Finite Group Databasebeta

← #11895876

Subgroups — #11895876

Order 1152.

793 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic6×D12C211yesmaximal, characteristic, complemented
2#10593879C211yesmaximal, characteristic, complemented
3#10592380C211yesmaximal, characteristic, complemented
4C3×C4×D24C211yesmaximal, characteristic
5C3×#4679C211yesmaximal, characteristic, complemented
6#10590895C212yesmaximal, complemented
7#10590805C212yesmaximal, complemented
8#10590755C212yesmaximal
9#10590747C212yesmaximal, complemented
10#10590365C211yesmaximal, characteristic, complemented
11#10590272C211yesmaximal, characteristic, complemented
12#79970—31nomaximal
13#79571—31nomaximal
14C2×D3×Dic6—21no—
15#64078C2211yescharacteristic
16#64078C2211yescharacteristic
17C2×C3×D24C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×C4×D12C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63918C2212yes—
22#63893—22no—
23Dic3×D12C2212yes—
24#63861—22no—
25#63860C2212yes—
26#63857—21no—
27#63856—21no—
28#63844C2212yes—
29#63841—21no—
30C2×#3716C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63643C2212yes—
33#63643C2212yes—
34C3×#821C2211yescharacteristic
35C3×#821C2211yescharacteristic
36C3×#818C2211yescharacteristic
37C3×#815C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63567C2212yes—
42#63563C2212yes—
43#5584—31no—
44Q8×D12—31no—
45#5542—31no—
46D4×Dic6—31no—
47C3×#446—31no—
48C3×C4×D8—31no—
49#5153—32no—
50#5019—31no—
51#5007—31no—
52#4875—32no—
53#4850—32no—
54#4846—31no—
55#4844—32no—
56#4841—31no—
57#4765—32no—
58#4757—32no—
59#4714—32no—
60#4710—32no—
61C4×D24D311yescharacteristic
62#4681—31no—
63#4681—31no—
64#4681—61no—
65#4679D311yescharacteristic, complemented
66C2×#634—21no—
67C2×#634C2312yes—
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×#627—22no—
74C2×D3×Dic3—22no—
75D3×Dic6—44no—
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C42C2311yescharacteristic
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2312yes—
83C3×(C2×D3)⋊C4—21no—
84C3×(C2×D3)⋊C4—21no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4D412yes—
89C3×C4×Dic3C2312yes—
90C2×C3×C3⋊C8C2312yes—
91C3×D24—22no—
92#3724—22no—
93Dic3⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3716—24no—
99#3367—91noSylow
100C2×D3×Q8—61no—
101C22×Dic6—61no—
102C2×C3×D8—31no—
103C3×C4×Q8—31no—
104C3×C4×D4—31no—
105C3×C4×D4—31no—
106#946—61no—
107#936—32no—
108D4×Dic3—32no—
109C2×#214—32no—
110#926—61no—
111#924—61no—
112#924—61no—
113C2×D24C2×D311yescharacteristic
114C2×#204—32no—
115#898—62no—
116#897—62no—
117#897—61no—
118#892—61no—
119#888—32no—
120#887—32no—
121#879—62no—
122#878—62no—
123#875—32no—
124C4×D12—32no—
125C4×D12C2×D311yescharacteristic
126C4×D12C2×D311yescharacteristic
127#869—31no—
128#869—31no—
129#869—32no—
130#869—31no—
131#869—31no—
132#869—61no—
133#869—61no—
134C4×Dic6—32no—
135C4×Dic6C2×D311yescharacteristic
136C3×#107—31no—
137C3×C4⋊C8—32no—
138C3×C4⋊C8—31no—
139C3×#102—31no—
140C3×#102—31no—
141C3×#97—32no—
142C3×C4×C8—21no—
143C3×C4×C8C2×D311yescharacteristic
144C3×C4×C8C2×D311yescharacteristic
145#832—32no—
146#821—32no—
147#821C2×D311yescharacteristic
148#821C2×D311yescharacteristic
149#818—32no—
150#818C2×D311yescharacteristic
151#816—32no—
152#816—32no—
153#816—32no—
154#816—32no—
155#816—32no—
156#816—62no—
157#816—62no—
158#815C2×D312yes—
159Dic3⋊C8C2×D312yes—
160#810—32no—
161#807—32no—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C22×C3×D3—21no—
164C22×C3×D3—21no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170#634—22no—
171#634—22no—
172#634—42no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12—21no—
180C3×D12#4112yes—
181C3×C4×D3—42no—
182C3×C4×D3—42no—
183C3×Dic6—22no—
184#627—44no—
185D3×Dic3—44no—
186C32×C8—21no—
187C32×C8—21no—
188C3×C3⋊C8—22no—
189#556—91no—
190D4×Q8—91no—
191#489—92no—
192#487—91no—
193#477—92no—
194#474—91no—
195#463—92no—
196#461—91no—
197#446—31no—
198#440—92no—
199C4×D8—31no—
200C2×C3×Q8—31no—
201C2×C3×D4—31no—
202C2×C3×D4—31no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×Dic3—62no—
206D3×Q8—124no—
207C2×D12C22×D311yescharacteristic
208C2×D12C22×D311yescharacteristic
209C2×C4×D3—21no—
210C2×C4×D3—21no—
211C2×C4×D3—62no—
212C2×Dic6—32no—
213C2×Dic6—32no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—62no—
219C2×Dic6—121no—
220C2×Dic6—124no—
221C2×Dic6D1211yescharacteristic
222C3×D8—62no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—32no—
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C3×C4⋊C4—31no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—31no—
234C3×C22⋊C4—61no—
235C3×C22⋊C4—61no—
236C3×C42—21no—
237C3×C42—32no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#217—62no—
241#217—62no—
242#217—62no—
243#214—64no—
244(C2×D3)⋊C4—21no—
245(C2×D3)⋊C4—21no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249C4⋊Dic3—32no—
250C4⋊Dic3—32no—
251C4⋊Dic3—62no—
252C4⋊Dic3—62no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3—121no—
260C4⋊Dic3—121no—
261C4⋊Dic3—121no—
262C4⋊Dic3D1211yescharacteristic
263C4⋊Dic3C22×D311yescharacteristic
264C4⋊Dic3C22×D311yescharacteristic
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4D1212yes—
269C4×Dic3—62no—
270C4×Dic3—62no—
271C4×Dic3C22×D312yes—
272C2×C3⋊C8C22×D312yes—
273D24—22no—
274#204—64no—
275C22×C32C22×D411yescharacteristic
276C2×C3×D3—22no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C32×C4—21no—
283C32×C4AGL(1,ℤ/8)12yes—
284C32×C4C2×#4111yescharacteristic
285C32×C42−1+411yescharacteristic
286C3⋊Dic3—42no—
287C3⋊Dic3—42no—
288C3×Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—41no—
291C3×Dic3—41no—
292C22×Q8—181no—
293C2×SD16—92no—
294C2×D8—31no—
295C4⋊Q8—92no—
296C4⋊Q8—91no—
297C4⋊Q8—91no—
298#126—182no—
299#124—92no—
300C22⋊Q8—182no—
301C22⋊Q8—181no—
302C22⋊Q8—181no—
303C4×Q8—31no—
304C4×Q8—92no—
305C4×D4—31no—
306C4×D4—31no—
307C4×D4—92no—
308#117—181no—
309#107—31no—
310#107—92no—
311C4⋊C8—32no—
312C4⋊C8—31no—
313#103—92no—
314#103—92no—
315#103—92no—
316#102—31no—
317#102—31no—
318#102—92no—
319#97—32no—
320C4×C8D3211yescharacteristic
321C23×C3—61no—
322C23×C3—61no—
323C22×D3—21no—
324C22×D3—21no—
325C3×Q8—62no—
326C3×D4—32no—
327C3×D4—61no—
328C3×D4—61no—
329C3×D4—61no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—122no—
338C2×C3×C4—122no—
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—122no—
352C2×Dic3—122no—
353C2×Dic3—124no—
354C2×Dic3C2×D1212yes—
355C2×Dic3C2×D1212yes—
356D12—21no—
357D12—21no—
358D12—21no—
359D12#23512yes—
360C4×D3—42no—
361C4×D3—42no—
362C4×D3—124no—
363Dic6—22no—
364Dic6—62no—
365Dic6—62no—
366Dic6—62no—
367Dic6—62no—
368Dic6—122no—
369Dic6—122no—
370Dic6—124no—
371Dic6—124no—
372Dic6—122no—
373Dic6—122no—
374Dic6—242no—
375C3×C8—21no—
376C3×C8—21no—
377C3×C8—21no—
378C3×C8—21no—
379C3×C8—41no—
380C3×C8—41no—
381C3×C8—62no—
382C3⋊C8—22no—
383C2×C32#54811yescharacteristic
384C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
385C2×C32#57811yescharacteristic
386C3×D3—42no—
387C3×D3—81no—
388C2×Q8—31no—
389C2×Q8—92no—
390C2×Q8—182no—
391C2×Q8—181no—
392C2×Q8—364no—
393C2×D4—31no—
394C2×D4—31no—
395C22×C4—61no—
396C22×C4—61no—
397C22×C4—182no—
398SD16—184no—
399D8—62no—
400C2×C8—32no—
401C2×C8C2×D3211yescharacteristic
402C2×C8C2×D3211yescharacteristic
403C4⋊C4—31no—
404C4⋊C4—32no—
405C4⋊C4—31no—
406C4⋊C4—31no—
407C4⋊C4—92no—
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4—181no—
411C4⋊C4—181no—
412C4⋊C4—181no—
413C22⋊C4—61no—
414C22⋊C4—61no—
415C22⋊C4—182no—
416C22⋊C4—182no—
417C22⋊C4—182no—
418C42—32no—
419C42—182no—
420C42C2×D3211yescharacteristic
421C22×C3—21no—
422C22×C3—62no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3—121no—
427C22×C3—121no—
428C22×C3C22×D1211yescharacteristic
429C22×C3C2×D3×D411yescharacteristic
430C2×D3—22no—
431C2×D3—41no—
432C2×D3—41no—
433C2×D3—41no—
434C2×D3—41no—
435C2×D3—41no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—22no—
442C3×C4—62no—
443C3×C4—62no—
444C3×C4—121no—
445C3×C4—121no—
446C3×C4#90812yes—
447C3×C4#91112yes—
448C3×C4C2×#23511yescharacteristic
449C3×C4#100711yescharacteristic
450C3×C4D3×#4111yescharacteristic
451C3×C4#101011yescharacteristic
452Dic3—22no—
453Dic3—22no—
454Dic3—41no—
455Dic3—41no—
456Dic3—122no—
457Dic3—122no—
458Dic3—122no—
459Dic3—122no—
460Dic3—242no—
461Dic3—242no—
462C32#336711yescharacteristic, complemented, Sylow
463C23—61no—
464C23—61no—
465Q8—62no—
466Q8—182no—
467Q8—182no—
468Q8—364no—
469Q8—362no—
470D4—32no—
471D4—61no—
472D4—61no—
473D4—61no—
474C2×C4—32no—
475C2×C4—32no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—122no—
479C2×C4—122no—
480C2×C4—182no—
481C2×C4—182no—
482C2×C4—364no—
483C2×C4D3×D1211yescharacteristic
484C2×C4D3×D1211yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—21no—
487C8—21no—
488C8—62no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—122no—
493C2×C3—241no—
494C2×C3#555211yescharacteristic
495C2×C3#557611yescharacteristic
496C2×C3C2×#90811yescharacteristic
497C2×C3#575311yescharacteristic
498C2×C3C2×#91111yescharacteristic
499C2×C3#577111yescharacteristic
500D3—42no—
501D3—81no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22C2×D3×D1211yescharacteristic
509C4—21no—
510C4—62no—
511C4—62no—
512C4—121no—
513C4—121no—
514C4—362no—
515C4—362no—
516C4#6379512yes—
517C4#6429711yescharacteristic
518C4D3×#23511yescharacteristic
519C3—21no—
520C3#7957111yescharacteristic, complemented
521C3#7997011yescharacteristic, complemented
522C2—122no—
523C2—241no—
524C2#1059389911yescharacteristic
525C2C2×#6379511yescharacteristic
526C2#1059469211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenterC4×C8D32
hypocenterC32#3367
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
1. Dic6×D12C2semidirect
2. #10593879C2semidirect
3. #10592380C2semidirect
5. C3×#4679C2semidirect
6. #10590895C2semidirect
7. #10590805C2semidirect
9. #10590747C2semidirect
10. #10590365C2semidirect
11. #10590272C2semidirect
65. #4679D3semidirect
462. C32#3367semidirect
520. C3#79571semidirect
521. C3#79970semidirect

Maximal subgroups

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

subgroupindex
Dic6×D122
#105938792
#105923802
C3×C4×D242
C3×#46792
#105908952
#105908052
#105907552
#105907472
#105903652
#105902722
#799703
#795713