Finite Group Databasebeta

← #11897671

Subgroups — #11897671

Order 1152.

727 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593956C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592378C211yesmaximal, characteristic, complemented
4C3×C4×#204C211yesmaximal, characteristic
5C3×#4682C211yesmaximal, characteristic, complemented
6#10590903C212yesmaximal, complemented
7#10590821C212yesmaximal, complemented
8#10590779C212yesmaximal
9#10590778C212yesmaximal
10#10590310C211yesmaximal, characteristic, complemented
11#10590266C211yesmaximal, characteristic
12#81954—31nomaximal
13#79634—31nomaximal
14C4×#634C2211yescharacteristic
15C2×C3×#204C2211yescharacteristic
16C3×C4×D12C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63919C2212yes—
21#63918—21no—
22#63898C2212yes—
23D3×C4⋊Dic3—21no—
24#63887—22no—
25#63872C2212yes—
26#63857—21no—
27#63844—21no—
28#63843C2212yes—
29#63839—22no—
30C32×C4×C8C2211yescharacteristic
31#63642C2212yes—
32#63641C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#821C2211yescharacteristic
35C3×#818C2212yes—
36C3×#818C2212yes—
37C3×#817C2211yescharacteristic
38C3×#816C2211yescharacteristic
39#63576C2212yes—
40#63574C2212yes—
41#63565C2212yes—
42#63562C2212yes—
43#5730—31no—
44#5722—31no—
45Q8×Dic6—31no—
46#5543—31no—
47C3×#500—31no—
48C3×C4×SD16—31no—
49#5164—32no—
50#5091—31no—
51#5084—31no—
52#5021—31no—
53#5008—31no—
54#4890—32no—
55#4889—32no—
56#4877—32no—
57#4876—32no—
58#4856—32no—
59#4796—32no—
60#4759—32no—
61C4×#204D311yescharacteristic
62#4682D311yescharacteristic, complemented
63#4679—31no—
64#4679—31no—
65#4679—61no—
66C2×#634D411yescharacteristic
67C2×C3×D12C2311yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C2×D3×Dic3—22no—
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)D411yescharacteristic
78#3750D412yes—
79C4×C3⋊Dic3C2312yes—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×(C2×D3)⋊C4—21no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2312yes—
85C3×C4⋊Dic3C2312yes—
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×C4×Dic3—21no—
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×Q8—31no—
102C3×C4×D4—31no—
103#946—62no—
104Q8×Dic3—32no—
105#944—62no—
106D4×Dic3—32no—
107C2×C4⋊Dic3—61no—
108#924—61no—
109C2×#204C2×D311yescharacteristic
110#897—61no—
111#893—32no—
112D3×C4⋊C4—61no—
113#890—32no—
114#890—32no—
115#888—32no—
116#888—32no—
117#888—61no—
118#888—62no—
119#887—32no—
120#887—61no—
121#878—62no—
122C4×D12C2×D311yescharacteristic
123#869—61no—
124#869C2×D311yescharacteristic
125#869C2×D311yescharacteristic
126C4×Dic6—31no—
127C4×Dic6—31no—
128C4×Dic6—61no—
129C4×Dic6—61no—
130C4×Dic6C2×D311yescharacteristic
131C3×#107—32no—
132C3×#107—32no—
133C3×#106—31no—
134C3×#103—31no—
135C3×#102—31no—
136C3×C4×C8—21no—
137C3×C4×C8C2×D311yescharacteristic
138C3×C4×C8C2×D311yescharacteristic
139#835—32no—
140#832—32no—
141#821C2×D311yescharacteristic
142#818C2×D312yes—
143#818C2×D312yes—
144#817C2×D311yescharacteristic
145#816C2×D311yescharacteristic
146#815—32no—
147#815—32no—
148#815—62no—
149Dic3⋊C8—32no—
150Dic3⋊C8—32no—
151Dic3⋊C8—62no—
152#810—32no—
153#809—32no—
154#808—32no—
155#808—32no—
156#807—32no—
157#807—32no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—31no—
160C4⋊(C3⋊C8)—61no—
161C22×C3×D3—21no—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3C2×D412yes—
166C2×C3⋊Dic3C2×D412yes—
167#634—22no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C3×D12—21no—
174C3×D12C2×Q812yes—
175C3×C4×D3—42no—
176C3×Dic6—21no—
177C3×Dic6—81no—
178C3×Dic6—81no—
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—31no—
189#479—92no—
190#477—91no—
191#476—91no—
192#474—92no—
193#446—91no—
194#440—92no—
195C4×SD16—31no—
196C2×C3×Q8—31no—
197C2×C3×Q8—61no—
198C2×C3×Q8—61no—
199C2×C3×D4—31no—
200C22×C3×C4—61no—
201C22×Dic3—62no—
202C2×D12C22×D311yescharacteristic
203C2×C4×D3—21no—
204C2×C4×D3—62no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—31no—
208C2×Dic6—31no—
209C2×Dic6—61no—
210C2×Dic6—62no—
211C2×Dic6—62no—
212C2×Dic6C22×D311yescharacteristic
213C3×SD16—34no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8C22×D311yescharacteristic
217C2×C3×C8C22×D311yescharacteristic
218C2×C3×C8C22×D311yescharacteristic
219C2×C3×C8C22×D311yescharacteristic
220C3×C4⋊C4—31no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C22⋊C4—61no—
228C3×C42—21no—
229C3×C42—61no—
230C3×C42C22×D311yescharacteristic
231C3×C42C22×D311yescharacteristic
232#217—62no—
233(C2×D3)⋊C4—21no—
234(C2×D3)⋊C4—62no—
235C4⋊Dic3—21no—
236C4⋊Dic3—21no—
237C4⋊Dic3—31no—
238C4⋊Dic3—31no—
239C4⋊Dic3—61no—
240C4⋊Dic3—62no—
241C4⋊Dic3—62no—
242C4⋊Dic3—62no—
243C4⋊Dic3C22×D311yescharacteristic
244C4⋊Dic3C22×D312yes—
245C4⋊Dic3C22×D311yescharacteristic
246C4⋊Dic3C22×D312yes—
247Dic3⋊C4—21no—
248Dic3⋊C4—32no—
249Dic3⋊C4—32no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256C4×Dic3—21no—
257C4×Dic3—32no—
258C4×Dic3—32no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—32no—
264C2×C3⋊C8—62no—
265#204Dic614yescomplemented
266C22×C32C22×D411yescharacteristic
267C2×C3×D3—22no—
268C2×C3×D3—41no—
269C2×C3×D3—41no—
270C32×C4—21no—
271C32×C4#13712yes—
272C32×C4C22×Q811yescharacteristic
273C32×C42−1+411yescharacteristic
274C3⋊Dic3—22no—
275C3⋊Dic3—22no—
276C3×Dic3—22no—
277C3×Dic3—41no—
278C3×Dic3—42no—
279C3×Dic3—41no—
280C3×Dic3—42no—
281C2×SD16—31no—
282C4⋊Q8—31no—
283C4⋊Q8—31no—
284C4⋊Q8—92no—
285C4⋊Q8—181no—
286C4⋊Q8—182no—
287#125—92no—
288C22⋊Q8—182no—
289C22⋊Q8—181no—
290C4×Q8—31no—
291C4×Q8—91no—
292C4×Q8—92no—
293C4×Q8—181no—
294C4×D4—31no—
295C4×D4—92no—
296C2×C4⋊C4—181no—
297#107—32no—
298#107—32no—
299#107—92no—
300#106—31no—
301#106—92no—
302C4⋊C8—92no—
303C4⋊C8—91no—
304#103—31no—
305#103—92no—
306#102—31no—
307#102—92no—
308#97—92no—
309C4×C8D3211yescharacteristic
310C23×C3—61no—
311C22×D3—21no—
312C3×Q8—32no—
313C3×Q8—61no—
314C3×Q8—241no—
315C3×Q8—241no—
316C3×D4—32no—
317C3×D4—61no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—61no—
322C2×C3×C4—62no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—62no—
326C2×C3×C4—122no—
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—22no—
336C2×Dic3—21no—
337C2×Dic3—22no—
338C2×Dic3—32no—
339C2×Dic3—32no—
340C2×Dic3—32no—
341C2×Dic3—32no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—242no—
345D12—21no—
346D12C2×Dic612yes—
347C4×D3—42no—
348C4×D3—242no—
349Dic6—21no—
350Dic6—62no—
351Dic6—62no—
352Dic6—81no—
353Dic6—81no—
354Dic6—122no—
355Dic6—242no—
356Dic6—242no—
357Dic6C2×Dic612yes—
358C3×C8—21no—
359C3×C8—21no—
360C3×C8—22no—
361C3×C8—41no—
362C3×C8C2×Dic612yes—
363C3×C8D3×Q812yes—
364C3⋊C8—62no—
365C3⋊C8—62no—
366C3⋊C8—122no—
367C2×C32D4×Q811yescharacteristic
368C2×C32C2×#13711yescharacteristic
369C2×C32#57611yescharacteristic
370C3×D3—42no—
371C2×Q8—31no—
372C2×Q8—61no—
373C2×Q8—61no—
374C2×Q8—91no—
375C2×Q8—182no—
376C2×D4—31no—
377C22×C4—61no—
378C22×C4—182no—
379SD16—34no—
380C2×C8—92no—
381C2×C8C2×D3211yescharacteristic
382C2×C8C2×D3211yescharacteristic
383C4⋊C4—31no—
384C4⋊C4—32no—
385C4⋊C4—31no—
386C4⋊C4—32no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—91no—
391C4⋊C4—92no—
392C4⋊C4—182no—
393C4⋊C4—182no—
394C4⋊C4—182no—
395C4⋊C4—182no—
396C22⋊C4—61no—
397C22⋊C4—182no—
398C42—61no—
399C42—92no—
400C42—182no—
401C42C2×D3211yescharacteristic
402C22×C3—21no—
403C22×C3—62no—
404C22×C3—121no—
405C22×C3—121no—
406C22×C3C2×D3×D411yescharacteristic
407C22×C3C2×D3×D411yescharacteristic
408C2×D3—22no—
409C2×D3—41no—
410C2×D3—41no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—22no—
416C3×C4—41no—
417C3×C4—62no—
418C3×C4—121no—
419C3×C4—121no—
420C3×C4—122no—
421C3×C4—122no—
422C3×C4#91512yes—
423C3×C4#91812yes—
424C3×C4C22×Dic611yescharacteristic
425C3×C4C2×D3×Q811yescharacteristic
426C3×C4#100711yescharacteristic
427C3×C4#101011yescharacteristic
428Dic3—22no—
429Dic3—42no—
430Dic3—42no—
431Dic3—41no—
432Dic3—41no—
433Dic3—62no—
434Dic3—62no—
435Dic3—62no—
436Dic3—62no—
437Dic3—122no—
438Dic3—122no—
439C32#338511yescharacteristic, complemented, Sylow
440C23—61no—
441Q8—32no—
442Q8—61no—
443Q8—182no—
444Q8—241no—
445Q8—241no—
446Q8—722no—
447D4—32no—
448D4—61no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—62no—
452C2×C4—61no—
453C2×C4—62no—
454C2×C4—92no—
455C2×C4—92no—
456C2×C4—122no—
457C2×C4—722no—
458C2×C4#380211yescharacteristic
459C2×C4#380211yescharacteristic
460C2×C4C22×D3211yescharacteristic
461C8—21no—
462C8—182no—
463C8D3×Dic612yes—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—122no—
468C2×C3D4×Dic611yescharacteristic
469C2×C3#572711yescharacteristic
470C2×C3#575711yescharacteristic
471C2×C3C2×#91511yescharacteristic
472C2×C3C2×#91811yescharacteristic
473C2×C3#576911yescharacteristic
474D3—42no—
475C22—62no—
476C22—121no—
477C22—121no—
478C22C2×#380211yescharacteristic
479C4—21no—
480C4—62no—
481C4—122no—
482C4—122no—
483C4—121no—
484C4—121no—
485C4—182no—
486C4—182no—
487C4#6381112yes—
488C4C2×D3×Dic611yescharacteristic
489C4#6429711yescharacteristic
490C3—21no—
491C3#7963411yescharacteristic, complemented
492C3#8195411yescharacteristic, complemented
493C2—122no—
494C2#1059390411yescharacteristic
495C2#1059468711yescharacteristic
496C2C2×#6381111yescharacteristic
subgroupG/H
centerC22C2×#3802
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. #10593856C2semidirect
3. #10592378C2semidirect
5. C3×#4682C2semidirect
6. #10590903C2semidirect
7. #10590821C2semidirect
10. #10590310C2semidirect
62. #4682D3semidirect
90. C3×#204Q8semidirect
265. #204Dic6semidirect
439. C32#3385semidirect
491. C3#79634semidirect
492. C3#81954semidirect

Maximal subgroups

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

subgroupindex
#105939562
#105938562
#105923782
C3×C4×#2042
C3×#46822
#105909032
#105908212
#105907792
#105907782
#105903102
#105902662
#819543
#796343