Finite Group Databasebeta

← #11896073

Subgroups — #11896073

Order 1152.

782 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596203C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3C3×#5090C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591632C212yesmaximal
6#10591630C212yesmaximal, complemented
7#10591582C212yesmaximal, complemented
8#10591579C212yesmaximal
9C4×#3717C211yesmaximal, characteristic
10#10590300C211yesmaximal, characteristic
11#10590296C211yesmaximal, characteristic, complemented
12#81626—31nomaximal
13#80464—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15#64156C2212yes—
16Q8×C3⋊Dic3C2212yes—
17#64107—22no—
18#64106—21no—
19#64101—21no—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#216C2212yes—
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63919C2212yes—
26#63918—21no—
27#63844—21no—
28#63843C2212yes—
29#63839—22no—
30C2×#3717C2211yescharacteristic
31C3×#835C2212yes—
32C3×#835C2212yes—
33C3×#835C2212yes—
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4×C3⋊C8C2211yescharacteristic
36#63573C2212yes—
37#63573C2211yescharacteristic
38#63572C2212yes—
39#63566C2211yescharacteristic
40#63564C2212yes—
41#63564C2211yescharacteristic
42#63555C2212yes—
43#5732—31no—
44#5732—31no—
45#5732—61no—
46#5722—31no—
47Q8×Dic6—31no—
48C3×#487—31no—
49C3×#462—31no—
50#5185—32no—
51#5184—32no—
52#5090D311yescharacteristic, complemented
53#5084—31no—
54#5079D311yescharacteristic, complemented
55C4×#215—31no—
56#4842—31no—
57#4831—31no—
58#4798—32no—
59#4794—32no—
60#4794—32no—
61#4791—32no—
62#4791—32no—
63#4789—32no—
64C4×#204—31no—
65#4679—31no—
66C2×C32×Q8C2312yes—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×#634D411yescharacteristic
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C32×C4⋊C4—21no—
74C32×C4⋊C4—21no—
75C32×C42C2311yescharacteristic
76#3752—21no—
77#3752—22no—
78#3752—22no—
79C4⋊(C3⋊Dic3)—22no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750D412yes—
83C4×C3⋊Dic3—22no—
84C4×C3⋊Dic3C2312yes—
85C3×#216—24no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×C4×Dic3—21no—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3717—22no—
98#3369—91noSylow
99C2×C3×Q16—32no—
100C3×C4⋊Q8—21no—
101C3×C4⋊Q8—31no—
102C3×C4⋊Q8C2×D311yescharacteristic
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×C4×Q8—31no—
105#947—32no—
106#947—32no—
107#947—62no—
108Q8×Dic3—32no—
109Q8×Dic3—32no—
110Q8×Dic3—32no—
111Q8×Dic3—62no—
112#944—62no—
113C2×#216C2×D312yes—
114C2×#215—31no—
115C2×#204—31no—
116#898—62no—
117#898—62no—
118#898—64no—
119#897—61no—
120#897—61no—
121#897—62no—
122#892—61no—
123#892—61no—
124#892—62no—
125#888—32no—
126#888—32no—
127#888—61no—
128#888—62no—
129#887—32no—
130#887—61no—
131C4×D12—31no—
132C4×D12—31no—
133C4×D12—61no—
134#869—61no—
135#869C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C4×Dic6—61no—
140C4×Dic6C2×D311yescharacteristic
141C3×C4⋊C8—31no—
142C3×#103—32no—
143C3×#103—32no—
144C3×#103—32no—
145C3×C4×C8—31no—
146#835—31no—
147#835C2×D312yes—
148#835C2×D312yes—
149#835C2×D312yes—
150#821—32no—
151#821—31no—
152#817—32no—
153#817—31no—
154#816—31no—
155#815—32no—
156#815—32no—
157Dic3⋊C8—32no—
158Dic3⋊C8—32no—
159#809—31no—
160#809—32no—
161#808—31no—
162#808—32no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C32×Q8—22no—
167C32×Q8—22no—
168C2×C32×C4—22no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3C2×D412yes—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)—21no—
177C4×C3⋊D3—42no—
178#634—22no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C3×Dic6—21no—
183C3×Dic6—81no—
184C3×Dic6#4112yes—
185#627—82no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—21no—
189Q82—91no—
190#556—91no—
191#489—92no—
192#487—31no—
193#476—91no—
194#475—92no—
195#464—92no—
196#462—31no—
197#446—91no—
198#441—92no—
199C4×SD16—91no—
200C2×C3×Q8—22no—
201C2×C3×Q8—31no—
202C2×C3×Q8—61no—
203C2×C3×Q8C22×D312yes—
204C2×C3×Q8C22×D312yes—
205C2×D12—31no—
206C2×D12—31no—
207C2×D12—61no—
208C2×C4×D3—62no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×Dic6—21no—
212C2×Dic6—31no—
213C2×Dic6—31no—
214C2×Dic6—61no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6C22×D311yescharacteristic
218C3×Q16—64no—
219C2×C3×C8—31no—
220C2×C3×C8—32no—
221C2×C3×C8—31no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C42—21no—
233C3×C42—61no—
234C3×C42C22×D311yescharacteristic
235C3×C42C22×D311yescharacteristic
236#216—24no—
237#215—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—61no—
246(C2×D3)⋊C4—61no—
247C4⋊Dic3—21no—
248C4⋊Dic3—31no—
249C4⋊Dic3—31no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—62no—
255C4⋊Dic3—62no—
256C4⋊Dic3—62no—
257C4⋊Dic3—64no—
258C4⋊Dic3C22×D311yescharacteristic
259C4⋊Dic3C22×D312yes—
260Dic3⋊C4—21no—
261Dic3⋊C4—32no—
262Dic3⋊C4—32no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267C4×Dic3—21no—
268C4×Dic3—32no—
269C4×Dic3—32no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3—62no—
273C4×Dic3—62no—
274C4×Dic3—62no—
275C4×Dic3—64no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D312yes—
279#204—62no—
280C22×C32C22×D411yescharacteristic
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C32×C4—21no—
285C32×C4—42no—
286C32×C4#13712yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3⋊Dic3—22no—
290C3⋊Dic3—22no—
291C3⋊Dic3—41no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C2×Q16—32no—
296C2×SD16—91no—
297C4⋊Q8—31no—
298C4⋊Q8—92no—
299C4⋊Q8—181no—
300C4⋊Q8—182no—
301C4⋊Q8D3211yescharacteristic
302#126—182no—
303#124—92no—
304C22⋊Q8—181no—
305C4×Q8—31no—
306C4×Q8—91no—
307C4×Q8—92no—
308C4×Q8—92no—
309C4×Q8—181no—
310C4×D4—91no—
311#117—181no—
312#106—91no—
313#106—92no—
314C4⋊C8—31no—
315C4⋊C8—92no—
316#103—32no—
317#103—32no—
318#103—32no—
319#103—91no—
320#102—91no—
321#102—92no—
322#97—92no—
323C4×C8—31no—
324C22×D3—62no—
325C22×D3—61no—
326C22×D3—61no—
327C3×Q8—22no—
328C3×Q8—22no—
329C3×Q8—22no—
330C3×Q8—22no—
331C3×Q8—32no—
332C3×Q8—42no—
333C3×Q8—42no—
334C3×Q8—61no—
335C3×Q8—241no—
336C2×C3×C4—24no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—61no—
343C2×C3×C4—62no—
344C2×C3×C4—61no—
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—22no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363D12—61no—
364D12—61no—
365D12—61no—
366D12—61no—
367D12—121no—
368D12—121no—
369C4×D3—124no—
370C4×D3—122no—
371C4×D3—122no—
372Dic6—21no—
373Dic6—62no—
374Dic6—62no—
375Dic6—81no—
376Dic6—122no—
377Dic6—242no—
378Dic6—242no—
379Dic6#23712yes—
380C3×C8—61no—
381C3×C8—62no—
382C3×C8—61no—
383C3⋊C8—22no—
384C3⋊C8—21no—
385C3⋊C8—21no—
386C2×C32#54811yescharacteristic
387C2×C32C2×#13711yescharacteristic
388C2×C32#57711yescharacteristic
389C3⋊D3—81no—
390C2×Q8—31no—
391C2×Q8—61no—
392C2×Q8—91no—
393C2×Q8—182no—
394C2×Q8C2×D3212yes—
395C2×D4—91no—
396C22×C4—181no—
397Q16—64no—
398SD16—182no—
399C2×C8—31no—
400C2×C8—31no—
401C2×C8—32no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—31no—
405C4⋊C4—32no—
406C4⋊C4—61no—
407C4⋊C4—61no—
408C4⋊C4—91no—
409C4⋊C4—92no—
410C4⋊C4—91no—
411C4⋊C4—182no—
412C4⋊C4—182no—
413C4⋊C4—182no—
414C22⋊C4—182no—
415C22⋊C4—182no—
416C22⋊C4—181no—
417C42—61no—
418C42—92no—
419C42—182no—
420C42—182no—
421C42C2×D3211yescharacteristic
422C22×C3—21no—
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C2×D3×D411yescharacteristic
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—121no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—121no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—41no—
440C3×C4—44no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—62no—
444C3×C4—121no—
445C3×C4—122no—
446C3×C4#91812yes—
447C3×C4#91812yes—
448C3×C4C2×#23711yescharacteristic
449C3×C4D3×#4111yescharacteristic
450C3×C4#101011yescharacteristic
451C3×C4#101011yescharacteristic
452Dic3—22no—
453Dic3—42no—
454Dic3—41no—
455Dic3—62no—
456Dic3—62no—
457Dic3—62no—
458Dic3—62no—
459Dic3—122no—
460Dic3—122no—
461Dic3—122no—
462Dic3—121no—
463Dic3—121no—
464C32#336911yescharacteristic, complemented, Sylow
465C23—181no—
466Q8—22no—
467Q8—22no—
468Q8—32no—
469Q8—61no—
470Q8—182no—
471Q8—241no—
472Q8—722no—
473D4—181no—
474D4—181no—
475C2×C4—22no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—62no—
479C2×C4—92no—
480C2×C4—92no—
481C2×C4—181no—
482C2×C4—362no—
483C2×C4#381111yescharacteristic
484C2×C4#381111yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—61no—
487C8—61no—
488C8—62no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3#559811yescharacteristic
493C2×C3#567711yescharacteristic
494C2×C3#576211yescharacteristic
495C2×C3C2×#91811yescharacteristic
496C2×C3C2×#91811yescharacteristic
497C2×C3#577811yescharacteristic
498D3—242no—
499D3—241no—
500D3—241no—
501C22—361no—
502C22—361no—
503C22—361no—
504C22C2×#381111yescharacteristic
505C4—21no—
506C4—42no—
507C4—62no—
508C4—122no—
509C4—121no—
510C4—182no—
511C4—182no—
512C4—361no—
513C4#6394512yes—
514C4#6430911yescharacteristic
515C4D3×#23711yescharacteristic
516C3—21no—
517C3#8046411yescharacteristic, complemented
518C3#8162611yescharacteristic, complemented
519C2—721no—
520C2#1059516111yescharacteristic
521C2#1059532411yescharacteristic
522C2C2×#6394511yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenterC4⋊Q8D32
hypocenterC32#3369
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
2. #10593856C2semidirect
3. C3×#5090C2semidirect
4. C3×#5079C2semidirect
6. #10591630C2semidirect
7. #10591582C2semidirect
11. #10590296C2semidirect
52. #5090D3semidirect
54. #5079D3semidirect
464. C32#3369semidirect
517. C3#80464semidirect
518. C3#81626semidirect

Maximal subgroups

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

subgroupindex
#105962032
#105938562
C3×#50902
C3×#50792
#105916322
#105916302
#105915822
#105915792
C4×#37172
#105903002
#105902962
#816263
#804643