Finite Group Databasebeta

← #11878906

Subgroups — #11878906

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 493 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic
3C3×#5092C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591603C214yesmaximal
6#10591580C214yesmaximal, complemented
7#10590386C211yesmaximal, characteristic, complemented
8#10590297C211yesmaximal, characteristic
9#10590288C211yesmaximal, characteristic, complemented
10#81802—31nomaximal
11#81604—31nomaximal
12C2×Q8×C3⋊D3C2212yes—
13C32×C4⋊Q8C2211yescharacteristic
14#64153C2212yes—
15C4⋊C4×C3⋊D3—21no—
16C4⋊C4×C3⋊D3—21no—
17#64097—21no—
18#64097—21no—
19C42×C3⋊D3C2211yescharacteristic
20#64078C2211yescharacteristic
21C2×C3×#216C2214yes—
22C3×#869C2211yescharacteristic
23C3×#869C2211yescharacteristic
24#63872—21no—
25#63871—21no—
26#63871C2212yes—
27#63849—21no—
28#63843—21no—
29#63843C2212yes—
30C2×#3719C2214yes—
31C3×#835C2214yes—
32C3×C4×C3⋊C8C2211yescharacteristic
33C3×C4×C3⋊C8C2211yescharacteristic
34#63572C2212yes—
35#63567C2214yes—
36#63557C2212yes—
37#5728—31no—
38#5728—31no—
39D3×C4⋊Q8—31no—
40D3×C4⋊Q8—31no—
41D3×C4⋊Q8—61no—
42C3×#494—31no—
43C3×#487—31no—
44#5186—34no—
45#5182—34no—
46#5093—31no—
47#5092—31no—
48#5092D311yescharacteristic, complemented
49#5079D311yescharacteristic, complemented
50#4809—34no—
51#4795—34no—
52#4699—31no—
53#4685—31no—
54#4685—31no—
55#4681—31no—
56C2×C32×Q8C2312yes—
57Q8×C3⋊D3—44no—
58C2×C4×C3⋊D3—22no—
59C2×C4×C3⋊D3D411yescharacteristic
60C2×C4×C3⋊D3D411yescharacteristic
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×#634—22no—
63C2×#634C2312yes—
64C2×C3×Dic6—21no—
65C2×C3×Dic6C2312yes—
66C32×C4⋊C4—21no—
67C32×C4⋊C4—21no—
68C32×C42C2311yescharacteristic
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)—21no—
71#3750—22no—
72#3750—22no—
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3D411yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76C3×#216—44no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3C2312yes—
81C2×C3×C3⋊C8C2312yes—
82C2×C3×C3⋊C8C2312yes—
83Dic3⋊Dic3—22no—
84Dic3⋊Dic3—22no—
85#3722—22no—
86Dic32—22no—
87#3719—44no—
88#3209—91noSylow
89C2×D3×Q8—32no—
90C2×D3×Q8—32no—
91C2×D3×Q8—62no—
92C2×C3×Q16—34no—
93C3×C4⋊Q8—21no—
94C3×C4⋊Q8—31no—
95C3×C4⋊Q8—31no—
96C3×C4⋊Q8C2×D311yescharacteristic
97C3×C4⋊Q8C2×D311yescharacteristic
98#946—32no—
99#946—61no—
100Q8×Dic3—32no—
101Q8×Dic3—61no—
102#944—32no—
103#944—32no—
104#944—62no—
105C2×#216—34no—
106C2×#216C2×D314yes—
107C2×Dic12—34no—
108#897—32no—
109#897—61no—
110#892—61no—
111#892—61no—
112D3×C4⋊C4—61no—
113D3×C4⋊C4—61no—
114D3×C4⋊C4—61no—
115D3×C4⋊C4—61no—
116D3×C4⋊C4—62no—
117D3×C4⋊C4—62no—
118#890—61no—
119#890—61no—
120#888—61no—
121#888—61no—
122#888—61no—
123#888—61no—
124#888—62no—
125#888—62no—
126#887—32no—
127#887—61no—
128C42×D3—31no—
129C42×D3—31no—
130C42×D3—61no—
131#869—31no—
132#869—31no—
133#869—61no—
134#869C2×D311yescharacteristic
135#869C2×D311yescharacteristic
136C3×#103—34no—
137C3×C4×C8—31no—
138C3×C4×C8—31no—
139#835C2×D314yes—
140(C2×D3)⋊C8—32no—
141(C2×D3)⋊C8—32no—
142#816—34no—
143Dic3⋊C8—32no—
144Dic3⋊C8—32no—
145#810—34no—
146C4×C3⋊C8C2×D311yescharacteristic
147C4×C3⋊C8C2×D311yescharacteristic
148C22×C3⋊D3C2×D411yescharacteristic
149C32×Q8—24no—
150C2×C32×C4—22no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3C2×D411yescharacteristic
156C2×C3⋊Dic3C2×D411yescharacteristic
157C2×C3⋊Dic3C2×D411yescharacteristic
158C4×C3⋊D3—22no—
159C4×C3⋊D3—22no—
160C4×C3⋊D3—44no—
161C4×C3⋊D3Q1614yescomplemented
162#634—24no—
163#634—44no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C3×Dic6—24no—
167C3×Dic6—42no—
168C3×C3⋊C8—22no—
169C3×C3⋊C8—22no—
170#533—91no—
171C2×C4⋊Q8—91no—
172#494—31no—
173#494—91no—
174#487—31no—
175#487—91no—
176#462—94no—
177#451—94no—
178#431—91no—
179C2×C3×Q8—22no—
180C2×C3×Q8—32no—
181C2×C3×Q8—61no—
182C2×C3×Q8C22×D312yes—
183C2×C3×Q8C22×D312yes—
184D3×Q8—124no—
185D3×Q8—124no—
186D3×Q8—128no—
187C2×C4×D3—31no—
188C2×C4×D3—31no—
189C2×C4×D3—31no—
190C2×C4×D3—31no—
191C2×C4×D3—31no—
192C2×C4×D3—31no—
193C2×C4×D3—61no—
194C2×C4×D3—61no—
195C2×C4×D3—61no—
196C2×C4×D3—62no—
197C2×C4×D3—62no—
198C2×C4×D3—64no—
199C2×Dic6—21no—
200C2×Dic6—32no—
201C2×Dic6—32no—
202C2×Dic6—62no—
203C2×Dic6—62no—
204C2×Dic6—62no—
205C2×Dic6—64no—
206C2×Dic6C22×D312yes—
207C3×Q16—124no—
208C2×C3×C8—32no—
209C2×C3×C8—32no—
210C3×C4⋊C4—22no—
211C3×C4⋊C4—22no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—32no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4—61no—
219C3×C4⋊C4—61no—
220C3×C42—21no—
221C3×C42C22×D311yescharacteristic
222C3×C42C22×D311yescharacteristic
223#216—44no—
224#216—124no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227C4⋊Dic3—21no—
228C4⋊Dic3—21no—
229C4⋊Dic3—21no—
230C4⋊Dic3—62no—
231C4⋊Dic3—62no—
232C4⋊Dic3—62no—
233C4⋊Dic3—62no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3C22×D312yes—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245Dic3⋊C4—64no—
246Dic3⋊C4—64no—
247C4×Dic3—31no—
248C4×Dic3—31no—
249C4×Dic3—31no—
250C4×Dic3—31no—
251C4×Dic3—31no—
252C4×Dic3—31no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C4×Dic3—62no—
257C4×Dic3—62no—
258C2×C3⋊C8C22×D312yes—
259C2×C3⋊C8C22×D312yes—
260Dic12—124no—
261C22×C32C22×D411yescharacteristic
262C2×C3⋊D3—21no—
263C2×C3⋊D3—21no—
264C2×C3⋊D3C2×Q1612yes—
265C32×C4—42no—
266C32×C4C2×Q1612yes—
267C32×C4#13712yes—
268C32×C4H(5,𝔽2)12yes—
269C3⋊Dic3—21no—
270C3⋊Dic3—21no—
271C3⋊Dic3—42no—
272C3⋊Dic3C2×Q1612yes—
273C3×Dic3—42no—
274C3×Dic3—42no—
275C22×Q8—92no—
276C2×Q16—34no—
277C2×Q16—94no—
278C4⋊Q8—31no—
279C4⋊Q8—31no—
280C4⋊Q8—92no—
281C4⋊Q8—91no—
282C4⋊Q8—181no—
283C4⋊Q8—181no—
284C4⋊Q8D3211yescharacteristic
285#125—181no—
286C22⋊Q8—92no—
287C22⋊Q8—181no—
288C4×Q8—92no—
289C4×Q8—181no—
290#117—181no—
291C2×C4⋊C4—181no—
292C2×C4⋊C4—181no—
293C2×C42—91no—
294C4⋊C8—92no—
295#103—34no—
296#103—94no—
297C22⋊C8—92no—
298C4×C8—31no—
299C4×C8—31no—
300C22×D3—31no—
301C22×D3—31no—
302C22×D3—61no—
303C3×Q8—24no—
304C3×Q8—24no—
305C3×Q8—44no—
306C3×Q8—64no—
307C3×Q8—122no—
308C2×C3×C4—24no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321C2×C3×C4C23×D311yescharacteristic
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—31no—
325C2×Dic3—31no—
326C2×Dic3—31no—
327C2×Dic3—31no—
328C2×Dic3—31no—
329C2×Dic3—31no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—64no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C4×D3—34no—
337C4×D3—34no—
338C4×D3—64no—
339C4×D3—64no—
340C4×D3—64no—
341C4×D3—62no—
342C4×D3—62no—
343C4×D3—62no—
344C4×D3—62no—
345C4×D3—128no—
346C4×D3—124no—
347C4×D3—124no—
348Dic6—24no—
349Dic6—42no—
350Dic6—64no—
351Dic6—64no—
352Dic6—124no—
353Dic6—128no—
354Dic6—124no—
355Dic6—124no—
356C3×C8—62no—
357C3×C8—62no—
358C3⋊C8—22no—
359C3⋊C8—22no—
360C2×C32#53511yescharacteristic
361C2×C32C22×Q1611yescharacteristic
362C2×C32C2×#13711yescharacteristic
363C3⋊D3—22no—
364C2×Q8—32no—
365C2×Q8—61no—
366C2×Q8—92no—
367C2×Q8—182no—
368C2×Q8—364no—
369C2×Q8C2×D3212yes—
370C22×C4—91no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—182no—
374Q16—124no—
375Q16—364no—
376C2×C8—32no—
377C2×C8—32no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—32no—
381C4⋊C4—61no—
382C4⋊C4—61no—
383C4⋊C4—61no—
384C4⋊C4—182no—
385C4⋊C4—182no—
386C4⋊C4—182no—
387C4⋊C4—182no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C22⋊C4—182no—
391C42—91no—
392C42—91no—
393C42—91no—
394C42—182no—
395C42C2×D3211yescharacteristic
396C22×C3—21no—
397C22×C3C2×D3×D411yescharacteristic
398C22×C3C2×D3×D411yescharacteristic
399C2×D3—32no—
400C2×D3—32no—
401C2×D3—62no—
402C2×D3—62no—
403C2×D3—62no—
404C2×D3—61no—
405C2×D3—61no—
406C2×D3—61no—
407C2×D3—61no—
408C3×C4—22no—
409C3×C4—22no—
410C3×C4—22no—
411C3×C4—44no—
412C3×C4—42no—
413C3×C4—42no—
414C3×C4—122no—
415C3×C4—122no—
416C3×C4#91512yes—
417C3×C4D3×Q1612yes—
418C3×C4D3×Q1612yes—
419C3×C4#91812yes—
420C3×C4#100412yes—
421C3×C4#100912yes—
422Dic3—32no—
423Dic3—32no—
424Dic3—42no—
425Dic3—42no—
426Dic3—62no—
427Dic3—62no—
428Dic3—62no—
429Dic3—61no—
430Dic3—61no—
431Dic3—61no—
432Dic3—61no—
433Dic3—124no—
434Dic3—122no—
435Dic3—122no—
436C32#320911yescharacteristic, complemented, Sylow
437C23—91no—
438Q8—24no—
439Q8—64no—
440Q8—122no—
441Q8—184no—
442Q8—364no—
443C2×C4—22no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—91no—
447C2×C4—94no—
448C2×C4—91no—
449C2×C4—91no—
450C2×C4—182no—
451C2×C4—182no—
452C2×C4—182no—
453C2×C4—364no—
454C2×C4#381111yescharacteristic
455C2×C4#381111yescharacteristic
456C2×C4C22×D3211yescharacteristic
457C8—62no—
458C8—62no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3#567411yescharacteristic
463C2×C3#571511yescharacteristic
464C2×C3C2×#91511yescharacteristic
465C2×C3C2×D3×Q1611yescharacteristic
466C2×C3C2×D3×Q1611yescharacteristic
467C2×C3C2×#91811yescharacteristic
468D3—64no—
469D3—62no—
470D3—62no—
471C22—92no—
472C22—181no—
473C22—181no—
474C22C2×#381111yescharacteristic
475C4—42no—
476C4—92no—
477C4—122no—
478C4—122no—
479C4—181no—
480C4—181no—
481C4—362no—
482C4#6394412yes—
483C4#6395112yes—
484C4#6431412yes—
485C3—21no—
486C3#8160411yescharacteristic, complemented
487C3#8180211yescharacteristic, complemented
488C2—182no—
489C2#1059516811yescharacteristic
490C2C2×#6394411yescharacteristic
491C2C2×#6395111yescharacteristic
subgroupG/H
centerC22C2×#3811
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. C3×#5092C2semidirect
4. C3×#5079C2semidirect
6. #10591580C2semidirect
7. #10590386C2semidirect
9. #10590288C2semidirect
48. #5092D3semidirect
49. #5079D3semidirect
161. C4×C3⋊D3Q16semidirect
436. C32#3209semidirect
486. C3#81604semidirect
487. C3#81802semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105938662
C3×#50922
C3×#50792
#105916032
#105915802
#105903862
#105902972
#105902882
#818023
#816043