Finite Group Databasebeta

← #11785324

Subgroups — #11785324

Order 1152.

779 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#837C212yesmaximal
3C4×#3724C211yesmaximal, characteristic, complemented
4#10591120C211yesmaximal, characteristic, complemented
5#10589162C212yesmaximal, complemented
6#70355—32nomaximal
7C2×C32×#41C2211yescharacteristic
8Q8×C3⋊Dic3C411yescharacteristic, complemented
9Q8×C3⋊Dic3C411yescharacteristic, complemented
10D4×C3⋊Dic3—21no—
11D4×C3⋊Dic3—21no—
12D4×C3⋊Dic3C411yescharacteristic, complemented
13D4×C3⋊Dic3C411yescharacteristic, complemented
14#64135—21no—
15#64135C2211yescharacteristic
16C2×C4×C3⋊Dic3—21no—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2212yes—
19C2×C3×#208C2212yes—
20C2×#3724—21no—
21C3×#837—24no—
22#63579—21no—
23#63572—21no—
24#63572—21no—
25Dic3×#41—32no—
26Dic3×#41—61no—
27C2×C3×#104—32no—
28C2×#837D312yes—
29#5118—32no—
30C4×Dic3⋊C4—32no—
31#4555—32no—
32#4523—32no—
33C32×#41—21no—
34C32×#41—21no—
35C32×#41D412yes—
36C32×#41Q812yes—
37C2×C32×Q8C2×C411yescharacteristic
38C2×C32×D4—21no—
39C2×C32×D4C2×C411yescharacteristic
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3D411yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3×Dic3—22no—
47#3757—21no—
48#3757—21no—
49#3757—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)C2×C411yescharacteristic
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3C2×C411yescharacteristic
58C4×C3⋊Dic3C2×C411yescharacteristic
59C4×C3⋊Dic3D411yescharacteristic
60C4×C3⋊Dic3D411yescharacteristic
61C3×C4×Dic3—22no—
62C3×C4×Dic3—22no—
63C3×#208—22no—
64C3×#208—22no—
65C2×C3×C3⋊C8—22no—
66#3724—24no—
67#1806—91noSylow
68C2×C3×#41—21no—
69C2×C3×#41C2×D312yes—
70C2×C3×M16—32no—
71C2×C3×C42—32no—
72Q8×Dic3—32no—
73Q8×Dic3—32no—
74Q8×Dic3—61no—
75Q8×Dic3—61no—
76D4×Dic3—32no—
77D4×Dic3—32no—
78D4×Dic3—61no—
79D4×Dic3—61no—
80D4×Dic3—62no—
81D4×Dic3—62no—
82D4×Dic3—62no—
83D4×Dic3—62no—
84#926—32no—
85#926—61no—
86#926—62no—
87#926—62no—
88C2×Dic3⋊C4—62no—
89C2×C4×Dic3—32no—
90C2×C4×Dic3—61no—
91C2×C4×Dic3—62no—
92C2×C4×Dic3—62no—
93C2×C4×Dic3C2×D312yes—
94C2×#208C2×D312yes—
95C3×#104—64no—
96#837—24no—
97C3⋊#95—62no—
98Dic3⋊C8—62no—
99Dic3⋊C8—62no—
100C23×C32—21no—
101C23×C32C2×D411yescharacteristic
102C32×Q8—21no—
103C32×Q8C4⋊C412yescomplemented
104C32×D4—22no—
105C32×D4—22no—
106C32×D4—21no—
107C32×D4C4⋊C412yescomplemented
108C2×C32×C4—21no—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×Q811yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—42no—
122C2×C3⋊Dic3—42no—
123C2×C3⋊Dic3C22⋊C411yescharacteristic
124C2×C3⋊Dic3C22⋊C411yescharacteristic
125C2×C3⋊Dic3C22⋊C411yescharacteristic
126C2×C3⋊Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3—24no—
128C2×C3×Dic3—42no—
129C2×C3×Dic3—42no—
130C3×C3⋊C8—42no—
131C4×#41—91no—
132#423—91no—
133C2×#104—32no—
134C4×C4⋊C4—91no—
135#339—92no—
136C3×#41—22no—
137C3×#41—22no—
138C3×#41—22no—
139C3×#41—22no—
140C3×#41—22no—
141C3×#41—22no—
142C3×#41Dic614yes—
143C3×#41#6714yes—
144C2×C3×Q8—21no—
145C2×C3×Q8C4×D312yes—
146C2×C3×D4—22no—
147C2×C3×D4—22no—
148C2×C3×D4—21no—
149C2×C3×D4C4×D312yes—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C22×C3×C4—21no—
153C22×C3×C4—62no—
154C22×C3×C4C22×D312yes—
155C22×Dic3—22no—
156C22×Dic3—32no—
157C22×Dic3—32no—
158C22×Dic3—61no—
159C22×Dic3—61no—
160C22×Dic3—62no—
161C22×Dic3—62no—
162C22×Dic3—62no—
163C22×Dic3—62no—
164C3×M16—62no—
165C3×M16—62no—
166C2×C3×C8—62no—
167C3×C42—62no—
168C3×C42—62no—
169#217—62no—
170#217—62no—
171#217—62no—
172#217—62no—
173#217—62no—
174#217—62no—
175C4⋊Dic3—32no—
176C4⋊Dic3—32no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—62no—
180C4⋊Dic3—62no—
181C4⋊Dic3—62no—
182C4⋊Dic3—62no—
183Dic3⋊C4—68no—
184C4×Dic3—22no—
185C4×Dic3—22no—
186C4×Dic3—32no—
187C4×Dic3—32no—
188C4×Dic3—32no—
189C4×Dic3—32no—
190C4×Dic3—61no—
191C4×Dic3—61no—
192C4×Dic3—61no—
193C4×Dic3—61no—
194C4×Dic3—62no—
195C4×Dic3—62no—
196C4×Dic3—62no—
197C4×Dic3—62no—
198C4×Dic3—62no—
199C4×Dic3—62no—
200#208—22no—
201#208—22no—
202C2×C3⋊C8—22no—
203C22×C32—22no—
204C22×C32—21no—
205C22×C32—21no—
206C22×C32—41no—
207C22×C32—41no—
208C22×C32C2×C22⋊C411yescharacteristic
209C22×C32#12111yescharacteristic
210C22×C32C22⋊Q811yescharacteristic
211C32×C4—22no—
212C32×C4C2×C4⋊C411yescharacteristic
213C32×C4#11711yescharacteristic
214C32×C4#12111yescharacteristic
215C32×C4C22⋊Q811yescharacteristic
216C3⋊Dic3—21no—
217C3⋊Dic3—21no—
218C3⋊Dic3—21no—
219C3⋊Dic3—41no—
220C3⋊Dic3—41no—
221C3⋊Dic3#10412yescomplemented
222C3×Dic3—44no—
223C2×#41D3211yescharacteristic
224C2×M16—32no—
225C4×Q8—91no—
226C4×Q8—91no—
227C4×D4—91no—
228C4×D4—91no—
229C4×D4—181no—
230C4×D4—181no—
231#117—91no—
232#117—181no—
233C2×C4⋊C4—181no—
234C2×C42—32no—
235C2×C42—91no—
236C2×C42—181no—
237C4⋊C8—181no—
238C4⋊C8—181no—
239#104—64no—
240#95—181no—
241C23×C3—22no—
242C23×C3—22no—
243C23×C3—21no—
244C23×C3D3×D412yes—
245C3×Q8—22no—
246C3×Q8—22no—
247C3×Q8—22no—
248C3×Q8Dic3⋊C414yescomplemented
249C3×D4—24no—
250C3×D4—24no—
251C3×D4—22no—
252C3×D4—24no—
253C3×D4—24no—
254C3×D4—22no—
255C3×D4—22no—
256C3×D4Dic3⋊C414yescomplemented
257C2×C3×C4—22no—
258C2×C3×C4—24no—
259C2×C3×C4—24no—
260C2×C3×C4—22no—
261C2×C3×C4—24no—
262C2×C3×C4—24no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—64no—
270C2×C3×C4—122no—
271C2×C3×C4—122no—
272C2×C3×C4C2×Dic612yes—
273C2×C3×C4C2×C4×D312yes—
274C2×C3×C4D3×D412yes—
275C2×C3×C4#23712yes—
276C2×C3×C4#23712yes—
277C2×C3×C4C2×#6712yes—
278C2×Dic3—24no—
279C2×Dic3—32no—
280C2×Dic3—32no—
281C2×Dic3—32no—
282C2×Dic3—32no—
283C2×Dic3—42no—
284C2×Dic3—42no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—64no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—122no—
295C2×Dic3—124no—
296C2×Dic3—122no—
297C2×Dic3—124no—
298C2×Dic3—122no—
299C2×Dic3—124no—
300C2×Dic3—124no—
301C3×C8—122no—
302C3⋊C8—42no—
303C2×C32—21no—
304C2×C32—21no—
305C2×C32—42no—
306C2×C32#38011yescharacteristic
307C2×C32C2×#10411yescharacteristic
308C2×C32#42111yescharacteristic
309#41—21no—
310#41—21no—
311#41#62512yes—
312#41#62712yes—
313C2×Q8#62411yescharacteristic
314C2×D4—21no—
315C2×D4#62411yescharacteristic
316C22×C4—21no—
317C22×C4—62no—
318C22×C4—91no—
319C22×C4—91no—
320C22×C4—181no—
321C22×C4—181no—
322C22×C4C2×D3211yescharacteristic
323M16—62no—
324M16—62no—
325C2×C8—62no—
326C4⋊C4—91no—
327C4⋊C4—91no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C4⋊C4—184no—
331C22⋊C4—181no—
332C22⋊C4—181no—
333C22⋊C4—181no—
334C42—62no—
335C42—62no—
336C42—91no—
337C42—91no—
338C42—91no—
339C42—91no—
340C42—181no—
341C42—181no—
342C42—181no—
343C22×C3—22no—
344C22×C3—22no—
345C22×C3—24no—
346C22×C3—24no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—42no—
353C22×C3—42no—
354C22×C3—42no—
355C22×C3—42no—
356C22×C3#87812yes—
357C22×C3D3×C22⋊C412yes—
358C22×C3#93912yes—
359C3×C4—24no—
360C3×C4—24no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—124no—
366C3×C4#87712yes—
367C3×C4#87812yes—
368C3×C4C2×Dic3⋊C412yes—
369C3×C4#93912yes—
370Dic3—34no—
371Dic3—44no—
372Dic3—62no—
373Dic3—62no—
374Dic3—62no—
375Dic3—62no—
376Dic3—62no—
377Dic3—121no—
378Dic3—121no—
379Dic3—122no—
380Dic3—122no—
381Dic3—122no—
382Dic3—122no—
383C32#180611yescharacteristic, complemented, Sylow
384C23—21no—
385C23#381111yescharacteristic
386Q8—21no—
387Q8#372412yescomplemented
388D4—22no—
389D4—22no—
390D4—21no—
391D4#372412yescomplemented
392C2×C4—21no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—64no—
396C2×C4—91no—
397C2×C4—91no—
398C2×C4—91no—
399C2×C4—91no—
400C2×C4—122no—
401C2×C4—122no—
402C2×C4—182no—
403C2×C4—181no—
404C2×C4—181no—
405C2×C4—362no—
406C2×C4—361no—
407C2×C4—362no—
408C2×C4#380511yescharacteristic
409C2×C4#380511yescharacteristic
410C2×C4C2×#62411yescharacteristic
411C2×C4C2×#62511yescharacteristic
412C2×C4C2×#62711yescharacteristic
413C2×C4#381111yescharacteristic
414C8—122no—
415C2×C3—22no—
416C2×C3—22no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3—44no—
423C2×C3—44no—
424C2×C3D3×#10412yes—
425C2×C3#482112yes—
426C2×C3#494212yes—
427C22—21no—
428C22—21no—
429C22—22no—
430C22—41no—
431C22—41no—
432C22#6397411yescharacteristic
433C22#6398011yescharacteristic
434C22#6398211yescharacteristic
435C4—22no—
436C4—92no—
437C4—124no—
438C4—181no—
439C4—181no—
440C4—181no—
441C4—361no—
442C4—361no—
443C4#6395711yescharacteristic
444C4C2×#372411yescharacteristic
445C4#6398011yescharacteristic
446C4#6398211yescharacteristic
447C3—21no—
448C3#7035512yescomplemented
449C2—21no—
450C2—21no—
451C2—42no—
452C2#1059167111yescharacteristic
453C2#1059167211yescharacteristic
454C2#1059172011yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1806
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
3. C4×#3724C2semidirect
4. #10591120C2semidirect
5. #10589162C2semidirect
8. Q8×C3⋊Dic3C4semidirect
9. Q8×C3⋊Dic3C4semidirect
12. D4×C3⋊Dic3C4semidirect
13. D4×C3⋊Dic3C4semidirect
103. C32×Q8C4⋊C4semidirect
107. C32×D4C4⋊C4semidirect
221. C3⋊Dic3#104semidirect
248. C3×Q8Dic3⋊C4semidirect
256. C3×D4Dic3⋊C4semidirect
383. C32#1806semidirect
387. Q8#3724semidirect
391. D4#3724semidirect
448. C3#70355semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
C2×C3×#8372
C4×#37242
#105911202
#105891622
#703553