Finite Group Databasebeta

← #11878895

Subgroups — #11878895

Order 1152.

829 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic
3#10592791C211yesmaximal, characteristic, complemented
4C3×#5092C211yesmaximal, characteristic, complemented
5#10591653C214yesmaximal
6#10591625C214yesmaximal, complemented
7#10590290C211yesmaximal, characteristic, complemented
8#10590288C211yesmaximal, characteristic, complemented
9#10590261C211yesmaximal, characteristic
10#83370—31nomaximal
11#81802—31nomaximal
12C2×D3×Dic6C2212yes—
13C32×C4⋊Q8C2211yescharacteristic
14C2×#3756C2214yes—
15#64078C2211yescharacteristic
16C3×#946C2212yes—
17C3×Q8×Dic3C2212yes—
18C2×C3×#216C2214yes—
19C3×#897—21no—
20C3×#892—21no—
21C3×#890—21no—
22C3×#887—21no—
23C3×C42×D3C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×#869C2211yescharacteristic
26#63918—21no—
27#63918—21no—
28D3×C4⋊Dic3—21no—
29D3×C4⋊Dic3—21no—
30#63866C2212yes—
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C3×C4×C3⋊C8C2211yescharacteristic
33Dic3⋊(C3⋊C8)C2212yes—
34#63567C2214yes—
35#63565C2214yes—
36(C2×D3)⋊(C3⋊C8)C2212yes—
37C3×#533—31no—
38#5728D311yescharacteristic
39D3×C4⋊Q8—31no—
40C2×#869—31no—
41C3×#494—31no—
42#5186—34no—
43#5182—34no—
44#5093—31no—
45#5093—31no—
46#5092—31no—
47#5092—31no—
48#5092—61no—
49#5092D311yescharacteristic, complemented
50#5079—31no—
51#5050—34no—
52#5031—34no—
53#4925—31no—
54#4685—31no—
55#4681—31no—
56C2×C32×Q8C2312yes—
57C2×#634C2312yes—
58C2×C3×C4×D3D411yescharacteristic
59C2×C3×C4×D3D411yescharacteristic
60C2×C3×C4×D3C2311yescharacteristic
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C2×#627—22no—
64C2×D3×Dic3—22no—
65D3×Dic6—44no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4—21no—
68C32×C42C2311yescharacteristic
69#3756—44no—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)—21no—
72C2×C3⋊(C3⋊C8)C2312yes—
73C3×#216—44no—
74C3×(C2×D3)⋊C4—22no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—22no—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3—22no—
82C3×C4×Dic3D411yescharacteristic
83C3×C4×Dic3D411yescharacteristic
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2312yes—
86Dic3⋊Dic3—22no—
87Dic3⋊Dic3—22no—
88#3209—91noSylow
89C2×D3×Q8—32no—
90C22×Dic6—32no—
91C2×C3×Q16—34no—
92C3×C4⋊Q8—21no—
93C3×C4⋊Q8—31no—
94C3×C4⋊Q8—31no—
95C3×C4⋊Q8C2×D311yescharacteristic
96C3×C4⋊Q8C2×D311yescharacteristic
97C3×#125—61no—
98C3×C22⋊Q8—32no—
99C3×C22⋊Q8—61no—
100C3×C4×Q8—32no—
101C3×C4×Q8—61no—
102C3×#117—61no—
103C2×C3×C42—31no—
104#946C2×D312yes—
105Q8×Dic3C2×D312yes—
106#944—32no—
107C2×#216—34no—
108C2×#216—34no—
109C2×#216—64no—
110C2×#216C2×D314yes—
111C2×C4⋊Dic3—61no—
112C2×C4⋊Dic3—61no—
113#897—21no—
114#892—21no—
115D3×C4⋊C4—61no—
116D3×C4⋊C4—61no—
117#890—21no—
118#888—61no—
119#888—61no—
120#887—21no—
121C42×D3C2×D311yescharacteristic
122#869—32no—
123#869—31no—
124#869—31no—
125#869—61no—
126#869—61no—
127#869—61no—
128#869C2×D311yescharacteristic
129#869C2×D311yescharacteristic
130C3×C4×C8—31no—
131#835—34no—
132#830—32no—
133(C2×D3)⋊C8—32no—
134#816—34no—
135Dic3⋊C8—32no—
136#810—34no—
137#810—34no—
138C4⋊(C3⋊C8)—32no—
139C4×C3⋊C8—31no—
140C4×C3⋊C8—31no—
141C4×C3⋊C8—61no—
142C4×C3⋊C8C2×D311yescharacteristic
143C22×C3×D3C2×D411yescharacteristic
144C32×Q8—24no—
145C2×C32×C4—22no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—22no—
150#634—24no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3C2×D411yescharacteristic
154C2×C3×Dic3C2×D411yescharacteristic
155C2×C3×Dic3C2×D411yescharacteristic
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×C4×D3Q1614yescomplemented
159C3×Dic6—24no—
160C3×Dic6—42no—
161#627—44no—
162D3×Dic3—44no—
163C3⋊(C3⋊C8)—22no—
164C3×C3⋊C8—22no—
165#533—31no—
166C2×C4⋊Q8—91no—
167#494—31no—
168#494—91no—
169#487—91no—
170#487—91no—
171#462—94no—
172#451—94no—
173#431—91no—
174C2×C3×Q8—22no—
175C2×C3×Q8—32no—
176C2×C3×Q8—61no—
177C2×C3×Q8C22×D312yes—
178C2×C3×Q8C22×D312yes—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—31no—
182C22×Dic3—62no—
183D3×Q8—124no—
184C2×C4×D3—62no—
185C2×C4×D3#6711yescharacteristic
186C2×C4×D3#6711yescharacteristic
187C2×C4×D3C22×D311yescharacteristic
188C2×Dic6—21no—
189C2×Dic6—32no—
190C2×Dic6—32no—
191C2×Dic6—62no—
192C2×Dic6—62no—
193C2×Dic6—62no—
194C2×Dic6—124no—
195C2×Dic6C22×D312yes—
196C3×Q16—124no—
197C2×C3×C8—32no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—41no—
204C3×C4⋊C4—41no—
205C3×C4⋊C4—62no—
206C3×C4⋊C4—62no—
207C3×C4⋊C4—61no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C22⋊C4—62no—
211C3×C42—21no—
212C3×C42—31no—
213C3×C42—31no—
214C3×C42—31no—
215C3×C42—62no—
216C3×C42C22×D311yescharacteristic
217C3×C42C22×D311yescharacteristic
218#216—44no—
219#216—124no—
220#216—124no—
221#216—128no—
222(C2×D3)⋊C4—22no—
223C4⋊Dic3—21no—
224C4⋊Dic3—21no—
225C4⋊Dic3—21no—
226C4⋊Dic3—22no—
227C4⋊Dic3—62no—
228C4⋊Dic3—62no—
229C4⋊Dic3—61no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3—121no—
234C4⋊Dic3—121no—
235C4⋊Dic3C22×D312yes—
236Dic3⋊C4—22no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239C4×Dic3—22no—
240C4×Dic3#6711yescharacteristic
241C4×Dic3#6711yescharacteristic
242C4×Dic3C22×D311yescharacteristic
243C2×C3⋊C8—32no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8C22×D312yes—
247C22×C32C22×D411yescharacteristic
248C2×C3×D3—21no—
249C2×C3×D3—21no—
250C2×C3×D3C2×Q1612yes—
251C32×C4—42no—
252C32×C4C2×Q1612yes—
253C32×C4#13712yes—
254C32×C4H(5,𝔽2)12yes—
255C3⋊Dic3—42no—
256C3×Dic3—21no—
257C3×Dic3—21no—
258C3×Dic3—42no—
259C3×Dic3—42no—
260C3×Dic3C2×Q1612yes—
261C22×Q8—92no—
262C2×Q16—34no—
263C2×Q16—94no—
264C4⋊Q8—31no—
265C4⋊Q8—31no—
266C4⋊Q8—92no—
267C4⋊Q8—91no—
268C4⋊Q8—181no—
269C4⋊Q8—181no—
270C4⋊Q8D3211yescharacteristic
271#125—61no—
272C22⋊Q8—32no—
273C22⋊Q8—61no—
274C4×Q8—32no—
275C4×Q8—61no—
276#117—61no—
277C2×C4⋊C4—181no—
278C2×C4⋊C4—181no—
279C2×C42—31no—
280C4⋊C8—92no—
281#103—94no—
282#103—94no—
283C22⋊C8—92no—
284C4×C8—31no—
285C4×C8—91no—
286C23×C3—31no—
287C22×D3C2×#6711yescharacteristic
288C3×Q8—24no—
289C3×Q8—24no—
290C3×Q8—44no—
291C3×Q8—64no—
292C3×Q8—122no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—31no—
299C2×C3×C4—34no—
300C2×C3×C4—31no—
301C2×C3×C4—31no—
302C2×C3×C4—42no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4C2×#6711yescharacteristic
310C2×C3×C4C2×#6711yescharacteristic
311C2×C3×C4C23×D311yescharacteristic
312C2×C3×C4C23×D311yescharacteristic
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—122no—
318C2×Dic3—124no—
319C2×Dic3C2×#6711yescharacteristic
320C2×Dic3C2×#6711yescharacteristic
321C2×Dic3C2×#6711yescharacteristic
322C4×D3—22no—
323C4×D3—22no—
324C4×D3—124no—
325C4×D3#21614yescomplemented
326Dic6—24no—
327Dic6—42no—
328Dic6—64no—
329Dic6—64no—
330Dic6—124no—
331Dic6—124no—
332Dic6—124no—
333C3×C8—62no—
334C3⋊C8—22no—
335C3⋊C8—64no—
336C3⋊C8—62no—
337C3⋊C8—62no—
338C2×C32#53511yescharacteristic
339C2×C32C22×Q1611yescharacteristic
340C2×C32C2×#13711yescharacteristic
341C3×D3—22no—
342C2×Q8—32no—
343C2×Q8—61no—
344C2×Q8—92no—
345C2×Q8—182no—
346C2×Q8—364no—
347C2×Q8C2×D3212yes—
348C22×C4—31no—
349C22×C4—31no—
350C22×C4—31no—
351C22×C4—182no—
352Q16—124no—
353Q16—364no—
354C2×C8—32no—
355C2×C8—92no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—32no—
359C4⋊C4—62no—
360C4⋊C4—62no—
361C4⋊C4—61no—
362C4⋊C4—61no—
363C4⋊C4—61no—
364C4⋊C4—182no—
365C4⋊C4—182no—
366C4⋊C4—181no—
367C4⋊C4—181no—
368C22⋊C4—62no—
369C42—31no—
370C42—31no—
371C42—31no—
372C42—62no—
373C42C2×D3211yescharacteristic
374C22×C3—21no—
375C22×C3—32no—
376C22×C3—61no—
377C22×C3—61no—
378C22×C3C2×D3×D411yescharacteristic
379C22×C3C22×#6711yescharacteristic
380C2×D3—21no—
381C2×D3—21no—
382C2×D3C2×#21612yes—
383C3×C4—22no—
384C3×C4—22no—
385C3×C4—22no—
386C3×C4—32no—
387C3×C4—42no—
388C3×C4—42no—
389C3×C4—61no—
390C3×C4—61no—
391C3×C4—82no—
392C3×C4—122no—
393C3×C4—122no—
394C3×C4D3×Q1612yes—
395C3×C4#91812yes—
396C3×C4C2×#21612yes—
397C3×C4#95112yes—
398C3×C4#100412yes—
399C3×C4#100912yes—
400Dic3—21no—
401Dic3—21no—
402Dic3—42no—
403Dic3—42no—
404Dic3—122no—
405Dic3—122no—
406Dic3—242no—
407Dic3C2×#21612yes—
408C32#320911yescharacteristic, complemented, Sylow
409C23—31no—
410Q8—24no—
411Q8—64no—
412Q8—122no—
413Q8—184no—
414Q8—364no—
415C2×C4—22no—
416C2×C4—31no—
417C2×C4—34no—
418C2×C4—31no—
419C2×C4—31no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—182no—
425C2×C4—364no—
426C2×C4D3×#6711yescharacteristic
427C2×C4D3×#6711yescharacteristic
428C2×C4C22×D3211yescharacteristic
429C8—62no—
430C8—182no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—62no—
435C2×C3#571511yescharacteristic
436C2×C3C2×D3×Q1611yescharacteristic
437C2×C3C2×#91811yescharacteristic
438C2×C3C22×#21611yescharacteristic
439C2×C3C2×#95111yescharacteristic
440C2×C3#583011yescharacteristic
441D3—22no—
442C22—32no—
443C22—61no—
444C22—61no—
445C22C2×D3×#6711yescharacteristic
446C4—32no—
447C4—42no—
448C4—61no—
449C4—61no—
450C4—122no—
451C4—122no—
452C4—362no—
453C4D3×#21612yes—
454C4#6394312yes—
455C4#6431412yes—
456C3—21no—
457C3#8180211yescharacteristic, complemented
458C3#8337011yescharacteristic, complemented
459C2—62no—
460C2#1059530311yescharacteristic
461C2C2×D3×#21611yescharacteristic
462C2C2×#6394311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32#3209
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10592791C2semidirect
4. C3×#5092C2semidirect
6. #10591625C2semidirect
7. #10590290C2semidirect
8. #10590288C2semidirect
49. #5092D3semidirect
158. C3×C4×D3Q16semidirect
325. C4×D3#216semidirect
408. C32#3209semidirect
457. C3#81802semidirect
458. C3#83370semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
D3×#8692
#105927912
C3×#50922
#105916532
#105916252
#105902902
#105902882
#105902612
#833703
#818023