Finite Group Databasebeta

← #11794347

Subgroups — #11794347

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#10592830C211yesmaximal, characteristic
2C2×C3×#822C211yesmaximal, characteristic, complemented
3#10591130C211yesmaximal, characteristic, complemented
4#10591119C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic
6C2×#63559C211yesmaximal, characteristic
7C3×#4554C211yesmaximal, characteristic, complemented
8#70715—31nomaximal
9#68996—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63648—21no—
18#63648—21no—
19C3×#822—22no—
20#63575—21no—
21#63573—21no—
22#63572—22no—
23#63564—22no—
24#63559—22no—
25C2×C3×#108—31no—
26#5131—31no—
27#5131—31no—
28#5131—61no—
29C2×#823—31no—
30C2×#823—31no—
31C2×#822D311yescharacteristic, complemented
32#5121—31no—
33#5119—31no—
34C2×#821—31no—
35#5102—31no—
36C2×#809—31no—
37#4964—31no—
38C3×#343—31no—
39#4554D311yescharacteristic, complemented
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×M16—21no—
50C32×M16—21no—
51C2×C32×C8—21no—
52#3757—21no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54C4⋊(C3⋊Dic3)D411yescharacteristic
55C4×C3⋊Dic3—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—21no—
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×M16C2×D311yescharacteristic
76C22×C3×C8—31no—
77C2×C3×C4⋊C4—31no—
78#926—31no—
79#926—31no—
80#926—61no—
81C2×C4⋊Dic3C2×D311yescharacteristic
82C2×#208C2×D311yescharacteristic
83C2×#208C2×D311yescharacteristic
84C22×C3⋊C8C2×D311yescharacteristic
85C3×#108—62no—
86#823—62no—
87#823—62no—
88#822—22no—
89#821—62no—
90#821—61no—
91#821—61no—
92#821—61no—
93#821—61no—
94#821—62no—
95#821—62no—
96#818—61no—
97#817—61no—
98Dic3⋊C8—62no—
99Dic3⋊C8—62no—
100#809—62no—
101#808—61no—
102#807—61no—
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×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×Q811yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—21no—
117C4⋊(C3⋊D3)—22no—
118C4⋊(C3⋊D3)—22no—
119C4⋊(C3⋊D3)—41no—
120C4⋊(C3⋊D3)—41no—
121C2×C3×Dic3—41no—
122C2×C3×Dic3—81no—
123C32×C8—41no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127C2×#108—31no—
128#428—91no—
129#424—91no—
130#418—91no—
131C2×#102—91no—
132C2×#100—91no—
133#343—31no—
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—21no—
161C3×M16—21no—
162C3×M16—21no—
163C3×M16—21no—
164C3×M16—32no—
165C3×M16—41no—
166C3×M16—41no—
167C3×M16—61no—
168C3×M16—61no—
169C3×M16—61no—
170C2×C3×C8—22no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—32no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C2×C3×C8—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180#217—61no—
181#217—61no—
182#217—121no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—31no—
186C4⋊Dic3—31no—
187C4⋊Dic3—31no—
188C4⋊Dic3—31no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4×Dic3—61no—
192C4×Dic3—61no—
193C4×Dic3—121no—
194#208—21no—
195#208—21no—
196#208—21no—
197#208#6712yes—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8D1212yes—
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#12111yescharacteristic
214C32×C4#12111yescharacteristic
215C32×C4C22⋊Q811yescharacteristic
216C32×C4C22⋊Q811yescharacteristic
217C3⋊Dic3—41no—
218C3⋊Dic3—41no—
219C3×Dic3—81no—
220C22×D4—91no—
221C2×M16—31no—
222C2×M16—31no—
223C2×M16D3211yescharacteristic
224C22×C8—31no—
225#117—91no—
226C2×C4⋊C4—31no—
227#108—62no—
228#107—181no—
229#106—181no—
230C4⋊C8—182no—
231#102—182no—
232#102—181no—
233#102—181no—
234#100—182no—
235C23×C3—21no—
236C23×C3#23511yescharacteristic
237C23×C3#23911yescharacteristic
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—121no—
260C2×C3×C4—241no—
261C2×C3×C4C2×D1211yescharacteristic
262C2×C3×C4#23511yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4#23511yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4#23711yescharacteristic
270C2×C3×C4D3×Q811yescharacteristic
271C2×C3×C4D3×Q811yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×Dic3—41no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—81no—
279C2×Dic3—121no—
280C2×Dic3—121no—
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—42no—
294C3×C8—41no—
295C3×C8—41no—
296C3×C8—62no—
297C3×C8—62no—
298C3×C8—121no—
299C3⋊C8—22no—
300C3⋊C8—22no—
301C3⋊C8—41no—
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—21no—
318M16—21no—
319M16—32no—
320M16—61no—
321M16—61no—
322M16—61no—
323C2×C8—21no—
324C2×C8—32no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—91no—
332C4⋊C4—91no—
333C22⋊C4—181no—
334C42—181no—
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#87611yescharacteristic
345C22×C3#88411yescharacteristic
346C22×C3#89511yescharacteristic
347C22×C3#89611yescharacteristic
348C22×C3#89811yescharacteristic
349C22×C3#94611yescharacteristic
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—241no—
370C3×C4#88411yescharacteristic
371C3×C4#88411yescharacteristic
372C3×C4#89611yescharacteristic
373C3×C4#89611yescharacteristic
374C3×C4#89611yescharacteristic
375C3×C4#89711yescharacteristic
376C3×C4#93011yescharacteristic
377C3×C4#93911yescharacteristic
378Dic3—81no—
379Dic3—121no—
380Dic3—121no—
381Dic3—121no—
382Dic3—121no—
383Dic3—241no—
384Dic3—241no—
385C32#206311yescharacteristic, complemented, Sylow
386C23—182no—
387C23—361no—
388C23—361no—
389C23—721no—
390C23—721no—
391C23#379911yescharacteristic
392D4—182no—
393D4—182no—
394D4—361no—
395D4—361no—
396C2×C4—121no—
397C2×C4—181no—
398C2×C4—181no—
399C2×C4—241no—
400C2×C4#379711yescharacteristic
401C2×C4#379811yescharacteristic
402C2×C4D3×D1211yescharacteristic
403C2×C4#380411yescharacteristic
404C2×C4D3×#6711yescharacteristic
405C2×C4#381111yescharacteristic
406C8—41no—
407C8—62no—
408C8—62no—
409C8—121no—
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#467611yescharacteristic
420C2×C3#474911yescharacteristic
421C2×C3#475411yescharacteristic
422C2×C3#489711yescharacteristic
423C2×C3#489811yescharacteristic
424C2×C3#499411yescharacteristic
425D3—244no—
426D3—242no—
427D3—242no—
428C22—21no—
429C22—21no—
430C22—362no—
431C22—722no—
432C22—722no—
433C22—721no—
434C22—721no—
435C22#6386811yescharacteristic
436C22#6388811yescharacteristic
437C22#6391011yescharacteristic
438C4—241no—
439C4—361no—
440C4—361no—
441C4#6386511yescharacteristic
442C4#6389511yescharacteristic
443C4#6390611yescharacteristic
444C4#6397111yescharacteristic
445C3—21no—
446C3#6899611yescharacteristic, complemented
447C3#7071511yescharacteristic, complemented
448C2—21no—
449C2—21no—
450C2—722no—
451C2#1059098711yescharacteristic
452C2#1059099011yescharacteristic
453C2#1059134711yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×M16D32
hypocenterC32#2063
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C3×#822C2semidirect
3. #10591130C2semidirect
4. #10591119C2semidirect
7. C3×#4554C2semidirect
31. C2×#822D3semidirect
39. #4554D3semidirect
385. C32#2063semidirect
446. C3#68996semidirect
447. C3#70715semidirect

Maximal subgroups

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

subgroupindex
#105928302
C2×C3×#8222
#105911302
#105911192
C2×#635642
C2×#635592
C3×#45542
#707153
#689963