Finite Group Databasebeta

← #11878485

Subgroups — #11878485

Order 1152.

883 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594923C212yesmaximal, complemented
2#10592809C211yesmaximal, characteristic, complemented
3C3×#5116C211yesmaximal, characteristic, complemented
4C3×#5115C211yesmaximal, characteristic, complemented
5#10591180C212yesmaximal, complemented
6#10590965C212yesmaximal, complemented
7#10590963C212yesmaximal, complemented
8#10590689C212yesmaximal, complemented
9#10590650C212yesmaximal, complemented
10#80768—31nomaximal
11#80724—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×#3796C2212yes—
14C22×C32×C8C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C3×#930C2212yes—
17C3×#924C2212yes—
18C2×C3×Dic12C2211yescharacteristic
19C2×C3×D24C2211yescharacteristic
20#63971—22no—
21#63958—22no—
22#63916C2212yes—
23#63910—22no—
24#63900C2212yes—
25#63896—22no—
26#63871C2212yes—
27C2×#3715C2212yes—
28#63647C2212yes—
29#63647C2212yes—
30C3×#821C2212yes—
31C3×#818C2211yescharacteristic
32C3×#818C2211yescharacteristic
33C3×#816C2212yes—
34#63576C2212yes—
35#63565C2212yes—
36#63562C2212yes—
37#5629—32no—
38#5608—32no—
39C3×#467—31no—
40C3×#466—31no—
41#5187—32no—
42#5158—32no—
43#5116D311yescharacteristic, complemented
44#5115D311yescharacteristic, complemented
45#5110—31no—
46#5110—31no—
47#5110—61no—
48#5049—32no—
49#5042—32no—
50#4884—32no—
51#4882—32no—
52#4811—32no—
53#4810—32no—
54#4783—32no—
55#4774—32no—
56C22×C32×C4C2311yescharacteristic
57C2×#638D412yes—
58#3828—41no—
59#3828—41no—
60C2×C4⋊(C3⋊D3)D411yescharacteristic
61C2×C4×C3⋊D3C2312yes—
62C2×#634D411yescharacteristic
63C2×C3×#67—22no—
64C2×C3×D12C2312yes—
65C2×C3×Dic6C2312yes—
66C2×#626—22no—
67C2×#626—22no—
68C2×#624—22no—
69C2×D3×Dic3—22no—
70#3796—42no—
71#3796—42no—
72C2×C32×C8—41no—
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75#3748—41no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×#217—22no—
78C3×(C2×D3)⋊C4—22no—
79C3×C4⋊Dic3C2312yes—
80C3×C4⋊Dic3C2312yes—
81C3×Dic3⋊C4—22no—
82C3×Dic12—41no—
83C3×D24—41no—
84#3724—22no—
85Dic3⋊Dic3—22no—
86#3722—22no—
87(C2×D3)⋊Dic3—22no—
88#3715—42no—
89#3203—91noSylow
90C2×#239—32no—
91C2×#237—32no—
92C2×#235—31no—
93C2×#235—31no—
94C2×#235—61no—
95C2×C3×Q16—31no—
96C2×C3×D8—31no—
97C22×C3×C8—21no—
98C22×C3×C8C2×D311yescharacteristic
99C22×C3×C8C2×D311yescharacteristic
100C3×C22⋊Q8—32no—
101C3×#121—32no—
102#946—32no—
103C2×#215—32no—
104#939—62no—
105#938—32no—
106#938—62no—
107C2×#214—32no—
108#930C2×D312yes—
109#924C2×D312yes—
110C2×#208—31no—
111C2×#208—31no—
112C2×#208—61no—
113C2×Dic12C2×D311yescharacteristic
114C2×D24C2×D311yescharacteristic
115#897—32no—
116#896—62no—
117#895—32no—
118#895—62no—
119D3×C4⋊C4—32no—
120D3×C4⋊C4—32no—
121#884—62no—
122#884—62no—
123#884—62no—
124#878—62no—
125C3×#107—31no—
126C3×#107—31no—
127C3×#103—32no—
128C3×#102—32no—
129#835—32no—
130#832—32no—
131#821C2×D312yes—
132(C2×D3)⋊C8—32no—
133(C2×D3)⋊C8—32no—
134(C2×D3)⋊C8—32no—
135(C2×D3)⋊C8—32no—
136(C2×D3)⋊C8—62no—
137(C2×D3)⋊C8—62no—
138#818C2×D311yescharacteristic
139#818C2×D311yescharacteristic
140#816C2×D312yes—
141#810—32no—
142#809—32no—
143#807—32no—
144#807—32no—
145C23×C32C2×D411yescharacteristic
146C22×C3⋊D3C2×D412yes—
147C22×C3×D3—22no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2411yescharacteristic
152#638—42no—
153C2×C3⋊Dic3C2×D412yes—
154C4⋊(C3⋊D3)—41no—
155C4×C3⋊D3—22no—
156C4×C3⋊D3—22no—
157#634—41no—
158C3×#67—82no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C3×D12—22no—
163C3×D12—22no—
164C3×Dic6—22no—
165C3×Dic6—22no—
166#626—44no—
167#626—82no—
168#624—82no—
169D3×Dic3—44no—
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—31no—
179#452—92no—
180#449—92no—
181#408—91no—
182C2×C3×Q8—32no—
183C2×C3×D4—32no—
184C2×C3×D4—62no—
185C22×C3×C4—21no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C2×#67—22no—
189C2×#67—32no—
190C2×#67—32no—
191C2×#67—62no—
192C2×#67—62no—
193C2×#67—62no—
194C22×Dic3—62no—
195#239—122no—
196#239—122no—
197#237—122no—
198#237—122no—
199#235—121no—
200#235—121no—
201#235—121no—
202#235—121no—
203#235—122no—
204#235—122no—
205C2×D12—31no—
206C2×D12—31no—
207C2×D12—61no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12C22×D312yes—
211C2×C4×D3—32no—
212C2×C4×D3—32no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×Dic6—31no—
218C2×Dic6—31no—
219C2×Dic6—61no—
220C2×Dic6C22×D312yes—
221C3×Q16—121no—
222C3×D8—121no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—41no—
226C2×C3×C8—41no—
227C2×C3×C8—42no—
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C3×C4⋊C4—32no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—62no—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—62no—
237#217—22no—
238#217—62no—
239#215—122no—
240#214—122no—
241(C2×D3)⋊C4—22no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245C4⋊Dic3—62no—
246C4⋊Dic3C22×D312yes—
247C4⋊Dic3C22×D312yes—
248Dic3⋊C4—22no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252#208—121no—
253#208—121no—
254#208—122no—
255C2×C3⋊C8—32no—
256C2×C3⋊C8—32no—
257C2×C3⋊C8—62no—
258Dic12—41no—
259D24—41no—
260C22×C32—21no—
261C22×C32—21no—
262C22×C32—21no—
263C22×C32C22×D411yescharacteristic
264C2×C3⋊D3—22no—
265C2×C3⋊D3—22no—
266C2×C3⋊D3—22no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C32×C4—21no—
271C32×C4H(5,𝔽2)11yescharacteristic
272C32×C4H(5,𝔽2)11yescharacteristic
273C3⋊Dic3—22no—
274C3×Dic3—42no—
275C3×Dic3—42no—
276C3×Dic3—42no—
277C2×#41—91no—
278C2×#41—92no—
279C2×Q16—31no—
280C2×SD16—92no—
281C2×D8—31no—
282C2×M16—91no—
283C22×C8D3211yescharacteristic
284C22⋊Q8—32no—
285C22⋊Q8—92no—
286C22⋊Q8—182no—
287#121—32no—
288#121—92no—
289#121—182no—
290#121—182no—
291#121—182no—
292C2×C4⋊C4—92no—
293#107—31no—
294#107—31no—
295#107—92no—
296#103—32no—
297#103—92no—
298#102—32no—
299#102—92no—
300C22⋊C8—92no—
301C22⋊C8—92no—
302C23×C3—21no—
303C23×C3—62no—
304C23×C3D3×D411yescharacteristic
305C23×C3D3×D411yescharacteristic
306C22×D3—22no—
307C22×D3—32no—
308C22×D3—32no—
309C22×D3—62no—
310C3×Q8—62no—
311C3×Q8—62no—
312C3×D4—62no—
313C3×D4—62no—
314C3×D4—242no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330#67—82no—
331#67—124no—
332#67—122no—
333#67—122no—
334#67—124no—
335#67—242no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—32no—
340C2×Dic3—32no—
341C2×Dic3—62no—
342C2×Dic3—124no—
343D12—22no—
344D12—22no—
345D12—121no—
346D12—121no—
347D12—122no—
348D12—124no—
349D12—242no—
350C4×D3—62no—
351C4×D3—62no—
352C4×D3—62no—
353C4×D3—62no—
354C4×D3—122no—
355C4×D3—122no—
356C4×D3—124no—
357C4×D3—242no—
358C4×D3—242no—
359Dic6—22no—
360Dic6—22no—
361Dic6—121no—
362Dic6—121no—
363Dic6—122no—
364C3×C8—21no—
365C3×C8—21no—
366C3×C8—21no—
367C3×C8—21no—
368C3×C8—41no—
369C3×C8—41no—
370C3⋊C8—62no—
371C3⋊C8—62no—
372C3⋊C8—122no—
373C2×C32—41no—
374C2×C32#53411yescharacteristic
375C2×C32#57611yescharacteristic
376C2×C32#57811yescharacteristic
377C3⋊D3—42no—
378C3×D3—82no—
379#41—361no—
380#41—361no—
381#41—362no—
382#41—362no—
383C2×Q8—32no—
384C2×Q8—91no—
385C2×D4—32no—
386C2×D4—62no—
387C2×D4—92no—
388C2×D4—91no—
389C2×D4—182no—
390C2×D4—182no—
391C22×C4—92no—
392C22×C4—182no—
393C22×C4—182no—
394C22×C4C2×D3211yescharacteristic
395Q16—121no—
396SD16—362no—
397D8—121no—
398M16—361no—
399C2×C8—41no—
400C2×C8—92no—
401C2×C8C2×D3211yescharacteristic
402C2×C8C2×D3211yescharacteristic
403C4⋊C4—32no—
404C4⋊C4—32no—
405C4⋊C4—62no—
406C4⋊C4—182no—
407C4⋊C4—182no—
408C22⋊C4—62no—
409C22⋊C4—62no—
410C22⋊C4—182no—
411C22⋊C4—182no—
412C22×C3—22no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3C2×D3×D411yescharacteristic
426C22×C3C2×D3×D411yescharacteristic
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—42no—
430C2×D3—62no—
431C2×D3—62no—
432C2×D3—62no—
433C2×D3—62no—
434C2×D3—62no—
435C2×D3—62no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C3×C4—22no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—122no—
445C3×C4—122no—
446C3×C4—122no—
447C3×C4#100411yescharacteristic
448C3×C4#100411yescharacteristic
449C3×C4#100911yescharacteristic
450C3×C4#100911yescharacteristic
451Dic3—42no—
452Dic3—42no—
453Dic3—42no—
454Dic3—62no—
455Dic3—62no—
456Dic3—122no—
457C32#320311yescharacteristic, complemented, Sylow
458C23—62no—
459C23—92no—
460C23#380211yescharacteristic
461Q8—62no—
462Q8—62no—
463Q8—361no—
464D4—62no—
465D4—62no—
466D4—242no—
467D4—361no—
468D4—364no—
469D4—362no—
470D4—722no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—92no—
477C2×C4—182no—
478C2×C4—182no—
479C2×C4—364no—
480C2×C4—722no—
481C2×C4#380211yescharacteristic
482C2×C4C22×D3211yescharacteristic
483C8—21no—
484C8—21no—
485C8—182no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—42no—
490C2×C3—41no—
491C2×C3—41no—
492C2×C3—242no—
493C2×C3#560511yescharacteristic
494C2×C3#560511yescharacteristic
495C2×C3#575711yescharacteristic
496C2×C3#576611yescharacteristic
497C2×C3#576911yescharacteristic
498C2×C3#577111yescharacteristic
499D3—82no—
500D3—122no—
501D3—122no—
502D3—242no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—122no—
507C22—122no—
508C22—122no—
509C22—182no—
510C22—182no—
511C22—182no—
512C22C2×#380211yescharacteristic
513C4—21no—
514C4—122no—
515C4—122no—
516C4—122no—
517C4—182no—
518C4#6430811yescharacteristic
519C4#6433011yescharacteristic
520C3—21no—
521C3#8072411yescharacteristic, complemented
522C3#8076811yescharacteristic, complemented
523C2—41no—
524C2—242no—
525C2—362no—
526C2#1059468711yescharacteristic
527C2#1059470311yescharacteristic
528C2#1059508411yescharacteristic
subgroupG/H
centerC22C2×#3802
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. #10594923C2semidirect
2. #10592809C2semidirect
3. C3×#5116C2semidirect
4. C3×#5115C2semidirect
5. #10591180C2semidirect
6. #10590965C2semidirect
7. #10590963C2semidirect
8. #10590689C2semidirect
9. #10590650C2semidirect
43. #5116D3semidirect
44. #5115D3semidirect
457. C32#3203semidirect
521. C3#80724semidirect
522. C3#80768semidirect

Maximal subgroups

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

subgroupindex
#105949232
#105928092
C3×#51162
C3×#51152
#105911802
#105909652
#105909632
#105906892
#105906502
#807683
#807243