Finite Group Databasebeta

← #11878905

Subgroups — #11878905

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×D3×C4⋊Q8C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic
3#10592791C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591595C214yesmaximal
6#10591575C214yesmaximal, complemented
7#10590386C211yesmaximal, characteristic, complemented
8#10590290C211yesmaximal, characteristic, complemented
9#10590261C211yesmaximal, characteristic
10#83222—31nomaximal
11#81604—31nomaximal
12C2×C3×D3×Q8C2212yes—
13C32×C4⋊Q8C2211yescharacteristic
14C2×#3756C2214yes—
15#64078C2211yescharacteristic
16C3×#944C2212yes—
17C3×D3×C4⋊C4—21no—
18C3×D3×C4⋊C4—21no—
19C3×#888—21no—
20C3×#888—21no—
21C3×C42×D3C2211yescharacteristic
22C3×#869C2211yescharacteristic
23C3×#869C2211yescharacteristic
24#63869—21no—
25#63857C2212yes—
26#63856—21no—
27#63844C2212yes—
28Dic3×Dic6—21no—
29#63841—21no—
30C2×#3719C2214yes—
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C3×#835C2214yes—
33C3×C4×C3⋊C8C2211yescharacteristic
34Dic3⋊(C3⋊C8)C2212yes—
35#63565C2214yes—
36(C2×D3)⋊(C3⋊C8)C2212yes—
37C2×C3×C4⋊Q8—31no—
38#5728—31no—
39D3×C4⋊Q8D311yescharacteristic
40#5470—31no—
41C3×#487—31no—
42#5228—34no—
43#5093—31no—
44#5092—31no—
45#5092—31no—
46#5092—31no—
47#5092—61no—
48#5090—34no—
49#5079—31no—
50#5079D311yescharacteristic, complemented
51#4925—31no—
52#4809—34no—
53#4795—34no—
54#4699—31no—
55#4685—31no—
56C2×C32×Q8C2312yes—
57C2×#634C2312yes—
58C3×D3×Q8—44no—
59C2×C3×C4×D3—22no—
60C2×C3×C4×D3D411yescharacteristic
61C2×C3×C4×D3D411yescharacteristic
62C2×C3×C4×D3C2311yescharacteristic
63C2×C3×Dic6—21no—
64C2×C3×Dic6—22no—
65C2×C3×Dic6C2312yes—
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×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3C2312yes—
77C3×Dic3⋊C4—22no—
78C3×Dic3⋊C4—22no—
79C3×C4×Dic3D411yescharacteristic
80C3×C4×Dic3D411yescharacteristic
81C3×C4×Dic3C2311yescharacteristic
82C2×C3×C3⋊C8C2312yes—
83#3724—22no—
84Dic3⋊Dic3—22no—
85(C2×D3)⋊Dic3—22no—
86Dic32—22no—
87#3719—44no—
88#3209—91noSylow
89C22×C3×Q8—32no—
90C2×D3×Q8C2×D312yes—
91C3×C4⋊Q8—21no—
92C3×C4⋊Q8—32no—
93C3×C4⋊Q8—31no—
94C3×C4⋊Q8—31no—
95C3×C4⋊Q8—61no—
96C3×C4⋊Q8—61no—
97C3×C4⋊Q8C2×D311yescharacteristic
98C3×C4⋊Q8C2×D311yescharacteristic
99C2×C3×C4⋊C4—61no—
100C2×C3×C4⋊C4—61no—
101C2×C3×C42—31no—
102#946—61no—
103Q8×Dic3—61no—
104#944C2×D312yes—
105C2×#216—34no—
106C2×#216—34no—
107C2×#216—34no—
108C2×#216—64no—
109#926—61no—
110#924—32no—
111#924—61no—
112C2×Dic12—34no—
113#897—32no—
114#892—61no—
115D3×C4⋊C4—21no—
116D3×C4⋊C4—21no—
117#890—61no—
118#888—21no—
119#888—21no—
120#887—32no—
121C42×D3C2×D311yescharacteristic
122#870—61no—
123#869—31no—
124#869—31no—
125#869—61no—
126#869C2×D311yescharacteristic
127#869C2×D311yescharacteristic
128C4×Dic6—32no—
129C4×Dic6—61no—
130C3×#103—34no—
131C3×C4×C8—31no—
132#835—34no—
133#835C2×D314yes—
134#830—32no—
135(C2×D3)⋊C8—32no—
136Dic3⋊C8—32no—
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×D3—44no—
159C3×C4×D3Q1614yescomplemented
160C3×Dic6—24no—
161C3×Dic6—44no—
162C3×Dic6—42no—
163C3⋊(C3⋊C8)—22no—
164C3×C3⋊C8—22no—
165#533—91no—
166C2×C4⋊Q8—31no—
167#494—91no—
168#494—91no—
169#487—31no—
170#487—91no—
171#462—94no—
172#451—94no—
173#431—91no—
174C2×C3×Q8—22no—
175C2×C3×Q8—32no—
176C2×C3×Q8—62no—
177C2×C3×Q8—61no—
178C2×C3×Q8—124no—
179C2×C3×Q8C22×D312yes—
180C2×C3×Q8C22×D312yes—
181C22×C3×C4—31no—
182C22×C3×C4—31no—
183C22×C3×C4—31no—
184C22×C3×C4—62no—
185D3×Q8—44no—
186C2×C4×D3—22no—
187C2×C4×D3#6711yescharacteristic
188C2×C4×D3#6711yescharacteristic
189C2×C4×D3C22×D311yescharacteristic
190C2×Dic6—21no—
191C2×Dic6—22no—
192C2×Dic6—32no—
193C2×Dic6—32no—
194C2×Dic6—62no—
195C2×Dic6C22×D312yes—
196C2×C3×C8—32no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—32no—
202C3×C4⋊C4—41no—
203C3×C4⋊C4—41no—
204C3×C4⋊C4—62no—
205C3×C4⋊C4—62no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C4⋊C4—61no—
209C3×C42—21no—
210C3×C42—31no—
211C3×C42—31no—
212C3×C42—31no—
213C3×C42C22×D311yescharacteristic
214C3×C42C22×D311yescharacteristic
215#217—62no—
216#216—124no—
217#216—124no—
218#216—124no—
219#216—128no—
220(C2×D3)⋊C4—62no—
221C4⋊Dic3—21no—
222C4⋊Dic3—21no—
223C4⋊Dic3—21no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226C4⋊Dic3—61no—
227C4⋊Dic3—61no—
228C4⋊Dic3—62no—
229C4⋊Dic3—121no—
230C4⋊Dic3—121no—
231C4⋊Dic3C22×D312yes—
232Dic3⋊C4—22no—
233Dic3⋊C4—22no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237C4×Dic3—62no—
238C4×Dic3—62no—
239C4×Dic3#6711yescharacteristic
240C4×Dic3#6711yescharacteristic
241C4×Dic3C22×D311yescharacteristic
242C2×C3⋊C8—32no—
243C2×C3⋊C8—32no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8C22×D312yes—
246Dic12—124no—
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—32no—
262C2×Q16—94no—
263C2×Q16—94no—
264C4⋊Q8—32no—
265C4⋊Q8—31no—
266C4⋊Q8—31no—
267C4⋊Q8—61no—
268C4⋊Q8—61no—
269C4⋊Q8—91no—
270C4⋊Q8D3211yescharacteristic
271#125—181no—
272C22⋊Q8—92no—
273C22⋊Q8—181no—
274C4×Q8—92no—
275C4×Q8—181no—
276#117—181no—
277C2×C4⋊C4—61no—
278C2×C4⋊C4—61no—
279C2×C42—31no—
280C4⋊C8—92no—
281#103—34no—
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—124no—
293C3×Q8—122no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—31no—
300C2×C3×C4—34no—
301C2×C3×C4—31no—
302C2×C3×C4—31no—
303C2×C3×C4—42no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—124no—
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—122no—
320C2×Dic3C2×#6711yescharacteristic
321C2×Dic3C2×#6711yescharacteristic
322C2×Dic3C2×#6711yescharacteristic
323C4×D3—22no—
324C4×D3—22no—
325C4×D3—44no—
326C4×D3#21614yescomplemented
327Dic6—24no—
328Dic6—44no—
329Dic6—42no—
330Dic6—64no—
331Dic6—64no—
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—62no—
344C2×Q8—61no—
345C2×Q8—92no—
346C2×Q8—124no—
347C2×Q8C2×D3212yes—
348C22×C4—31no—
349C22×C4—31no—
350C22×C4—31no—
351C22×C4—62no—
352Q16—364no—
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—182no—
369C42—31no—
370C42—31no—
371C42—31no—
372C42—182no—
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×C4#91512yes—
395C3×C4D3×Q1612yes—
396C3×C4#94212yes—
397C3×C4C2×#21612yes—
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—124no—
413Q8—122no—
414Q8—184no—
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—124no—
425C2×C4—182no—
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#567411yescharacteristic
436C2×C3C2×#91511yescharacteristic
437C2×C3C2×D3×Q1611yescharacteristic
438C2×C3#580511yescharacteristic
439C2×C3C2×#94211yescharacteristic
440C2×C3C22×#21611yescharacteristic
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#6394612yes—
455C4#6431412yes—
456C3—21no—
457C3#8160411yescharacteristic, complemented
458C3#8322211yescharacteristic, complemented
459C2—62no—
460C2#1059523511yescharacteristic
461C2C2×D3×#21611yescharacteristic
462C2C2×#6394611yescharacteristic
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×#5079C2semidirect
6. #10591575C2semidirect
7. #10590386C2semidirect
8. #10590290C2semidirect
50. #5079D3semidirect
159. C3×C4×D3Q16semidirect
326. C4×D3#216semidirect
408. C32#3209semidirect
457. C3#81604semidirect
458. C3#83222semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
#105938592
#105927912
C3×#50792
#105915952
#105915752
#105903862
#105902902
#105902612
#832223
#816043