Finite Group Databasebeta

← #11794356

Subgroups — #11794356

Order 1152.

551 conjugacy classes of subgroups.

The subgroup lattice has 455 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592700C211yesmaximal, characteristic
2C3×#4999C211yesmaximal, characteristic, complemented
3C3×#4995C211yesmaximal, characteristic, complemented
4C2×#63577C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic
6C2×#63559C211yesmaximal, characteristic
7#10589167C211yesmaximal, characteristic, complemented
8#70676—31nomaximal
9#70542—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63636—21no—
18#63636—21no—
19C3×#808—21no—
20C3×#807—21no—
21C3×C4⋊(C3⋊C8)—22no—
22#63577—22no—
23#63564—22no—
24#63559—22no—
25C3×#428—31no—
26C3×#424—31no—
27C2×#823—31no—
28C2×#823—31no—
29C2×#822—31no—
30C2×#821—31no—
31C2×#819—31no—
32#5001—31no—
33#5001—31no—
34#5001—61no—
35#4999D311yescharacteristic, complemented
36#4995D311yescharacteristic, complemented
37C2×#809—31no—
38#4554—31no—
39#4530—31no—
40C23×C3⋊D3—21no—
41C22×C32×C4C2311yescharacteristic
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)Q812yes—
48C22×C3×Dic3—21no—
49C32×C4⋊C4D411yescharacteristic
50C32×C4⋊C4D411yescharacteristic
51C32×C22⋊C4—21no—
52C32×C42—21no—
53#3748—21no—
54#3748—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208D412yes—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8D412yes—
67#2063—91noSylow
68C22×D12—31no—
69C22×D12—31no—
70C22×D12—61no—
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C22×C3×C8—31no—
74C3×#117—21no—
75C3×#117C2×D311yescharacteristic
76C3×#117C2×D311yescharacteristic
77C2×C3×C4⋊C4—31no—
78C2×C4⋊Dic3C2×D311yescharacteristic
79C2×#208—31no—
80C2×#208—31no—
81C2×#208—61no—
82C2×#208C2×D311yescharacteristic
83C2×#208C2×D311yescharacteristic
84C22×C3⋊C8C2×D311yescharacteristic
85C3×#107—61no—
86C3×#106—61no—
87C3×C4⋊C8—62no—
88#823—62no—
89#823—62no—
90#822—62no—
91#821—62no—
92#819—62no—
93#809—62no—
94#809—62no—
95#809—61no—
96#809—61no—
97#809—61no—
98#809—61no—
99#809—62no—
100#808—21no—
101#807—21no—
102C4⋊(C3⋊C8)—22no—
103C23×C32#4111yescharacteristic
104C22×C3⋊D3—22no—
105C22×C3⋊D3—41no—
106C22×C3⋊D3—41no—
107C22×C3⋊D3—81no—
108C22×C3⋊D3—81no—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×Q811yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C4⋊(C3⋊D3)—22no—
118C4⋊(C3⋊D3)—22no—
119C4⋊(C3⋊D3)—41no—
120C4⋊(C3⋊D3)—41no—
121C2×C3×Dic3—41no—
122C2×C3×Dic3—81no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127C2×#108—91no—
128#428—31no—
129#424—31no—
130#418—91no—
131C2×#102—91no—
132C2×#100—91no—
133#343—91no—
134C23×D3—61no—
135C23×D3—61no—
136C23×D3—121no—
137C22×C3×C4—21no—
138C22×C3×C4—61no—
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C22×D311yescharacteristic
141C22×Dic3—21no—
142C2×D12—32no—
143C2×D12—32no—
144C2×D12—62no—
145C2×D12—62no—
146C2×D12—62no—
147C2×D12—61no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—121no—
158C2×D12—121no—
159C2×D12—121no—
160C3×M16—32no—
161C3×M16—61no—
162C3×M16—61no—
163C3×M16—61no—
164C2×C3×C8—32no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4D1211yescharacteristic
174C3×C4⋊C4D1211yescharacteristic
175C3×C4⋊C4#6711yescharacteristic
176C3×C4⋊C4#6711yescharacteristic
177C3×C22⋊C4—21no—
178C3×C22⋊C4—21no—
179C3×C22⋊C4—41no—
180C3×C42—21no—
181C3×C42—21no—
182C3×C42—41no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185#208—21no—
186#208—21no—
187#208—21no—
188#208—61no—
189#208—61no—
190#208—61no—
191#208—61no—
192#208—121no—
193#208—121no—
194#208D1212yes—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—62no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8#6712yes—
203C22×C32—21no—
204C22×C32—21no—
205C22×C32#12111yescharacteristic
206C22×C32C22⋊Q811yescharacteristic
207C22×C32#12611yescharacteristic
208C2×C3⋊D3—42no—
209C2×C3⋊D3—82no—
210C2×C3⋊D3—81no—
211C2×C3⋊D3—81no—
212C2×C3⋊D3—82no—
213C32×C4—41no—
214C32×C4—41no—
215C32×C4#12111yescharacteristic
216C32×C4#12111yescharacteristic
217C32×C4C22⋊Q811yescharacteristic
218C32×C4C22⋊Q811yescharacteristic
219C3×Dic3—81no—
220C22×D4—91no—
221C2×M16—31no—
222C2×M16—31no—
223C2×M16—91no—
224C22×C8—31no—
225#117D3211yescharacteristic
226C2×C4⋊C4—31no—
227#108—182no—
228#107—61no—
229#106—61no—
230C4⋊C8—62no—
231#102—182no—
232#102—181no—
233#102—181no—
234#100—182no—
235C23×C3—21no—
236C23×C3#23511yescharacteristic
237C23×C3#23711yescharacteristic
238C22×D3—62no—
239C22×D3—62no—
240C22×D3—122no—
241C22×D3—122no—
242C22×D3—122no—
243C22×D3—121no—
244C22×D3—121no—
245C22×D3—121no—
246C22×D3—121no—
247C22×D3—242no—
248C22×D3—242no—
249C22×D3—241no—
250C22×D3—241no—
251C22×D3—241no—
252C22×D3—241no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—121no—
266C2×C3×C4—241no—
267C2×C3×C4C2×D1211yescharacteristic
268C2×C3×C4C2×D1211yescharacteristic
269C2×C3×C4#23511yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4#23711yescharacteristic
273C2×C3×C4D3×Q811yescharacteristic
274C2×C3×C4D3×Q811yescharacteristic
275C2×C3×C4#23911yescharacteristic
276C2×C3×C4#23911yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279C2×Dic3—41no—
280C2×Dic3—81no—
281D12—64no—
282D12—62no—
283D12—62no—
284D12—62no—
285D12—62no—
286D12—122no—
287D12—122no—
288D12—122no—
289D12—121no—
290D12—121no—
291D12—121no—
292D12—121no—
293C3×C8—62no—
294C3×C8—62no—
295C3×C8—121no—
296C3⋊C8—22no—
297C3⋊C8—22no—
298C3⋊C8—41no—
299C3⋊C8—122no—
300C3⋊C8—121no—
301C3⋊C8—121no—
302C2×C32—21no—
303C2×C32—21no—
304C2×C32#39611yescharacteristic
305C2×C32#47111yescharacteristic
306C2×C32#47211yescharacteristic
307C3⋊D3—82no—
308C24—181no—
309C2×D4—92no—
310C2×D4—181no—
311C2×D4—181no—
312C2×D4—181no—
313C2×D4—181no—
314C2×D4—181no—
315C22×C4—61no—
316C22×C4C2×D3211yescharacteristic
317M16—32no—
318M16—61no—
319M16—61no—
320M16—61no—
321M16—181no—
322M16—181no—
323C2×C8—32no—
324C2×C8—61no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—181no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4#62611yescharacteristic
332C4⋊C4#62611yescharacteristic
333C22⋊C4—21no—
334C42—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3#89611yescharacteristic
345C22×C3#89711yescharacteristic
346C22×C3#89811yescharacteristic
347C22×C3#89811yescharacteristic
348C22×C3#93011yescharacteristic
349C22×C3#93911yescharacteristic
350C2×D3—124no—
351C2×D3—122no—
352C2×D3—122no—
353C2×D3—242no—
354C2×D3—242no—
355C2×D3—242no—
356C2×D3—242no—
357C2×D3—244no—
358C2×D3—244no—
359C2×D3—241no—
360C2×D3—241no—
361C2×D3—241no—
362C2×D3—241no—
363C2×D3—242no—
364C2×D3—242no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—41no—
370C3×C4—41no—
371C3×C4—41no—
372C3×C4—41no—
373C3×C4—81no—
374C3×C4—81no—
375C3×C4—241no—
376C3×C4#89511yescharacteristic
377C3×C4#89511yescharacteristic
378C3×C4#89611yescharacteristic
379C3×C4#89711yescharacteristic
380C3×C4#93011yescharacteristic
381C3×C4#93911yescharacteristic
382C3×C4#94611yescharacteristic
383C3×C4#94611yescharacteristic
384Dic3—81no—
385C32#206311yescharacteristic, complemented, Sylow
386C23—182no—
387C23—361no—
388C23—361no—
389C23—721no—
390C23—721no—
391C23#380411yescharacteristic
392D4—182no—
393D4—182no—
394D4—361no—
395D4—361no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—121no—
399C2×C4—241no—
400C2×C4#379611yescharacteristic
401C2×C4#379711yescharacteristic
402C2×C4#379911yescharacteristic
403C2×C4D3×D1211yescharacteristic
404C2×C4C2×#62611yescharacteristic
405C2×C4D3×#6711yescharacteristic
406C8—62no—
407C8—62no—
408C8—121no—
409C8—361no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3#499411yescharacteristic
420C2×C3#499411yescharacteristic
421C2×C3#514111yescharacteristic
422C2×C3#514211yescharacteristic
423C2×C3#519911yescharacteristic
424C2×C3#520311yescharacteristic
425D3—244no—
426D3—242no—
427D3—242no—
428C22—21no—
429C22—21no—
430C22—362no—
431C22—722no—
432C22—722no—
433C22—721no—
434C22—721no—
435C22#6384811yescharacteristic
436C22#6389511yescharacteristic
437C22#6397811yescharacteristic
438C4—41no—
439C4—41no—
440C4—241no—
441C4#6387111yescharacteristic
442C4#6388611yescharacteristic
443C4#6388811yescharacteristic
444C4#6390911yescharacteristic
445C3—21no—
446C3#7054211yescharacteristic, complemented
447C3#7067611yescharacteristic, complemented
448C2—21no—
449C2—21no—
450C2—722no—
451C2#1059131111yescharacteristic
452C2#1059167711yescharacteristic
453C2#1059168011yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#121
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#117D32
hypocenterC32#2063
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#4999C2semidirect
3. C3×#4995C2semidirect
4. C2×#63577C2semidirect
7. #10589167C2semidirect
35. #4999D3semidirect
36. #4995D3semidirect
385. C32#2063semidirect
446. C3#70542semidirect
447. C3#70676semidirect

Maximal subgroups

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

subgroupindex
#105927002
C3×#49992
C3×#49952
C2×#635772
C2×#635642
C2×#635592
#105891672
#706763
#705423