Finite Group Databasebeta

← #11796532

Subgroups — #11796532

Order 1152.

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

normal subgroups only

This group has 490 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#10595399C211yesmaximal, characteristic
2C3×D3×#101C211yesmaximal, characteristic, complemented
3D3×#836C211yesmaximal, characteristic, complemented
4#10589344C211yesmaximal, characteristic, complemented
5C3×#4477C211yesmaximal, characteristic, complemented
6#10589185C211yesmaximal, characteristic, complemented
7#10589182C211yesmaximal, characteristic, complemented
8#70128—31nomaximal
9#69164—31nomaximal
10C2×C3×D3×Q8C2211yescharacteristic
11C2×#3795C411yescharacteristic
12#64153C2211yescharacteristic
13C3×#947C2211yescharacteristic
14C3×D3×M16—21no—
15#63905—21no—
16#63905—21no—
17#63887—21no—
18#63887—21no—
19#63866C411yescharacteristic
20#63863C411yescharacteristic
21#63855C411yescharacteristic
22D3×#208—21no—
23C32×#101C2211yescharacteristic
24#63663C2211yescharacteristic
25C3×#836C2211yescharacteristic
26C3×#836C2211yescharacteristic
27C3×#824—21no—
28#63560—21no—
29#5816—31no—
30#5675—31no—
31C2×C3×#101—31no—
32C2×#836—31no—
33D3×#101—31no—
34D3×#101D311yescharacteristic, complemented
35C3×#355—31no—
36#4542—31no—
37#4478—31no—
38#4478—31no—
39#4478—31no—
40#4478—31no—
41#4478—61no—
42#4477—31no—
43#4477D311yescharacteristic, complemented
44C2×C32×Q8C2311yescharacteristic
45C2×#634C2×C411yescharacteristic
46C3×D3×Q8—41no—
47C3×D3×Q8—41no—
48C2×C3×D12C2×C411yescharacteristic
49C2×C3×C4×D3C2×C411yescharacteristic
50C2×C3×C4×D3D411yescharacteristic
51C2×C3×C4×D3D411yescharacteristic
52C2×C3×Dic6C2×C411yescharacteristic
53C2×C3×Dic6D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×#625—21no—
56C2×D3×Dic3—21no—
57#3795—41no—
58#3795—41no—
59C32×M16—21no—
60#3750—21no—
61#3750—21no—
62C4×C3⋊Dic3C2×C411yescharacteristic
63#3748—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4×Dic3C2×C411yescharacteristic
67C3×#208—21no—
68C3×#208—21no—
69C3×ΓL(1,𝔽25)—41no—
70C3×D3×C8—41no—
71Dic3⋊Dic3—21no—
72Dic3⋊Dic3—21no—
73Dic3⋊Dic3—21no—
74(C2×D3)⋊Dic3—21no—
75(C2×D3)⋊Dic3—21no—
76(C2×D3)⋊Dic3—21no—
77#3711—41no—
78D3×C3⋊C8—41no—
79#2133—91noSylow
80C22×C3×Q8—31no—
81C2×D3×Q8C2×D311yescharacteristic
82C2×#237—31no—
83C2×#235—31no—
84C2×C3×M16—61no—
85C3×#124—31no—
86#947—31no—
87#947C2×D311yescharacteristic
88#946—61no—
89#946—61no—
90#944—31no—
91#944—31no—
92#944—31no—
93#944—61no—
94#936—31no—
95#929—61no—
96#929—61no—
97#926—31no—
98C2×#208—61no—
99D3×M16—21no—
100D3×M16—61no—
101#883—61no—
102#883—61no—
103#878—61no—
104#878—61no—
105#872—31no—
106#869—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—
128C2×C3⋊Dic3—21no—
129#634—41no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3C22⋊C411yescharacteristic
132C2×C3×Dic3C22⋊C411yescharacteristic
133C2×C3×Dic3C22⋊C411yescharacteristic
134C3×D12—41no—
135C3×C4×D3—21no—
136C3×C4×D3—21no—
137C3×C4×D3—21no—
138C3×C4×D3—21no—
139C3×C4×D3—21no—
140C3×C4×D3—21no—
141C3×Dic6—41no—
142C3×Dic6—41no—
143C3×Dic6—41no—
144#625—41no—
145#625—41no—
146D3×Dic3—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—91no—
155#356—91no—
156#355—31no—
157#355—91no—
158C2×C3×Q8—21no—
159C2×C3×Q8—31no—
160C2×C3×Q8—31no—
161C2×C3×Q8—31no—
162C2×C3×Q8—121no—
163C2×C3×Q8—121no—
164C2×C3×Q8C22×D311yescharacteristic
165C2×C3×Q8C22×D311yescharacteristic
166C2×C3×D4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C2×#67—61no—
171C2×#67—61no—
172C22×Dic3—61no—
173D3×Q8—41no—
174D3×Q8—41no—
175#237—121no—
176#237—121no—
177#235—121no—
178#235—121no—
179C2×D12C4×D311yescharacteristic
180C2×C4×D3—61no—
181C2×C4×D3C4×D311yescharacteristic
182C2×C4×D3D1211yescharacteristic
183C2×C4×D3#6711yescharacteristic
184C2×Dic6—31no—
185C2×Dic6—31no—
186C2×Dic6—61no—
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×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C42—31no—
200#217—61no—
201#217—61no—
202#217—61no—
203(C2×D3)⋊C4—21no—
204(C2×D3)⋊C4—21no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—121no—
219Dic3⋊C4—121no—
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—41no—
237C2×C3×D3—42no—
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—41no—
246C3×Dic3—21no—
247C3×Dic3—21no—
248C3×Dic3—21no—
249C3×Dic3—41no—
250C2×#41—91no—
251C22×Q8—31no—
252C2×M16—61no—
253C2×M16—181no—
254C4⋊Q8—91no—
255C4⋊Q8—91no—
256#124—31no—
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—
270C23×C3—61no—
271C22×D3—21no—
272C22×D3(C2×D3)⋊C411yescharacteristic
273C3×Q8—41no—
274C3×Q8—41no—
275C3×Q8—81no—
276C3×Q8—121no—
277C3×Q8—121no—
278C3×Q8—121no—
279C3×D4—121no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—31no—
284C2×C3×C4—31no—
285C2×C3×C4—31no—
286C2×C3×C4—61no—
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×C4C2×C4×D311yescharacteristic
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4C2×D1211yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299#67—121no—
300#67—121no—
301#67—121no—
302#67—121no—
303C2×Dic3—21no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—121no—
309C2×Dic3—121no—
310C2×Dic3—122no—
311C2×Dic3(C2×D3)⋊C411yescharacteristic
312C2×Dic3(C2×D3)⋊C411yescharacteristic
313C2×Dic3(C2×D3)⋊C411yescharacteristic
314D12—41no—
315C4×D3—21no—
316C4×D3—21no—
317C4×D3—21no—
318C4×D3—21no—
319C4×D3—21no—
320C4×D3—21no—
321C4×D3—122no—
322Dic6—41no—
323Dic6—41no—
324Dic6—41no—
325Dic6—121no—
326Dic6—121no—
327Dic6—241no—
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—21no—
341C3×D3—21no—
342C3×D3—81no—
343#41—361no—
344#41—361no—
345C2×Q8—31no—
346C2×Q8—31no—
347C2×Q8—31no—
348C2×Q8—91no—
349C2×Q8—121no—
350C2×Q8—121no—
351C2×Q8C2×D3211yescharacteristic
352C2×D4—31no—
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—181no—
367C4⋊C4—181no—
368C4⋊C4—181no—
369C4⋊C4—181no—
370C4⋊C4—181no—
371C22⋊C4—61no—
372C22⋊C4—61no—
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×C3—122no—
383C22×C3—121no—
384C22×C3D3×C22⋊C411yescharacteristic
385C22×C3C2×(C2×D3)⋊C411yescharacteristic
386C2×D3—41no—
387C2×D3—42no—
388C2×D3—41no—
389C2×D3#80611yescharacteristic
390C2×D3#80611yescharacteristic
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—41no—
400C3×C4—61no—
401C3×C4—61no—
402C3×C4—61no—
403C3×C4—121no—
404Dic3—21no—
405Dic3—21no—
406Dic3—21no—
407Dic3—41no—
408Dic3—121no—
409Dic3—121no—
410Dic3—122no—
411Dic3—121no—
412Dic3—121no—
413Dic3—241no—
414C32#213311yescharacteristic, complemented, Sylow
415C23—31no—
416C23—61no—
417Q8—41no—
418Q8—121no—
419Q8—121no—
420Q8—121no—
421Q8—361no—
422D4—121no—
423D4—361no—
424D4—361no—
425C2×C4—31no—
426C2×C4—31no—
427C2×C4—31no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—181no—
436C2×C4—181no—
437C2×C4—362no—
438C2×C4C4×D3211yescharacteristic
439C2×C4D3×D1211yescharacteristic
440C2×C4D3×#6711yescharacteristic
441C8—41no—
442C8—121no—
443C8—121no—
444C8—361no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—41no—
449C2×C3—61no—
450C2×C3—61no—
451C2×C3—241no—
452C2×C3D3×#9911yescharacteristic
453C2×C3C2×#80611yescharacteristic
454D3—21no—
455D3—21no—
456D3—81no—
457C22—31no—
458C22—31no—
459C22—121no—
460C22—122no—
461C22—121no—
462C22D3×(C2×D3)⋊C411yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—61no—
467C4—61no—
468C4—61no—
469C4—121no—
470C4—361no—
471C4—361no—
472C3—21no—
473C3#6916411yescharacteristic, complemented
474C3#7012811yescharacteristic, complemented
475C2—21no—
476C2—61no—
477C2—61no—
478C2—241no—
479C2D3×#80611yescharacteristic
subgroupG/H
centerC2D3×#806
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C2×D32
FittingC32×#101C22
socleC2×C32C2×#99
prime radicalC2×#3795C4
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. #10589344C2semidirect
5. C3×#4477C2semidirect
6. #10589185C2semidirect
7. #10589182C2semidirect
34. D3×#101D3semidirect
43. #4477D3semidirect
414. C32#2133semidirect
473. C3#69164semidirect
474. C3#70128semidirect

Maximal subgroups

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

subgroupindex
#105953992
C3×D3×#1012
D3×#8362
#105893442
C3×#44772
#105891852
#105891822
#701283
#691643