Finite Group Databasebeta

← #11794341

Subgroups — #11794341

Order 1152.

557 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63648C211yesmaximal, characteristic
2C2×C3×#819C211yesmaximal, characteristic, complemented
3C3×#5102C211yesmaximal, characteristic, complemented
4#10591131C211yesmaximal, characteristic, complemented
5#10591096C211yesmaximal, characteristic
6C2×#63559C211yesmaximal, characteristic
7#10589168C211yesmaximal, characteristic, complemented
8#70715—31nomaximal
9#70542—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63648—22no—
18C3×#819—22no—
19C3×Dic3⋊C8—22no—
20#63575—21no—
21#63573—21no—
22#63564—21no—
23#63564—21no—
24#63559—22no—
25C2×C3×#108—31no—
26C3×#424—31no—
27#5131—31no—
28C2×#823—31no—
29C2×#823—31no—
30#5121—31no—
31C2×#821—31no—
32C2×#821—31no—
33C2×#821—61no—
34C2×#819D311yescharacteristic, complemented
35#5102D311yescharacteristic, complemented
36#5001—31no—
37#4995—31no—
38#4554—31no—
39#4554—31no—
40C23×C3⋊D3—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3—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)—21no—
48C2×C4⋊(C3⋊D3)Q812yes—
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C2×C32×C8D412yes—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C3×#217—21no—
55C3×C4⋊Dic3D411yescharacteristic
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4×Dic3—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208D412yes—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#2063—91noSylow
68C22×D12—31no—
69C22×D12—31no—
70C22×D12—61no—
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C22×C3×C8—21no—
75C22×C3×C8C2×D311yescharacteristic
76C22×C3×C8C2×D311yescharacteristic
77C3×#117—31no—
78#926C2×D311yescharacteristic
79C2×C4⋊Dic3—31no—
80C2×C4⋊Dic3—31no—
81C2×C4⋊Dic3—61no—
82C2×#208C2×D311yescharacteristic
83C2×#208C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C3×#108—62no—
86C3×C4⋊C8—62no—
87#823—62no—
88#823—62no—
89#821—64no—
90#821—62no—
91#821—62no—
92#821—61no—
93#821—61no—
94#819—22no—
95#818—61no—
96#817—61no—
97Dic3⋊C8—22no—
98#809—61no—
99#809—61no—
100#808—61no—
101#807—61no—
102C23×C32#4111yescharacteristic
103C22×C3⋊D3—22no—
104C22×C3⋊D3—41no—
105C22×C3⋊D3—41no—
106C22×C3⋊D3—81no—
107C22×C3⋊D3—81no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×Q811yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C3⋊Dic3—41no—
115C2×C3⋊Dic3—81no—
116C4⋊(C3⋊D3)—22no—
117C4⋊(C3⋊D3)—22no—
118C4⋊(C3⋊D3)—41no—
119C4⋊(C3⋊D3)—41no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C32×C8—22no—
123C3×C3⋊C8—22no—
124C3×C3⋊C8—41no—
125C3×C3⋊C8—41no—
126C2×#108—31no—
127#428—91no—
128#424—31no—
129#418—91no—
130C2×#102—91no—
131C2×#100—91no—
132#343—91no—
133C23×D3—61no—
134C23×D3—61no—
135C23×D3—121no—
136C22×C3×C4—21no—
137C22×C3×C4C22×D311yescharacteristic
138C22×C3×C4C22×D311yescharacteristic
139C22×Dic3—61no—
140C22×Dic3—61no—
141C22×Dic3—121no—
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—
164C3×M16—61no—
165C3×M16—61no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—22no—
171C2×C3×C8—41no—
172C2×C3×C8—41no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C2×C3×C8D1212yes—
177C2×C3×C8#6712yes—
178C3×C4⋊C4—31no—
179C3×C4⋊C4—31no—
180C3×C22⋊C4—61no—
181C3×C42—61no—
182#217—21no—
183C4⋊Dic3—62no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—121no—
189C4⋊Dic3D1211yescharacteristic
190C4⋊Dic3D1211yescharacteristic
191C4×Dic3—21no—
192#208—21no—
193#208—21no—
194#208—21no—
195#208—21no—
196#208—21no—
197#208#6712yes—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C22×C32—21no—
202C22×C32—21no—
203C22×C32#12111yescharacteristic
204C22×C32C22⋊Q811yescharacteristic
205C22×C32#12611yescharacteristic
206C2×C3⋊D3—42no—
207C2×C3⋊D3—82no—
208C2×C3⋊D3—81no—
209C2×C3⋊D3—81no—
210C2×C3⋊D3—82no—
211C32×C4#12111yescharacteristic
212C32×C4#12111yescharacteristic
213C32×C4C22⋊Q811yescharacteristic
214C32×C4C22⋊Q811yescharacteristic
215C3⋊Dic3—81no—
216C3×Dic3—41no—
217C3×Dic3—41no—
218C22×D4—91no—
219C2×M16—31no—
220C2×M16—31no—
221C2×M16—31no—
222C22×C8D3211yescharacteristic
223#117—31no—
224C2×C4⋊C4—91no—
225#108—62no—
226#107—181no—
227#106—181no—
228C4⋊C8—62no—
229#102—181no—
230#102—181no—
231#102—182no—
232#100—182no—
233C23×C3—21no—
234C23×C3#23511yescharacteristic
235C23×C3#23911yescharacteristic
236C22×D3—62no—
237C22×D3—62no—
238C22×D3—122no—
239C22×D3—122no—
240C22×D3—122no—
241C22×D3—121no—
242C22×D3—121no—
243C22×D3—121no—
244C22×D3—121no—
245C22×D3—242no—
246C22×D3—242no—
247C22×D3—241no—
248C22×D3—241no—
249C22×D3—241no—
250C22×D3—241no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4C2×D1211yescharacteristic
260C2×C3×C4C2×D1211yescharacteristic
261C2×C3×C4#23511yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4#23711yescharacteristic
265C2×C3×C4#23711yescharacteristic
266C2×C3×C4D3×Q811yescharacteristic
267C2×C3×C4D3×Q811yescharacteristic
268C2×C3×C4#23911yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×Dic3—21no—
272C2×Dic3—21no—
273C2×Dic3—122no—
274C2×Dic3—121no—
275C2×Dic3—121no—
276C2×Dic3—242no—
277C2×Dic3—241no—
278C2×Dic3—241no—
279D12—64no—
280D12—62no—
281D12—62no—
282D12—62no—
283D12—62no—
284D12—122no—
285D12—122no—
286D12—122no—
287D12—121no—
288D12—121no—
289D12—121no—
290D12—121no—
291C3×C8—22no—
292C3×C8—22no—
293C3×C8—42no—
294C3×C8—62no—
295C3×C8—121no—
296C3×C8—121no—
297C3⋊C8—22no—
298C3⋊C8—41no—
299C3⋊C8—41no—
300C2×C32—21no—
301C2×C32—21no—
302C2×C32#39611yescharacteristic
303C2×C32#47111yescharacteristic
304C2×C32#47211yescharacteristic
305C3⋊D3—82no—
306C24—181no—
307C2×D4—92no—
308C2×D4—181no—
309C2×D4—181no—
310C2×D4—181no—
311C2×D4—181no—
312C2×D4—181no—
313C22×C4—181no—
314C22×C4C2×D3211yescharacteristic
315M16—32no—
316M16—61no—
317M16—61no—
318M16—61no—
319M16—61no—
320M16—61no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—61no—
324C2×C8—61no—
325C2×C8—61no—
326C2×C8#62612yes—
327C4⋊C4—31no—
328C4⋊C4—31no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C22⋊C4—61no—
332C42—61no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3#89511yescharacteristic
343C22×C3#89611yescharacteristic
344C22×C3#89811yescharacteristic
345C22×C3#89811yescharacteristic
346C22×C3#93011yescharacteristic
347C22×C3#94611yescharacteristic
348C2×D3—124no—
349C2×D3—122no—
350C2×D3—122no—
351C2×D3—244no—
352C2×D3—244no—
353C2×D3—242no—
354C2×D3—242no—
355C2×D3—242no—
356C2×D3—242no—
357C2×D3—241no—
358C2×D3—241no—
359C2×D3—241no—
360C2×D3—241no—
361C2×D3—242no—
362C2×D3—242no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—121no—
368C3×C4—121no—
369C3×C4#89511yescharacteristic
370C3×C4#89611yescharacteristic
371C3×C4#89711yescharacteristic
372C3×C4#89711yescharacteristic
373C3×C4#93011yescharacteristic
374C3×C4#93911yescharacteristic
375C3×C4#93911yescharacteristic
376C3×C4#94611yescharacteristic
377Dic3—41no—
378Dic3—41no—
379Dic3—242no—
380Dic3—241no—
381Dic3—241no—
382C32#206311yescharacteristic, complemented, Sylow
383C23—182no—
384C23—361no—
385C23—361no—
386C23—721no—
387C23—721no—
388C23#379911yescharacteristic
389D4—182no—
390D4—182no—
391D4—361no—
392D4—361no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—361no—
396C2×C4—721no—
397C2×C4#379611yescharacteristic
398C2×C4#379711yescharacteristic
399C2×C4D3×D1211yescharacteristic
400C2×C4#380411yescharacteristic
401C2×C4C2×#62611yescharacteristic
402C2×C4D3×#6711yescharacteristic
403C8—22no—
404C8—62no—
405C8—121no—
406C8—121no—
407C2×C3—22no—
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#489711yescharacteristic
417C2×C3#489811yescharacteristic
418C2×C3#499411yescharacteristic
419C2×C3#499411yescharacteristic
420C2×C3#514111yescharacteristic
421C2×C3#514211yescharacteristic
422D3—244no—
423D3—242no—
424D3—242no—
425C22—21no—
426C22—21no—
427C22—362no—
428C22—722no—
429C22—722no—
430C22—721no—
431C22—721no—
432C22#6384811yescharacteristic
433C22#6388811yescharacteristic
434C22#6390911yescharacteristic
435C4—121no—
436C4—121no—
437C4—721no—
438C4#6387111yescharacteristic
439C4#6388611yescharacteristic
440C4#6389511yescharacteristic
441C4#6397811yescharacteristic
442C3—21no—
443C3#7054211yescharacteristic, complemented
444C3#7071511yescharacteristic, complemented
445C2—21no—
446C2—21no—
447C2—722no—
448C2#1059092711yescharacteristic
449C2#1059093111yescharacteristic
450C2#1059131111yescharacteristic
subgroupG/H
centerC22#63909
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32#121
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×C8D32
hypocenterC32#2063
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#819C2semidirect
3. C3×#5102C2semidirect
4. #10591131C2semidirect
7. #10589168C2semidirect
34. C2×#819D3semidirect
35. #5102D3semidirect
382. C32#2063semidirect
443. C3#70542semidirect
444. C3#70715semidirect

Maximal subgroups

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

subgroupindex
C2×#636482
C2×C3×#8192
C3×#51022
#105911312
#105910962
C2×#635592
#105891682
#707153
#705423