C411yescharacteristic
106C9×C22⋊C4C2×C411yescharacteristic
107C42×C9C2311yescharacteristic
108#3676C2×C411yescharacteristic
109#3676C2×C411yescharacteristic
110(C2×D9)⋊C4C2×C411yescharacteristic
111(C2×D9)⋊C4C2×C411yescharacteristic
112(C2×D9)⋊C4C2×C411yescharacteristic
113(C2×D9)⋊C4C2×C411yescharacteristic
114(C2×D9)⋊C4C2×C411yescharacteristic
115(C2×D9)⋊C4C2×C411yescharacteristic
116C4⋊Dic9C2×C411yescharacteristic
117Dic9⋊C4C2×C411yescharacteristic
118Dic9⋊C4C2×C411yescharacteristic
119Dic9⋊C4C2×C411yescharacteristic
120Dic9⋊C4C2×C411yescharacteristic
121C4×Dic9C2311yescharacteristic
122#3667—22no—
123C2×C9⋊C8—22no—
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126C2×C9⋊C8C2311yescharacteristic
127C2×C9⋊C8C2311yescharacteristic
128#3663—22no—
129#3663—22no—
130#3663—22no—
131#3663—22no—
132#3663—22no—
133C8×D9—22no—
134C8×D9—22no—
135C8×D9D414yescomplemented
136#2930—91noSylow
137C2×#235—31no—
138C22×C4×D3—31no—
139C2×C3×M16C2×D311yescharacteristic
140C2×C3×M16C2×D311yescharacteristic
141C3×C4×D4C2×D311yescharacteristic
142#939—31no—
143#937—31no—
144C4×#67—31no—
145C4×#67—31no—
146C2×#208—31no—
147C22×C3⋊C8—31no—
148#907—64no—
149D3×M16—64no—
150C2×ΓL(1,𝔽25)—31no—
151C2×ΓL(1,𝔽25)—31no—
152C2×ΓL(1,𝔽25)—31no—
153C2×ΓL(1,𝔽25)—31no—
154C2×ΓL(1,𝔽25)—31no—
155C2×D3×C8—31no—
156C2×D3×C8—31no—
157C2×D3×C8—31no—
158#896—31no—
159#894—31no—
160#884—31no—
161#883—31no—
162#882—31no—
163#878—31no—
164C4×D12—31no—
165#872—31no—
166C3×C4⋊C8C2×D311yescharacteristic
167C3×C22⋊C8C2×D311yescharacteristic
168C3×C22⋊C8C2×D311yescharacteristic
169C3×C4×C8C2×D311yescharacteristic
170#830—31no—
171#830—31no—
172(C2×D3)⋊C8—31no—
173(C2×D3)⋊C8—31no—
174(C2×D3)⋊C8—31no—
175(C2×D3)⋊C8—31no—
176#815—31no—
177Dic3⋊C8—31no—
178Dic3⋊C8—31no—
179C8×Dic3—31no—
180C4⋊(C3⋊C8)—31no—
181#803—31no—
182C23×C9C22×C411yescharacteristic
183C23×C9C22×C411yescharacteristic
184C22×D9—22no—
185C22×D9—41no—
186C22×D9—41no—
187C22×D9C22×C411yescharacteristic
188C22×D9C22×C411yescharacteristic
189C22×D9C22×C411yescharacteristic
190D4×C9—41no—
191C2×C4×C9—21no—
192C2×C4×C9—21no—
193C2×C4×C9—21no—
194C2×C4×C9—21no—
195C2×C4×C9C22×C411yescharacteristic
196C2×C4×C9C22×C411yescharacteristic
197C2×C4×C9C22×C411yescharacteristic
198C2×C4×C9C22×C411yescharacteristic
199C2×C4×C9C2411yescharacteristic
200#611—22no—
201#611—22no—
202#611—41no—
203#611—41no—
204C2×Dic9—22no—
205C2×Dic9C22×C411yescharacteristic
206C2×Dic9C22×C411yescharacteristic
207C2×Dic9C22×C411yescharacteristic
208C2×Dic9C22×C411yescharacteristic
209C2×Dic9C22×C411yescharacteristic
210D36—22no—
211D36—41no—
212C4×D9—22no—
213C4×D9—21no—
214C4×D9—21no—
215C4×D9—21no—
216C4×D9—21no—
217C4×D9—22no—
218C4×D9C2×D412yes—
219C4×D9#4112yes—
220Dic18—22no—
221C8×C9—21no—
222C8×C9—21no—
223C8×C9—21no—
224C8×C9C2×D412yes—
225C9⋊C8—21no—
226C9⋊C8—21no—
227C9⋊C8—21no—
228C9⋊C8C2×D412yes—
229C2×#131—91no—
230C22×M16—91no—
231#525—91no—
232#436—91no—
233#436—91no—
234#436—91no—
235#436D911yescharacteristic, 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—31no—
245C2×C3×D4C4×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C2×#67—31no—
249C2×#67—31no—
250C2×#67—31no—
251C2×#67—31no—
252C22×Dic3—31no—
253#235—62no—
254#235—62no—
255C2×D12—31no—
256C2×D12—31no—
257C2×C4×D3—31no—
258C2×C4×D3—31no—
259C2×C4×D3—31no—
260C2×C4×D3—31no—
261C2×C4×D3—31no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×Dic6—31no—
265C3×M16—22no—
266C3×M16—22no—
267C2×C3×C8C22×D311yescharacteristic
268C2×C3×C8C22×D311yescharacteristic
269C2×C3×C8C22×D311yescharacteristic
270C2×C3×C8C22×D311yescharacteristic
271C3×C4⋊C4C4×D311yescharacteristic
272C3×C22⋊C4C4×D311yescharacteristic
273C3×C22⋊C4C4×D311yescharacteristic
274C3×C42C22×D311yescharacteristic
275#217—31no—
276#217—31no—
277(C2×D3)⋊C4—31no—
278(C2×D3)⋊C4—31no—
279(C2×D3)⋊C4—31no—
280(C2×D3)⋊C4—31no—
281(C2×D3)⋊C4—31no—
282(C2×D3)⋊C4—31no—
283C4⋊Dic3—31no—
284Dic3⋊C4—31no—
285Dic3⋊C4—31no—
286Dic3⋊C4—31no—
287Dic3⋊C4—31no—
288C4×Dic3—31no—
289#208—62no—
290C2×C3⋊C8—31no—
291C2×C3⋊C8—31no—
292C2×C3⋊C8—31no—
293C2×C3⋊C8—31no—
294C2×C3⋊C8—62no—
295ΓL(1,𝔽25)—62no—
296ΓL(1,𝔽25)—62no—
297ΓL(1,𝔽25)—62no—
298ΓL(1,𝔽25)—62no—
299ΓL(1,𝔽25)—62no—
300D3×C8—34no—
301D3×C8—62no—
302D3×C8—62no—
303C22×C9—21no—
304C22×C9—21no—
305C22×C9—21no—
306C22×C9—21no—
307C22×C9—21no—
308C22×C9—21no—
309C22×C9C23×C411yescharacteristic
310C2×D9—21no—
311C2×D9—21no—
312C2×D9—21no—
313C2×D9—21no—
314C2×D9—21no—
315C2×D9—21no—
316C2×D9—21no—
317C2×D9—21no—
318C2×D9—44no—
319C2×D9C4×D412yes—
320C4×C9—21no—
321C4×C9—21no—
322C4×C9—21no—
323C4×C9—21no—
324C4×C9C22×D411yescharacteristic
325C4×C9C2×#4111yescharacteristic
326Dic9—21no—
327Dic9—21no—
328Dic9—21no—
329Dic9—21no—
330Dic9C4×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×D911yescharacteristic
342C2×M16C2×D911yescharacteristic, 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×D911yescharacteristic
359#117—91no—
360C4⋊C8—91no—
361C4⋊C8—91no—
362C4⋊C8—91no—
363C4⋊C8C2×D911yescharacteristic, complemented
364C22⋊C8—91no—
365C22⋊C8—91no—
366C22⋊C8—91no—
367C22⋊C8—91no—
368C22⋊C8—91no—
369C22⋊C8—91no—
370C22⋊C8C2×D911yescharacteristic
371C22⋊C8C2×D911yescharacteristic, complemented
372#97—91no—
373#97—91no—
374C4×C8—91no—
375C4×C8C2×D911yescharacteristic, complemented
376C23×C3C2×C4×D311yescharacteristic
377C23×C3C2×C4×D311yescharacteristic
378C22×D3—31no—
379C22×D3—31no—
380C22×D3—31no—
381C22×D3—62no—
382C22×D3—121no—
383C22×D3—121no—
384C3×D4—41no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4C2×C4×D311yescharacteristic
390C2×C3×C4C2×C4×D311yescharacteristic
391C2×C3×C4C2×C4×D311yescharacteristic
392C2×C3×C4C2×C4×D311yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394#67—62no—
395#67—62no—
396#67—121no—
397#67—121no—
398C2×Dic3—31no—
399C2×Dic3—31no—
400C2×Dic3—31no—
401C2×Dic3—31no—
402C2×Dic3—31no—
403C2×Dic3—62no—
404D12—62no—
405D12—121no—
406C4×D3—32no—
407C4×D3—32no—
408C4×D3—62no—
409C4×D3—62no—
410C4×D3—61no—
411C4×D3—61no—
412C4×D3—61no—
413C4×D3—61no—
414Dic6—62no—
415C3×C8—21no—
416C3×C8—21no—
417C3×C8—21no—
418C3×C8D3×D412yes—
419C3⋊C8—32no—
420C3⋊C8—61no—
421C3⋊C8—61no—
422C3⋊C8—61no—
423C2×C9—41no—
424C2×C9—41no—
425C2×C9C2×C4×D411yescharacteristic
426C2×C9#56811yescharacteristic
427C2×C9#56811yescharacteristic
428D9—22no—
429D9—41no—
430D9—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×D911yescharacteristic
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×D911yescharacteristic
451C22×C4C22×D911yescharacteristic
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×D911yescharacteristic
469C2×C8C22×D911yescharacteristic
470C2×C8C22×D911yescharacteristic
471C2×C8C22×D911yescharacteristic
472C4⋊C4—91no—
473C4⋊C4—91no—
474C4⋊C4—91no—
475C4⋊C4—91no—
476C4⋊C4—91no—
477C4⋊C4C4×D911yescharacteristic
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×D911yescharacteristic
487C22⋊C4C4×D911yescharacteristic
488C42—91no—
489C42C22×D911yescharacteristic
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3C22×C4×D311yescharacteristic
497C2×D3—32no—
498C2×D3—61no—
499C2×D3—61no—
500C2×D3—61no—
501C2×D3—61no—
502C2×D3—61no—
503C2×D3—61no—
504C2×D3—61no—
505C2×D3—61no—
506C2×D3—124no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4C2×D3×D411yescharacteristic
512C3×C4D3×#4111yescharacteristic
513Dic3—32no—
514Dic3—61no—
515Dic3—61no—
516Dic3—61no—
517Dic3—61no—
518C9#293011yescharacteristic, complemented, Sylow
519C23—91no—
520C23—91no—
521C23—91no—
522C23—182no—
523C23—361no—
524C23—361no—
525C23C2×C4×D911yescharacteristic
526C23C2×C4×D911yescharacteristic
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×D911yescharacteristic
554C2×C4C2×C4×D911yescharacteristic
555C2×C4C2×C4×D911yescharacteristic
556C2×C4C2×C4×D911yescharacteristic
557C2×C4C23×D911yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—92no—
562C8—181no—
563C8—181no—
564C8—181no—
565C8D4×D912yes—
566C2×C3—41no—
567C2×C3—41no—
568C2×C3C4×D3×D411yescharacteristic
569C2×C3#574511yescharacteristic
570C2×C3#575011yescharacteristic
571D3—62no—
572D3—121no—
573D3—121no—
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×D911yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—92no—
596C4—181no—
597C4—181no—
598C4—181no—
599C4—181no—
600C4C2×D4×D911yescharacteristic
601C4#41×D911yescharacteristic
602C3#7953711yescharacteristic
603C2—41no—
604C2—41no—
605C2—182no—
606C2—361no—
607C2—361no—
608C2C4×D4×D911yescharacteristic
609C2#1058984711yescharacteristic
610C2#1058985211yescharacteristic
subgroupG/H
centerC2×C4C23×D9
commutatorC22×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC9×#436C2
socleC22×C3C22×C4×D3
prime radical#10589649C2
cosocleC2×C4×C9C24
hypercenter#436D9
hypocenterC9#2930
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#63469C2semidirect
2. C2×M16×D9C2semidirect
4. C9×#436C2semidirect
5. #10588810C2semidirect
6. #10588810C2semidirect
7. #10588688C2semidirect
8. #10588523C2semidirect
9. #10588520C2semidirect
10. #10588412C2semidirect
11. #10588410C2semidirect
12. #10588409C2semidirect
13. #10588408C2semidirect
14. #10588371C2semidirect
15. #10588370C2semidirect
20. C2×C9×M16C22semidirect
27. C22×C9⋊C8C22semidirect
34. C2×#3663C22semidirect
37. C2×C8×D9C22semidirect
46. C9×C4⋊C8C22semidirect
48. C9×C22⋊C8C22semidirect
49. C4×C8×C9C22semidirect
51. #63389C22semidirect
54. (C2×D9)⋊C8C22semidirect
55. (C2×D9)⋊C8C22semidirect
56. #63375C22semidirect
57. Dic9⋊C8C22semidirect
58. Dic9⋊C8C22semidirect
59. C8×Dic9C22semidirect
60. C4⋊(C9⋊C8)C22semidirect
61. #63362C22semidirect
135. C8×D9D4semidirect
235. #436D9semidirect
342. C2×M16C2×D9semidirect
363. C4⋊C8C2×D9semidirect
371. C22⋊C8C2×D9semidirect
375. C4×C8C2×D9semidirect
518. C9#2930semidirect

Maximal subgroups

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

subgroupindex
C2×#634692
C2×M16×D92
#105896492
C9×#4362
#105888102
#105886882
#105885232
#105885202
#105884122
#105884102
#105884092
#105884082
#105883712
#105883702
#795373