Finite Group Databasebeta

← #11897660

Subgroups — #11897660

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2#10593958C211yesmaximal, characteristic
3C4×#3755C211yesmaximal, characteristic
4C3×#5021C211yesmaximal, characteristic, complemented
5#10591545C212yesmaximal, complemented
6#10591540C212yesmaximal
7#10590464C212yesmaximal
8#10590420C212yesmaximal, complemented
9#10590312C211yesmaximal, characteristic, complemented
10#10590300C211yesmaximal, characteristic
11#10590259C211yesmaximal, characteristic, complemented
12#83706—31nomaximal
13#81137—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15C2×#3755C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×Q8×Dic3C2212yes—
18C3×#888—22no—
19C3×#888C2212yes—
20C3×#869—21no—
21C3×#869C2211yescharacteristic
22C3×#869C2211yescharacteristic
23C3×C4×Dic6—21no—
24C3×C4×Dic6C2211yescharacteristic
25#63900—21no—
26#63894C2212yes—
27#63888—22no—
28#63871—21no—
29#63869C2212yes—
30#63662C2211yescharacteristic
31#63636C2211yescharacteristic
32#63635C2211yescharacteristic
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#835C2212yes—
35C3×#807C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63576C2212yes—
38#63576C2212yes—
39#63573C2212yes—
40Dic3⋊(C3⋊C8)C2212yes—
41#63564C2212yes—
42#63554C2212yes—
43C3×Q82—31no—
44#5730—31no—
45#5579—31no—
46Q8×Dic6D311yescharacteristic, complemented
47C3×#477—31no—
48#5087—32no—
49#5084—31no—
50#5081—32no—
51#5078—31no—
52#5078—31no—
53#5026—32no—
54C4×#215—31no—
55C4×#215—31no—
56C4×#215—61no—
57#5024—31no—
58#5022—32no—
59#5021D311yescharacteristic, complemented
60#4890—32no—
61#4876—32no—
62#4842—31no—
63#4831—31no—
64#4817—32no—
65#4799—32no—
66C2×C32×Q8C2311yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—22no—
72C2×C3×Dic6D411yescharacteristic
73C2×#624—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2311yescharacteristic
76C32×C42—21no—
77C32×C42C2311yescharacteristic
78#3755Q814yescomplemented
79#3752—21no—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—22no—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94#3724—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97#3385—91noSylow
98C3×C4⋊Q8—32no—
99C3×C4⋊Q8—31no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8—61no—
102C3×C4⋊Q8—62no—
103C3×C4×Q8—21no—
104C3×C4×Q8—31no—
105C3×C4×Q8—32no—
106C3×C4×Q8—61no—
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×Q8C2×D311yescharacteristic
109#946—61no—
110#946—62no—
111Q8×Dic3C2×D312yes—
112C2×#215—31no—
113C2×#215—31no—
114C2×#215—61no—
115#897—61no—
116#896—62no—
117#893—32no—
118D3×C4⋊C4—61no—
119D3×C4⋊C4—61no—
120#890—32no—
121#888—22no—
122#888C2×D312yes—
123C4×D12—31no—
124C4×D12—31no—
125C4×D12—32no—
126C4×D12—61no—
127#870—32no—
128#869—21no—
129#869C2×D311yescharacteristic
130#869C2×D311yescharacteristic
131C4×Dic6—21no—
132C4×Dic6C2×D311yescharacteristic
133C3×#107—32no—
134C3×C4⋊C8—31no—
135C3×#103—32no—
136#835—31no—
137#835—31no—
138#835—61no—
139#835C2×D312yes—
140#821—32no—
141#817—32no—
142#815—32no—
143Dic3⋊C8—32no—
144#809—31no—
145#809—31no—
146#809—32no—
147#809—61no—
148#808—31no—
149#808—31no—
150#808—32no—
151#808—61no—
152#807—32no—
153#807—32no—
154#807—32no—
155#807—32no—
156#807C2×D312yes—
157C4⋊(C3⋊C8)—32no—
158C4⋊(C3⋊C8)C2×D311yescharacteristic
159#803—32no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C22×C3⋊D3—21no—
164C32×Q8—21no—
165C32×Q8C2×Q812yes—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—21no—
172C4⋊(C3⋊D3)—21no—
173C4⋊(C3⋊D3)C2×Q812yes—
174C4×C3⋊D3—42no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×Dic6—22no—
180C3×Dic6—82no—
181C3×Dic6—81no—
182C3×Dic6—81no—
183#624—82no—
184C3⋊(C3⋊C8)—21no—
185C3⋊(C3⋊C8)C2×Q812yes—
186C3×C3⋊C8—22no—
187Q82—31no—
188#554—91no—
189#501—92no—
190#500—91no—
191#479—92no—
192#477—31no—
193#476—91no—
194#474—92no—
195#446—91no—
196#440—92no—
197C4×SD16—91no—
198C2×C3×Q8—21no—
199C2×C3×Q8—31no—
200C2×C3×Q8—62no—
201C2×C3×Q8—61no—
202C2×C3×Q8—61no—
203C2×C3×Q8C22×D311yescharacteristic
204C2×C3×Q8C22×D311yescharacteristic
205C2×D12—31no—
206C2×D12—31no—
207C2×D12—61no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—121no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6—22no—
216C2×Dic6#6711yescharacteristic
217C2×C3×C8—32no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—31no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—41no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4—62no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4C22×D311yescharacteristic
231C3×C4⋊C4C22×D311yescharacteristic
232C3×C42—21no—
233C3×C42—21no—
234C3×C42—21no—
235C3×C42—32no—
236C3×C42—41no—
237C3×C42—62no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#215—34no—
241#215—34no—
242#215—64no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—61no—
245(C2×D3)⋊C4—61no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—121no—
248C4⋊Dic3—21no—
249C4⋊Dic3—21no—
250C4⋊Dic3—22no—
251C4⋊Dic3—31no—
252C4⋊Dic3—31no—
253C4⋊Dic3—61no—
254C4⋊Dic3—62no—
255C4⋊Dic3#6711yescharacteristic
256C4⋊Dic3C22×D312yes—
257C4⋊Dic3C22×D312yes—
258Dic3⋊C4—22no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4#6712yes—
263C4×Dic3—22no—
264C4×Dic3C22×D312yes—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8C22×D312yes—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—22no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C32×C4—22no—
277C32×C4—21no—
278C32×C4—41no—
279C32×C4#13712yes—
280C32×C4C22×Q811yescharacteristic
281C32×C42−1+411yescharacteristic
282C3⋊Dic3—41no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—42no—
286C3×Dic3—42no—
287C2×SD16—91no—
288C4⋊Q8—32no—
289C4⋊Q8—31no—
290C4⋊Q8—31no—
291C4⋊Q8—61no—
292C4⋊Q8—62no—
293#125—92no—
294C22⋊Q8—182no—
295C22⋊Q8—181no—
296C4×Q8—31no—
297C4×Q8—32no—
298C4×Q8—61no—
299C4×Q8D3211yescharacteristic
300C4×D4—92no—
301C4×D4—91no—
302C2×C4⋊C4—181no—
303#107—32no—
304#107—92no—
305#107—92no—
306#106—92no—
307#106—91no—
308C4⋊C8—31no—
309C4⋊C8—92no—
310#103—32no—
311#103—91no—
312#102—92no—
313#102—91no—
314#97—92no—
315C4×C8—91no—
316C22×D3—61no—
317C22×D3—61no—
318C22×D3—121no—
319C3×Q8—21no—
320C3×Q8—21no—
321C3×Q8—22no—
322C3×Q8—41no—
323C3×Q8—62no—
324C3×Q8—241no—
325C3×Q8—241no—
326C3×Q8—242no—
327C3×Q8D3×Q812yes—
328C3×Q8D3×Q812yes—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—121no—
353C2×Dic3C2×#6712yes—
354C2×Dic3C2×#6712yes—
355D12—32no—
356D12—32no—
357D12—62no—
358D12—61no—
359D12—61no—
360D12—121no—
361C4×D3—122no—
362C4×D3—122no—
363C4×D3—242no—
364C4×D3—242no—
365C4×D3—242no—
366Dic6—22no—
367Dic6—82no—
368Dic6—81no—
369Dic6—81no—
370C3×C8—62no—
371C3⋊C8—22no—
372C3⋊C8—32no—
373C3⋊C8—32no—
374C3⋊C8—62no—
375C3⋊C8—61no—
376C3⋊C8—61no—
377C3⋊C8—121no—
378C2×C32D4×Q811yescharacteristic
379C2×C32C2×#13711yescharacteristic
380C2×C32#57611yescharacteristic
381C3⋊D3—42no—
382C2×Q8—31no—
383C2×Q8—62no—
384C2×Q8—61no—
385C2×Q8—61no—
386C2×Q8C2×D3211yescharacteristic
387C2×D4—91no—
388C22×C4—182no—
389C22×C4—181no—
390SD16—94no—
391C2×C8—32no—
392C2×C8—91no—
393C2×C8—91no—
394C4⋊C4—21no—
395C4⋊C4—31no—
396C4⋊C4—32no—
397C4⋊C4—32no—
398C4⋊C4—32no—
399C4⋊C4—62no—
400C4⋊C4—62no—
401C4⋊C4—61no—
402C4⋊C4—61no—
403C4⋊C4—91no—
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4C2×D3211yescharacteristic
407C22⋊C4—182no—
408C22⋊C4—181no—
409C42—21no—
410C42—32no—
411C42—62no—
412C42C2×D3211yescharacteristic
413C22×C3—21no—
414C22×C3C2×D3×D411yescharacteristic
415C22×C3C22×#6711yescharacteristic
416C2×D3—62no—
417C2×D3—62no—
418C2×D3—122no—
419C2×D3—121no—
420C2×D3—121no—
421C2×D3—121no—
422C2×D3—121no—
423C2×D3—241no—
424C2×D3—241no—
425C3×C4—22no—
426C3×C4—21no—
427C3×C4—22no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4—42no—
434C3×C4—41no—
435C3×C4—41no—
436C3×C4—62no—
437C3×C4—62no—
438C3×C4—81no—
439C3×C4—122no—
440C3×C4—122no—
441C3×C4#91812yes—
442C3×C4#94212yes—
443C3×C4C2×D3×Q811yescharacteristic
444C3×C4C2×D3×Q811yescharacteristic
445C3×C4#100711yescharacteristic
446C3×C4#101011yescharacteristic
447Dic3—22no—
448Dic3—22no—
449Dic3—42no—
450Dic3—42no—
451Dic3—121no—
452Dic3—121no—
453Dic3—241no—
454C32#338511yescharacteristic, complemented, Sylow
455C23—181no—
456Q8—21no—
457Q8—62no—
458Q8—241no—
459Q8—241no—
460Q8—242no—
461Q8#379712yes—
462D4—92no—
463D4—181no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—181no—
471C2×C4—362no—
472C2×C4—722no—
473C2×C4D3×#6711yescharacteristic
474C2×C4D3×#6711yescharacteristic
475C2×C4C22×D3211yescharacteristic
476C8—62no—
477C8—92no—
478C8—181no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3#563211yescharacteristic
483C2×C3C2×#91811yescharacteristic
484C2×C3#577411yescharacteristic
485C2×C3C2×#94211yescharacteristic
486C2×C3Q8×#6711yescharacteristic
487C2×C3#583511yescharacteristic
488D3—122no—
489D3—122no—
490D3—242no—
491C22—182no—
492C22—361no—
493C22—361no—
494C22C2×D3×#6711yescharacteristic
495C4—21no—
496C4—22no—
497C4—41no—
498C4—62no—
499C4—62no—
500C4—122no—
501C4—122no—
502C4—361no—
503C4#6394812yes—
504C4#6429711yescharacteristic
505C4C2×#379711yescharacteristic
506C3—21no—
507C3#8113711yescharacteristic, complemented
508C3#8370611yescharacteristic, complemented
509C2—362no—
510C2#1059480311yescharacteristic
511C2C2×#6394811yescharacteristic
512C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenterC4×Q8D32
hypocenterC32#3385
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
1. C3×Q8×Dic6C2semidirect
4. C3×#5021C2semidirect
5. #10591545C2semidirect
8. #10590420C2semidirect
9. #10590312C2semidirect
11. #10590259C2semidirect
46. Q8×Dic6D3semidirect
59. #5021D3semidirect
78. #3755Q8semidirect
454. C32#3385semidirect
507. C3#81137semidirect
508. C3#83706semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
#105939582
C4×#37552
C3×#50212
#105915452
#105915402
#105904642
#105904202
#105903122
#105903002
#105902592
#837063
#811373