Finite Group Databasebeta

← #11897604

Subgroups — #11897604

Order 1152.

510 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589824C211yesmaximal, characteristic, complemented
2#10589641C211yesmaximal, characteristic
3C9×#474C211yesmaximal, characteristic
4#10588761C211yesmaximal, characteristic, complemented
5#10588694C211yesmaximal, characteristic
6#10588557C211yesmaximal, characteristic, complemented
7#10588556C211yesmaximal, characteristic, complemented
8#10588555C211yesmaximal, characteristic, complemented
9#10588554C211yesmaximal, characteristic, complemented
10#10588511C211yesmaximal, characteristic, complemented
11#10588510C211yesmaximal, characteristic, complemented
12#10588441C211yesmaximal, characteristic
13#10588439C211yesmaximal, characteristic
14#10588438C211yesmaximal, characteristic
15#10588437C211yesmaximal, characteristic
16#80960—31nomaximal
17C9×C4⋊Q8C2211yescharacteristic
18C4×D4×C9C2211yescharacteristic
19#63506—21no—
20#63506—21no—
21D4×Dic9C2211yescharacteristic
22D4×Dic9C2211yescharacteristic
23C2×#3672C2211yescharacteristic
24#63486—21no—
25C2×Dic9⋊C4—21no—
26#63452C2211yescharacteristic
27#63450—21no—
28#63450C2211yescharacteristic
29#63450C2211yescharacteristic
30#63450C2211yescharacteristic
31#63449—21no—
32#63449C2211yescharacteristic
33#63449C2211yescharacteristic
34#63440—21no—
35#63440—21no—
36#63432C2211yescharacteristic
37C4×Dic18C2211yescharacteristic
38C4×Dic18C2211yescharacteristic
39C9×#107C2211yescharacteristic
40C9×#107C2211yescharacteristic
41C9×C4⋊C8C2211yescharacteristic
42C9×#102C2211yescharacteristic
43C9×#102C2211yescharacteristic
44#63392C2211yescharacteristic
45#63378C2211yescharacteristic
46#63377C2211yescharacteristic
47#63376C2211yescharacteristic
48#63376C2211yescharacteristic
49#63375C2211yescharacteristic
50Dic9⋊C8C2211yescharacteristic
51Dic9⋊C8C2211yescharacteristic
52C8×Dic9C2211yescharacteristic
53#63368C2211yescharacteristic
54#63367C2211yescharacteristic
55#63367C2211yescharacteristic
56#63366C2211yescharacteristic
57#63366C2211yescharacteristic
58#63366C2211yescharacteristic
59#63362C2211yescharacteristic
60#5722—31no—
61#5539—31no—
62C3×#474D311yescharacteristic
63#5081—31no—
64#5018—31no—
65#4877—31no—
66#4876—31no—
67#4875—31no—
68#4874—31no—
69#4829—31no—
70#4828—31no—
71#4761—31no—
72#4759—31no—
73#4758—31no—
74#4757—31no—
75C2×Q8×C9—21no—
76C2×D4×C9C2311yescharacteristic
77C22×C4×C9—21no—
78C22×Dic9—21no—
79C22×Dic9—21no—
80C2×Dic18—21no—
81C2×Dic18—21no—
82C2×Dic18—21no—
83C2×Dic18D411yescharacteristic
84C2×Dic18C2311yescharacteristic
85C2×C8×C9C2311yescharacteristic
86C2×C8×C9C2311yescharacteristic
87C9×C4⋊C4—21no—
88C9×C4⋊C4C2311yescharacteristic
89C9×C4⋊C4C2311yescharacteristic
90C9×C4⋊C4C2311yescharacteristic
91C9×C22⋊C4—21no—
92C42×C9C2311yescharacteristic
93#3676—21no—
94#3676—21no—
95#3672Q814yescomplemented
96C4⋊Dic9—21no—
97C4⋊Dic9D411yescharacteristic
98C4⋊Dic9C2311yescharacteristic
99C4⋊Dic9C2311yescharacteristic
100C4⋊Dic9C2311yescharacteristic
101Dic9⋊C4—21no—
102Dic9⋊C4—21no—
103Dic9⋊C4—21no—
104Dic9⋊C4—21no—
105Dic9⋊C4—21no—
106Dic9⋊C4—21no—
107Dic9⋊C4—21no—
108Dic9⋊C4—21no—
109Dic9⋊C4—21no—
110Dic9⋊C4D411yescharacteristic
111Dic9⋊C4D411yescharacteristic
112C4×Dic9—21no—
113C4×Dic9—21no—
114C4×Dic9—21no—
115C4×Dic9C2311yescharacteristic
116C4×Dic9C2311yescharacteristic
117C2×C9⋊C8C2311yescharacteristic
118C2×C9⋊C8C2311yescharacteristic
119#3385—91noSylow
120C3×C4⋊Q8C2×D311yescharacteristic
121C3×C4×D4C2×D311yescharacteristic
122#944—61no—
123#944—61no—
124D4×Dic3—31no—
125D4×Dic3—31no—
126C2×#214—31no—
127#924—61no—
128C2×Dic3⋊C4—61no—
129#890—31no—
130#888—31no—
131#888—31no—
132#888—31no—
133#888—61no—
134#887—31no—
135#887—31no—
136#887—61no—
137#878—61no—
138#878—61no—
139#870—31no—
140C4×Dic6—31no—
141C4×Dic6—31no—
142C3×#107C2×D311yescharacteristic
143C3×#107C2×D311yescharacteristic
144C3×C4⋊C8C2×D311yescharacteristic
145C3×#102C2×D311yescharacteristic
146C3×#102C2×D311yescharacteristic
147#832—31no—
148#818—31no—
149#817—31no—
150#816—31no—
151#816—31no—
152#815—31no—
153Dic3⋊C8—31no—
154Dic3⋊C8—31no—
155C8×Dic3—31no—
156#810—31no—
157#808—31no—
158#808—31no—
159#807—31no—
160#807—31no—
161#807—31no—
162#803—31no—
163C23×C9—21no—
164Q8×C9—81no—
165D4×C9—21no—
166D4×C9C2×Q812yes—
167C2×C4×C9—21no—
168C2×C4×C9—21no—
169C2×C4×C9—21no—
170C2×C4×C9—81no—
171C2×C4×C9C2×D411yescharacteristic
172C2×C4×C9C2×D411yescharacteristic
173C2×C4×C9C2411yescharacteristic
174C2×Dic9—21no—
175C2×Dic9—21no—
176C2×Dic9—21no—
177C2×Dic9—21no—
178C2×Dic9—42no—
179C2×Dic9—81no—
180C2×Dic9C2×D411yescharacteristic
181C2×Dic9C2×D411yescharacteristic
182C2×Dic9C2×D411yescharacteristic
183C2×Dic9C2×D411yescharacteristic
184Dic18—21no—
185Dic18—22no—
186Dic18—81no—
187Dic18—81no—
188Dic18—81no—
189Dic18C2×Q812yes—
190C8×C9—21no—
191C8×C9—21no—
192C9⋊C8—21no—
193C9⋊C8C2×Q812yes—
194Q82—91no—
195#554—91no—
196#501—91no—
197#501—91no—
198#500—91no—
199#479—91no—
200#479—91no—
201#477—91no—
202#476—91no—
203#474—91no—
204#474D911yescharacteristic
205#446—91no—
206#440—91no—
207#440—91no—
208C4×SD16—91no—
209C2×C3×Q8—21no—
210C2×C3×D4C22×D311yescharacteristic
211C22×C3×C4—21no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×C3×C8C22×D311yescharacteristic
220C2×C3×C8C22×D311yescharacteristic
221C3×C4⋊C4—21no—
222C3×C4⋊C4C22×D311yescharacteristic
223C3×C4⋊C4C22×D311yescharacteristic
224C3×C4⋊C4C22×D311yescharacteristic
225C3×C22⋊C4—21no—
226C3×C42C22×D311yescharacteristic
227#217—61no—
228#217—61no—
229#214—34no—
230C4⋊Dic3—31no—
231C4⋊Dic3—31no—
232C4⋊Dic3—31no—
233C4⋊Dic3—31no—
234C4⋊Dic3—61no—
235Dic3⋊C4—31no—
236Dic3⋊C4—31no—
237Dic3⋊C4—61no—
238Dic3⋊C4—61no—
239Dic3⋊C4—61no—
240Dic3⋊C4—61no—
241Dic3⋊C4—61no—
242Dic3⋊C4—61no—
243Dic3⋊C4—61no—
244Dic3⋊C4—61no—
245Dic3⋊C4—61no—
246C4×Dic3—31no—
247C4×Dic3—31no—
248C4×Dic3—61no—
249C4×Dic3—61no—
250C4×Dic3—61no—
251C2×C3⋊C8—31no—
252C2×C3⋊C8—31no—
253C22×C9—22no—
254C22×C9—41no—
255C22×C9—41no—
256C22×C9C22×D411yescharacteristic
257C4×C9—21no—
258C4×C9—21no—
259C4×C9—41no—
260C4×C9—41no—
261C4×C9—41no—
262C4×C9C22×Q811yescharacteristic
263C4×C92−1+411yescharacteristic
264Dic9—22no—
265Dic9—21no—
266Dic9—21no—
267Dic9—21no—
268Dic9—41no—
269Dic9—41no—
270Dic9—41no—
271Dic9#13712yes—
272C2×SD16—91no—
273C4⋊Q8—91no—
274C4⋊Q8—91no—
275C4⋊Q8—91no—
276C4⋊Q8—181no—
277C4⋊Q8—181no—
278C4⋊Q8—181no—
279C4⋊Q8C2×D911yescharacteristic
280#125—91no—
281#125—91no—
282C22⋊Q8—181no—
283C22⋊Q8—181no—
284C22⋊Q8—181no—
285C4×Q8—91no—
286C4×Q8—91no—
287C4×Q8—91no—
288C4×Q8—91no—
289C4×Q8—181no—
290C4×D4—91no—
291C4×D4—91no—
292C4×D4C2×D911yescharacteristic
293C2×C4⋊C4—181no—
294#107—91no—
295#107—91no—
296#107—91no—
297#107—91no—
298#107C2×D911yescharacteristic
299#107C2×D911yescharacteristic
300#106—91no—
301#106—91no—
302#106—91no—
303C4⋊C8—91no—
304C4⋊C8—91no—
305C4⋊C8C2×D911yescharacteristic
306#103—91no—
307#103—91no—
308#103—91no—
309#102—91no—
310#102C2×D911yescharacteristic
311#102C2×D911yescharacteristic
312#97—91no—
313#97—91no—
314C4×C8—91no—
315C23×C3—21no—
316C3×Q8—81no—
317C3×D4—21no—
318C3×D4D3×Q812yes—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—81no—
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326C2×Dic3—31no—
327C2×Dic3—31no—
328C2×Dic3—31no—
329C2×Dic3—31no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—122no—
335C2×Dic3—241no—
336Dic6—32no—
337Dic6—62no—
338Dic6—61no—
339Dic6—241no—
340Dic6—241no—
341Dic6—241no—
342C3×C8—21no—
343C3×C8—21no—
344C3⋊C8—32no—
345C3⋊C8—61no—
346C2×C9—42no—
347C2×C9D4×Q811yescharacteristic
348C2×C9C2×#13711yescharacteristic
349C2×C9#57611yescharacteristic
350C2×Q8—21no—
351C2×Q8—91no—
352C2×Q8—91no—
353C2×Q8—181no—
354C2×Q8—181no—
355C2×Q8—181no—
356C2×D4C22×D911yescharacteristic
357C22×C4—21no—
358C22×C4—181no—
359C22×C4—181no—
360SD16—94no—
361C2×C8—91no—
362C2×C8—91no—
363C2×C8C22×D911yescharacteristic
364C2×C8C22×D911yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—91no—
367C4⋊C4—91no—
368C4⋊C4—91no—
369C4⋊C4—91no—
370C4⋊C4—91no—
371C4⋊C4—91no—
372C4⋊C4—181no—
373C4⋊C4—181no—
374C4⋊C4—181no—
375C4⋊C4—181no—
376C4⋊C4—181no—
377C4⋊C4—181no—
378C4⋊C4—181no—
379C4⋊C4—181no—
380C4⋊C4—181no—
381C4⋊C4—181no—
382C4⋊C4C22×D911yescharacteristic
383C4⋊C4C22×D911yescharacteristic
384C4⋊C4C22×D911yescharacteristic
385C22⋊C4—21no—
386C22⋊C4—181no—
387C22⋊C4—181no—
388C42—91no—
389C42—91no—
390C42—181no—
391C42—181no—
392C42—181no—
393C42C22×D911yescharacteristic
394C22×C3—22no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3C2×D3×D411yescharacteristic
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—41no—
401C3×C4—41no—
402C3×C4—41no—
403C3×C4C2×D3×Q811yescharacteristic
404C3×C4#101011yescharacteristic
405Dic3—32no—
406Dic3—62no—
407Dic3—61no—
408Dic3—61no—
409Dic3—61no—
410Dic3—121no—
411Dic3—121no—
412Dic3—121no—
413C9#338511yescharacteristic, complemented, Sylow
414C23—21no—
415Q8—81no—
416Q8—92no—
417Q8—182no—
418Q8—181no—
419Q8—721no—
420Q8—721no—
421Q8—721no—
422D4—21no—
423D4Q8×D912yes—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—81no—
428C2×C4—91no—
429C2×C4—91no—
430C2×C4—91no—
431C2×C4—91no—
432C2×C4—181no—
433C2×C4—181no—
434C2×C4—181no—
435C2×C4—181no—
436C2×C4—362no—
437C2×C4—721no—
438C2×C4D4×D911yescharacteristic
439C2×C4D4×D911yescharacteristic
440C2×C4C23×D911yescharacteristic
441C8—21no—
442C8—21no—
443C8—92no—
444C8—181no—
445C2×C3—42no—
446C2×C3#563211yescharacteristic
447C2×C3#575711yescharacteristic
448C2×C3D3×#13711yescharacteristic
449C22—22no—
450C22—41no—
451C22—41no—
452C22C2×D4×D911yescharacteristic
453C4—21no—
454C4—21no—
455C4—41no—
456C4—41no—
457C4—41no—
458C4—92no—
459C4—182no—
460C4—181no—
461C4—181no—
462C4—181no—
463C4—361no—
464C4—361no—
465C4—361no—
466C4C2×Q8×D911yescharacteristic
467C4#6371611yescharacteristic
468C3#8096011yescharacteristic
469C2—42no—
470C2#1058973411yescharacteristic
471C2#1058985911yescharacteristic
472C2D9×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#474C2
socleC22×C3C2×D3×D4
prime radicalC2×C3×D4C22×D3
hypercenter#474D9
hypocenterC9#3385
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10589824C2semidirect
4. #10588761C2semidirect
6. #10588557C2semidirect
7. #10588556C2semidirect
8. #10588555C2semidirect
9. #10588554C2semidirect
10. #10588511C2semidirect
11. #10588510C2semidirect
95. #3672Q8semidirect
413. C9#3385semidirect

Maximal subgroups

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

subgroupindex
#105898242
#105896412
C9×#4742
#105887612
#105886942
#105885572
#105885562
#105885552
#105885542
#105885112
#105885102
#105884412
#105884392
#105884382
#105884372
#809603