Finite Group Databasebeta

← #11872568

Subgroups — #11872568

Order 1152.

555 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589636C211yesmaximal, characteristic
2#10589618C211yesmaximal, characteristic, complemented
3C9×#433C211yesmaximal, characteristic, complemented
4#10588529C211yesmaximal, characteristic, complemented
5#10588529C211yesmaximal, characteristic, complemented
6#10588515C211yesmaximal, characteristic, complemented
7#10588514C211yesmaximal, characteristic, complemented
8#10588419C211yesmaximal, characteristic
9#10588405C211yesmaximal, characteristic, complemented
10#10588404C211yesmaximal, characteristic
11#10588403C211yesmaximal, characteristic, complemented
12#10588391C211yesmaximal, characteristic, complemented
13#10588384C211yesmaximal, characteristic, complemented
14C4×#3664C211yesmaximal, characteristic, complemented
15C4×Dic36C211yesmaximal, characteristic, complemented
16#79394—31nomaximal
17C22×Dic18C2211yescharacteristic
18C9×#117C2211yescharacteristic
19#63492C2211yescharacteristic
20#63488C2211yescharacteristic
21#63486C2211yescharacteristic
22C2×#3664C2211yescharacteristic
23C2×#3664C2211yescharacteristic
24C2×Dic36C2211yescharacteristic
25C2×Dic36C2211yescharacteristic
26#63460—21no—
27#63458—21no—
28#63449—21no—
29#63449—21no—
30#63447—21no—
31#63445—21no—
32#63439—21no—
33#63439—21no—
34#63437C2211yescharacteristic
35C4×D36C2211yescharacteristic
36#63431C2211yescharacteristic
37C4×Dic18C2211yescharacteristic
38C4×Dic18C2211yescharacteristic
39C4×Dic18C2211yescharacteristic
40C4×Dic18C2211yescharacteristic
41C4×Dic18C2211yescharacteristic
42C9×C4⋊C8C2211yescharacteristic
43C9×C4⋊C8C2211yescharacteristic
44C9×C22⋊C8C2211yescharacteristic
45C9×C22⋊C8C2211yescharacteristic
46C9×#97C2211yescharacteristic
47C4×C8×C9C2211yescharacteristic
48#63380C2211yescharacteristic
49#63380C2211yescharacteristic
50#63378C2211yescharacteristic
51#63378C2211yescharacteristic
52#63377C2211yescharacteristic
53#63377C2211yescharacteristic
54#63376C2211yescharacteristic
55#63376C2211yescharacteristic
56#63376C2211yescharacteristic
57#63376C2211yescharacteristic
58#63376C2211yescharacteristic
59#63376C2211yescharacteristic
60#5534—31no—
61#5516—31no—
62C3×#433D311yescharacteristic
63#4851—31no—
64#4850—31no—
65#4845—31no—
66#4845—31no—
67#4739—31no—
68#4738—31no—
69#4737—31no—
70#4723—31no—
71#4716—31no—
72#4710—31no—
73C4×Dic12—31no—
74C4×#204—31no—
75C22×C4×C9C2311yescharacteristic
76C2×#611—21no—
77C22×Dic9—21no—
78C2×D36C2311yescharacteristic
79C2×C4×D9—21no—
80C2×Dic18—21no—
81C2×Dic18—22no—
82C2×Dic18—22no—
83C2×Dic18—21no—
84C2×Dic18C2311yescharacteristic
85C2×Dic18C2311yescharacteristic
86C2×Dic18C2311yescharacteristic
87C2×C8×C9C2311yescharacteristic
88C2×C8×C9C2311yescharacteristic
89C2×C8×C9C2311yescharacteristic
90C2×C8×C9C2311yescharacteristic
91C9×C4⋊C4D411yescharacteristic
92C9×C4⋊C4D411yescharacteristic
93C9×C22⋊C4D411yescharacteristic
94C9×C22⋊C4D411yescharacteristic
95C42×C9C2311yescharacteristic
96C42×C9C2311yescharacteristic
97#3676—21no—
98#3676—21no—
99(C2×D9)⋊C4—21no—
100(C2×D9)⋊C4—21no—
101(C2×D9)⋊C4—21no—
102(C2×D9)⋊C4—21no—
103C4⋊Dic9—21no—
104C4⋊Dic9C2311yescharacteristic
105C4⋊Dic9C2311yescharacteristic
106C4⋊Dic9C2311yescharacteristic
107C4⋊Dic9C2311yescharacteristic
108Dic9⋊C4—21no—
109Dic9⋊C4—21no—
110Dic9⋊C4—21no—
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114C4×Dic9—21no—
115C4×Dic9—21no—
116C4×Dic9—21no—
117C4×Dic9—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120#3664—22no—
121#3664—22no—
122Dic36—22no—
123Dic36—22no—
124#3121—91noSylow
125C22×Dic6—31no—
126C3×#117C2×D311yescharacteristic
127#930—31no—
128#926—31no—
129#924—31no—
130C2×Dic12—31no—
131C2×Dic12—31no—
132C2×#204—31no—
133C2×#204—31no—
134#898—61no—
135#896—61no—
136#887—61no—
137#887—61no—
138#885—61no—
139#883—61no—
140#877—61no—
141#877—61no—
142#875—31no—
143C4×D12—31no—
144#869—31no—
145C4×Dic6—31no—
146C4×Dic6—31no—
147C4×Dic6—31no—
148C4×Dic6—31no—
149C4×Dic6—31no—
150C3×C4⋊C8C2×D311yescharacteristic
151C3×C4⋊C8C2×D311yescharacteristic
152C3×C22⋊C8C2×D311yescharacteristic
153C3×C22⋊C8C2×D311yescharacteristic
154C3×#97C2×D311yescharacteristic
155C3×C4×C8C2×D311yescharacteristic
156#821—31no—
157#821—31no—
158#818—31no—
159#818—31no—
160#817—31no—
161#817—31no—
162#816—31no—
163#816—31no—
164#816—31no—
165#816—31no—
166#816—31no—
167#816—31no—
168C23×C9C2×D411yescharacteristic
169C22×D9—21no—
170C2×C4×C9—21no—
171C2×C4×C9—21no—
172C2×C4×C9C2×D411yescharacteristic
173C2×C4×C9C2×D411yescharacteristic
174C2×C4×C9C2×D411yescharacteristic
175C2×C4×C9C2×D411yescharacteristic
176C2×C4×C9C2×D411yescharacteristic
177C2×C4×C9C2411yescharacteristic
178#611—81no—
179C2×Dic9—24no—
180C2×Dic9—21no—
181C2×Dic9—21no—
182C2×Dic9—21no—
183C2×Dic9—21no—
184C2×Dic9—21no—
185C2×Dic9—21no—
186C2×Dic9—21no—
187D36—21no—
188D36—21no—
189C4×D9—81no—
190Dic18—24no—
191Dic18—21no—
192Dic18—21no—
193Dic18—21no—
194Dic18—21no—
195Dic18—81no—
196Dic18#4112yes—
197Dic18#4112yes—
198C8×C9—21no—
199C8×C9—21no—
200C8×C9—21no—
201C8×C9—21no—
202#542—91no—
203#519—91no—
204#485—91no—
205#482—91no—
206#477—91no—
207#475—91no—
208#464—91no—
209#464—91no—
210#451—91no—
211#448—91no—
212#441—91no—
213#440—91no—
214C4×Q16—91no—
215C4×SD16—91no—
216#433D911yescharacteristic, complemented
217C22×C3×C4C22×D311yescharacteristic
218C2×#67—61no—
219C22×Dic3—61no—
220C2×D12—31no—
221C2×C4×D3—61no—
222C2×Dic6—31no—
223C2×Dic6—31no—
224C2×Dic6—31no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×Dic6—61no—
228C2×Dic6—61no—
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C22×D311yescharacteristic
233C3×C4⋊C4D1211yescharacteristic
234C3×C4⋊C4D1211yescharacteristic
235C3×C22⋊C4D1211yescharacteristic
236C3×C22⋊C4D1211yescharacteristic
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D311yescharacteristic
239#217—61no—
240#217—61no—
241(C2×D3)⋊C4—61no—
242(C2×D3)⋊C4—61no—
243(C2×D3)⋊C4—61no—
244(C2×D3)⋊C4—61no—
245C4⋊Dic3—31no—
246C4⋊Dic3—31no—
247C4⋊Dic3—31no—
248C4⋊Dic3—31no—
249C4⋊Dic3—61no—
250Dic3⋊C4—61no—
251Dic3⋊C4—61no—
252Dic3⋊C4—61no—
253Dic3⋊C4—61no—
254Dic3⋊C4—61no—
255Dic3⋊C4—61no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C4×Dic3—61no—
259C4×Dic3—61no—
260C4×Dic3—61no—
261C4×Dic3—61no—
262Dic12—62no—
263Dic12—62no—
264#204—62no—
265#204—62no—
266C22×C9—21no—
267C22×C9—21no—
268C22×C9—21no—
269C22×C9C22×D411yescharacteristic
270C2×D9—41no—
271C2×D9—41no—
272C2×D9—41no—
273C4×C9—21no—
274C4×C9—21no—
275C4×C9—21no—
276C4×C9—21no—
277C4×C9—21no—
278C4×C9C2×#4111yescharacteristic
279C4×C9C2×#4111yescharacteristic
280Dic9—22no—
281Dic9—22no—
282Dic9—41no—
283Dic9—41no—
284Dic9—41no—
285Dic9—41no—
286Dic9—41no—
287C22×Q8—91no—
288C2×Q16—91no—
289C2×Q16—91no—
290C2×SD16—91no—
291C2×SD16—91no—
292C4⋊Q8—91no—
293#126—181no—
294#124—91no—
295#124—181no—
296#123—181no—
297C22⋊Q8—91no—
298C22⋊Q8—181no—
299#121—91no—
300C4×Q8—91no—
301C4×Q8—91no—
302C4×Q8—91no—
303C4×Q8—91no—
304C4×Q8—91no—
305C4×Q8—181no—
306C4×Q8—181no—
307C4×D4—91no—
308#117—91no—
309#117—181no—
310#117—181no—
311#117C2×D911yescharacteristic
312#107—91no—
313#107—91no—
314#106—91no—
315#106—91no—
316C4⋊C8C2×D911yescharacteristic
317C4⋊C8C2×D911yescharacteristic
318#103—91no—
319#103—91no—
320#103—91no—
321#103—91no—
322#103—91no—
323#103—91no—
324#102—91no—
325#102—91no—
326C22⋊C8C2×D911yescharacteristic
327C22⋊C8C2×D911yescharacteristic
328#97C2×D911yescharacteristic
329C4×C8C2×D911yescharacteristic
330C23×C3C2×D1211yescharacteristic
331C22×D3—61no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340#67—241no—
341C2×Dic3—64no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349D12—61no—
350D12—61no—
351C4×D3—241no—
352Dic6—32no—
353Dic6—32no—
354Dic6—64no—
355Dic6—61no—
356Dic6—61no—
357Dic6—61no—
358Dic6—61no—
359Dic6—241no—
360C3×C8—21no—
361C3×C8—21no—
362C3×C8—21no—
363C3×C8—21no—
364C2×C9—41no—
365C2×C9#52511yescharacteristic
366C2×C9#57711yescharacteristic
367C2×C9#57811yescharacteristic
368D9—81no—
369C2×Q8—91no—
370C2×Q8—91no—
371C2×Q8—91no—
372C2×Q8—182no—
373C2×Q8—182no—
374C2×Q8—181no—
375C2×Q8—181no—
376C2×D4—91no—
377C2×D4—181no—
378C22×C4—181no—
379C22×C4—181no—
380C22×C4C22×D911yescharacteristic
381Q16—182no—
382Q16—182no—
383SD16—182no—
384SD16—182no—
385C2×C8C22×D911yescharacteristic
386C2×C8C22×D911yescharacteristic
387C2×C8C22×D911yescharacteristic
388C2×C8C22×D911yescharacteristic
389C4⋊C4—91no—
390C4⋊C4—91no—
391C4⋊C4—91no—
392C4⋊C4—91no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C4⋊C4D3611yescharacteristic
401C4⋊C4D3611yescharacteristic
402C22⋊C4—181no—
403C22⋊C4—181no—
404C22⋊C4—181no—
405C22⋊C4—181no—
406C22⋊C4—181no—
407C22⋊C4—181no—
408C22⋊C4D3611yescharacteristic
409C22⋊C4D3611yescharacteristic
410C42—181no—
411C42—181no—
412C42—181no—
413C42—181no—
414C42—181no—
415C42—181no—
416C42C22×D911yescharacteristic
417C42C22×D911yescharacteristic
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3C22×D1211yescharacteristic
422C2×D3—121no—
423C2×D3—121no—
424C2×D3—121no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4D3×#4111yescharacteristic
431C3×C4D3×#4111yescharacteristic
432Dic3—62no—
433Dic3—62no—
434Dic3—121no—
435Dic3—121no—
436Dic3—121no—
437Dic3—121no—
438Dic3—121no—
439C9#312111yescharacteristic, complemented, Sylow
440C23—181no—
441C23C2×D3611yescharacteristic
442Q8—92no—
443Q8—92no—
444Q8—184no—
445Q8—181no—
446Q8—181no—
447Q8—181no—
448Q8—181no—
449Q8—721no—
450D4—181no—
451D4—181no—
452D4—721no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—184no—
456C2×C4—181no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4—181no—
462C2×C4—181no—
463C2×C4—721no—
464C2×C4C2×D3611yescharacteristic
465C2×C4C2×D3611yescharacteristic
466C2×C4C2×D3611yescharacteristic
467C2×C4C2×D3611yescharacteristic
468C2×C4C2×D3611yescharacteristic
469C2×C4C23×D911yescharacteristic
470C8—21no—
471C8—21no—
472C8—21no—
473C8—21no—
474C2×C3—41no—
475C2×C3#552411yescharacteristic
476C2×C3#575111yescharacteristic
477C2×C3#575311yescharacteristic
478D3—241no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—361no—
483C22—361no—
484C22—361no—
485C22C22×D3611yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—182no—
492C4—182no—
493C4—361no—
494C4—361no—
495C4—361no—
496C4—361no—
497C4—361no—
498C4#41×D911yescharacteristic
499C4#41×D911yescharacteristic
500C3#7939411yescharacteristic
501C2—41no—
502C2—721no—
503C2#1058962611yescharacteristic
504C2#1058985311yescharacteristic
505C2#1058985511yescharacteristic
subgroupG/H
centerC22C22×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#433C2
socleC22×C3C22×D12
prime radical#63492C22
hypercenter#433D9
hypocenterC9#3121
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #10589618C2semidirect
3. C9×#433C2semidirect
4. #10588529C2semidirect
5. #10588529C2semidirect
6. #10588515C2semidirect
7. #10588514C2semidirect
9. #10588405C2semidirect
11. #10588403C2semidirect
12. #10588391C2semidirect
13. #10588384C2semidirect
14. C4×#3664C2semidirect
15. C4×Dic36C2semidirect
216. #433D9semidirect
439. C9#3121semidirect

Maximal subgroups

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

subgroupindex
#105896362
#105896182
C9×#4332
#105885292
#105885152
#105885142
#105884192
#105884052
#105884042
#105884032
#105883912
#105883842
C4×#36642
C4×Dic362
#793943