Finite Group Databasebeta

← #11889323

Subgroups — #11889323

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
1Q8×#611C211yesmaximal, characteristic
2#10589741C211yesmaximal, characteristic
3C9×#451C211yesmaximal, characteristic, complemented
4#10588906C211yesmaximal, characteristic, complemented
5#10588868C211yesmaximal, characteristic, complemented
6#10588866C211yesmaximal, characteristic, complemented
7#10588864C211yesmaximal, characteristic, complemented
8#10588862C211yesmaximal, characteristic, complemented
9#10588728C211yesmaximal, characteristic, complemented
10#10588485C211yesmaximal, characteristic, complemented
11D9×#103C211yesmaximal, characteristic, complemented
12#10588477C211yesmaximal, characteristic, complemented
13#10588476C211yesmaximal, characteristic, complemented
14#10588410C211yesmaximal, characteristic
15#10588403C211yesmaximal, characteristic, complemented
16#80196—31nomaximal
17C22×Q8×C9C2211yescharacteristic
18C2×Q8×D9C2211yescharacteristic
19C2×C9×Q16C2211yescharacteristic
20C2×C9×Q16C2211yescharacteristic
21C9×C22⋊Q8C2211yescharacteristic
22#63508—21no—
23#63508C2211yescharacteristic
24#63508C2211yescharacteristic
25Q8×Dic9C2211yescharacteristic
26Q8×Dic9C2211yescharacteristic
27#63506—21no—
28#63506C2211yescharacteristic
29C2×#3674C2211yescharacteristic
30C4×#611—21no—
31C4×#611C2211yescharacteristic
32#63488C2211yescharacteristic
33#63486—21no—
34#63486C2211yescharacteristic
35C2×#3667C2211yescharacteristic
36C2×C8×D9C2211yescharacteristic
37#63454—21no—
38C4⋊C4×D9C2211yescharacteristic
39#63452C2211yescharacteristic
40#63451—21no—
41#63445—21no—
42#63441—21no—
43C9×#103C2211yescharacteristic
44C9×#103C2211yescharacteristic
45C9×C22⋊C8C2211yescharacteristic
46#63395C2211yescharacteristic
47#63395C2211yescharacteristic
48#63395C2211yescharacteristic
49#63395C2211yescharacteristic
50#63395C2211yescharacteristic
51(C2×D9)⋊C8C2211yescharacteristic
52#63378C2211yescharacteristic
53#63377C2211yescharacteristic
54#63376C2211yescharacteristic
55#63376C2211yescharacteristic
56#63375C2211yescharacteristic
57Dic9⋊C8C2211yescharacteristic
58#63368C2211yescharacteristic
59#63367C2211yescharacteristic
60Q8×#67—31no—
61#5639—31no—
62C3×#451D311yescharacteristic
63#5225—31no—
64#5188—31no—
65#5186—31no—
66#5184—31no—
67#5182—31no—
68#5052—31no—
69#4805—31no—
70D3×#103—31no—
71#4797—31no—
72#4796—31no—
73#4728—31no—
74#4723—31no—
75C2×Q8×C9—21no—
76C2×Q8×C9—22no—
77C2×Q8×C9—41no—
78C2×Q8×C9C2311yescharacteristic
79C2×Q8×C9C2311yescharacteristic
80C2×Q8×C9C2311yescharacteristic
81C22×C4×C9—21no—
82C22×C4×C9C2311yescharacteristic
83C2×#611D411yescharacteristic
84Q8×D9—22no—
85Q8×D9—41no—
86C2×C4×D9—21no—
87C2×C4×D9—21no—
88C2×C4×D9C2311yescharacteristic
89C2×Dic18—21no—
90C2×Dic18C2311yescharacteristic
91C9×Q16—22no—
92C9×Q16—41no—
93C2×C8×C9C2311yescharacteristic
94C2×C8×C9C2311yescharacteristic
95C9×C4⋊C4—21no—
96C9×C4⋊C4C2311yescharacteristic
97C9×C22⋊C4—21no—
98#3676—21no—
99#3676—21no—
100#3676D411yescharacteristic
101#3674—41no—
102(C2×D9)⋊C4—21no—
103(C2×D9)⋊C4—21no—
104(C2×D9)⋊C4D411yescharacteristic
105C4⋊Dic9—21no—
106C4⋊Dic9—21no—
107C4⋊Dic9—21no—
108C4⋊Dic9C2311yescharacteristic
109C4⋊Dic9C2311yescharacteristic
110C4⋊Dic9C2311yescharacteristic
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4D411yescharacteristic
119C4×Dic9—21no—
120C4×Dic9—21no—
121C4×Dic9—21no—
122C4×Dic9C2311yescharacteristic
123#3667—41no—
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126C8×D9—41no—
127#3312—91noSylow
128C22×C3×Q8C2×D311yescharacteristic
129C2×D3×Q8—31no—
130C2×C3×Q16C2×D311yescharacteristic
131C2×C3×Q16C2×D311yescharacteristic
132C3×C22⋊Q8C2×D311yescharacteristic
133#946—31no—
134#946—31no—
135#946—61no—
136Q8×Dic3—31no—
137Q8×Dic3—31no—
138#944—31no—
139#944—61no—
140C2×#216—31no—
141C4×#67—31no—
142C4×#67—61no—
143#926—31no—
144#924—31no—
145#924—61no—
146C2×#208—31no—
147C2×D3×C8—31no—
148#892—61no—
149D3×C4⋊C4—31no—
150#890—31no—
151#889—61no—
152#883—61no—
153#879—61no—
154C3×#103C2×D311yescharacteristic
155C3×#103C2×D311yescharacteristic
156C3×C22⋊C8C2×D311yescharacteristic
157#835—31no—
158#835—31no—
159#835—31no—
160#835—31no—
161#835—31no—
162(C2×D3)⋊C8—31no—
163#818—31no—
164#817—31no—
165#816—31no—
166#816—31no—
167#815—31no—
168Dic3⋊C8—31no—
169#810—31no—
170#808—31no—
171C23×C9C2×D411yescharacteristic
172C22×D9C2×D411yescharacteristic
173Q8×C9—21no—
174Q8×C9—21no—
175Q8×C9—21no—
176Q8×C9—21no—
177Q8×C9—21no—
178Q8×C9—42no—
179Q8×C9#4112yes—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9—42no—
187C2×C4×C9C2×D411yescharacteristic
188C2×C4×C9C2411yescharacteristic
189#611—22no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—21no—
194C2×Dic9C2×D411yescharacteristic
195C2×Dic9C2×D411yescharacteristic
196C2×Dic9C2×D411yescharacteristic
197C4×D9—21no—
198C4×D9—21no—
199C4×D9—42no—
200C4×D9—42no—
201Dic18—21no—
202Dic18—21no—
203Dic18—42no—
204C8×C9—21no—
205C8×C9—21no—
206C9⋊C8—21no—
207C9⋊C8—21no—
208#552—91no—
209D4×Q8—91no—
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#451D911yescharacteristic, complemented
219#441—91no—
220#435—91no—
221#419—91no—
222C2×#103—91no—
223C2×C3×Q8—21no—
224C2×C3×Q8—22no—
225C2×C3×Q8—41no—
226C2×C3×Q8C22×D311yescharacteristic
227C2×C3×Q8C22×D311yescharacteristic
228C2×C3×Q8C22×D311yescharacteristic
229C22×C3×C4—21no—
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—31no—
232D3×Q8—62no—
233D3×Q8—121no—
234C2×C4×D3—31no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×Dic6—31no—
238C2×Dic6—61no—
239C3×Q16—22no—
240C3×Q16—41no—
241C2×C3×C8C22×D311yescharacteristic
242C2×C3×C8C22×D311yescharacteristic
243C3×C4⋊C4—21no—
244C3×C4⋊C4C22×D311yescharacteristic
245C3×C22⋊C4—21no—
246#217—31no—
247#217—61no—
248#217—61no—
249#216—121no—
250(C2×D3)⋊C4—31no—
251(C2×D3)⋊C4—61no—
252(C2×D3)⋊C4—61no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259Dic3⋊C4—31no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266Dic3⋊C4—61no—
267C4×Dic3—31no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271#208—121no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274D3×C8—121no—
275C22×C9—21no—
276C22×C9—21no—
277C22×C9—21no—
278C22×C9C22×D411yescharacteristic
279C2×D9—21no—
280C2×D9—21no—
281C2×D9#13712yes—
282C4×C9—22no—
283C4×C9—21no—
284C4×C9—41no—
285C4×C9—41no—
286C4×C9—41no—
287C4×C9C2×#4111yescharacteristic
288C4×C9H(5,𝔽2)11yescharacteristic
289Dic9—21no—
290Dic9—21no—
291Dic9—21no—
292Dic9—41no—
293Dic9—41no—
294Dic9—41no—
295Dic9—41no—
296C22×Q8—91no—
297C22×Q8C2×D911yescharacteristic
298C2×Q16—91no—
299C2×Q16C2×D911yescharacteristic
300C2×Q16C2×D911yescharacteristic
301C2×M16—91no—
302C22×C8—91no—
303C4⋊Q8—91no—
304C4⋊Q8—181no—
305#126—181no—
306#125—91no—
307#125—181no—
308#123—181no—
309C22⋊Q8—91no—
310C22⋊Q8—91no—
311C22⋊Q8—91no—
312C22⋊Q8—181no—
313C22⋊Q8—181no—
314C22⋊Q8C2×D911yescharacteristic
315C4×Q8—91no—
316C4×Q8—91no—
317C4×D4—91no—
318C4×D4—181no—
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#103C2×D911yescharacteristic
335#103C2×D911yescharacteristic
336C22⋊C8—91no—
337C22⋊C8C2×D911yescharacteristic
338#97—91no—
339C23×C3D3×D411yescharacteristic
340C22×D3—31no—
341C3×Q8—21no—
342C3×Q8—21no—
343C3×Q8—21no—
344C3×Q8—21no—
345C3×Q8—21no—
346C3×Q8—42no—
347C3×Q8#23712yes—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—42no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357#67—62no—
358C2×Dic3—31no—
359C2×Dic3—31no—
360C2×Dic3—31no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C4×D3—61no—
366C4×D3—61no—
367C4×D3—122no—
368C4×D3—122no—
369Dic6—61no—
370Dic6—61no—
371Dic6—122no—
372C3×C8—21no—
373C3×C8—21no—
374C3⋊C8—61no—
375C3⋊C8—61no—
376C2×C9—41no—
377C2×C9#54611yescharacteristic
378C2×C9C2×#13711yescharacteristic
379C2×C9#57811yescharacteristic
380D9—22no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—41no—
384C2×Q8—91no—
385C2×Q8—181no—
386C2×Q8—182no—
387C2×Q8—361no—
388C2×Q8C22×D911yescharacteristic
389C2×Q8C22×D911yescharacteristic
390C2×Q8C22×D911yescharacteristic
391C2×D4—91no—
392C22×C4—21no—
393C22×C4—91no—
394C22×C4—181no—
395C22×C4—181no—
396C22×C4C22×D911yescharacteristic
397Q16—22no—
398Q16—41no—
399Q16—361no—
400M16—361no—
401C2×C8—91no—
402C2×C8—91no—
403C2×C8—361no—
404C2×C8C22×D911yescharacteristic
405C2×C8C22×D911yescharacteristic
406C4⋊C4—21no—
407C4⋊C4—91no—
408C4⋊C4—91no—
409C4⋊C4—91no—
410C4⋊C4—91no—
411C4⋊C4—181no—
412C4⋊C4—181no—
413C4⋊C4—181no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4C22×D911yescharacteristic
422C22⋊C4—21no—
423C22⋊C4—91no—
424C22⋊C4—91no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C42—91no—
430C42—181no—
431C42—181no—
432C42—181no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3C2×D3×D411yescharacteristic
437C2×D3—32no—
438C2×D3—61no—
439C2×D3—61no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4C2×#23711yescharacteristic
446C3×C4#100411yescharacteristic
447Dic3—61no—
448Dic3—61no—
449Dic3—61no—
450Dic3—121no—
451Dic3—121no—
452Dic3—121no—
453Dic3—121no—
454C9#331211yescharacteristic, complemented, Sylow
455C23—91no—
456C23D4×D911yescharacteristic
457Q8—21no—
458Q8—21no—
459Q8—21no—
460Q8—21no—
461Q8—21no—
462Q8—42no—
463Q8—181no—
464Q8—181no—
465Q8—362no—
466Q8#369912yes—
467D4—182no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—42no—
475C2×C4—91no—
476C2×C4—91no—
477C2×C4—91no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—362no—
485C2×C4—362no—
486C2×C4D4×D911yescharacteristic
487C2×C4C23×D911yescharacteristic
488C8—21no—
489C8—21no—
490C8—181no—
491C8—181no—
492C2×C3—41no—
493C2×C3#559111yescharacteristic
494C2×C3#576611yescharacteristic
495C2×C3D3×#13711yescharacteristic
496D3—62no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—92no—
501C22—181no—
502C22—181no—
503C22C2×D4×D911yescharacteristic
504C4—21no—
505C4—22no—
506C4—41no—
507C4—41no—
508C4—41no—
509C4—181no—
510C4—181no—
511C4—181no—
512C4—361no—
513C4—361no—
514C4—361no—
515C4—361no—
516C4C2×#369911yescharacteristic
517C4#6371011yescharacteristic
518C3#8019611yescharacteristic
519C2—41no—
520C2—182no—
521C2#1058969311yescharacteristic
522C2#1058986811yescharacteristic
523C2D9×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#451C2
socleC22×C3C2×D3×D4
prime radicalC2×#611D4
hypercenter#451D9
hypocenterC9#3312
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. C9×#451C2semidirect
4. #10588906C2semidirect
5. #10588868C2semidirect
6. #10588866C2semidirect
7. #10588864C2semidirect
8. #10588862C2semidirect
9. #10588728C2semidirect
10. #10588485C2semidirect
11. D9×#103C2semidirect
12. #10588477C2semidirect
13. #10588476C2semidirect
15. #10588403C2semidirect
218. #451D9semidirect
454. C9#3312semidirect

Maximal subgroups

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

subgroupindex
Q8×#6112
#105897412
C9×#4512
#105889062
#105888682
#105888662
#105888642
#105888622
#105887282
#105884852
D9×#1032
#105884772
#105884762
#105884102
#105884032
#801963