Finite Group Databasebeta

← #11796530

Subgroups — #11796530

Order 1152.

492 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595340C211yesmaximal, characteristic
2C3×D3×#101C211yesmaximal, characteristic, complemented
3D3×#836C211yesmaximal, characteristic, complemented
4#10589343C211yesmaximal, characteristic, complemented
5C3×#4478C211yesmaximal, characteristic, complemented
6#10589184C211yesmaximal, characteristic, complemented
7#10589183C211yesmaximal, characteristic, complemented
8#70128—31nomaximal
9#69171—31nomaximal
10C2×C3×D3×Q8C2211yescharacteristic
11C2×#3799C411yescharacteristic
12#64156C2211yescharacteristic
13C3×#944C2211yescharacteristic
14C3×D3×M16—21no—
15#63888—21no—
16#63888—21no—
17#63873C411yescharacteristic
18#63864C411yescharacteristic
19#63855C411yescharacteristic
20#63850—21no—
21#63850—21no—
22D3×#208—21no—
23C32×#101C2211yescharacteristic
24#63663C2211yescharacteristic
25C3×#836C2211yescharacteristic
26C3×#836C2211yescharacteristic
27C3×#824—21no—
28#63560—21no—
29#5816—31no—
30#5724—31no—
31C2×C3×#101—31no—
32C2×#836—31no—
33D3×#101—31no—
34D3×#101D311yescharacteristic, complemented
35C3×#356—31no—
36#4548—31no—
37#4478—31no—
38#4478D311yescharacteristic, complemented
39#4477—31no—
40#4477—31no—
41#4477—31no—
42#4477—31no—
43#4477—61no—
44C2×C32×Q8C2311yescharacteristic
45C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
46C3×D3×Q8—41no—
47C3×D3×Q8—41no—
48C2×C3×C4×D3C2×C411yescharacteristic
49C2×C3×C4×D3D411yescharacteristic
50C2×C3×C4×D3D411yescharacteristic
51C2×C3×Dic6C2×C411yescharacteristic
52C2×C3×Dic6C2×C411yescharacteristic
53C2×C3×Dic6D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×#626—21no—
56C2×#624—21no—
57#3799—41no—
58#3799—41no—
59C32×M16—21no—
60#3752—21no—
61#3752—21no—
62C4×C3⋊Dic3C2×C411yescharacteristic
63#3748—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×C4×Dic3C2×C411yescharacteristic
67C3×#208—21no—
68C3×#208—21no—
69C3×ΓL(1,𝔽25)—41no—
70C3×D3×C8—41no—
71#3724—21no—
72#3724—21no—
73Dic3⋊Dic3—21no—
74#3722—21no—
75#3722—21no—
76(C2×D3)⋊Dic3—21no—
77#3711—41no—
78D3×C3⋊C8—41no—
79#2133—91noSylow
80C22×C3×Q8—31no—
81C2×#239—31no—
82C2×D3×Q8C2×D311yescharacteristic
83C2×#235—31no—
84C2×C3×M16—61no—
85C3×C4⋊Q8—31no—
86#947—31no—
87#947—31no—
88#947—31no—
89#947—61no—
90#946—61no—
91#946—61no—
92#944—31no—
93#944—31no—
94#944C2×D311yescharacteristic
95#929—61no—
96#929—61no—
97#926—31no—
98C2×#208—61no—
99D3×M16—21no—
100D3×M16—61no—
101#896—61no—
102#896—61no—
103#894—61no—
104#894—61no—
105#875—31no—
106#872—31no—
107C3×#101—21no—
108C3×#101—31no—
109C3×#101—31no—
110C3×#101—61no—
111C3×#101C2×D311yescharacteristic
112C3×#101C2×D311yescharacteristic
113#836—31no—
114#836—31no—
115#836—61no—
116#836—61no—
117#836C2×D311yescharacteristic
118#836C2×D311yescharacteristic
119#824—21no—
120#824—61no—
121C22×C3⋊D3—21no—
122C22×C3×D3C22⋊C411yescharacteristic
123C32×Q8—41no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C3⋊Dic3—21no—
128C4⋊(C3⋊D3)—41no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3C22⋊C411yescharacteristic
132C2×C3×Dic3C22⋊C411yescharacteristic
133C2×C3×Dic3C22⋊C411yescharacteristic
134C3×C4×D3—21no—
135C3×C4×D3—21no—
136C3×C4×D3—21no—
137C3×C4×D3—21no—
138C3×C4×D3—21no—
139C3×C4×D3—21no—
140C3×Dic6—41no—
141C3×Dic6—41no—
142C3×Dic6—41no—
143C3×Dic6—41no—
144#626—41no—
145#626—41no—
146#624—42no—
147C32×C8—41no—
148C3⋊(C3⋊C8)—41no—
149C3×C3⋊C8—41no—
150C3×C3⋊C8—41no—
151#536—91no—
152C2×#101—31no—
153C2×#101—91no—
154#356—31no—
155#356—91no—
156#355—91no—
157#355—91no—
158C2×C3×Q8—21no—
159C2×C3×Q8—31no—
160C2×C3×Q8—31no—
161C2×C3×Q8—31no—
162C2×C3×Q8—31no—
163C2×C3×Q8—121no—
164C2×C3×Q8—121no—
165C2×C3×Q8C22×D311yescharacteristic
166C2×C3×Q8C22×D311yescharacteristic
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C2×#67—61no—
171#239—121no—
172#239—121no—
173D3×Q8—41no—
174D3×Q8—41no—
175#235—121no—
176#235—121no—
177C2×D12—31no—
178C2×D12—31no—
179C2×D12—61no—
180C2×D12—61no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3C4×D311yescharacteristic
184C2×C4×D3D1211yescharacteristic
185C2×C4×D3#6711yescharacteristic
186C2×Dic6C4×D311yescharacteristic
187C2×Dic6C4×D311yescharacteristic
188C2×Dic6D1211yescharacteristic
189C2×Dic6#6711yescharacteristic
190C3×M16—21no—
191C3×M16—21no—
192C3×M16—41no—
193C3×M16—61no—
194C3×M16—61no—
195C3×M16—121no—
196C2×C3×C8—121no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4—61no—
199C3×C42—31no—
200#217—61no—
201(C2×D3)⋊C4—61no—
202(C2×D3)⋊C4—61no—
203(C2×D3)⋊C4—61no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—121no—
211(C2×D3)⋊C4—121no—
212C4⋊Dic3—61no—
213Dic3⋊C4—21no—
214Dic3⋊C4—21no—
215Dic3⋊C4—61no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220C4×Dic3—31no—
221C4×Dic3—31no—
222C4×Dic3—61no—
223C4×Dic3C4×D311yescharacteristic
224#208—21no—
225#208—21no—
226#208—61no—
227#208—61no—
228#208—121no—
229#208—121no—
230C2×C3⋊C8—121no—
231ΓL(1,𝔽25)—41no—
232ΓL(1,𝔽25)—121no—
233D3×C8—41no—
234D3×C8—121no—
235C22×C32C2×C22⋊C411yescharacteristic
236C2×C3⋊D3—42no—
237C2×C3⋊D3—41no—
238C2×C3×D3—41no—
239C2×C3×D3#9911yescharacteristic
240C2×C3×D3#9911yescharacteristic
241C32×C4—21no—
242C32×C4—21no—
243C32×C4—21no—
244C3⋊Dic3—41no—
245C3×Dic3—21no—
246C3×Dic3—21no—
247C3×Dic3—21no—
248C3×Dic3—41no—
249C3×Dic3—41no—
250C2×#41—91no—
251C22×Q8—31no—
252C2×M16—61no—
253C2×M16—181no—
254C4⋊Q8—31no—
255C4⋊Q8—91no—
256#124—91no—
257#124—91no—
258#123—181no—
259#123—181no—
260C22⋊Q8—181no—
261C22⋊Q8—181no—
262#117—91no—
263#101—31no—
264#101—31no—
265#101—61no—
266#101—91no—
267#101—181no—
268#101D3211yescharacteristic
269C23×C3—31no—
270C22×D3—61no—
271C22×D3—61no—
272C22×D3—121no—
273C22×D3(C2×D3)⋊C411yescharacteristic
274C3×Q8—41no—
275C3×Q8—41no—
276C3×Q8—81no—
277C3×Q8—121no—
278C3×Q8—121no—
279C3×Q8—121no—
280C3×Q8—121no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—31no—
285C2×C3×C4—31no—
286C2×C3×C4—31no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×D1211yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301#67—121no—
302#67—121no—
303C2×Dic3—21no—
304C2×Dic3—21no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—121no—
308C2×Dic3(C2×D3)⋊C411yescharacteristic
309C2×Dic3(C2×D3)⋊C411yescharacteristic
310C2×Dic3(C2×D3)⋊C411yescharacteristic
311D12—121no—
312D12—121no—
313D12—121no—
314D12—121no—
315D12—241no—
316C4×D3—21no—
317C4×D3—21no—
318C4×D3—21no—
319C4×D3—21no—
320C4×D3—21no—
321C4×D3—21no—
322C4×D3—122no—
323C4×D3—122no—
324Dic6—41no—
325Dic6—41no—
326Dic6—41no—
327Dic6—41no—
328C3×C8—41no—
329C3×C8—41no—
330C3×C8—81no—
331C3×C8—121no—
332C3×C8—121no—
333C3⋊C8—41no—
334C3⋊C8—41no—
335C3⋊C8—121no—
336C3⋊C8—121no—
337C3⋊C8—241no—
338C2×C32—21no—
339C2×C32C2×#9911yescharacteristic
340C3⋊D3—81no—
341C3×D3—21no—
342C3×D3—21no—
343#41—361no—
344#41—361no—
345C2×Q8—31no—
346C2×Q8—31no—
347C2×Q8—31no—
348C2×Q8—31no—
349C2×Q8—121no—
350C2×Q8—121no—
351C2×Q8C2×D3211yescharacteristic
352C2×D4—91no—
353C2×D4—181no—
354C22×C4—31no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—181no—
358M16—21no—
359M16—61no—
360M16—61no—
361M16—121no—
362M16—181no—
363M16—361no—
364C2×C8—121no—
365C2×C8—361no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—181no—
369C4⋊C4—181no—
370C4⋊C4—181no—
371C22⋊C4—181no—
372C22⋊C4—181no—
373C22⋊C4—181no—
374C22⋊C4—181no—
375C22⋊C4—181no—
376C42—31no—
377C42—91no—
378C22×C3—21no—
379C22×C3—31no—
380C22×C3—31no—
381C22×C3—121no—
382C22×C3D3×C22⋊C411yescharacteristic
383C22×C3C2×(C2×D3)⋊C411yescharacteristic
384C2×D3—41no—
385C2×D3—122no—
386C2×D3—122no—
387C2×D3—121no—
388C2×D3—121no—
389C2×D3—241no—
390C2×D3—242no—
391C2×D3#80611yescharacteristic
392C2×D3#80611yescharacteristic
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—41no—
400C3×C4—41no—
401C3×C4—41no—
402C3×C4—61no—
403C3×C4—61no—
404C3×C4—61no—
405C3×C4—121no—
406C3×C4—121no—
407Dic3—21no—
408Dic3—21no—
409Dic3—21no—
410Dic3—41no—
411Dic3—41no—
412Dic3—121no—
413Dic3—121no—
414Dic3—241no—
415C32#213311yescharacteristic, complemented, Sylow
416C23—31no—
417C23—181no—
418Q8—41no—
419Q8—121no—
420Q8—121no—
421Q8—121no—
422Q8—121no—
423D4—361no—
424D4—361no—
425D4—361no—
426C2×C4—31no—
427C2×C4—31no—
428C2×C4—31no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—181no—
438C2×C4—362no—
439C2×C4C4×D3211yescharacteristic
440C2×C4D3×D1211yescharacteristic
441C2×C4D3×#6711yescharacteristic
442C8—41no—
443C8—121no—
444C8—121no—
445C8—361no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—41no—
450C2×C3—61no—
451C2×C3—61no—
452C2×C3D3×#9911yescharacteristic
453C2×C3C2×#80611yescharacteristic
454D3—21no—
455D3—21no—
456D3—241no—
457D3—241no—
458D3—481no—
459C22—31no—
460C22—31no—
461C22—121no—
462C22—362no—
463C22—361no—
464C22D3×(C2×D3)⋊C411yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—61no—
469C4—61no—
470C4—61no—
471C4—121no—
472C4—121no—
473C4—361no—
474C3—21no—
475C3#6917111yescharacteristic, complemented
476C3#7012811yescharacteristic, complemented
477C2—21no—
478C2—61no—
479C2—61no—
480C2—721no—
481C2D3×#80611yescharacteristic
subgroupG/H
centerC2D3×#806
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C2×D32
FittingC32×#101C22
socleC2×C32C2×#99
prime radicalC2×#3799C4
cosocleC2×C32×Q8C23
hypercenter#101D32
hypocenterC32#2133
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
2. C3×D3×#101C2semidirect
3. D3×#836C2semidirect
4. #10589343C2semidirect
5. C3×#4478C2semidirect
6. #10589184C2semidirect
7. #10589183C2semidirect
34. D3×#101D3semidirect
38. #4478D3semidirect
415. C32#2133semidirect
475. C3#69171semidirect
476. C3#70128semidirect

Maximal subgroups

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

subgroupindex
#105953402
C3×D3×#1012
D3×#8362
#105893432
C3×#44782
#105891842
#105891832
#701283
#691713