Finite Group Databasebeta

← #11789716

Subgroups — #11789716

Order 1152.

517 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63632C211yesmaximal, characteristic
2C3×C4×#208C211yesmaximal, characteristic, complemented
3#10591141C211yesmaximal, characteristic, complemented
4#10591113C211yesmaximal, characteristic
5#10591078C211yesmaximal, characteristic
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#69874—31nomaximal
9#68750—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63632—21no—
18#63632—21no—
19C3×#803—21no—
20C3×C4×C3⋊C8—21no—
21#63577—22no—
22#63570—22no—
23#63561C412yescomplemented
24#63559C412yescomplemented
25C3×C4×M16—31no—
26#5139—31no—
27#5132—31no—
28#5132—31no—
29#5125—31no—
30#5124—31no—
31#5005—31no—
32C2×#805—31no—
33C2×#805—31no—
34C2×#805—61no—
35C4×#208D311yescharacteristic, complemented
36C3×#339—31no—
37#4559—31no—
38#4533—31no—
39#4523D311yescharacteristic, complemented
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C2×#638—21no—
43#3828—21no—
44#3828—21no—
45#3828—21no—
46#3828—21no—
47C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
48C2×C4×C3⋊D3—21no—
49C2×#634C2×C411yescharacteristic
50C32×C42—21no—
51C32×C42D411yescharacteristic
52C32×C42D411yescharacteristic
53#3748—21no—
54#3748—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4×Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208C2×C412yes—
63C3×#208C2×C412yes—
64C3×#208D412yes—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1932—91noSylow
69C2×#235—31no—
70C2×#235—31no—
71C2×#235—61no—
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C2×C3×M16—31no—
75C3×#117—31no—
76C2×C3×C42—21no—
77C2×C3×C42C2×D311yescharacteristic
78C2×C3×C42C2×D311yescharacteristic
79#926C2×D311yescharacteristic
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C3×#97—61no—
87C3×C4×C8—61no—
88#825—62no—
89#824—32no—
90#824—32no—
91#823—32no—
92#823—32no—
93#822—62no—
94#819—62no—
95#805—62no—
96#805—62no—
97#805—61no—
98#805—61no—
99#805—61no—
100#805—61no—
101#805—62no—
102#803—21no—
103C4×C3⋊C8—21no—
104C23×C32#4111yescharacteristic
105C22×C3⋊D3—21no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4—42no—
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115#638—41no—
116#638—41no—
117C2×C3⋊Dic3—21no—
118C4⋊(C3⋊D3)—21no—
119C4⋊(C3⋊D3)—21no—
120C4×C3⋊D3—41no—
121C4×C3⋊D3—41no—
122#634—21no—
123#634—21no—
124C2×C3×Dic3—41no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—22no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—22no—
129#430—91no—
130#421—91no—
131C2×#104—91no—
132#413—91no—
133C4×M16—31no—
134#344—91no—
135#339—31no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—41no—
140C22×C3×C4C22×D311yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C2×#67—61no—
143C2×#67—61no—
144C2×#67—121no—
145#235—62no—
146#235—62no—
147#235—61no—
148#235—61no—
149#235—61no—
150#235—61no—
151#235—61no—
152#235—61no—
153#235—61no—
154#235—61no—
155#235—121no—
156#235—121no—
157C2×D12—31no—
158C2×D12—31no—
159C2×D12—61no—
160C2×C4×D3—61no—
161C2×C4×D3—61no—
162C2×C4×D3—121no—
163C2×Dic6—31no—
164C2×Dic6—31no—
165C2×Dic6—61no—
166C3×M16—32no—
167C3×M16—32no—
168C3×M16—32no—
169C3×M16—61no—
170C3×M16—61no—
171C3×M16—61no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C3×C4⋊C4—61no—
176C3×C22⋊C4—61no—
177C3×C42—21no—
178C3×C42—21no—
179C3×C42—21no—
180C3×C42—21no—
181C3×C42—41no—
182C3×C42—61no—
183C3×C42D1211yescharacteristic
184C3×C42D1211yescharacteristic
185C3×C42#6711yescharacteristic
186C3×C42#6711yescharacteristic
187#217—21no—
188C4⋊Dic3—21no—
189C4×Dic3—21no—
190#208—21no—
191#208—21no—
192#208—21no—
193#208—62no—
194#208—61no—
195#208—61no—
196#208—61no—
197#208—61no—
198#208—121no—
199#208C4×D312yes—
200#208C4×D312yes—
201#208D1212yes—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—121no—
208C22×C32—41no—
209C22×C32#11711yescharacteristic
210C22×C32#12311yescharacteristic
211C22×C32#12411yescharacteristic
212C2×C3⋊D3—41no—
213C2×C3⋊D3—81no—
214C32×C4—22no—
215C32×C4—41no—
216C32×C4C4×D411yescharacteristic
217C32×C4C4×D411yescharacteristic
218C32×C4#12111yescharacteristic
219C32×C4#12611yescharacteristic
220C3⋊Dic3—41no—
221C3×Dic3—81no—
222C2×#41—91no—
223C2×M16—31no—
224C2×M16—31no—
225C2×M16—31no—
226C2×M16—91no—
227#117—31no—
228C2×C42D3211yescharacteristic
229#108—182no—
230#104—182no—
231#104—181no—
232#104—181no—
233#101—92no—
234#100—92no—
235#97—61no—
236C4×C8—61no—
237C23×C3—21no—
238C23×C3#23511yescharacteristic
239C23×C3#23711yescharacteristic
240C22×D3—61no—
241C22×D3—61no—
242C22×D3—121no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—42no—
256C2×C3×C4—42no—
257C2×C3×C4—44no—
258C2×C3×C4—121no—
259C2×C3×C4C2×C4×D311yescharacteristic
260C2×C3×C4C2×C4×D311yescharacteristic
261C2×C3×C4C2×D1211yescharacteristic
262C2×C3×C4C2×D1211yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4#23511yescharacteristic
265C2×C3×C4#23511yescharacteristic
266C2×C3×C4#23511yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4#23711yescharacteristic
269C2×C3×C4#23911yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271#67—122no—
272#67—122no—
273#67—121no—
274#67—121no—
275#67—121no—
276#67—121no—
277C2×Dic3—41no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—121no—
281D12—62no—
282D12—61no—
283D12—61no—
284D12—61no—
285D12—61no—
286D12—121no—
287C4×D3—122no—
288C4×D3—122no—
289C4×D3—121no—
290C4×D3—121no—
291C4×D3—121no—
292C4×D3—121no—
293Dic6—62no—
294Dic6—61no—
295Dic6—61no—
296Dic6—61no—
297Dic6—61no—
298Dic6—121no—
299C3×C8—62no—
300C3×C8—62no—
301C3×C8—62no—
302C3⋊C8—22no—
303C3⋊C8—22no—
304C3⋊C8—22no—
305C3⋊C8—122no—
306C3⋊C8—121no—
307C3⋊C8—121no—
308C2×C32—21no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32#38811yescharacteristic
312C3⋊D3—81no—
313#41—181no—
314#41—181no—
315#41—181no—
316#41—181no—
317C2×Q8—91no—
318C2×D4—91no—
319C2×D4—181no—
320C22×C4—21no—
321C22×C4—181no—
322C22×C4C2×D3211yescharacteristic
323M16—32no—
324M16—32no—
325M16—32no—
326M16—61no—
327M16—61no—
328M16—61no—
329M16—181no—
330M16—181no—
331C2×C8—61no—
332C2×C8—61no—
333C2×C8—61no—
334C2×C8—181no—
335C4⋊C4—61no—
336C22⋊C4—61no—
337C42—21no—
338C42—61no—
339C42#62611yescharacteristic
340C42#62611yescharacteristic
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—42no—
347C22×C3#87211yescharacteristic
348C22×C3#87511yescharacteristic
349C22×C3#88511yescharacteristic
350C22×C3#88611yescharacteristic
351C22×C3#89211yescharacteristic
352C22×C3#92911yescharacteristic
353C2×D3—122no—
354C2×D3—121no—
355C2×D3—121no—
356C2×D3—242no—
357C2×D3—241no—
358C2×D3—241no—
359C3×C4—22no—
360C3×C4—22no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—42no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—42no—
369C3×C4—241no—
370C3×C4C4×D1211yescharacteristic
371C3×C4C4×D1211yescharacteristic
372C3×C4#87611yescharacteristic
373C3×C4#67⋊C411yescharacteristic
374C3×C4#89511yescharacteristic
375C3×C4#89811yescharacteristic
376C3×C4C4×#6711yescharacteristic
377C3×C4#93011yescharacteristic
378Dic3—81no—
379Dic3—122no—
380Dic3—121no—
381Dic3—121no—
382C32#193211yescharacteristic, complemented, Sylow
383C23—181no—
384C23#380411yescharacteristic
385Q8—181no—
386Q8—181no—
387D4—181no—
388D4—181no—
389D4—361no—
390D4—361no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—42no—
394C2×C4—121no—
395C2×C4—181no—
396C2×C4—361no—
397C2×C4—361no—
398C2×C4#379811yescharacteristic
399C2×C4#379911yescharacteristic
400C2×C4C4×D3211yescharacteristic
401C2×C4D3×D1211yescharacteristic
402C2×C4#380411yescharacteristic
403C2×C4C2×#62611yescharacteristic
404C8—62no—
405C8—62no—
406C8—62no—
407C8—361no—
408C2×C3—22no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—41no—
417C2×C3—41no—
418C2×C3#467011yescharacteristic
419C2×C3#494011yescharacteristic
420D3—242no—
421D3—241no—
422D3—241no—
423C22—41no—
424C22—361no—
425C22—721no—
426C22#6383611yescharacteristic
427C22#6385211yescharacteristic
428C22#6396611yescharacteristic
429C4—22no—
430C4—41no—
431C4—241no—
432C4—361no—
433C4#6386811yescharacteristic
434C4#6388011yescharacteristic
435C4C4×#62611yescharacteristic
436C4#6390911yescharacteristic
437C3—21no—
438C3#6875011yescharacteristic, complemented
439C3#6987411yescharacteristic, complemented
440C2—21no—
441C2—21no—
442C2—21no—
443C2—721no—
444C2#1059119411yescharacteristic
subgroupG/H
centerC4#63909
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC2×C32#388
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1932
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×#208C2semidirect
3. #10591141C2semidirect
6. C3×#4523C2semidirect
7. #10589170C2semidirect
23. #63561C4semidirect
24. #63559C4semidirect
35. C4×#208D3semidirect
39. #4523D3semidirect
382. C32#1932semidirect
438. C3#68750semidirect
439. C3#69874semidirect

Maximal subgroups

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

subgroupindex
C2×#636322
C3×C4×#2082
#105911412
#105911132
#105910782
C3×#45232
#105891702
#698743
#687503