Finite Group Databasebeta

← #11870568

Subgroups — #11870568

Order 1152.

1188 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#10595950C211yesmaximal, characteristic, complemented
2C4×#3828C211yesmaximal, characteristic, complemented
3C32×#431C211yesmaximal, characteristic, complemented
4#10592546C211yesmaximal, characteristic, complemented
5#10592544C211yesmaximal, characteristic, complemented
6#10592543C211yesmaximal, characteristic, complemented
7#10592528C211yesmaximal, characteristic, complemented
8#10592436C211yesmaximal, characteristic, complemented
9#10592433C211yesmaximal, characteristic
10#10592432C211yesmaximal, characteristic, complemented
11#10592422C211yesmaximal, characteristic, complemented
12C4×#3746C211yesmaximal, characteristic, complemented
13C4×#3745C211yesmaximal, characteristic, complemented
14C4×#3744C211yesmaximal, characteristic, complemented
15C4×#3744C211yesmaximal, characteristic, complemented
16#79299—34nomaximal
17C2×#3828C2211yescharacteristic
18C2×C32×C42C2211yescharacteristic
19#64139C2211yescharacteristic
20#64138—21no—
21C4×#638—21no—
22C4×#638—21no—
23C4×#638—21no—
24#64135C2211yescharacteristic
25#64133C2211yescharacteristic
26C2×#3746C2211yescharacteristic
27C2×#3745C2211yescharacteristic
28C2×#3744C2211yescharacteristic
29C2×#3744C2211yescharacteristic
30#64085—21no—
31#64084C2211yescharacteristic
32C4×C4⋊(C3⋊D3)C2211yescharacteristic
33C4×C4⋊(C3⋊D3)C2211yescharacteristic
34C4×C4⋊(C3⋊D3)C2211yescharacteristic
35#64081—21no—
36#64081—21no—
37C42×C3⋊D3—21no—
38#64079C2211yescharacteristic
39C4×#634C2211yescharacteristic
40C4×#634C2211yescharacteristic
41C4×#634C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C32×C4×C8C2211yescharacteristic
47C32×C4×C8C2211yescharacteristic
48#63648C2211yescharacteristic
49#63648C2211yescharacteristic
50#63648C2211yescharacteristic
51#63648C2211yescharacteristic
52#63645C2211yescharacteristic
53#63645C2211yescharacteristic
54#63644C2211yescharacteristic
55#63644C2211yescharacteristic
56#63643C2211yescharacteristic
57#63643C2211yescharacteristic
58#63643C2211yescharacteristic
59#63643C2211yescharacteristic
60#5479—34no—
61C4×#235—34no—
62C3×#431D314yescomplemented
63#4847—34no—
64#4845—34no—
65#4844—34no—
66#4829—34no—
67#4737—34no—
68#4734—34no—
69#4733—34no—
70#4723—34no—
71C4×Dic12—34no—
72C4×D24—34no—
73C4×#204—34no—
74C4×#204—34no—
75C22×C32×C4D411yescharacteristic
76C22×C32×C4D411yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C2×#638—21no—
79C2×#638—21no—
80#3828—22no—
81#3828—22no—
82C2×C4⋊(C3⋊D3)C2311yescharacteristic
83C2×C4⋊(C3⋊D3)C2311yescharacteristic
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×#634C2311yescharacteristic
89C2×#634C2311yescharacteristic
90C2×C32×C8C2311yescharacteristic
91C2×C32×C8C2311yescharacteristic
92C2×C32×C8C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C32×C42D411yescharacteristic
95C32×C42D411yescharacteristic
96C32×C42C2311yescharacteristic
97C32×C42C2311yescharacteristic
98#3757—21no—
99#3757—21no—
100#3752—21no—
101#3752—21no—
102#3752—21no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111#3750—21no—
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120#3746—22no—
121#3745—22no—
122#3744—22no—
123#3744—22no—
124#3102—91noSylow
125C2×#235—34no—
126C2×C3×C42C2×D314yes—
127#930—34no—
128#929—64no—
129C4×#67—64no—
130C4×#67—64no—
131C4×#67—64no—
132#926—34no—
133#924—34no—
134C2×Dic12—34no—
135C2×D24—34no—
136C2×#204—34no—
137C2×#204—34no—
138#876—64no—
139#875—34no—
140C4×D12—34no—
141C4×D12—34no—
142C4×D12—34no—
143#872—64no—
144#872—64no—
145C42×D3—64no—
146#870—34no—
147C4×Dic6—34no—
148C4×Dic6—34no—
149C4×Dic6—34no—
150C3×C4⋊C8C2×D314yes—
151C3×C4⋊C8C2×D314yes—
152C3×C22⋊C8C2×D314yes—
153C3×C22⋊C8C2×D314yes—
154C3×C4×C8C2×D314yes—
155C3×C4×C8C2×D314yes—
156#821—34no—
157#821—34no—
158#821—34no—
159#821—34no—
160#818—34no—
161#818—34no—
162#817—34no—
163#817—34no—
164#816—34no—
165#816—34no—
166#816—34no—
167#816—34no—
168C23×C32C2×D411yescharacteristic
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C2×C32×C4—22no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—41no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181#638—24no—
182#638—42no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C4⋊(C3⋊D3)—21no—
190C4⋊(C3⋊D3)—21no—
191C4⋊(C3⋊D3)—21no—
192C4⋊(C3⋊D3)#4112yes—
193C4×C3⋊D3—24no—
194C4×C3⋊D3—42no—
195C4×C3⋊D3—42no—
196C4×C3⋊D3—42no—
197#634—21no—
198#634—21no—
199#634—21no—
200#634#4112yes—
201C32×C8—21no—
202C32×C8—21no—
203C32×C8—21no—
204C32×C8—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#431C3⋊D311yescharacteristic, complemented
220C22×C3×C4D1214yes—
221C22×C3×C4D1214yes—
222C22×C3×C4C22×D314yes—
223C2×#67—64no—
224C2×#67—64no—
225#235—68no—
226#235—68no—
227C2×D12—34no—
228C2×D12—34no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C2×Dic6—34no—
234C2×Dic6—34no—
235C2×C3×C8C22×D314yes—
236C2×C3×C8C22×D314yes—
237C2×C3×C8C22×D314yes—
238C2×C3×C8C22×D314yes—
239C3×C42D1214yes—
240C3×C42D1214yes—
241C3×C42C22×D314yes—
242C3×C42C22×D314yes—
243#217—64no—
244#217—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251C4⋊Dic3—34no—
252C4⋊Dic3—34no—
253C4⋊Dic3—34no—
254C4⋊Dic3—34no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259Dic3⋊C4—64no—
260Dic3⋊C4—64no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C4×Dic3—64no—
264C4×Dic3—64no—
265Dic12—68no—
266D24—68no—
267#204—68no—
268#204—68no—
269C22×C32—21no—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—22no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C32×C4—21no—
280C32×C4—21no—
281C32×C4—21no—
282C32×C4—21no—
283C32×C4#13512yes—
284C32×C4C2×#4111yescharacteristic
285C32×C4C2×#4111yescharacteristic
286C3⋊Dic3—22no—
287C3⋊Dic3—41no—
288C3⋊Dic3—41no—
289C3⋊Dic3—41no—
290C3⋊Dic3—41no—
291C3⋊Dic3—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×C3⋊D311yescharacteristic
317#107—91no—
318#107—91no—
319#106—91no—
320#106—91no—
321C4⋊C8C2×C3⋊D311yescharacteristic
322C4⋊C8C2×C3⋊D311yescharacteristic
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×C3⋊D311yescharacteristic
332C22⋊C8C2×C3⋊D311yescharacteristic
333C4×C8C2×C3⋊D311yescharacteristic
334C4×C8C2×C3⋊D311yescharacteristic
335C23×C3C2×D1214yes—
336C22×D3—64no—
337C22×D3—64no—
338C2×C3×C4—28no—
339C2×C3×C4—24no—
340C2×C3×C4—24no—
341C2×C3×C4—44no—
342C2×C3×C4C2×D1214yes—
343C2×C3×C4C2×D1214yes—
344C2×C3×C4C2×D1214yes—
345C2×C3×C4C2×D1214yes—
346C2×C3×C4C2×D1214yes—
347C2×C3×C4C23×D314yes—
348#67—616no—
349#67—128no—
350C2×Dic3—64no—
351C2×Dic3—64no—
352C2×Dic3—64no—
353C2×Dic3—64no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356D12—38no—
357D12—64no—
358D12—64no—
359D12—64no—
360C4×D3—616no—
361C4×D3—128no—
362C4×D3—128no—
363C4×D3—128no—
364Dic6—38no—
365Dic6—64no—
366Dic6—64no—
367Dic6—64no—
368C3×C8—24no—
369C3×C8—24no—
370C3×C8—24no—
371C3×C8—24no—
372C2×C32—41no—
373C2×C32#52511yescharacteristic
374C2×C32C2×#13511yescharacteristic
375C2×C32#57511yescharacteristic
376C3⋊D3—42no—
377C3⋊D3—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×C4C4⋊(C3⋊D3)11yescharacteristic
391C22×C4C4⋊(C3⋊D3)11yescharacteristic
392C22×C4C22×C3⋊D311yescharacteristic
393Q16—182no—
394SD16—182no—
395SD16—182no—
396D8—182no—
397C2×C8C22×C3⋊D311yescharacteristic
398C2×C8C22×C3⋊D311yescharacteristic
399C2×C8C22×C3⋊D311yescharacteristic
400C2×C8C22×C3⋊D311yescharacteristic
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—
423C42C4⋊(C3⋊D3)11yescharacteristic
424C42C4⋊(C3⋊D3)11yescharacteristic
425C42C22×C3⋊D311yescharacteristic
426C42C22×C3⋊D311yescharacteristic
427C22×C3—24no—
428C22×C3—24no—
429C22×C3—24no—
430C22×C3C22×D1214yes—
431C2×D3—68no—
432C2×D3—124no—
433C2×D3—124no—
434C2×D3—124no—
435C2×D3—124no—
436C2×D3—124no—
437C3×C4—24no—
438C3×C4—24no—
439C3×C4—24no—
440C3×C4—24no—
441C3×C4#90418yes—
442C3×C4D3×#4114yes—
443C3×C4D3×#4114yes—
444Dic3—68no—
445Dic3—124no—
446Dic3—124no—
447Dic3—124no—
448Dic3—124no—
449Dic3—124no—
450C32#310211yescharacteristic, complemented, Sylow
451C23—181no—
452C23—181no—
453C23C2×C4⋊(C3⋊D3)11yescharacteristic
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×C4⋊(C3⋊D3)11yescharacteristic
479C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
480C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
481C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
482C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
483C2×C4C23×C3⋊D311yescharacteristic
484C8—21no—
485C8—21no—
486C8—21no—
487C8—21no—
488C2×C3—44no—
489C2×C3#552414yes—
490C2×C3C2×#90414yes—
491C2×C3#574814yes—
492D3—128no—
493D3—244no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—182no—
498C22—361no—
499C22—361no—
500C22—361no—
501C22—361no—
502C22—361no—
503C22C22×C4⋊(C3⋊D3)11yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—182no—
509C4—361no—
510C4—361no—
511C4—361no—
512C4—361no—
513C4—361no—
514C4#6411312yes—
515C4#41×C3⋊D311yescharacteristic
516C4#41×C3⋊D311yescharacteristic
517C3#7929914yescomplemented
518C2—41no—
519C2—362no—
520C2—721no—
521C2#1059599511yescharacteristic
522C2C2×#6411311yescharacteristic
523C2#1059621911yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#431C2
socleC22×C32C22×D4
prime radical#10592433C2
hypercenter#431C3⋊D3
hypocenterC32#3102
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #10595950C2semidirect
2. C4×#3828C2semidirect
3. C32×#431C2semidirect
4. #10592546C2semidirect
5. #10592544C2semidirect
6. #10592543C2semidirect
7. #10592528C2semidirect
8. #10592436C2semidirect
10. #10592432C2semidirect
11. #10592422C2semidirect
12. C4×#3746C2semidirect
13. C4×#3745C2semidirect
14. C4×#3744C2semidirect
15. C4×#3744C2semidirect
62. C3×#431D3semidirect
219. #431C3⋊D3semidirect
450. C32#3102semidirect
517. C3#79299semidirect

Maximal subgroups

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

subgroupindex
#105959502
C4×#38282
C32×#4312
#105925462
#105925442
#105925432
#105925282
#105924362
#105924332
#105924322
#105924222
C4×#37462
C4×#37452
C4×#37442
#792993