Finite Group Databasebeta

← #11793114

Subgroups — #11793114

Order 1152.

573 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595050C211yesmaximal, characteristic, complemented
2C2×#63652C211yesmaximal, characteristic
3#10591232C211yesmaximal, characteristic
4#10591113C211yesmaximal, characteristic
5C3×#4559C211yesmaximal, characteristic, complemented
6C3×#4557C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#69042—31nomaximal
9#68714—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63982—22no—
18#63919—21no—
19C4×#627—22no—
20#63872—21no—
21#63652—21no—
22#63652—21no—
23#63581—22no—
24#63570—22no—
25#5517—31no—
26#5517—31no—
27#5139—31no—
28C2×#825—31no—
29C2×#825—31no—
30C2×#825—61no—
31#5006—31no—
32#5006—31no—
33#5005—31no—
34C3×#344—31no—
35C3×H(3,ℤ/4)—31no—
36#4559D311yescharacteristic, complemented
37#4557D311yescharacteristic, complemented
38#4555—31no—
39#4532—31no—
40C22×C32×C4C2311yescharacteristic
41C2×#638—21no—
42C22×C3⋊Dic3—21no—
43#3828—21no—
44#3828—21no—
45#3828—21no—
46#3828—21no—
47C2×C4⋊(C3⋊D3)Q811yescharacteristic, complemented
48C2×C4×C3⋊D3—21no—
49C2×#634Q811yescharacteristic, complemented
50C2×#627—22no—
51C32×M16—21no—
52C32×M16—21no—
53C2×C32×C8—21no—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C3×#217—21no—
58C3×#217—21no—
59C3×#217D412yes—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4×Dic3—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3D412yes—
66C3×#208—21no—
67C3×#208—21no—
68C2×C3×C3⋊C8—21no—
69#3724—22no—
70Dic3⋊Dic3—22no—
71Dic3⋊Dic3—22no—
72#2031—91noSylow
73C2×#235—31no—
74C2×#235—31no—
75C2×#235—61no—
76C2×C3×M16—21no—
77C2×C3×M16—31no—
78C2×C3×M16C2×D311yescharacteristic
79C2×C3×M16C2×D311yescharacteristic
80C3×#117—31no—
81C3×#117—31no—
82C3×#117—31no—
83#926C2×D311yescharacteristic
84#926C2×D311yescharacteristic
85#926C2×D311yescharacteristic
86C2×C4×Dic3—31no—
87C2×C4×Dic3—31no—
88C2×C4×Dic3—61no—
89C2×#208C2×D311yescharacteristic
90#890—61no—
91#890—61no—
92#888—61no—
93#888—61no—
94#878—62no—
95#878—62no—
96C4×Dic6—62no—
97C4×Dic6—62no—
98#825—61no—
99#825—61no—
100#825—61no—
101#825—61no—
102#825—62no—
103#825—62no—
104#825—62no—
105#806—62no—
106#806—62no—
107#805—62no—
108C23×C32C2×D411yescharacteristic
109C22×C3⋊D3—21no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×Q811yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116#638—41no—
117#638—41no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—42no—
122C4⋊(C3⋊D3)—21no—
123C4⋊(C3⋊D3)—21no—
124C4×C3⋊D3—41no—
125C4×C3⋊D3—41no—
126#634—21no—
127#634—21no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—41no—
131#627—44no—
132C32×C8—41no—
133C3×C3⋊C8—41no—
134#533—91no—
135#421—91no—
136C2×#104—91no—
137#410—91no—
138#344—31no—
139#339—91no—
140H(3,ℤ/4)—31no—
141C22×C3×C4—21no—
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C2×#67—61no—
145C2×#67—61no—
146C2×#67—121no—
147C22×Dic3—61no—
148C22×Dic3—61no—
149C22×Dic3—121no—
150#235—62no—
151#235—62no—
152#235—61no—
153#235—61no—
154#235—61no—
155#235—61no—
156#235—61no—
157#235—61no—
158#235—61no—
159#235—61no—
160#235—121no—
161#235—121no—
162C2×D12—31no—
163C2×D12—31no—
164C2×D12—61no—
165C2×C4×D3—61no—
166C2×C4×D3—61no—
167C2×C4×D3—121no—
168C2×Dic6—31no—
169C2×Dic6—31no—
170C2×Dic6—61no—
171C2×Dic6—62no—
172C2×Dic6—62no—
173C3×M16—22no—
174C3×M16—21no—
175C3×M16—21no—
176C3×M16—21no—
177C3×M16—21no—
178C3×M16—41no—
179C3×M16—61no—
180C3×M16—61no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—41no—
184C2×C3×C8—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C22⋊C4—32no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C42—32no—
192C3×C42—61no—
193C3×C42—61no—
194#217—21no—
195#217—21no—
196#217D1212yes—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—62no—
201C4⋊Dic3—62no—
202Dic3⋊C4—62no—
203Dic3⋊C4—62no—
204Dic3⋊C4—62no—
205Dic3⋊C4—62no—
206C4×Dic3—21no—
207C4×Dic3—21no—
208C4×Dic3—31no—
209C4×Dic3—31no—
210C4×Dic3—31no—
211C4×Dic3—31no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—121no—
217C4×Dic3D1212yes—
218#208—21no—
219#208—21no—
220C2×C3⋊C8—21no—
221C22×C32—41no—
222C22×C32#12011yescharacteristic
223C22×C32C22⋊Q811yescharacteristic
224C22×C32#12411yescharacteristic
225C2×C3⋊D3—41no—
226C2×C3⋊D3—81no—
227C32×C4C22⋊Q811yescharacteristic
228C32×C4C22⋊Q811yescharacteristic
229C32×C4#12411yescharacteristic
230C32×C4#12411yescharacteristic
231C3⋊Dic3—22no—
232C3⋊Dic3—41no—
233C3⋊Dic3—41no—
234C3×Dic3—42no—
235C3×Dic3—42no—
236C3×Dic3—81no—
237C2×#41—91no—
238C2×M16—31no—
239C2×M16D3211yescharacteristic
240C4⋊Q8—181no—
241#125—181no—
242C22⋊Q8—182no—
243C4×Q8—182no—
244#117—31no—
245#117—31no—
246#117—31no—
247C2×C42—91no—
248#104—182no—
249#104—181no—
250#104—181no—
251#99—182no—
252C23×C3—21no—
253C23×C3C2×D1211yescharacteristic
254C23×C3D3×D411yescharacteristic
255C22×D3—61no—
256C22×D3—61no—
257C22×D3—121no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—121no—
267C2×C3×C4C2×D1211yescharacteristic
268C2×C3×C4#23511yescharacteristic
269C2×C3×C4#23511yescharacteristic
270C2×C3×C4#23511yescharacteristic
271C2×C3×C4#23511yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4#23711yescharacteristic
276C2×C3×C4#23711yescharacteristic
277C2×C3×C4D3×Q811yescharacteristic
278C2×C3×C4D3×Q811yescharacteristic
279#67—122no—
280#67—122no—
281#67—121no—
282#67—121no—
283#67—121no—
284#67—121no—
285C2×Dic3—22no—
286C2×Dic3—22no—
287C2×Dic3—41no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—121no—
295C2×Dic3—121no—
296C2×Dic3—121no—
297C2×Dic3—122no—
298C2×Dic3—122no—
299C2×Dic3—124no—
300D12—62no—
301D12—61no—
302D12—61no—
303D12—61no—
304D12—61no—
305D12—121no—
306C4×D3—122no—
307C4×D3—122no—
308C4×D3—121no—
309C4×D3—121no—
310C4×D3—121no—
311C4×D3—121no—
312Dic6—62no—
313Dic6—61no—
314Dic6—61no—
315Dic6—61no—
316Dic6—61no—
317Dic6—121no—
318Dic6—124no—
319Dic6—124no—
320C3×C8—42no—
321C3×C8—41no—
322C3×C8—41no—
323C3×C8—121no—
324C3⋊C8—41no—
325C2×C32—21no—
326C2×C32—21no—
327C2×C32—21no—
328C2×C32#39311yescharacteristic
329C3⋊D3—81no—
330#41—181no—
331#41—181no—
332#41—181no—
333#41—181no—
334C2×Q8—91no—
335C2×Q8—182no—
336C2×D4—91no—
337C2×D4—181no—
338C22×C4—181no—
339C22×C4—181no—
340C22×C4C2×D3211yescharacteristic
341M16—21no—
342M16—21no—
343M16—61no—
344M16—61no—
345C2×C8—21no—
346C2×C8—61no—
347C4⋊C4—61no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—182no—
351C4⋊C4—182no—
352C4⋊C4—182no—
353C22⋊C4—32no—
354C22⋊C4—61no—
355C22⋊C4—61no—
356C42—32no—
357C42—61no—
358C42—61no—
359C42—91no—
360C42—91no—
361C42—181no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—42no—
368C22×C3#87511yescharacteristic
369C22×C3#88211yescharacteristic
370C22×C3#88211yescharacteristic
371C22×C3#88511yescharacteristic
372C22×C3#89611yescharacteristic
373C22×C3#89711yescharacteristic
374C2×D3—122no—
375C2×D3—121no—
376C2×D3—121no—
377C2×D3—242no—
378C2×D3—241no—
379C2×D3—241no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—122no—
385C3×C4—122no—
386C3×C4—241no—
387C3×C4#87511yescharacteristic
388C3×C4#88511yescharacteristic
389C3×C4#88511yescharacteristic
390C3×C4#88511yescharacteristic
391C3×C4#89611yescharacteristic
392C3×C4#89611yescharacteristic
393C3×C4#89611yescharacteristic
394C3×C4#89711yescharacteristic
395Dic3—42no—
396Dic3—42no—
397Dic3—62no—
398Dic3—62no—
399Dic3—81no—
400Dic3—122no—
401Dic3—122no—
402Dic3—121no—
403Dic3—121no—
404Dic3—122no—
405Dic3—121no—
406Dic3—121no—
407C32#203111yescharacteristic, complemented, Sylow
408C23—181no—
409C23D3×D1211yescharacteristic
410Q8—181no—
411Q8—181no—
412Q8—364no—
413D4—181no—
414D4—181no—
415D4—361no—
416D4—361no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—121no—
420C2×C4—181no—
421C2×C4—181no—
422C2×C4—181no—
423C2×C4—362no—
424C2×C4—361no—
425C2×C4—361no—
426C2×C4#379711yescharacteristic
427C2×C4#379811yescharacteristic
428C2×C4D3×D1211yescharacteristic
429C2×C4#380411yescharacteristic
430C2×C4#380411yescharacteristic
431C2×C4#381111yescharacteristic
432C8—41no—
433C8—121no—
434C2×C3—22no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—41no—
443C2×C3—41no—
444C2×C3#467311yescharacteristic
445C2×C3#467311yescharacteristic
446D3—242no—
447D3—241no—
448D3—241no—
449C22—41no—
450C22—361no—
451C22—721no—
452C22#6385211yescharacteristic
453C22#6389511yescharacteristic
454C22#6392311yescharacteristic
455C4—122no—
456C4—122no—
457C4—182no—
458C4—241no—
459C4—361no—
460C4—361no—
461C4#6385211yescharacteristic
462C4#6386511yescharacteristic
463C4#6389511yescharacteristic
464C4#6395311yescharacteristic
465C3—21no—
466C3#6871411yescharacteristic, complemented
467C3#6904211yescharacteristic, complemented
468C2—21no—
469C2—21no—
470C2—21no—
471C2—721no—
472C2#1059120511yescharacteristic
subgroupG/H
centerC4#63852
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#393
prime radicalC2×#3828C22
hypercenterC2×M16D32
hypocenterC32#2031
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10595050C2semidirect
5. C3×#4559C2semidirect
6. C3×#4557C2semidirect
7. #10589160C2semidirect
36. #4559D3semidirect
37. #4557D3semidirect
47. C2×C4⋊(C3⋊D3)Q8semidirect
49. C2×#634Q8semidirect
407. C32#2031semidirect
466. C3#68714semidirect
467. C3#69042semidirect

Maximal subgroups

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

subgroupindex
#105950502
C2×#636522
#105912322
#105911132
C3×#45592
C3×#45572
#105891602
#690423
#687143