Finite Group Databasebeta

← #11774713

Subgroups — #11774713

Order 1152.

539 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
1C4×D3×Dic6C211yesmaximal, characteristic
2C3×#4835C211yesmaximal, characteristic
3C4×#3711C211yesmaximal, characteristic
4#10589350C211yesmaximal, characteristic, complemented
5C3×#4484C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#70802—31nomaximal
9#68239—31nomaximal
10C2×D3×Dic6C411yescharacteristic
11C4×#634C2211yescharacteristic
12C3×C42×D3C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14C4×#627—21no—
15D3×C4⋊Dic3C411yescharacteristic
16D3×Dic3⋊C4—21no—
17C4×D3×Dic3—21no—
18#63844C411yescharacteristic
19Dic3×Dic6C411yescharacteristic
20#63837—21no—
21C2×#3711—21no—
22C32×C4⋊C8C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×(C2×D3)⋊C8—21no—
25C3×#815—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×C4×C3⋊C8C2211yescharacteristic
28#63554—21no—
29C4×D3×Q8—31no—
30C2×C4×Dic6—31no—
31C3×#432—31no—
32C4×#208—31no—
33#4835D311yescharacteristic
34C4×ΓL(1,𝔽25)—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4484—31no—
38#4484—31no—
39#4484—31no—
40#4484—31no—
41#4484—61no—
42#4484D311yescharacteristic, complemented
43#4456—31no—
44C2×#634C2×C411yescharacteristic
45C2×C3×C4×D3C2×C411yescharacteristic
46C2×C3×C4×D3D411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×Dic6C2×C411yescharacteristic
49C2×#627—21no—
50C2×D3×Dic3—21no—
51C2×D3×Dic3—21no—
52D3×Dic6—22no—
53D3×Dic6—22no—
54C2×C32×C8—21no—
55C32×C42C2311yescharacteristic
56C4⋊(C3⋊Dic3)C2×C411yescharacteristic
57#3750—21no—
58C4×C3⋊Dic3—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×C4⋊Dic3C2×C411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3C2×C411yescharacteristic
64C3×C4×Dic3D411yescharacteristic
65C3×C4×Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#3724—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71Dic32—21no—
72Dic32—21no—
73#3711—24no—
74#1491—91noSylow
75C2×D3×Q8—31no—
76C22×Dic6—31no—
77C3×C4×Q8—31no—
78C2×C3×C42—31no—
79Q8×Dic3—31no—
80C2×C4⋊Dic3—31no—
81C2×Dic3⋊C4—61no—
82C2×C4×Dic3—61no—
83C2×#208—61no—
84C2×ΓL(1,𝔽25)—61no—
85D3×C4⋊C4—31no—
86D3×C4⋊C4—61no—
87#887—31no—
88#887—61no—
89C42×D3—61no—
90C42×D3C2×D311yescharacteristic
91C4×Dic6—31no—
92C4×Dic6—31no—
93C4×Dic6—31no—
94C4×Dic6—31no—
95C4×Dic6—61no—
96C4×Dic6—61no—
97C4×Dic6—61no—
98C4×Dic6—61no—
99C4×Dic6C2×D311yescharacteristic
100C3×C4⋊C8—21no—
101C3×C4⋊C8—31no—
102C3×C4⋊C8C2×D311yescharacteristic
103C3×C4⋊C8C2×D311yescharacteristic
104C3×C22⋊C8—61no—
105C3×#97—61no—
106C3×C4×C8—31no—
107(C2×D3)⋊C8—21no—
108#815—21no—
109#815—61no—
110C4⋊(C3⋊C8)C2×D311yescharacteristic
111#803—61no—
112C4×C3⋊C8—31no—
113C4×C3⋊C8—31no—
114C4×C3⋊C8—61no—
115C4×C3⋊C8C2×D311yescharacteristic
116C22×C3×D3C22⋊C411yescharacteristic
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122#634—21no—
123#634M1612yescomplemented
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3C22⋊C411yescharacteristic
128C2×C3×Dic3C22⋊C411yescharacteristic
129C3×C4×D3—22no—
130C3×C4×D3—21no—
131C3×C4×D3—21no—
132C3×C4×D3—21no—
133C3×C4×D3—21no—
134C3×Dic6—21no—
135C3×Dic6M1612yescomplemented
136#627—24no—
137D3×Dic3—24no—
138D3×Dic3—42no—
139C32×C8—41no—
140C3⋊(C3⋊C8)—22no—
141C3×C3⋊C8—22no—
142C3×C3⋊C8—41no—
143C2×C4×Q8—91no—
144#432—31no—
145C4×M16—91no—
146Q8⋊C8—31no—
147Q8⋊C8—91no—
148Q8⋊C8—91no—
149Q8⋊C8—91no—
150C2×C3×Q8—31no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×Dic3—61no—
155C22×Dic3—61no—
156D3×Q8—62no—
157D3×Q8—62no—
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×C4×D3C4×D311yescharacteristic
161C2×C4×D3D1211yescharacteristic
162C2×C4×D3#6711yescharacteristic
163C2×Dic6—31no—
164C2×Dic6—31no—
165C2×Dic6—61no—
166C2×Dic6—62no—
167C2×Dic6—61no—
168C2×Dic6—61no—
169C2×Dic6—62no—
170C2×Dic6C4×D311yescharacteristic
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—41no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—61no—
178C3×C42—21no—
179C3×C42—31no—
180C3×C42—31no—
181C3×C42—31no—
182C3×C42—61no—
183C3×C42C22×D311yescharacteristic
184C3×C42C22×D311yescharacteristic
185C4⋊Dic3—31no—
186C4⋊Dic3—31no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3C4×D311yescharacteristic
191Dic3⋊C4—21no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—121no—
199C4×Dic3—21no—
200C4×Dic3—61no—
201C4×Dic3—61no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—121no—
207C4×Dic3C4×D311yescharacteristic
208C4×Dic3D1211yescharacteristic
209C4×Dic3#6711yescharacteristic
210#208—64no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—121no—
216ΓL(1,𝔽25)—64no—
217C22×C32C2×C22⋊C411yescharacteristic
218C2×C3×D3—21no—
219C2×C3×D3—21no—
220C2×C3×D3#10412yes—
221C32×C4—21no—
222C32×C4C2×M1611yescharacteristic
223C32×C4C2×M1611yescharacteristic
224C32×C4#13711yescharacteristic
225C32×C4#13711yescharacteristic
226C3⋊Dic3—22no—
227C3⋊Dic3—41no—
228C3×Dic3—22no—
229C3×Dic3—21no—
230C3×Dic3—21no—
231C3×Dic3—21no—
232C3×Dic3—41no—
233C22×Q8—91no—
234C2×M16—181no—
235C4×Q8—31no—
236C4×Q8—91no—
237C4×Q8—91no—
238C4×Q8—91no—
239C4×Q8—181no—
240C4×Q8—181no—
241C2×C4⋊C4—91no—
242C2×C4⋊C4—181no—
243C2×C42—31no—
244C2×C42—181no—
245C4⋊C8—31no—
246C4⋊C8D3211yescharacteristic
247C22⋊C8—61no—
248#97—61no—
249#97—181no—
250C4×C8—31no—
251C4×C8—91no—
252C23×C3—31no—
253C22×D3(C2×D3)⋊C411yescharacteristic
254C3×Q8—32no—
255C3×Q8—61no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—31no—
260C2×C3×C4—31no—
261C2×C3×C4—31no—
262C2×C3×C4—62no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4C2×D1211yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—64no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—121no—
283C2×Dic3—121no—
284C2×Dic3—122no—
285C2×Dic3(C2×D3)⋊C411yescharacteristic
286C2×Dic3(C2×D3)⋊C411yescharacteristic
287C2×Dic3(C2×D3)⋊C411yescharacteristic
288C4×D3—22no—
289C4×D3—21no—
290C4×D3—21no—
291C4×D3—21no—
292C4×D3—21no—
293C4×D3—64no—
294C4×D3—122no—
295Dic6—21no—
296Dic6—32no—
297Dic6—32no—
298Dic6—62no—
299Dic6—64no—
300Dic6—64no—
301Dic6—61no—
302Dic6—61no—
303Dic6—121no—
304Dic6ΓL(1,𝔽25)12yescomplemented
305C3×C8—41no—
306C3×C8—41no—
307C3×C8—62no—
308C3×C8—81no—
309C3×C8—121no—
310C3⋊C8—22no—
311C3⋊C8—41no—
312C3⋊C8—62no—
313C3⋊C8—62no—
314C3⋊C8—122no—
315C2×C32#40711yescharacteristic
316C2×C32#41911yescharacteristic
317C2×C32C2×#10411yescharacteristic
318C3×D3—22no—
319C2×Q8—31no—
320C2×Q8—91no—
321C2×Q8—181no—
322C2×Q8—182no—
323C2×Q8—182no—
324C22×C4—31no—
325C22×C4—31no—
326C22×C4—31no—
327C22×C4—181no—
328C22×C4—181no—
329M16—184no—
330C2×C8—21no—
331C2×C8—61no—
332C2×C8—61no—
333C2×C8—181no—
334C4⋊C4—31no—
335C4⋊C4—61no—
336C4⋊C4—91no—
337C4⋊C4—181no—
338C4⋊C4—181no—
339C4⋊C4—181no—
340C4⋊C4—181no—
341C42—31no—
342C42—31no—
343C42—31no—
344C42—61no—
345C42—181no—
346C42—181no—
347C42—181no—
348C42C2×D3211yescharacteristic
349C22×C3—21no—
350C22×C3—32no—
351C22×C3—61no—
352C22×C3—61no—
353C22×C3D3×C22⋊C411yescharacteristic
354C22×C3C2×(C2×D3)⋊C411yescharacteristic
355C2×D3—21no—
356C2×D3—21no—
357C2×D3#82512yes—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—41no—
365C3×C4—62no—
366C3×C4—61no—
367C3×C4—61no—
368C3×C4—61no—
369C3×C4—121no—
370C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
371C3×C4D3×M1611yescharacteristic
372C3×C4D3×M1611yescharacteristic
373C3×C4D3×M1611yescharacteristic
374C3×C4#91511yescharacteristic
375C3×C4#91811yescharacteristic
376C3×C4#95111yescharacteristic
377C3×C4#95111yescharacteristic
378Dic3—21no—
379Dic3—21no—
380Dic3—22no—
381Dic3—21no—
382Dic3—41no—
383Dic3—62no—
384Dic3—62no—
385Dic3—122no—
386Dic3—121no—
387Dic3—121no—
388Dic3—241no—
389C32#149111yescharacteristic, complemented, Sylow
390C23—31no—
391Q8—32no—
392Q8—61no—
393Q8—92no—
394Q8—184no—
395Q8—181no—
396C2×C4—31no—
397C2×C4—31no—
398C2×C4—31no—
399C2×C4—62no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—184no—
407C2×C4—181no—
408C2×C4—181no—
409C2×C4—362no—
410C2×C4C4×D3211yescharacteristic
411C2×C4D3×D1211yescharacteristic
412C2×C4D3×#6711yescharacteristic
413C8—41no—
414C8—62no—
415C8—121no—
416C8—182no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—62no—
421C2×C3#472611yescharacteristic
422C2×C3#480211yescharacteristic
423C2×C3D3×#10411yescharacteristic
424C2×C3#500411yescharacteristic
425C2×C3#512611yescharacteristic
426C2×C3C2×#82511yescharacteristic
427D3—22no—
428C22—32no—
429C22—61no—
430C22—61no—
431C22D3×(C2×D3)⋊C411yescharacteristic
432C4—21no—
433C4—61no—
434C4—61no—
435C4—61no—
436C4—62no—
437C4—121no—
438C4—182no—
439C4—361no—
440C4D3×ΓL(1,𝔽25)11yescharacteristic
441C4#6379111yescharacteristic
442C4#6392911yescharacteristic
443C4#6394311yescharacteristic
444C3—21no—
445C3#6823911yescharacteristic, complemented
446C3#7080211yescharacteristic, complemented
447C2—62no—
448C2#1059060011yescharacteristic
449C2#1059093611yescharacteristic
450C2D3×#82511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #10589350C2semidirect
5. C3×#4484C2semidirect
6. #10589085C2semidirect
7. #10589083C2semidirect
42. #4484D3semidirect
123. #634M16semidirect
135. C3×Dic6M16semidirect
304. Dic6ΓL(1,𝔽25)semidirect
389. C32#1491semidirect
445. C3#68239semidirect
446. C3#70802semidirect

Maximal subgroups

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

subgroupindex
C4×D3×Dic62
C3×#48352
C4×#37112
#105893502
C3×#44842
#105890852
#105890832
#708023
#682393