Finite Group Databasebeta

← #11889344

Subgroups — #11889344

Order 1152.

564 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Q8×C9C211yesmaximal, characteristic
2#10589643C211yesmaximal, characteristic
3#10588907C211yesmaximal, characteristic, complemented
4#10588907C211yesmaximal, characteristic, complemented
5#10588906C211yesmaximal, characteristic, complemented
6C2×#63395C211yesmaximal, characteristic, complemented
7#10588763C211yesmaximal, characteristic, complemented
8#10588762C211yesmaximal, characteristic, complemented
9#10588728C211yesmaximal, characteristic, complemented
10#10588727C211yesmaximal, characteristic, complemented
11#10588725C211yesmaximal, characteristic, complemented
12#10588723C211yesmaximal, characteristic, complemented
13#10588706C211yesmaximal, characteristic, complemented
14#10588704C211yesmaximal, characteristic, complemented
15#10588688C211yesmaximal, characteristic
16#83552—31nomaximal
17C22×Q8×C9C2211yescharacteristic
18C22×Q8×C9C2211yescharacteristic
19C9×C4⋊Q8—21no—
20C9×C4⋊Q8C2211yescharacteristic
21C9×C22⋊Q8—21no—
22C9×C22⋊Q8—21no—
23C9×C22⋊Q8C2211yescharacteristic
24C9×C22⋊Q8C2211yescharacteristic
25C4×Q8×C9C2211yescharacteristic
26C4×D4×C9—21no—
27C4×D4×C9C2211yescharacteristic
28C2×#3674C2211yescharacteristic
29C2×#3674C2211yescharacteristic
30C2×#3674C2211yescharacteristic
31#63497—21no—
32#63488C2211yescharacteristic
33C2×C4⋊Dic9C2211yescharacteristic
34#63486C2211yescharacteristic
35#63486C2211yescharacteristic
36C2×#3667C2211yescharacteristic
37C22×C9⋊C8C2211yescharacteristic
38#63451—21no—
39#63441—21no—
40#63439—21no—
41#63432C2211yescharacteristic
42C4×Dic18C2211yescharacteristic
43#63395C2211yescharacteristic
44#63395C2211yescharacteristic
45#63395C2211yescharacteristic
46#63395C2211yescharacteristic
47#63395C2211yescharacteristic
48#63395C2211yescharacteristic
49#63395C2211yescharacteristic
50#63395C2211yescharacteristic
51#63395C2211yescharacteristic
52#63389C2211yescharacteristic
53#63389C2211yescharacteristic
54#63368C2211yescharacteristic
55#63367C2211yescharacteristic
56#63367C2211yescharacteristic
57#63366C2211yescharacteristic
58C4⋊(C9⋊C8)C2211yescharacteristic
59#63362C2211yescharacteristic
60C3×D4×Q8D311yescharacteristic
61#5541—31no—
62#5228—31no—
63#5228—31no—
64#5225—31no—
65C2×#835—31no—
66#5090—31no—
67#5082—31no—
68#5052—31no—
69#5051—31no—
70#5045—31no—
71#5043—31no—
72#5030—31no—
73#5022—31no—
74#5011—31no—
75C2×Q8×C9—21no—
76C2×Q8×C9—21no—
77C2×Q8×C9—22no—
78C2×Q8×C9—22no—
79C2×Q8×C9—41no—
80C2×Q8×C9—41no—
81C2×Q8×C9C2311yescharacteristic
82C2×Q8×C9C2311yescharacteristic
83C2×Q8×C9C2311yescharacteristic
84C2×D4×C9D411yescharacteristic
85C22×C4×C9—21no—
86C22×C4×C9—21no—
87C22×C4×C9C2311yescharacteristic
88C22×C4×C9C2311yescharacteristic
89C22×Dic9—21no—
90C2×Dic18C2311yescharacteristic
91C9×C4⋊C4—21no—
92C9×C4⋊C4—21no—
93C9×C4⋊C4—21no—
94C9×C4⋊C4—21no—
95C9×C4⋊C4—21no—
96C9×C4⋊C4D411yescharacteristic
97C9×C4⋊C4C2311yescharacteristic
98C9×C22⋊C4—21no—
99C9×C22⋊C4—21no—
100C9×C22⋊C4D411yescharacteristic
101C9×C22⋊C4D411yescharacteristic
102C42×C9—21no—
103C42×C9C2311yescharacteristic
104#3676—21no—
105#3676—21no—
106#3676—21no—
107#3674—22no—
108#3674—41no—
109#3674—41no—
110C4⋊Dic9—21no—
111C4⋊Dic9C2311yescharacteristic
112C4⋊Dic9C2311yescharacteristic
113C4⋊Dic9C2311yescharacteristic
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4—21no—
119C4×Dic9—21no—
120C4×Dic9—21no—
121#3667—41no—
122C2×C9⋊C8—41no—
123C2×C9⋊C8C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126C2×C9⋊C8C2311yescharacteristic
127#3312—91noSylow
128C22×C3×Q8C2×D311yescharacteristic
129C22×C3×Q8C2×D311yescharacteristic
130C3×C4⋊Q8—21no—
131C3×C4⋊Q8C2×D311yescharacteristic
132C3×C22⋊Q8—21no—
133C3×C22⋊Q8—21no—
134C3×C22⋊Q8C2×D311yescharacteristic
135C3×C22⋊Q8C2×D311yescharacteristic
136C3×C4×Q8C2×D311yescharacteristic
137C3×C4×D4—21no—
138C3×C4×D4C2×D311yescharacteristic
139C2×#216—31no—
140C2×#216—31no—
141C2×#216—31no—
142#935—61no—
143#926—31no—
144C2×C4⋊Dic3—31no—
145#924—31no—
146#924—31no—
147C2×#208—31no—
148C22×C3⋊C8—31no—
149#889—61no—
150#879—61no—
151#877—61no—
152#870—31no—
153C4×Dic6—31no—
154#835—31no—
155#835—31no—
156#835—31no—
157#835—31no—
158#835—31no—
159#835—31no—
160#835—31no—
161#835—31no—
162#835—31no—
163#830—31no—
164#830—31no—
165#810—31no—
166#808—31no—
167#808—31no—
168#807—31no—
169C4⋊(C3⋊C8)—31no—
170#803—31no—
171C23×C9C2×D411yescharacteristic
172C23×C9C2×D411yescharacteristic
173Q8×C9—21no—
174Q8×C9—21no—
175Q8×C9—21no—
176Q8×C9—21no—
177Q8×C9—21no—
178Q8×C9—42no—
179Q8×C9—42no—
180Q8×C9#4112yes—
181D4×C9—22no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9—21no—
188C2×C4×C9—21no—
189C2×C4×C9—21no—
190C2×C4×C9—42no—
191C2×C4×C9—42no—
192C2×C4×C9C2×D411yescharacteristic
193C2×C4×C9C2×D411yescharacteristic
194C2×C4×C9C2×D411yescharacteristic
195C2×C4×C9C2×D411yescharacteristic
196C2×C4×C9C2411yescharacteristic
197C2×Dic9—21no—
198C2×Dic9—21no—
199C2×Dic9—21no—
200C2×Dic9—21no—
201C2×Dic9—42no—
202Dic18—21no—
203Dic18—21no—
204C9⋊C8—21no—
205C9⋊C8—21no—
206C9⋊C8—21no—
207C9⋊C8—21no—
208#552—91no—
209D4×Q8D911yescharacteristic
210#491—91no—
211#485—91no—
212#483—91no—
213#479—91no—
214#470—91no—
215#467—91no—
216#462—91no—
217#451—91no—
218#451—91no—
219#441—91no—
220#435—91no—
221#419—91no—
222C2×#103—91no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—22no—
226C2×C3×Q8—22no—
227C2×C3×Q8—41no—
228C2×C3×Q8—41no—
229C2×C3×Q8C22×D311yescharacteristic
230C2×C3×Q8C22×D311yescharacteristic
231C2×C3×Q8C22×D311yescharacteristic
232C2×C3×D4#6711yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×Dic3—61no—
238C2×Dic6—31no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4#6711yescharacteristic
245C3×C4⋊C4C22×D311yescharacteristic
246C3×C22⋊C4—21no—
247C3×C22⋊C4—21no—
248C3×C22⋊C4#6711yescharacteristic
249C3×C22⋊C4#6711yescharacteristic
250C3×C42—21no—
251C3×C42C22×D311yescharacteristic
252#217—61no—
253#217—61no—
254#217—61no—
255#216—62no—
256#216—121no—
257#216—121no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266Dic3⋊C4—61no—
267C4×Dic3—61no—
268C4×Dic3—61no—
269#208—121no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—121no—
275C22×C9—21no—
276C22×C9—21no—
277C22×C9—21no—
278C22×C9—21no—
279C22×C9—21no—
280C22×C9#13712yes—
281C22×C9C22×D411yescharacteristic
282C4×C9—21no—
283C4×C9—21no—
284C4×C9—22no—
285C4×C9—21no—
286C4×C9—21no—
287C4×C9—41no—
288C4×C9—41no—
289C4×C9—41no—
290C4×C9C2×#4111yescharacteristic
291C4×C9H(5,𝔽2)11yescharacteristic
292Dic9—41no—
293Dic9—41no—
294Dic9—41no—
295Dic9—41no—
296C22×Q8C2×D911yescharacteristic
297C22×Q8C2×D911yescharacteristic
298C2×Q16—91no—
299C2×Q16—91no—
300C2×Q16—91no—
301C2×M16—91no—
302C22×C8—91no—
303C4⋊Q8—21no—
304C4⋊Q8C2×D911yescharacteristic
305#126—181no—
306#125—91no—
307#125—181no—
308#123—181no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—91no—
312C22⋊Q8—91no—
313C22⋊Q8C2×D911yescharacteristic
314C22⋊Q8C2×D911yescharacteristic
315C4×Q8—91no—
316C4×Q8C2×D911yescharacteristic
317C4×D4—21no—
318C4×D4C2×D911yescharacteristic
319#117—91no—
320#117—181no—
321C2×C4⋊C4—91no—
322#107—91no—
323#106—91no—
324#106—91no—
325C4⋊C8—91no—
326#103—91no—
327#103—91no—
328#103—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336C22⋊C8—91no—
337C22⋊C8—91no—
338#97—91no—
339C23×C3C2×#6711yescharacteristic
340C23×C3C2×#6711yescharacteristic
341C3×Q8—21no—
342C3×Q8—21no—
343C3×Q8—21no—
344C3×Q8—21no—
345C3×Q8—21no—
346C3×Q8—42no—
347C3×Q8—42no—
348C3×Q8#23712yes—
349C3×D4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—122no—
370Dic6—61no—
371Dic6—61no—
372C3⋊C8—61no—
373C3⋊C8—61no—
374C3⋊C8—61no—
375C3⋊C8—61no—
376C2×C9—22no—
377C2×C9—41no—
378C2×C9#54611yescharacteristic
379C2×C9C2×#13711yescharacteristic
380C2×C9#57811yescharacteristic
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8—91no—
388C2×Q8C22×D911yescharacteristic
389C2×Q8C22×D911yescharacteristic
390C2×Q8C22×D911yescharacteristic
391C2×D4#61111yescharacteristic
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—181no—
395C22×C4C22×D911yescharacteristic
396C22×C4C22×D911yescharacteristic
397Q16—182no—
398Q16—361no—
399Q16—361no—
400M16—361no—
401C2×C8—91no—
402C2×C8—91no—
403C2×C8—91no—
404C2×C8—91no—
405C2×C8—361no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—91no—
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4#61111yescharacteristic
421C4⋊C4C22×D911yescharacteristic
422C22⋊C4—21no—
423C22⋊C4—21no—
424C22⋊C4—181no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4#61111yescharacteristic
428C22⋊C4#61111yescharacteristic
429C42—21no—
430C42—181no—
431C42—181no—
432C42C22×D911yescharacteristic
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3#94212yes—
439C22×C3C22×#6711yescharacteristic
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—22no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—41no—
446C3×C4—41no—
447C3×C4—41no—
448C3×C4C2×#23711yescharacteristic
449C3×C4#100411yescharacteristic
450Dic3—121no—
451Dic3—121no—
452Dic3—121no—
453Dic3—121no—
454C9#331211yescharacteristic, complemented, Sylow
455C23C2×#61111yescharacteristic
456C23C2×#61111yescharacteristic
457Q8—21no—
458Q8—21no—
459Q8—21no—
460Q8—21no—
461Q8—21no—
462Q8—42no—
463Q8—42no—
464Q8—181no—
465Q8—181no—
466Q8#369912yes—
467D4—22no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—362no—
483C2×C4C2×#61111yescharacteristic
484C2×C4C2×#61111yescharacteristic
485C2×C4C2×#61111yescharacteristic
486C2×C4C2×#61111yescharacteristic
487C2×C4C23×D911yescharacteristic
488C8—181no—
489C8—181no—
490C8—181no—
491C8—181no—
492C2×C3—22no—
493C2×C3—41no—
494C2×C3#580611yescharacteristic
495C2×C3C2×#94211yescharacteristic
496C2×C3#583811yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22#6350512yes—
503C22C22×#61111yescharacteristic
504C4—21no—
505C4—21no—
506C4—22no—
507C4—21no—
508C4—21no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—361no—
513C4—361no—
514C4—361no—
515C4—361no—
516C4C2×#369911yescharacteristic
517C4#6371011yescharacteristic
518C3#8355211yescharacteristic
519C2—22no—
520C2—41no—
521C2#1058990811yescharacteristic
522C2C2×#6350511yescharacteristic
523C2#1058994011yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingD4×Q8×C9C2
socleC22×C3C22×#67
prime radicalC2×C3×D4#67
hypercenterD4×Q8D9
hypocenterC9#3312
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
3. #10588907C2semidirect
4. #10588907C2semidirect
5. #10588906C2semidirect
6. C2×#63395C2semidirect
7. #10588763C2semidirect
8. #10588762C2semidirect
9. #10588728C2semidirect
10. #10588727C2semidirect
11. #10588725C2semidirect
12. #10588723C2semidirect
13. #10588706C2semidirect
14. #10588704C2semidirect
454. C9#3312semidirect

Maximal subgroups

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

subgroupindex
D4×Q8×C92
#105896432
#105889072
#105889062
C2×#633952
#105887632
#105887622
#105887282
#105887272
#105887252
#105887232
#105887062
#105887042
#105886882
#835523