Finite Group Databasebeta

← #11878484

Subgroups — #11878484

Order 1152.

871 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#10594894C212yesmaximal, complemented
2#10592814C211yesmaximal, characteristic, complemented
3C3×#5116C211yesmaximal, characteristic, complemented
4C3×#5110C211yesmaximal, characteristic, complemented
5#10591178C212yesmaximal, complemented
6#10590967C212yesmaximal, complemented
7#10590966C212yesmaximal, complemented
8#10590682C212yesmaximal, complemented
9#10590679C212yesmaximal, complemented
10#80768—31nomaximal
11#78676—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C2×#3799C2212yes—
14C22×C32×C8C2211yescharacteristic
15#64139C2212yes—
16C2×#3745C2211yescharacteristic
17C3×#924C2212yes—
18C2×C3×#208C2211yescharacteristic
19C2×C3×Dic12C2211yescharacteristic
20#63971—22no—
21#63958—22no—
22#63909C2212yes—
23D3×C4⋊Dic3C2212yes—
24#63888—22no—
25#63886—22no—
26#63856C2212yes—
27C2×#3717C2212yes—
28#63648C2212yes—
29#63645C2211yescharacteristic
30C3×(C2×D3)⋊C8C2212yes—
31C3×(C2×D3)⋊C8C2212yes—
32C3×#818C2211yescharacteristic
33C3×#816C2212yes—
34#63575C2212yes—
35#63566C2212yes—
36#63564C2212yes—
37#5833—32no—
38#5629—32no—
39C3×#467—31no—
40C3×#408—31no—
41#5187—32no—
42#5134—32no—
43#5116D311yescharacteristic, complemented
44#5115—31no—
45#5115—31no—
46#5115—61no—
47#5110D311yescharacteristic, complemented
48#5049—32no—
49#4882—32no—
50#4811—32no—
51#4810—32no—
52#4736—32no—
53#4734—32no—
54#4733—32no—
55#4722—32no—
56C22×C32×C4C2311yescharacteristic
57C2×#638—22no—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C3×#67D412yes—
60C3×#235—41no—
61C3×#235—41no—
62C2×C3×D12D411yescharacteristic
63C2×C3×C4×D3C2312yes—
64C2×C3×Dic6D411yescharacteristic
65C2×C3×Dic6C2312yes—
66C2×#626—22no—
67C2×#626—22no—
68C2×#624—22no—
69C2×D3×Dic3—22no—
70#3799—42no—
71#3799—42no—
72C2×C32×C8—41no—
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75#3752—22no—
76C4⋊(C3⋊Dic3)C2312yes—
77#3745—41no—
78C3×#217—22no—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×#208—41no—
82C2×C3×C3⋊C8C2312yes—
83C3×Dic12—41no—
84#3724—22no—
85Dic3⋊Dic3—22no—
86#3722—22no—
87(C2×D3)⋊Dic3—22no—
88#3717—42no—
89#3203—91noSylow
90C2×C3×#41—31no—
91C2×#239—32no—
92C2×#235—32no—
93C2×#235C2×D311yescharacteristic
94C2×C3×Q16—31no—
95C2×C3×M16—31no—
96C22×C3×C8—21no—
97C22×C3×C8C2×D311yescharacteristic
98C22×C3×C8C2×D311yescharacteristic
99C3×C22⋊Q8—32no—
100#946—32no—
101#946—62no—
102C2×#215—32no—
103#939—62no—
104#939—62no—
105#938—62no—
106#930—32no—
107#930—32no—
108#930—32no—
109#930—62no—
110C2×C4⋊Dic3—32no—
111#924—32no—
112#924C2×D312yes—
113C2×#208C2×D311yescharacteristic
114C2×Dic12C2×D311yescharacteristic
115C2×D24—31no—
116C2×D24—31no—
117C2×D24—61no—
118C2×#204—32no—
119#896—62no—
120#895—32no—
121#895—62no—
122D3×C4⋊C4—32no—
123#884—62no—
124#884—62no—
125C3×#107—31no—
126C3×#103—32no—
127C3×C22⋊C8—32no—
128C3×C22⋊C8—32no—
129#835—32no—
130#821—32no—
131#821—32no—
132#821—32no—
133#821—62no—
134(C2×D3)⋊C8C2×D312yes—
135(C2×D3)⋊C8C2×D312yes—
136#818—31no—
137#818—31no—
138#818—32no—
139#818—61no—
140#818C2×D311yescharacteristic
141#816—32no—
142#816C2×D312yes—
143#809—32no—
144#807—32no—
145C23×C32C2×D411yescharacteristic
146C22×C3⋊D3—22no—
147C22×C3×D3C2×D412yes—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2411yescharacteristic
152#638—82no—
153C2×C3⋊Dic3—22no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—22no—
156C3×#67—42no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3C2×D412yes—
160C3×D12—41no—
161C3×C4×D3—22no—
162C3×C4×D3—22no—
163C3×Dic6—22no—
164C3×Dic6—22no—
165C3×Dic6—41no—
166#626—44no—
167#626—82no—
168#624—44no—
169D3×Dic3—82no—
170C32×C8—21no—
171C32×C8—21no—
172C3×C3⋊C8—22no—
173#537—92no—
174#484—92no—
175#480—92no—
176#468—92no—
177#467—31no—
178#466—91no—
179#452—92no—
180#449—92no—
181#408—31no—
182C3×#41—121no—
183C3×#41—121no—
184C2×C3×Q8—31no—
185C2×C3×Q8—32no—
186C2×C3×D4—32no—
187C2×C3×D4—31no—
188C22×C3×C4—21no—
189C22×C3×C4—32no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C2×#67—62no—
193C2×#67—62no—
194C2×#67—62no—
195C2×#67—62no—
196C2×#67—122no—
197C2×#67D1212yes—
198C22×Dic3—62no—
199#239—122no—
200#239—122no—
201#235—41no—
202#235—41no—
203#235—122no—
204#235—122no—
205C2×D12—32no—
206C2×D12—32no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12D1211yescharacteristic
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3C22×D312yes—
215C2×Dic6D1211yescharacteristic
216C2×Dic6C22×D312yes—
217C3×Q16—121no—
218C3×M16—121no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—32no—
222C2×C3×C8—41no—
223C2×C3×C8—41no—
224C2×C3×C8—42no—
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C3×C4⋊C4—32no—
230C3×C4⋊C4—62no—
231C3×C22⋊C4—62no—
232#217—22no—
233#217—62no—
234#215—122no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—122no—
241C4⋊Dic3—32no—
242C4⋊Dic3—32no—
243C4⋊Dic3—62no—
244C4⋊Dic3—62no—
245C4⋊Dic3C22×D312yes—
246Dic3⋊C4—22no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250#208—41no—
251C2×C3⋊C8C22×D312yes—
252Dic12—41no—
253D24—121no—
254D24—121no—
255D24—122no—
256#204—122no—
257C22×C32—21no—
258C22×C32—21no—
259C22×C32—21no—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—42no—
264C2×C3×D3—22no—
265C2×C3×D3—22no—
266C2×C3×D3—22no—
267C32×C4—21no—
268C32×C4H(5,𝔽2)11yescharacteristic
269C32×C4H(5,𝔽2)11yescharacteristic
270C3⋊Dic3—42no—
271C3×Dic3—22no—
272C3×Dic3—42no—
273C3×Dic3—42no—
274C2×#41—31no—
275C2×#41—92no—
276C2×Q16—31no—
277C2×SD16—92no—
278C2×D8—91no—
279C2×M16—31no—
280C22×C8D3211yescharacteristic
281C22⋊Q8—32no—
282C22⋊Q8—92no—
283C22⋊Q8—182no—
284#121—92no—
285#121—92no—
286#121—182no—
287#121—182no—
288#121—182no—
289C2×C4⋊C4—92no—
290#107—31no—
291#107—92no—
292#107—91no—
293#103—32no—
294#103—92no—
295#102—92no—
296#102—92no—
297C22⋊C8—32no—
298C22⋊C8—32no—
299C23×C3—21no—
300C23×C3—32no—
301C23×C3C2×D1211yescharacteristic
302C23×C3D3×D411yescharacteristic
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—122no—
306C22×D3C2×D1212yes—
307C3×Q8—62no—
308C3×Q8—62no—
309C3×Q8—121no—
310C3×D4—121no—
311C3×D4—122no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—32no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328C2×C3×C4C23×D311yescharacteristic
329#67—42no—
330#67—124no—
331#67—242no—
332#67—242no—
333#67—242no—
334#67—244no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—122no—
340C2×Dic3—242no—
341C2×Dic3C2×D1212yes—
342D12—41no—
343D12—62no—
344D12—62no—
345D12—62no—
346D12—62no—
347D12—122no—
348D12—122no—
349D12—124no—
350D12—242no—
351C4×D3—22no—
352C4×D3—22no—
353C4×D3—124no—
354C4×D3—124no—
355C4×D3—242no—
356Dic6—22no—
357Dic6—22no—
358Dic6—41no—
359C3×C8—22no—
360C3×C8—21no—
361C3×C8—21no—
362C3×C8—21no—
363C3×C8—21no—
364C3×C8—41no—
365C3×C8—62no—
366C3⋊C8—22no—
367C2×C32—41no—
368C2×C32#53411yescharacteristic
369C2×C32#57611yescharacteristic
370C2×C32#57811yescharacteristic
371C3⋊D3—82no—
372C3×D3—42no—
373#41—121no—
374#41—121no—
375#41—362no—
376#41—362no—
377C2×Q8—31no—
378C2×Q8—32no—
379C2×D4—32no—
380C2×D4—31no—
381C2×D4—92no—
382C2×D4—182no—
383C2×D4—182no—
384C2×D4—182no—
385C22×C4—32no—
386C22×C4—182no—
387C22×C4—182no—
388C22×C4C2×D3211yescharacteristic
389Q16—121no—
390SD16—362no—
391D8—361no—
392M16—121no—
393C2×C8—32no—
394C2×C8—41no—
395C2×C8C2×D3211yescharacteristic
396C2×C8C2×D3211yescharacteristic
397C4⋊C4—32no—
398C4⋊C4—62no—
399C4⋊C4—92no—
400C4⋊C4—182no—
401C4⋊C4—182no—
402C22⋊C4—62no—
403C22⋊C4—182no—
404C22⋊C4—182no—
405C22⋊C4—182no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—62no—
417C22×C3—62no—
418C22×C3—62no—
419C22×C3C22×D1211yescharacteristic
420C22×C3C2×D3×D411yescharacteristic
421C2×D3—22no—
422C2×D3—22no—
423C2×D3—22no—
424C2×D3—122no—
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—242no—
431C2×D3—242no—
432C2×D3—242no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—41no—
438C3×C4—62no—
439C3×C4—122no—
440C3×C4—122no—
441C3×C4#100411yescharacteristic
442C3×C4#100411yescharacteristic
443C3×C4#100411yescharacteristic
444C3×C4#100911yescharacteristic
445Dic3—22no—
446Dic3—42no—
447Dic3—42no—
448Dic3—122no—
449Dic3—122no—
450Dic3—242no—
451C32#320311yescharacteristic, complemented, Sylow
452C23—32no—
453C23—182no—
454C23D3×D1211yescharacteristic
455Q8—62no—
456Q8—62no—
457Q8—121no—
458D4—121no—
459D4—122no—
460D4—182no—
461D4—182no—
462D4—364no—
463D4—722no—
464D4—722no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—32no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—182no—
473C2×C4—364no—
474C2×C4—722no—
475C2×C4D3×D1211yescharacteristic
476C2×C4C22×D3211yescharacteristic
477C8—21no—
478C8—21no—
479C8—62no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—42no—
484C2×C3—41no—
485C2×C3—41no—
486C2×C3—122no—
487C2×C3#549311yescharacteristic
488C2×C3#560511yescharacteristic
489C2×C3#575211yescharacteristic
490C2×C3#575311yescharacteristic
491C2×C3#576611yescharacteristic
492C2×C3#576911yescharacteristic
493D3—42no—
494D3—242no—
495D3—242no—
496D3—482no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—62no—
501C22—62no—
502C22—62no—
503C22—362no—
504C22—362no—
505C22—362no—
506C22C2×D3×D1211yescharacteristic
507C4—21no—
508C4—62no—
509C4—122no—
510C4—122no—
511C4—362no—
512C4#6430711yescharacteristic
513C4#6433011yescharacteristic
514C3—21no—
515C3#7867611yescharacteristic, complemented
516C3#8076811yescharacteristic, complemented
517C2—41no—
518C2—122no—
519C2—722no—
520C2#1059468011yescharacteristic
521C2#1059469111yescharacteristic
522C2#1059507211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3203
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #10594894C2semidirect
2. #10592814C2semidirect
3. C3×#5116C2semidirect
4. C3×#5110C2semidirect
5. #10591178C2semidirect
6. #10590967C2semidirect
7. #10590966C2semidirect
8. #10590682C2semidirect
9. #10590679C2semidirect
43. #5116D3semidirect
47. #5110D3semidirect
451. C32#3203semidirect
515. C3#78676semidirect
516. C3#80768semidirect

Maximal subgroups

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

subgroupindex
#105948942
#105928142
C3×#51162
C3×#51102
#105911782
#105909672
#105909662
#105906822
#105906792
#807683
#786763