Finite Group Databasebeta

← #11870567

Subgroups — #11870567

Order 1152.

594 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#10589581C211yesmaximal, characteristic, complemented
2C4×#3697C211yesmaximal, characteristic, complemented
3C9×#431C211yesmaximal, characteristic, complemented
4#10588531C211yesmaximal, characteristic, complemented
5#10588529C211yesmaximal, characteristic, complemented
6#10588528C211yesmaximal, characteristic, complemented
7#10588511C211yesmaximal, characteristic, complemented
8#10588419C211yesmaximal, characteristic, complemented
9#10588416C211yesmaximal, characteristic
10#10588415C211yesmaximal, characteristic, complemented
11#10588403C211yesmaximal, characteristic, complemented
12C4×D72C211yesmaximal, characteristic, complemented
13C4×#3664C211yesmaximal, characteristic, complemented
14C4×#3664C211yesmaximal, characteristic, complemented
15C4×Dic36C211yesmaximal, characteristic, complemented
16#79299—31nomaximal
17C2×#3697C2211yescharacteristic
18C2×C42×C9C2211yescharacteristic
19#63492C2211yescharacteristic
20#63491—21no—
21C4×#611—21no—
22C4×#611—21no—
23C4×#611—21no—
24#63488C2211yescharacteristic
25#63486C2211yescharacteristic
26C2×D72C2211yescharacteristic
27C2×#3664C2211yescharacteristic
28C2×#3664C2211yescharacteristic
29C2×Dic36C2211yescharacteristic
30#63438—21no—
31#63437C2211yescharacteristic
32C4×D36C2211yescharacteristic
33C4×D36C2211yescharacteristic
34C4×D36C2211yescharacteristic
35#63434—21no—
36#63434—21no—
37C42×D9—21no—
38#63432C2211yescharacteristic
39C4×Dic18C2211yescharacteristic
40C4×Dic18C2211yescharacteristic
41C4×Dic18C2211yescharacteristic
42C9×C4⋊C8C2211yescharacteristic
43C9×C4⋊C8C2211yescharacteristic
44C9×C22⋊C8C2211yescharacteristic
45C9×C22⋊C8C2211yescharacteristic
46C4×C8×C9C2211yescharacteristic
47C4×C8×C9C2211yescharacteristic
48#63380C2211yescharacteristic
49#63380C2211yescharacteristic
50#63380C2211yescharacteristic
51#63380C2211yescharacteristic
52#63378C2211yescharacteristic
53#63378C2211yescharacteristic
54#63377C2211yescharacteristic
55#63377C2211yescharacteristic
56#63376C2211yescharacteristic
57#63376C2211yescharacteristic
58#63376C2211yescharacteristic
59#63376C2211yescharacteristic
60#5479—31no—
61C4×#235—31no—
62C3×#431D311yescharacteristic
63#4847—31no—
64#4845—31no—
65#4844—31no—
66#4829—31no—
67#4737—31no—
68#4734—31no—
69#4733—31no—
70#4723—31no—
71C4×Dic12—31no—
72C4×D24—31no—
73C4×#204—31no—
74C4×#204—31no—
75C22×C4×C9D411yescharacteristic
76C22×C4×C9D411yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C2×#611—21no—
79C2×#611—21no—
80#3697—22no—
81#3697—22no—
82C2×D36C2311yescharacteristic
83C2×D36C2311yescharacteristic
84C2×C4×D9—21no—
85C2×C4×D9—21no—
86C2×C4×D9—21no—
87C2×C4×D9—21no—
88C2×Dic18C2311yescharacteristic
89C2×Dic18C2311yescharacteristic
90C2×C8×C9C2311yescharacteristic
91C2×C8×C9C2311yescharacteristic
92C2×C8×C9C2311yescharacteristic
93C2×C8×C9C2311yescharacteristic
94C42×C9D411yescharacteristic
95C42×C9D411yescharacteristic
96C42×C9C2311yescharacteristic
97C42×C9C2311yescharacteristic
98#3676—21no—
99#3676—21no—
100(C2×D9)⋊C4—21no—
101(C2×D9)⋊C4—21no—
102(C2×D9)⋊C4—21no—
103(C2×D9)⋊C4—21no—
104(C2×D9)⋊C4—21no—
105(C2×D9)⋊C4—21no—
106C4⋊Dic9C2311yescharacteristic
107C4⋊Dic9C2311yescharacteristic
108C4⋊Dic9C2311yescharacteristic
109C4⋊Dic9C2311yescharacteristic
110Dic9⋊C4—21no—
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116C4×Dic9—21no—
117C4×Dic9—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120D72—22no—
121#3664—22no—
122#3664—22no—
123Dic36—22no—
124#3102—91noSylow
125C2×#235—31no—
126C2×C3×C42C2×D311yescharacteristic
127#930—31no—
128#929—61no—
129C4×#67—61no—
130C4×#67—61no—
131C4×#67—61no—
132#926—31no—
133#924—31no—
134C2×Dic12—31no—
135C2×D24—31no—
136C2×#204—31no—
137C2×#204—31no—
138#876—61no—
139#875—31no—
140C4×D12—31no—
141C4×D12—31no—
142C4×D12—31no—
143#872—61no—
144#872—61no—
145C42×D3—61no—
146#870—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×C4×C8C2×D311yescharacteristic
155C3×C4×C8C2×D311yescharacteristic
156#821—31no—
157#821—31no—
158#821—31no—
159#821—31no—
160#818—31no—
161#818—31no—
162#817—31no—
163#817—31no—
164#816—31no—
165#816—31no—
166#816—31no—
167#816—31no—
168C23×C9C2×D411yescharacteristic
169C22×D9—21no—
170C22×D9—21no—
171C2×C4×C9—22no—
172C2×C4×C9—21no—
173C2×C4×C9—21no—
174C2×C4×C9—41no—
175C2×C4×C9C2×D411yescharacteristic
176C2×C4×C9C2×D411yescharacteristic
177C2×C4×C9C2×D411yescharacteristic
178C2×C4×C9C2×D411yescharacteristic
179C2×C4×C9C2×D411yescharacteristic
180C2×C4×C9C2411yescharacteristic
181#611—24no—
182#611—42no—
183C2×Dic9—21no—
184C2×Dic9—21no—
185C2×Dic9—21no—
186C2×Dic9—21no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189D36—21no—
190D36—21no—
191D36—21no—
192D36#4112yes—
193C4×D9—24no—
194C4×D9—42no—
195C4×D9—42no—
196C4×D9—42no—
197Dic18—21no—
198Dic18—21no—
199Dic18—21no—
200Dic18#4112yes—
201C8×C9—21no—
202C8×C9—21no—
203C8×C9—21no—
204C8×C9—21no—
205#529—91no—
206C4×#41—91no—
207#485—91no—
208#482—91no—
209#479—91no—
210#478—91no—
211#464—91no—
212#463—91no—
213#452—91no—
214#449—91no—
215C4×Q16—91no—
216C4×SD16—91no—
217C4×SD16—91no—
218C4×D8—91no—
219#431D911yescharacteristic, complemented
220C22×C3×C4D1211yescharacteristic
221C22×C3×C4D1211yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C2×#67—61no—
224C2×#67—61no—
225#235—62no—
226#235—62no—
227C2×D12—31no—
228C2×D12—31no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×Dic6—31no—
234C2×Dic6—31no—
235C2×C3×C8C22×D311yescharacteristic
236C2×C3×C8C22×D311yescharacteristic
237C2×C3×C8C22×D311yescharacteristic
238C2×C3×C8C22×D311yescharacteristic
239C3×C42D1211yescharacteristic
240C3×C42D1211yescharacteristic
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#217—61no—
244#217—61no—
245(C2×D3)⋊C4—61no—
246(C2×D3)⋊C4—61no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—61no—
251C4⋊Dic3—31no—
252C4⋊Dic3—31no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255Dic3⋊C4—61no—
256Dic3⋊C4—61no—
257Dic3⋊C4—61no—
258Dic3⋊C4—61no—
259Dic3⋊C4—61no—
260Dic3⋊C4—61no—
261C4×Dic3—61no—
262C4×Dic3—61no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265Dic12—62no—
266D24—62no—
267#204—62no—
268#204—62no—
269C22×C9—21no—
270C22×C9—21no—
271C22×C9—21no—
272C22×C9C22×D411yescharacteristic
273C2×D9—22no—
274C2×D9—41no—
275C2×D9—41no—
276C2×D9—41no—
277C2×D9—41no—
278C2×D9—41no—
279C4×C9—21no—
280C4×C9—21no—
281C4×C9—21no—
282C4×C9—21no—
283C4×C9#13512yes—
284C4×C9C2×#4111yescharacteristic
285C4×C9C2×#4111yescharacteristic
286Dic9—22no—
287Dic9—41no—
288Dic9—41no—
289Dic9—41no—
290Dic9—41no—
291Dic9—41no—
292C2×#41—91no—
293C2×Q16—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×D8—91no—
297#126—181no—
298#125—91no—
299#124—91no—
300#123—181no—
301C22⋊Q8—91no—
302#121—91no—
303C4×Q8—91no—
304C4×Q8—91no—
305C4×Q8—91no—
306C4×D4—91no—
307C4×D4—91no—
308C4×D4—91no—
309C4×D4—181no—
310C4×D4—181no—
311C4×D4—181no—
312#117—91no—
313#117—181no—
314#117—181no—
315C2×C42—181no—
316C2×C42C2×D911yescharacteristic
317#107—91no—
318#107—91no—
319#106—91no—
320#106—91no—
321C4⋊C8C2×D911yescharacteristic
322C4⋊C8C2×D911yescharacteristic
323#103—91no—
324#103—91no—
325#103—91no—
326#103—91no—
327#102—91no—
328#102—91no—
329#102—91no—
330#102—91no—
331C22⋊C8C2×D911yescharacteristic
332C22⋊C8C2×D911yescharacteristic
333C4×C8C2×D911yescharacteristic
334C4×C8C2×D911yescharacteristic
335C23×C3C2×D1211yescharacteristic
336C22×D3—61no—
337C22×D3—61no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—41no—
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348#67—64no—
349#67—122no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356D12—32no—
357D12—61no—
358D12—61no—
359D12—61no—
360C4×D3—64no—
361C4×D3—122no—
362C4×D3—122no—
363C4×D3—122no—
364Dic6—32no—
365Dic6—61no—
366Dic6—61no—
367Dic6—61no—
368C3×C8—21no—
369C3×C8—21no—
370C3×C8—21no—
371C3×C8—21no—
372C2×C9—41no—
373C2×C9#52511yescharacteristic
374C2×C9C2×#13511yescharacteristic
375C2×C9#57511yescharacteristic
376D9—42no—
377D9—81no—
378#41—182no—
379#41—182no—
380C2×Q8—91no—
381C2×Q8—91no—
382C2×D4—91no—
383C2×D4—91no—
384C2×D4—181no—
385C2×D4—181no—
386C22×C4—181no—
387C22×C4—181no—
388C22×C4—181no—
389C22×C4—181no—
390C22×C4D3611yescharacteristic
391C22×C4D3611yescharacteristic
392C22×C4C22×D911yescharacteristic
393Q16—182no—
394SD16—182no—
395SD16—182no—
396D8—182no—
397C2×C8C22×D911yescharacteristic
398C2×C8C22×D911yescharacteristic
399C2×C8C22×D911yescharacteristic
400C2×C8C22×D911yescharacteristic
401C4⋊C4—91no—
402C4⋊C4—91no—
403C4⋊C4—91no—
404C4⋊C4—91no—
405C4⋊C4—181no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C22⋊C4—181no—
412C22⋊C4—181no—
413C22⋊C4—181no—
414C22⋊C4—181no—
415C22⋊C4—181no—
416C22⋊C4—181no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C42—181no—
420C42—181no—
421C42—181no—
422C42—181no—
423C42D3611yescharacteristic
424C42D3611yescharacteristic
425C42C22×D911yescharacteristic
426C42C22×D911yescharacteristic
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3C22×D1211yescharacteristic
431C2×D3—62no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—121no—
435C2×D3—121no—
436C2×D3—121no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4#90412yes—
442C3×C4D3×#4111yescharacteristic
443C3×C4D3×#4111yescharacteristic
444Dic3—62no—
445Dic3—121no—
446Dic3—121no—
447Dic3—121no—
448Dic3—121no—
449Dic3—121no—
450C9#310211yescharacteristic, complemented, Sylow
451C23—181no—
452C23—181no—
453C23C2×D3611yescharacteristic
454Q8—92no—
455Q8—181no—
456Q8—181no—
457Q8—181no—
458D4—92no—
459D4—184no—
460D4—181no—
461D4—181no—
462D4—181no—
463D4—362no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—184no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—362no—
476C2×C4—362no—
477C2×C4—362no—
478C2×C4C2×D3611yescharacteristic
479C2×C4C2×D3611yescharacteristic
480C2×C4C2×D3611yescharacteristic
481C2×C4C2×D3611yescharacteristic
482C2×C4C2×D3611yescharacteristic
483C2×C4C23×D911yescharacteristic
484C8—21no—
485C8—21no—
486C8—21no—
487C8—21no—
488C2×C3—41no—
489C2×C3#552411yescharacteristic
490C2×C3C2×#90411yescharacteristic
491C2×C3#574811yescharacteristic
492D3—122no—
493D3—241no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—182no—
498C22—361no—
499C22—361no—
500C22—361no—
501C22—361no—
502C22—361no—
503C22C22×D3611yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—182no—
509C4—361no—
510C4—361no—
511C4—361no—
512C4—361no—
513C4—361no—
514C4#6346712yes—
515C4#41×D911yescharacteristic
516C4#41×D911yescharacteristic
517C3#7929911yescharacteristic
518C2—41no—
519C2—362no—
520C2—721no—
521C2#1058962611yescharacteristic
522C2C2×#6346711yescharacteristic
523C2#1058985011yescharacteristic
subgroupG/H
centerC2×C4C2×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#431C2
socleC22×C3C22×D12
prime radical#10588416C2
hypercenter#431D9
hypocenterC9#3102
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #10589581C2semidirect
2. C4×#3697C2semidirect
3. C9×#431C2semidirect
4. #10588531C2semidirect
5. #10588529C2semidirect
6. #10588528C2semidirect
7. #10588511C2semidirect
8. #10588419C2semidirect
10. #10588415C2semidirect
11. #10588403C2semidirect
12. C4×D72C2semidirect
13. C4×#3664C2semidirect
14. C4×#3664C2semidirect
15. C4×Dic36C2semidirect
219. #431D9semidirect
450. C9#3102semidirect

Maximal subgroups

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

subgroupindex
#105895812
C4×#36972
C9×#4312
#105885312
#105885292
#105885282
#105885112
#105884192
#105884162
#105884152
#105884032
C4×D722
C4×#36642
C4×Dic362
#792993