Finite Group Databasebeta

← #11897673

Subgroups — #11897673

Order 1152.

729 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593960C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592381C211yesmaximal, characteristic, complemented
4C3×C4×#204C211yesmaximal, characteristic
5C3×#4679C211yesmaximal, characteristic, complemented
6#10590892C212yesmaximal, complemented
7#10590811C212yesmaximal, complemented
8#10590766C212yesmaximal
9#10590762C212yesmaximal
10#10590283C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic
12#79976—31nomaximal
13#79634—31nomaximal
14#64078C2211yescharacteristic
15#64078C2211yescharacteristic
16C2×C3×#204C2211yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63918—21no—
21#63918C2212yes—
22#63896—22no—
23Dic3×D12C2212yes—
24D3×C4⋊Dic3—21no—
25#63869C2212yes—
26#63856—21no—
27Dic3×Dic6—21no—
28Dic3×Dic6C2212yes—
29#63840—22no—
30C32×C4×C8C2211yescharacteristic
31#63645C2212yes—
32#63645C2212yes—
33C3×#821C2211yescharacteristic
34C3×#817C2211yescharacteristic
35C3×#816C2211yescharacteristic
36C3×#815C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39#63575C2212yes—
40#63573C2212yes—
41#63566C2212yes—
42#63563C2212yes—
43#5579—31no—
44Q8×Dic6—31no—
45Q8×Dic6—31no—
46#5543—31no—
47C3×#446—31no—
48C3×C4×SD16—31no—
49#5164—32no—
50#5021—31no—
51#5008—31no—
52#4856—32no—
53#4850—31no—
54#4846—32no—
55#4842—31no—
56#4829—32no—
57#4796—32no—
58#4759—32no—
59#4710—32no—
60#4702—32no—
61C4×#204D311yescharacteristic
62#4682—31no—
63#4682—31no—
64#4682—61no—
65#4679D311yescharacteristic, complemented
66C2×#634—21no—
67C2×#634—21no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C2×D3×Dic3—22no—
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2312yes—
80C4⋊(C3⋊Dic3)C2312yes—
81C3×(C2×D3)⋊C4—21no—
82C3×C4⋊Dic3D411yescharacteristic
83C3×C4⋊Dic3C2311yescharacteristic
84C3×C4⋊Dic3C2311yescharacteristic
85C3×Dic3⋊C4—21no—
86C3×Dic3⋊C4D412yes—
87C3×C4×Dic3—21no—
88C3×C4×Dic3C2312yes—
89C2×C3×C3⋊C8C2312yes—
90C3×#204Q814yescomplemented
91#3724—22no—
92Dic3⋊Dic3—22no—
93Dic3⋊Dic3—22no—
94Dic3⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97#3385—91noSylow
98C2×C3×SD16—31no—
99C3×C4×Q8—31no—
100C3×C4×Q8—31no—
101C3×C4×D4—31no—
102#946—61no—
103Q8×Dic3—32no—
104Q8×Dic3—61no—
105D4×Dic3—32no—
106C2×C4⋊Dic3—61no—
107#924—61no—
108C2×#204C2×D311yescharacteristic
109#896—62no—
110D3×C4⋊C4—61no—
111#890—32no—
112#888—32no—
113#888—61no—
114#888—62no—
115#888—62no—
116#878—62no—
117C4×D12—32no—
118C4×D12C2×D311yescharacteristic
119#870—32no—
120#869—31no—
121#869—31no—
122#869—31no—
123#869—31no—
124#869—32no—
125#869—61no—
126#869—61no—
127#869—61no—
128C4×Dic6—32no—
129C4×Dic6—61no—
130C4×Dic6C2×D311yescharacteristic
131C4×Dic6C2×D311yescharacteristic
132C3×#106—31no—
133C3×C4⋊C8—32no—
134C3×C4⋊C8—31no—
135C3×#103—31no—
136C3×#102—31no—
137C3×#97—32no—
138C3×C4×C8—21no—
139C3×C4×C8C2×D311yescharacteristic
140C3×C4×C8C2×D311yescharacteristic
141#835—32no—
142#832—32no—
143#821—32no—
144#821C2×D311yescharacteristic
145#818—32no—
146#818—32no—
147#818—32no—
148#818—32no—
149#818—32no—
150#818—62no—
151#818—62no—
152#817—32no—
153#817C2×D311yescharacteristic
154#816—32no—
155#816C2×D311yescharacteristic
156#815C2×D312yes—
157Dic3⋊C8C2×D312yes—
158#808—32no—
159#807—32no—
160C4⋊(C3⋊C8)C2×D311yescharacteristic
161C22×C3×D3—21no—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167#634—81no—
168#634—81no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3C2×D412yes—
173C2×C3×Dic3C2×D412yes—
174C3×D12—21no—
175C3×D12C2×Q812yes—
176C3×C4×D3—42no—
177C3×Dic6—22no—
178C3×Dic6—21no—
179C3×Dic6C2×Q812yes—
180#627—82no—
181D3×Dic3—82no—
182C32×C8—21no—
183C32×C8C2×Q812yes—
184C3×C3⋊C8—22no—
185Q82—91no—
186#554—91no—
187#501—92no—
188#500—91no—
189#479—92no—
190#477—91no—
191#476—91no—
192#474—92no—
193#446—31no—
194#440—92no—
195C4×SD16—31no—
196C2×C3×Q8—31no—
197C2×C3×Q8—31no—
198C2×C3×D4—31no—
199C22×C3×C4—61no—
200C22×Dic3—62no—
201C2×D12C22×D311yescharacteristic
202C2×C4×D3—21no—
203C2×C4×D3—62no—
204C2×Dic6—62no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—62no—
210C2×Dic6—121no—
211C2×Dic6—121no—
212C2×Dic6D1211yescharacteristic
213C2×Dic6C22×D311yescharacteristic
214C3×SD16—34no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—32no—
218C2×C3×C8C22×D311yescharacteristic
219C2×C3×C8C22×D311yescharacteristic
220C2×C3×C8C22×D311yescharacteristic
221C2×C3×C8C22×D311yescharacteristic
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—61no—
227C3×C22⋊C4—61no—
228C3×C42—21no—
229C3×C42—32no—
230C3×C42—61no—
231C3×C42C22×D311yescharacteristic
232C3×C42C22×D311yescharacteristic
233#217—62no—
234(C2×D3)⋊C4—21no—
235(C2×D3)⋊C4—62no—
236C4⋊Dic3—32no—
237C4⋊Dic3—32no—
238C4⋊Dic3—32no—
239C4⋊Dic3—32no—
240C4⋊Dic3—62no—
241C4⋊Dic3—62no—
242C4⋊Dic3—62no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—62no—
248C4⋊Dic3—62no—
249C4⋊Dic3—121no—
250C4⋊Dic3—121no—
251C4⋊Dic3D1211yescharacteristic
252C4⋊Dic3C22×D311yescharacteristic
253C4⋊Dic3C22×D311yescharacteristic
254Dic3⋊C4—21no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4D1212yes—
261C4×Dic3—21no—
262C4×Dic3—62no—
263C4×Dic3—62no—
264C4×Dic3C22×D312yes—
265C2×C3⋊C8C22×D312yes—
266#204Dic614yescomplemented
267C22×C32C22×D411yescharacteristic
268C2×C3×D3—22no—
269C2×C3×D3—41no—
270C2×C3×D3—41no—
271C32×C4—21no—
272C32×C4#13712yes—
273C32×C4C22×Q811yescharacteristic
274C32×C42−1+411yescharacteristic
275C3⋊Dic3—42no—
276C3⋊Dic3—42no—
277C3×Dic3—22no—
278C3×Dic3—22no—
279C3×Dic3—22no—
280C3×Dic3—41no—
281C3×Dic3—41no—
282C2×SD16—31no—
283C4⋊Q8—92no—
284C4⋊Q8—91no—
285C4⋊Q8—91no—
286C4⋊Q8—181no—
287C4⋊Q8—182no—
288#125—92no—
289C22⋊Q8—182no—
290C22⋊Q8—181no—
291C4×Q8—31no—
292C4×Q8—31no—
293C4×Q8—92no—
294C4×Q8—181no—
295C4×D4—31no—
296C4×D4—92no—
297C2×C4⋊C4—181no—
298#107—92no—
299#107—92no—
300#107—92no—
301#106—31no—
302#106—92no—
303C4⋊C8—32no—
304C4⋊C8—31no—
305#103—31no—
306#103—92no—
307#102—31no—
308#102—92no—
309#97—32no—
310C4×C8D3211yescharacteristic
311C23×C3—61no—
312C22×D3—21no—
313C3×Q8—32no—
314C3×Q8—62no—
315C3×Q8—61no—
316C3×D4—32no—
317C3×D4—61no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—122no—
327C2×C3×C4C2×D1211yescharacteristic
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—122no—
341C2×Dic3—122no—
342C2×Dic3—242no—
343C2×Dic3C2×D1212yes—
344C2×Dic3C2×D1212yes—
345D12—21no—
346D12C2×Dic612yes—
347C4×D3—42no—
348C4×D3—242no—
349Dic6—22no—
350Dic6—21no—
351Dic6—242no—
352Dic6—242no—
353Dic6—241no—
354Dic6—241no—
355Dic6—241no—
356Dic6—241no—
357Dic6—242no—
358Dic6—242no—
359Dic6C2×Dic612yes—
360C3×C8—22no—
361C3×C8—21no—
362C3×C8—21no—
363C3×C8—22no—
364C3×C8—62no—
365C3×C8C2×Dic612yes—
366C3×C8D3×Q812yes—
367C3⋊C8—22no—
368C2×C32D4×Q811yescharacteristic
369C2×C32C2×#13711yescharacteristic
370C2×C32#57611yescharacteristic
371C3×D3—42no—
372C2×Q8—31no—
373C2×Q8—31no—
374C2×Q8—182no—
375C2×Q8—181no—
376C2×Q8—181no—
377C2×D4—31no—
378C22×C4—61no—
379C22×C4—182no—
380SD16—34no—
381C2×C8—32no—
382C2×C8C2×D3211yescharacteristic
383C2×C8C2×D3211yescharacteristic
384C4⋊C4—31no—
385C4⋊C4—32no—
386C4⋊C4—31no—
387C4⋊C4—31no—
388C4⋊C4—61no—
389C4⋊C4—92no—
390C4⋊C4—92no—
391C4⋊C4—182no—
392C4⋊C4—182no—
393C4⋊C4—182no—
394C4⋊C4—182no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C22⋊C4—61no—
398C22⋊C4—182no—
399C42—32no—
400C42—61no—
401C42—182no—
402C42C2×D3211yescharacteristic
403C22×C3—21no—
404C22×C3—62no—
405C22×C3—121no—
406C22×C3—121no—
407C22×C3C22×D1211yescharacteristic
408C22×C3C2×D3×D411yescharacteristic
409C2×D3—22no—
410C2×D3—41no—
411C2×D3—41no—
412C3×C4—22no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—22no—
418C3×C4—62no—
419C3×C4—62no—
420C3×C4—62no—
421C3×C4—121no—
422C3×C4—121no—
423C3×C4#90912yes—
424C3×C4#91512yes—
425C3×C4C22×Dic611yescharacteristic
426C3×C4C2×D3×Q811yescharacteristic
427C3×C4#101011yescharacteristic
428C3×C4#101011yescharacteristic
429Dic3—22no—
430Dic3—22no—
431Dic3—22no—
432Dic3—41no—
433Dic3—41no—
434Dic3—122no—
435Dic3—122no—
436Dic3—122no—
437Dic3—122no—
438Dic3—242no—
439Dic3—242no—
440C32#338511yescharacteristic, complemented, Sylow
441C23—61no—
442Q8—32no—
443Q8—61no—
444Q8—62no—
445Q8—721no—
446Q8—721no—
447Q8—722no—
448D4—32no—
449D4—61no—
450C2×C4—32no—
451C2×C4—32no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—122no—
456C2×C4—182no—
457C2×C4—182no—
458C2×C4—722no—
459C2×C4D3×D1211yescharacteristic
460C2×C4D3×D1211yescharacteristic
461C2×C4C22×D3211yescharacteristic
462C8—21no—
463C8—62no—
464C8D3×Dic612yes—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—122no—
469C2×C3D4×Dic611yescharacteristic
470C2×C3Q8×D1211yescharacteristic
471C2×C3C2×#90911yescharacteristic
472C2×C3#575211yescharacteristic
473C2×C3C2×#91511yescharacteristic
474C2×C3#576911yescharacteristic
475D3—42no—
476C22—62no—
477C22—121no—
478C22—121no—
479C22C2×D3×D1211yescharacteristic
480C4—21no—
481C4—62no—
482C4—62no—
483C4—62no—
484C4—121no—
485C4—121no—
486C4—362no—
487C4—362no—
488C4#6380012yes—
489C4C2×D3×Dic611yescharacteristic
490C4#6429811yescharacteristic
491C3—21no—
492C3#7963411yescharacteristic, complemented
493C3#7997611yescharacteristic, complemented
494C2—122no—
495C2Dic6×D1211yescharacteristic
496C2#1059468011yescharacteristic
497C2C2×#6380011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4×C8D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. Dic62C2semidirect
3. #10592381C2semidirect
5. C3×#4679C2semidirect
6. #10590892C2semidirect
7. #10590811C2semidirect
10. #10590283C2semidirect
65. #4679D3semidirect
90. C3×#204Q8semidirect
266. #204Dic6semidirect
440. C32#3385semidirect
492. C3#79634semidirect
493. C3#79976semidirect

Maximal subgroups

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

subgroupindex
#105939602
Dic622
#105923812
C3×C4×#2042
C3×#46792
#105908922
#105908112
#105907662
#105907622
#105902832
#105902682
#799763
#796343