Finite Group Databasebeta

← #11906257

Subgroups — #11906257

Order 1152.

1446 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#557C211yesmaximal, characteristic, complemented
2#10589831C213yesmaximal
3#10589824C213yesmaximal, complemented
4#10589791C213yesmaximal
5#10589790C213yesmaximal
6#10589787C213yesmaximal, complemented
7#10589787C213yesmaximal, complemented
8#10589680C213yesmaximal
9#10589674C211yesmaximal, characteristic
10#10589674C211yesmaximal, characteristic
11C4×Q8×D9C211yesmaximal, characteristic
12#10589671C211yesmaximal, characteristic, complemented
13#10589671C211yesmaximal, characteristic, complemented
14#10589669C213yesmaximal, complemented
15Q8×Dic18C211yesmaximal, characteristic, complemented
16#87032—31nomaximal
17C2×Q8×D9C2211yescharacteristic
18C9×C4⋊Q8C2213yes—
19C9×#125C2213yes—
20C9×#125C2213yes—
21C4×Q8×C9C2211yescharacteristic
22C4×Q8×C9C2213yes—
23C4×Q8×C9C2211yescharacteristic
24C4×Q8×C9C2211yescharacteristic
25#63508C2213yes—
26Q8×Dic9C2211yescharacteristic
27Q8×Dic9C2211yescharacteristic
28Q8×Dic9C2211yescharacteristic
29#63506C2213yes—
30#63506C2216yes—
31#63459C2213yes—
32#63458C2213yes—
33#63458C2216yes—
34#63458C2211yescharacteristic
35#63454C2213yes—
36#63454C2213yes—
37C4⋊C4×D9C2213yes—
38#63452C2213yes—
39#63452C2213yes—
40#63451C2216yes—
41#63451C2213yes—
42#63451C2216yes—
43#63451C2213yes—
44#63450C2213yes—
45#63450C2213yes—
46#63450C2216yes—
47#63450C2213yes—
48#63450C2213yes—
49#63450C2213yes—
50#63449C2213yes—
51#63449C2216yes—
52#63449C2216yes—
53#63449C2213yes—
54#63449C2213yes—
55#63434C2213yes—
56#63434C2213yes—
57C42×D9C2213yes—
58#63432C2213yes—
59#63432C2213yes—
60#63431C2213yes—
61C4×Dic18C2213yes—
62C4×Dic18C2213yes—
63C4×Dic18C2213yes—
64C4×Dic18C2213yes—
65C4×Dic18C2213yes—
66C4×Dic18C2213yes—
67C3×#557D311yescharacteristic
68#5729—33no—
69#5722—33no—
70#5689—33no—
71#5688—33no—
72#5685—33no—
73#5685—33no—
74#5578—33no—
75#5572—31no—
76#5572—31no—
77C4×D3×Q8—31no—
78#5569—31no—
79#5569—31no—
80#5567—33no—
81Q8×Dic6—31no—
82C2×Q8×C9C2313yes—
83C2×Q8×C9C2311yescharacteristic
84Q8×D9Q818yescomplemented
85C2×C4×D9C2311yescharacteristic
86C2×C4×D9C2313yes—
87C2×C4×D9C2313yes—
88C2×Dic18C2311yescharacteristic
89C2×Dic18C2313yes—
90C2×Dic18C2313yes—
91C2×Dic18C2316yes—
92C2×Dic18C2313yes—
93C9×C4⋊C4C2311yescharacteristic
94C9×C4⋊C4C2313yes—
95C9×C4⋊C4C2313yes—
96C9×C4⋊C4C2313yes—
97C9×C4⋊C4C2313yes—
98C9×C4⋊C4C2313yes—
99C9×C4⋊C4C2316yes—
100C42×C9C2313yes—
101C42×C9C2313yes—
102C42×C9C2313yes—
103(C2×D9)⋊C4C2311yescharacteristic
104(C2×D9)⋊C4C2313yes—
105(C2×D9)⋊C4C2311yescharacteristic
106(C2×D9)⋊C4C2313yes—
107C4⋊Dic9C2313yes—
108C4⋊Dic9C2313yes—
109C4⋊Dic9C2313yes—
110C4⋊Dic9C2313yes—
111C4⋊Dic9C2313yes—
112C4⋊Dic9C2313yes—
113Dic9⋊C4C2311yescharacteristic
114Dic9⋊C4C2313yes—
115Dic9⋊C4C2313yes—
116Dic9⋊C4C2313yes—
117Dic9⋊C4C2316yes—
118Dic9⋊C4C2316yes—
119Dic9⋊C4C2313yes—
120Dic9⋊C4C2313yes—
121Dic9⋊C4C2311yescharacteristic
122Dic9⋊C4C2313yes—
123Dic9⋊C4C2313yes—
124Dic9⋊C4C2316yes—
125Dic9⋊C4C2313yes—
126C4×Dic9C2316yes—
127C4×Dic9C2313yes—
128C4×Dic9C2313yes—
129C4×Dic9C2313yes—
130C4×Dic9C2313yes—
131C4×Dic9C2313yes—
132C4×Dic9C2316yes—
133#3502—91noSylow
134C2×D3×Q8—31no—
135C3×C4⋊Q8C2×D313yes—
136C3×#125C2×D313yes—
137C3×#125C2×D313yes—
138C3×C4×Q8C2×D311yescharacteristic
139C3×C4×Q8C2×D313yes—
140C3×C4×Q8C2×D311yescharacteristic
141C3×C4×Q8C2×D311yescharacteristic
142#946—33no—
143Q8×Dic3—31no—
144Q8×Dic3—31no—
145Q8×Dic3—31no—
146#944—33no—
147#944—36no—
148#897—33no—
149#896—33no—
150#896—36no—
151#896—31no—
152#892—33no—
153#892—33no—
154D3×C4⋊C4—33no—
155#890—33no—
156#890—33no—
157#889—36no—
158#889—33no—
159#889—36no—
160#889—33no—
161#888—33no—
162#888—33no—
163#888—36no—
164#888—33no—
165#888—33no—
166#888—33no—
167#887—33no—
168#887—36no—
169#887—36no—
170#887—33no—
171#887—33no—
172#872—33no—
173#872—33no—
174C42×D3—33no—
175#870—33no—
176#870—33no—
177#869—33no—
178C4×Dic6—33no—
179C4×Dic6—33no—
180C4×Dic6—33no—
181C4×Dic6—33no—
182C4×Dic6—33no—
183C4×Dic6—33no—
184C22×D9C2411yescharacteristic
185Q8×C9—43no—
186Q8×C9C2×Q814yes—
187C2×C4×C9C2411yescharacteristic
188C2×C4×C9C2413yes—
189C2×C4×C9C2413yes—
190C2×C4×C9C2413yes—
191C2×C4×C9C2411yescharacteristic
192C2×C4×C9C2411yescharacteristic
193C2×C4×C9C2413yes—
194C2×Dic9C2413yes—
195C2×Dic9C2411yescharacteristic
196C2×Dic9C2411yescharacteristic
197C2×Dic9C2413yes—
198C2×Dic9C2413yes—
199C2×Dic9C2413yes—
200C2×Dic9C2411yescharacteristic
201C4×D9—22no—
202C4×D9—43no—
203C4×D9C2×Q8112yes—
204Dic18—22no—
205Dic18—26no—
206Dic18—43no—
207Dic18—46no—
208Dic18C2×Q8112yes—
209Q82—93no—
210Q82—91no—
211#557—93no—
212#557—93no—
213#557—93no—
214#557—91no—
215#557—91no—
216#557D911yescharacteristic, complemented
217#544—93no—
218#544—93no—
219#533—93no—
220#533—93no—
221#519—91no—
222#519—91no—
223C2×C4×Q8—91no—
224C2×C3×Q8C22×D313yes—
225C2×C3×Q8C22×D311yescharacteristic
226D3×Q8—38no—
227C2×C4×D3—33no—
228C2×C4×D3—31no—
229C2×C4×D3—33no—
230C2×Dic6—33no—
231C2×Dic6—31no—
232C2×Dic6—33no—
233C2×Dic6—33no—
234C2×Dic6—36no—
235C3×C4⋊C4C22×D313yes—
236C3×C4⋊C4C22×D313yes—
237C3×C4⋊C4C22×D316yes—
238C3×C4⋊C4C22×D313yes—
239C3×C4⋊C4C22×D313yes—
240C3×C4⋊C4C22×D313yes—
241C3×C4⋊C4C22×D311yescharacteristic
242C3×C42C22×D313yes—
243C3×C42C22×D313yes—
244C3×C42C22×D313yes—
245(C2×D3)⋊C4—31no—
246(C2×D3)⋊C4—31no—
247(C2×D3)⋊C4—33no—
248(C2×D3)⋊C4—33no—
249C4⋊Dic3—33no—
250C4⋊Dic3—33no—
251C4⋊Dic3—33no—
252C4⋊Dic3—33no—
253C4⋊Dic3—33no—
254C4⋊Dic3—33no—
255Dic3⋊C4—31no—
256Dic3⋊C4—31no—
257Dic3⋊C4—33no—
258Dic3⋊C4—33no—
259Dic3⋊C4—33no—
260Dic3⋊C4—33no—
261Dic3⋊C4—33no—
262Dic3⋊C4—36no—
263Dic3⋊C4—33no—
264Dic3⋊C4—36no—
265Dic3⋊C4—36no—
266Dic3⋊C4—33no—
267Dic3⋊C4—33no—
268C4×Dic3—33no—
269C4×Dic3—33no—
270C4×Dic3—33no—
271C4×Dic3—33no—
272C4×Dic3—36no—
273C4×Dic3—36no—
274C4×Dic3—33no—
275C22×C9C2511yescharacteristic
276C2×D9—21no—
277C2×D9—21no—
278C2×D9C22×Q812yes—
279C4×C9—23no—
280C4×C9—21no—
281C4×C9—21no—
282C4×C9—23no—
283C4×C9—23no—
284C4×C9—21no—
285C4×C9C22×Q816yes—
286Dic9—21no—
287Dic9—23no—
288Dic9—21no—
289Dic9—23no—
290Dic9—23no—
291Dic9C22×Q816yes—
292Dic92−1+412yes—
293C22×Q8—91no—
294C4⋊Q8—93no—
295C4⋊Q8—96no—
296C4⋊Q8—93no—
297C4⋊Q8—93no—
298C4⋊Q8—93no—
299C4⋊Q8—96no—
300C4⋊Q8—93no—
301C4⋊Q8—93no—
302C4⋊Q8—93no—
303C4⋊Q8C2×D913yes—
304#125—93no—
305#125—93no—
306#125—96no—
307#125—96no—
308#125—93no—
309#125—93no—
310#125—93no—
311#125—93no—
312#125C2×D913yes—
313#125C2×D913yes—
314C22⋊Q8—93no—
315C22⋊Q8—93no—
316C22⋊Q8—91no—
317C22⋊Q8—96no—
318C22⋊Q8—93no—
319C4×Q8—91no—
320C4×Q8—91no—
321C4×Q8—91no—
322C4×Q8—93no—
323C4×Q8—93no—
324C4×Q8—93no—
325C4×Q8—96no—
326C4×Q8—96no—
327C4×Q8—93no—
328C4×Q8—93no—
329C4×Q8—93no—
330C4×Q8—93no—
331C4×Q8—93no—
332C4×Q8—93no—
333C4×Q8C2×D911yescharacteristic
334C4×Q8C2×D911yescharacteristic
335C4×Q8C2×D911yescharacteristic
336C4×Q8C2×D913yes—
337#117—93no—
338#117—93no—
339#117—93no—
340#117—93no—
341C2×C4⋊C4—93no—
342C2×C42—93no—
343C22×D3—31no—
344C3×Q8—43no—
345C3×Q8D3×Q814yes—
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D313yes—
348C2×C3×C4C23×D313yes—
349C2×C3×C4C23×D313yes—
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×C3×C4C23×D313yes—
353C2×Dic3—33no—
354C2×Dic3—31no—
355C2×Dic3—31no—
356C2×Dic3—33no—
357C2×Dic3—31no—
358C2×Dic3—33no—
359C2×Dic3—33no—
360C4×D3—312no—
361C4×D3—62no—
362C4×D3—123no—
363Dic6—312no—
364Dic6—62no—
365Dic6—66no—
366Dic6—123no—
367Dic6—126no—
368C2×C9C23×Q811yescharacteristic
369C2×C9C2×2−1+411yescharacteristic
370C2×C9#58511yescharacteristic
371D9—22no—
372C2×Q8—98no—
373C2×Q8—93no—
374C2×Q8—93no—
375C2×Q8—91no—
376C2×Q8—93no—
377C2×Q8—96no—
378C2×Q8C22×D913yes—
379C2×Q8C22×D911yescharacteristic
380C22×C4—93no—
381C22×C4—91no—
382C22×C4—93no—
383C4⋊C4—96no—
384C4⋊C4—93no—
385C4⋊C4—93no—
386C4⋊C4—93no—
387C4⋊C4—93no—
388C4⋊C4—93no—
389C4⋊C4—93no—
390C4⋊C4—93no—
391C4⋊C4—93no—
392C4⋊C4—91no—
393C4⋊C4—93no—
394C4⋊C4—91no—
395C4⋊C4—96no—
396C4⋊C4—93no—
397C4⋊C4—96no—
398C4⋊C4—93no—
399C4⋊C4—93no—
400C4⋊C4—93no—
401C4⋊C4—93no—
402C4⋊C4C22×D913yes—
403C4⋊C4C22×D913yes—
404C4⋊C4C22×D913yes—
405C4⋊C4C22×D913yes—
406C4⋊C4C22×D916yes—
407C4⋊C4C22×D911yescharacteristic
408C4⋊C4C22×D913yes—
409C22⋊C4—93no—
410C22⋊C4—91no—
411C22⋊C4—93no—
412C22⋊C4—91no—
413C42—93no—
414C42—93no—
415C42—93no—
416C42—96no—
417C42—96no—
418C42—93no—
419C42—93no—
420C42C22×D913yes—
421C42C22×D913yes—
422C42C22×D913yes—
423C22×C3C24×D311yescharacteristic
424C2×D3—32no—
425C2×D3—61no—
426C2×D3—61no—
427C3×C4—23no—
428C3×C4—23no—
429C3×C4—21no—
430C3×C4—23no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4C2×D3×Q816yes—
434Dic3—36no—
435Dic3—32no—
436Dic3—61no—
437Dic3—63no—
438Dic3—63no—
439Dic3—61no—
440Dic3—63no—
441C9#350211yescharacteristic, complemented, Sylow
442C23—91no—
443Q8—43no—
444Q8—912no—
445Q8—186no—
446Q8—182no—
447Q8—363no—
448Q8—366no—
449Q8Q8×D914yes—
450C2×C4—93no—
451C2×C4—91no—
452C2×C4—912no—
453C2×C4—91no—
454C2×C4—93no—
455C2×C4—91no—
456C2×C4—93no—
457C2×C4—93no—
458C2×C4—182no—
459C2×C4—363no—
460C2×C4C23×D911yescharacteristic
461C2×C4C23×D913yes—
462C2×C4C23×D913yes—
463C2×C4C23×D913yes—
464C2×C4C23×D911yescharacteristic
465C2×C4C23×D911yescharacteristic
466C2×C4C23×D913yes—
467C2×C3C22×D3×Q811yescharacteristic
468C2×C3#596411yescharacteristic
469C2×C3D3×2−1+411yescharacteristic
470D3—62no—
471C22—92no—
472C22—181no—
473C22—181no—
474C22C24×D911yescharacteristic
475C4—23no—
476C4—21no—
477C4—23no—
478C4—21no—
479C4—23no—
480C4—21no—
481C4—96no—
482C4—92no—
483C4—183no—
484C4—181no—
485C4—183no—
486C4—181no—
487C4—183no—
488C4C2×Q8×D916yes—
489C3#8703211yescharacteristic
490C2—182no—
491C2C22×Q8×D911yescharacteristic
492C2#1059313911yescharacteristic
493C2D9×2−1+411yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#557C2
prime radicalC22×D9C24
hypercenter#557D9
hypocenterC9#3502
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C9×#557C2semidirect
3. #10589824C2semidirect
6. #10589787C2semidirect
7. #10589787C2semidirect
12. #10589671C2semidirect
13. #10589671C2semidirect
14. #10589669C2semidirect
15. Q8×Dic18C2semidirect
84. Q8×D9Q8semidirect
216. #557D9semidirect
441. C9#3502semidirect

Maximal subgroups

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

subgroupindex
C9×#5572
#105898312
#105898242
#105897912
#105897902
#105897872
#105896802
#105896742
C4×Q8×D92
#105896712
#105896692
Q8×Dic182
#870323