Finite Group Databasebeta

← #11789727

Subgroups — #11789727

Order 1152.

509 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592704C211yesmaximal, characteristic
2#10591141C211yesmaximal, characteristic, complemented
3C2×#63570C211yesmaximal, characteristic
4#10591078C211yesmaximal, characteristic
5Dic3×#208C211yesmaximal, characteristic, complemented
6C3×#4533C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8#69012—31nomaximal
9#68750—31nomaximal
10C2×#3828C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63632—22no—
18#63577—22no—
19#63570—21no—
20#63570—21no—
21#63561C412yescomplemented
22#63559C412yescomplemented
23#63554—21no—
24Dic3×C3⋊C8—21no—
25C2×#825—31no—
26#5132—31no—
27#5132—31no—
28#5125—31no—
29#5124—31no—
30Dic3×M16—31no—
31#5005—31no—
32#5005—31no—
33#5005—61no—
34C2×#805—31no—
35C4×#208—31no—
36C3×#344—31no—
37C3×#339—31no—
38#4533D311yescharacteristic, complemented
39#4532D311yescharacteristic, complemented
40C22×C32×C4C2311yescharacteristic
41C2×#638—21no—
42#3828—21no—
43#3828—21no—
44#3828—21no—
45#3828—21no—
46C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
47C2×C4×C3⋊D3—21no—
48C2×#634C2×C411yescharacteristic
49C22×C3×Dic3—21no—
50C32×C4⋊C4—21no—
51C32×C22⋊C4—21no—
52C32×C42—21no—
53#3748—21no—
54#3748D412yes—
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4×Dic3—21no—
57C3×C4×Dic3D411yescharacteristic
58C3×C4×Dic3D411yescharacteristic
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208C2×C412yes—
64C3×#208C2×C412yes—
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—21no—
76C3×#117C2×D311yescharacteristic
77C3×#117C2×D311yescharacteristic
78C2×C3×C42—31no—
79C2×C4×Dic3C2×D311yescharacteristic
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86#825—61no—
87#825—61no—
88#824—32no—
89#824—32no—
90#823—32no—
91#823—32no—
92#822—62no—
93#819—62no—
94#815—61no—
95C8×Dic3—61no—
96#805—61no—
97#805—61no—
98#805—62no—
99#805—62no—
100#805—64no—
101#803—61no—
102C4×C3⋊C8—61no—
103C23×C32#4111yescharacteristic
104C22×C3⋊D3—21no—
105C2×C32×C4—41no—
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112#638—41no—
113#638—41no—
114C2×C3⋊Dic3—21no—
115C4⋊(C3⋊D3)—21no—
116C4⋊(C3⋊D3)—21no—
117C4×C3⋊D3—41no—
118C4×C3⋊D3—41no—
119#634—21no—
120#634—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—42no—
124C3⋊(C3⋊C8)—22no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—22no—
127C3×C3⋊C8—41no—
128#430—91no—
129#421—91no—
130C2×#104—91no—
131#413—91no—
132C4×M16—91no—
133#344—31no—
134#339—31no—
135C22×C3×C4—21no—
136C22×C3×C4—61no—
137C22×C3×C4C22×D311yescharacteristic
138C22×C3×C4C22×D311yescharacteristic
139C2×#67—61no—
140C2×#67—61no—
141C2×#67—121no—
142C22×Dic3—21no—
143#235—62no—
144#235—62no—
145#235—61no—
146#235—61no—
147#235—61no—
148#235—61no—
149#235—61no—
150#235—61no—
151#235—61no—
152#235—61no—
153#235—121no—
154#235—121no—
155C2×D12—31no—
156C2×D12—31no—
157C2×D12—61no—
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×C4×D3—121no—
161C2×Dic6—31no—
162C2×Dic6—31no—
163C2×Dic6—61no—
164C3×M16—32no—
165C3×M16—32no—
166C3×M16—61no—
167C3×M16—61no—
168C3×M16—61no—
169C3×M16—61no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—41no—
176C3×C22⋊C4—21no—
177C3×C22⋊C4—21no—
178C3×C22⋊C4—41no—
179C3×C42—22no—
180C3×C42—21no—
181C3×C42—21no—
182C3×C42—31no—
183C3×C42—31no—
184C3×C42—61no—
185C4×Dic3—21no—
186C4×Dic3D1211yescharacteristic
187C4×Dic3D1211yescharacteristic
188#208—21no—
189#208—21no—
190#208—21no—
191#208—21no—
192#208—32no—
193#208—32no—
194#208—62no—
195#208—61no—
196#208—61no—
197#208—121no—
198#208C4×D312yes—
199#208C4×D312yes—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—121no—
206C22×C32—41no—
207C22×C32#11711yescharacteristic
208C22×C32#12311yescharacteristic
209C22×C32#12411yescharacteristic
210C2×C3⋊D3—41no—
211C2×C3⋊D3—81no—
212C32×C4—81no—
213C32×C4C4×D411yescharacteristic
214C32×C4C4×D411yescharacteristic
215C32×C4#12111yescharacteristic
216C32×C4#12611yescharacteristic
217C3⋊Dic3—41no—
218C3×Dic3—22no—
219C3×Dic3—41no—
220C2×#41—91no—
221C2×M16—31no—
222C2×M16—31no—
223C2×M16—31no—
224C2×M16—91no—
225#117D3211yescharacteristic
226C2×C42—31no—
227#108—182no—
228#104—182no—
229#104—181no—
230#104—181no—
231#101—92no—
232#100—92no—
233#97—181no—
234C4×C8—181no—
235C23×C3—21no—
236C23×C3#23511yescharacteristic
237C23×C3#23711yescharacteristic
238C22×D3—61no—
239C22×D3—61no—
240C22×D3—121no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—42no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—61no—
251C2×C3×C4—61no—
252C2×C3×C4—122no—
253C2×C3×C4C2×C4×D311yescharacteristic
254C2×C3×C4C2×C4×D311yescharacteristic
255C2×C3×C4C2×D1211yescharacteristic
256C2×C3×C4#23511yescharacteristic
257C2×C3×C4#23511yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4#23711yescharacteristic
262C2×C3×C4#23711yescharacteristic
263C2×C3×C4#23911yescharacteristic
264C2×C3×C4#23911yescharacteristic
265#67—122no—
266#67—122no—
267#67—121no—
268#67—121no—
269#67—121no—
270#67—121no—
271C2×Dic3—21no—
272C2×Dic3—21no—
273C2×Dic3—42no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—121no—
277D12—62no—
278D12—61no—
279D12—61no—
280D12—61no—
281D12—61no—
282D12—121no—
283C4×D3—122no—
284C4×D3—122no—
285C4×D3—121no—
286C4×D3—121no—
287C4×D3—121no—
288C4×D3—121no—
289Dic6—62no—
290Dic6—61no—
291Dic6—61no—
292Dic6—61no—
293Dic6—61no—
294Dic6—121no—
295C3×C8—62no—
296C3×C8—62no—
297C3×C8—121no—
298C3⋊C8—22no—
299C3⋊C8—22no—
300C3⋊C8—41no—
301C3⋊C8—62no—
302C3⋊C8—62no—
303C3⋊C8—122no—
304C2×C32—21no—
305C2×C32—21no—
306C2×C32—21no—
307C2×C32#38811yescharacteristic
308C3⋊D3—81no—
309#41—181no—
310#41—181no—
311#41—181no—
312#41—181no—
313C2×Q8—91no—
314C2×D4—91no—
315C2×D4—181no—
316C22×C4—61no—
317C22×C4—181no—
318C22×C4C2×D3211yescharacteristic
319M16—32no—
320M16—32no—
321M16—61no—
322M16—61no—
323M16—61no—
324M16—61no—
325M16—92no—
326M16—181no—
327C2×C8—61no—
328C2×C8—61no—
329C2×C8—61no—
330C2×C8—181no—
331C4⋊C4—21no—
332C22⋊C4—21no—
333C42—21no—
334C42—31no—
335C42—31no—
336C42—61no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—81no—
343C22×C3#87211yescharacteristic
344C22×C3#88511yescharacteristic
345C22×C3#88511yescharacteristic
346C22×C3#88611yescharacteristic
347C22×C3#89211yescharacteristic
348C22×C3#89411yescharacteristic
349C2×D3—122no—
350C2×D3—121no—
351C2×D3—121no—
352C2×D3—242no—
353C2×D3—241no—
354C2×D3—241no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—62no—
360C3×C4—81no—
361C3×C4—81no—
362C3×C4—82no—
363C3×C4—121no—
364C3×C4C4×D1211yescharacteristic
365C3×C4#67⋊C411yescharacteristic
366C3×C4#67⋊C411yescharacteristic
367C3×C4#88411yescharacteristic
368C3×C4#89311yescharacteristic
369C3×C4#89511yescharacteristic
370C3×C4#89811yescharacteristic
371C3×C4#89811yescharacteristic
372Dic3—22no—
373Dic3—41no—
374Dic3—122no—
375Dic3—121no—
376Dic3—121no—
377C32#193211yescharacteristic, complemented, Sylow
378C23—181no—
379C23#380411yescharacteristic
380Q8—181no—
381Q8—181no—
382D4—181no—
383D4—181no—
384D4—361no—
385D4—361no—
386C2×C4—41no—
387C2×C4—61no—
388C2×C4—61no—
389C2×C4—122no—
390C2×C4—181no—
391C2×C4—361no—
392C2×C4—361no—
393C2×C4#379611yescharacteristic
394C2×C4#379911yescharacteristic
395C2×C4C4×D3211yescharacteristic
396C2×C4D3×D1211yescharacteristic
397C2×C4#380411yescharacteristic
398C2×C4#381111yescharacteristic
399C8—62no—
400C8—62no—
401C8—121no—
402C8—182no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—41no—
411C2×C3—41no—
412C2×C3—41no—
413C2×C3#466911yescharacteristic
414C2×C3#467011yescharacteristic
415D3—242no—
416D3—241no—
417D3—241no—
418C22—41no—
419C22—361no—
420C22—721no—
421C22#6383611yescharacteristic
422C22#6389011yescharacteristic
423C22#6395311yescharacteristic
424C4—62no—
425C4—81no—
426C4—121no—
427C4—361no—
428C4#6384811yescharacteristic
429C4#6388011yescharacteristic
430C4#6388111yescharacteristic
431C4#6391011yescharacteristic
432C3—21no—
433C3#6875011yescharacteristic, complemented
434C3#6901211yescharacteristic, complemented
435C2—21no—
436C2—21no—
437C2—21no—
438C2—721no—
439C2#1059125911yescharacteristic
subgroupG/H
centerC4#63910
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#388
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1932
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10591141C2semidirect
5. Dic3×#208C2semidirect
6. C3×#4533C2semidirect
7. C3×#4532C2semidirect
21. #63561C4semidirect
22. #63559C4semidirect
38. #4533D3semidirect
39. #4532D3semidirect
377. C32#1932semidirect
433. C3#68750semidirect
434. C3#69012semidirect

Maximal subgroups

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

subgroupindex
#105927042
#105911412
C2×#635702
#105910782
Dic3×#2082
C3×#45332
C3×#45322
#690123
#687503