Finite Group Databasebeta

← #11889350

Subgroups — #11889350

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
1#10589643C211yesmaximal, characteristic
2D4×Dic18C211yesmaximal, characteristic
3C9×#435C211yesmaximal, characteristic
4#10588807C211yesmaximal, characteristic, complemented
5#10588804C211yesmaximal, characteristic, complemented
6#10588788C211yesmaximal, characteristic, complemented
7C2×#63376C211yesmaximal, characteristic, complemented
8#10588513C211yesmaximal, characteristic, complemented
9#10588511C211yesmaximal, characteristic, complemented
10#10588405C211yesmaximal, characteristic, complemented
11#10588405C211yesmaximal, characteristic, complemented
12#10588403C211yesmaximal, characteristic, complemented
13#10588401C211yesmaximal, characteristic, complemented
14#10588384C211yesmaximal, characteristic, complemented
15#10588383C211yesmaximal, characteristic, complemented
16#79511—31nomaximal
17C22×Dic18C2211yescharacteristic
18C22×Dic18C2211yescharacteristic
19C2×C9×M16C2211yescharacteristic
20C22×C8×C9C2211yescharacteristic
21C4×D4×C9C2211yescharacteristic
22#63497—21no—
23D4×Dic9—21no—
24#63488C2211yescharacteristic
25C2×C4⋊Dic9C2211yescharacteristic
26#63486C2211yescharacteristic
27#63486C2211yescharacteristic
28#63486C2211yescharacteristic
29#63486C2211yescharacteristic
30C2×Dic36C2211yescharacteristic
31C2×Dic36C2211yescharacteristic
32C2×Dic36C2211yescharacteristic
33#63451—21no—
34#63450—21no—
35#63441—21no—
36#63440—21no—
37#63440—21no—
38#63439—21no—
39#63432C2211yescharacteristic
40#63431C2211yescharacteristic
41C4×Dic18C2211yescharacteristic
42C4×Dic18C2211yescharacteristic
43C9×C4⋊C8C2211yescharacteristic
44C9×C22⋊C8C2211yescharacteristic
45C9×C22⋊C8C2211yescharacteristic
46C9×#97C2211yescharacteristic
47#63378C2211yescharacteristic
48#63377C2211yescharacteristic
49#63377C2211yescharacteristic
50#63376C2211yescharacteristic
51#63376C2211yescharacteristic
52#63376C2211yescharacteristic
53#63376C2211yescharacteristic
54#63376C2211yescharacteristic
55#63376C2211yescharacteristic
56#63376C2211yescharacteristic
57#63376C2211yescharacteristic
58#63376C2211yescharacteristic
59#63376C2211yescharacteristic
60#5541—31no—
61D4×Dic6—31no—
62C3×#435D311yescharacteristic
63#5137—31no—
64#5120—31no—
65#5116—31no—
66C2×#816—31no—
67#4849—31no—
68#4829—31no—
69#4739—31no—
70#4739—31no—
71#4723—31no—
72#4721—31no—
73#4716—31no—
74#4703—31no—
75C2×D4×C9D411yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C22×Dic9—21no—
79C22×Dic9—21no—
80C22×Dic9—21no—
81C2×Dic18—22no—
82C2×Dic18—22no—
83C2×Dic18—21no—
84C2×Dic18—21no—
85C2×Dic18—41no—
86C2×Dic18—41no—
87C2×Dic18C2311yescharacteristic
88C2×Dic18C2311yescharacteristic
89C2×Dic18C2311yescharacteristic
90C2×Dic18C2311yescharacteristic
91C9×M16—41no—
92C2×C8×C9—41no—
93C2×C8×C9C2311yescharacteristic
94C2×C8×C9C2311yescharacteristic
95C2×C8×C9C2311yescharacteristic
96C2×C8×C9C2311yescharacteristic
97C9×C4⋊C4D411yescharacteristic
98C9×C22⋊C4D411yescharacteristic
99C9×C22⋊C4D411yescharacteristic
100C42×C9C2311yescharacteristic
101#3676—21no—
102#3676—21no—
103#3676—21no—
104#3676—21no—
105#3676—21no—
106C4⋊Dic9—21no—
107C4⋊Dic9—21no—
108C4⋊Dic9—21no—
109C4⋊Dic9C2311yescharacteristic
110C4⋊Dic9C2311yescharacteristic
111C4⋊Dic9C2311yescharacteristic
112C4⋊Dic9C2311yescharacteristic
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4—21no—
119Dic9⋊C4—21no—
120Dic9⋊C4—21no—
121C4×Dic9—21no—
122C4×Dic9—21no—
123C4×Dic9—21no—
124Dic36—22no—
125Dic36—41no—
126Dic36—41no—
127#3312—91noSylow
128C22×Dic6—31no—
129C22×Dic6—31no—
130C2×C3×M16C2×D311yescharacteristic
131C22×C3×C8C2×D311yescharacteristic
132C3×C4×D4C2×D311yescharacteristic
133#935—61no—
134D4×Dic3—61no—
135#926—31no—
136C2×C4⋊Dic3—31no—
137#924—31no—
138#924—31no—
139#924—31no—
140#924—31no—
141C2×Dic12—31no—
142C2×Dic12—31no—
143C2×Dic12—31no—
144#889—61no—
145#888—61no—
146#879—61no—
147#878—61no—
148#878—61no—
149#877—61no—
150#870—31no—
151#869—31no—
152C4×Dic6—31no—
153C4×Dic6—31no—
154C3×C4⋊C8C2×D311yescharacteristic
155C3×C22⋊C8C2×D311yescharacteristic
156C3×C22⋊C8C2×D311yescharacteristic
157C3×#97C2×D311yescharacteristic
158#818—31no—
159#817—31no—
160#817—31no—
161#816—31no—
162#816—31no—
163#816—31no—
164#816—31no—
165#816—31no—
166#816—31no—
167#816—31no—
168#816—31no—
169#816—31no—
170#816—31no—
171C23×C9C2×D411yescharacteristic
172C23×C9C2×D411yescharacteristic
173D4×C9—22no—
174C2×C4×C9—21no—
175C2×C4×C9—21no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9C2×D411yescharacteristic
179C2×C4×C9C2×D411yescharacteristic
180C2×C4×C9C2×D411yescharacteristic
181C2×C4×C9C2×D411yescharacteristic
182C2×C4×C9C2411yescharacteristic
183C2×Dic9—21no—
184C2×Dic9—21no—
185C2×Dic9—21no—
186C2×Dic9—21no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9—42no—
192C2×Dic9—42no—
193C2×Dic9—42no—
194Dic18—21no—
195Dic18—21no—
196Dic18—21no—
197Dic18—21no—
198Dic18—21no—
199Dic18—21no—
200Dic18—21no—
201Dic18—42no—
202Dic18—42no—
203Dic18#4112yes—
204C8×C9—21no—
205C8×C9—21no—
206C8×C9—21no—
207C8×C9—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#451—91no—
219#441—91no—
220#435D911yescharacteristic
221#419—91no—
222C2×#103—91no—
223C2×C3×D4D1211yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C2×Dic6—31no—
230C2×Dic6—31no—
231C2×Dic6—31no—
232C2×Dic6—31no—
233C2×Dic6—62no—
234C2×Dic6—62no—
235C2×Dic6—61no—
236C2×Dic6—61no—
237C2×Dic6—121no—
238C2×Dic6—121no—
239C3×M16—41no—
240C2×C3×C8—41no—
241C2×C3×C8C22×D311yescharacteristic
242C2×C3×C8C22×D311yescharacteristic
243C2×C3×C8C22×D311yescharacteristic
244C2×C3×C8C22×D311yescharacteristic
245C3×C4⋊C4D1211yescharacteristic
246C3×C22⋊C4D1211yescharacteristic
247C3×C22⋊C4D1211yescharacteristic
248C3×C42C22×D311yescharacteristic
249#217—61no—
250#217—61no—
251#217—61no—
252#217—61no—
253#217—61no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266Dic3⋊C4—61no—
267Dic3⋊C4—61no—
268Dic3⋊C4—61no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272Dic12—62no—
273Dic12—121no—
274Dic12—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—21no—
285C4×C9—21no—
286C4×C9C2×#4111yescharacteristic
287C4×C9H(5,𝔽2)11yescharacteristic
288Dic9—22no—
289Dic9—41no—
290Dic9—41no—
291Dic9—41no—
292Dic9—41no—
293Dic9—41no—
294Dic9—41no—
295Dic9—41no—
296C22×Q8—91no—
297C22×Q8—91no—
298C2×Q16—91no—
299C2×Q16—91no—
300C2×Q16—91no—
301C2×M16C2×D911yescharacteristic
302C22×C8C2×D911yescharacteristic
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—91no—
313C22⋊Q8—181no—
314C22⋊Q8—181no—
315C4×Q8—91no—
316C4×Q8—91no—
317C4×D4—181no—
318C4×D4C2×D911yescharacteristic
319#117—91no—
320#117—181no—
321C2×C4⋊C4—91no—
322#107—91no—
323#106—91no—
324#106—91no—
325C4⋊C8C2×D911yescharacteristic
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⋊C8C2×D911yescharacteristic
337C22⋊C8C2×D911yescharacteristic
338#97C2×D911yescharacteristic
339C23×C3C2×D1211yescharacteristic
340C23×C3C2×D1211yescharacteristic
341C3×D4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—122no—
360C2×Dic3—122no—
361C2×Dic3—122no—
362Dic6—32no—
363Dic6—61no—
364Dic6—61no—
365Dic6—61no—
366Dic6—61no—
367Dic6—61no—
368Dic6—61no—
369Dic6—61no—
370Dic6—122no—
371Dic6—122no—
372C3×C8—21no—
373C3×C8—21no—
374C3×C8—21no—
375C3×C8—21no—
376C2×C9—22no—
377C2×C9—41no—
378C2×C9#54611yescharacteristic
379C2×C9C2×#13711yescharacteristic
380C2×C9#57811yescharacteristic
381C2×Q8—91no—
382C2×Q8—91no—
383C2×Q8—91no—
384C2×Q8—91no—
385C2×Q8—182no—
386C2×Q8—182no—
387C2×Q8—181no—
388C2×Q8—181no—
389C2×Q8—361no—
390C2×Q8—361no—
391C2×D4D3611yescharacteristic
392C22×C4—181no—
393C22×C4—181no—
394C22×C4—181no—
395C22×C4C22×D911yescharacteristic
396C22×C4C22×D911yescharacteristic
397Q16—182no—
398Q16—361no—
399Q16—361no—
400M16—41no—
401C2×C8—41no—
402C2×C8C22×D911yescharacteristic
403C2×C8C22×D911yescharacteristic
404C2×C8C22×D911yescharacteristic
405C2×C8C22×D911yescharacteristic
406C4⋊C4—91no—
407C4⋊C4—91no—
408C4⋊C4—91no—
409C4⋊C4—91no—
410C4⋊C4—181no—
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⋊C4D3611yescharacteristic
422C22⋊C4—181no—
423C22⋊C4—181no—
424C22⋊C4—181no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4D3611yescharacteristic
428C22⋊C4D3611yescharacteristic
429C42—181no—
430C42—181no—
431C42—181no—
432C42C22×D911yescharacteristic
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3#90912yes—
439C22×C3C22×D1211yescharacteristic
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4#100411yescharacteristic
445C3×C4D3×#4111yescharacteristic
446Dic3—62no—
447Dic3—121no—
448Dic3—121no—
449Dic3—121no—
450Dic3—121no—
451Dic3—121no—
452Dic3—121no—
453Dic3—121no—
454C9#331211yescharacteristic, complemented, Sylow
455C23C2×D3611yescharacteristic
456C23C2×D3611yescharacteristic
457Q8—92no—
458Q8—181no—
459Q8—181no—
460Q8—181no—
461Q8—181no—
462Q8—181no—
463Q8—181no—
464Q8—181no—
465Q8—362no—
466Q8—362no—
467D4—22no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—362no—
481C2×C4—362no—
482C2×C4—362no—
483C2×C4C2×D3611yescharacteristic
484C2×C4C2×D3611yescharacteristic
485C2×C4C2×D3611yescharacteristic
486C2×C4C2×D3611yescharacteristic
487C2×C4C23×D911yescharacteristic
488C8—21no—
489C8—21no—
490C8—21no—
491C8—21no—
492C2×C3—22no—
493C2×C3—41no—
494C2×C3#555411yescharacteristic
495C2×C3C2×#90911yescharacteristic
496C2×C3#575311yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22#6347112yes—
503C22C22×D3611yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—182no—
509C4—361no—
510C4—361no—
511C4—361no—
512C4—361no—
513C4—361no—
514C4—361no—
515C4—361no—
516C4#6371011yescharacteristic
517C4#41×D911yescharacteristic
518C3#7951111yescharacteristic
519C2—22no—
520C2—41no—
521C2#1058965611yescharacteristic
522C2C2×#6347111yescharacteristic
523C2#1058985511yescharacteristic
subgroupG/H
centerC22C22×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#435C2
socleC22×C3C22×D12
prime radicalC2×C3×D4D12
hypercenter#435D9
hypocenterC9#3312
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
4. #10588807C2semidirect
5. #10588804C2semidirect
6. #10588788C2semidirect
7. C2×#63376C2semidirect
8. #10588513C2semidirect
9. #10588511C2semidirect
10. #10588405C2semidirect
11. #10588405C2semidirect
12. #10588403C2semidirect
13. #10588401C2semidirect
14. #10588384C2semidirect
15. #10588383C2semidirect
454. C9#3312semidirect

Maximal subgroups

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

subgroupindex
#105896432
D4×Dic182
C9×#4352
#105888072
#105888042
#105887882
C2×#633762
#105885132
#105885112
#105884052
#105884032
#105884012
#105883842
#105883832
#795113