Finite Group Databasebeta

← #37575762

Subgroups — #37575762

Order 24448.

696 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×C4×C22⋊D191C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D191C211yesmaximal, characteristic, complemented
3C2×#20259281C211yesmaximal, characteristic, complemented
4#27132596C211yesmaximal, characteristic, complemented
5#27132591C211yesmaximal, characteristic, complemented
6#27132586C211yesmaximal, characteristic, complemented
7#27132585C211yesmaximal, characteristic, complemented
8#27132579C211yesmaximal, characteristic, complemented
9#27132578C211yesmaximal, characteristic, complemented
10#27132577C211yesmaximal, characteristic, complemented
11#27132571C211yesmaximal, characteristic
12C4×Dic191⋊C4C211yesmaximal, characteristic, complemented
13C4×(C2×D191)⋊C4C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic191C211yesmaximal, characteristic, complemented
15C2×C4×D4×C191C211yesmaximal, characteristic, complemented
16C22×C22⋊D191C2211yescharacteristic
17C22×C22⋊D191C2211yescharacteristic
18C22×C4×D191C2211yescharacteristic
19C4×C22⋊D191—24no—
20C4×C22⋊D191—24no—
21#20259281—24no—
22C2×C4⋊Dic191C2211yescharacteristic
23C2×C4⋊Dic191C2211yescharacteristic
24C2×Dic191⋊C4C2211yescharacteristic
25C2×Dic191⋊C4C2211yescharacteristic
26C2×Dic191⋊C4C2211yescharacteristic
27C2×Dic191⋊C4C2211yescharacteristic
28C2×C22⋊Dic191C2211yescharacteristic
29C2×C22⋊Dic191C2211yescharacteristic
30C2×C22⋊Dic191C2211yescharacteristic
31C2×C22⋊Dic191C2211yescharacteristic
32C2×C22⋊Dic191C2211yescharacteristic
33C2×C22⋊Dic191C2211yescharacteristic
34C2×(C2×D191)⋊C4C2211yescharacteristic
35C2×(C2×D191)⋊C4C2211yescharacteristic
36C2×(C2×D191)⋊C4C2211yescharacteristic
37C2×(C2×D191)⋊C4C2211yescharacteristic
38C2×C4×Dic191C2211yescharacteristic
39C2×C4×Dic191C2211yescharacteristic
40C2×C4×Dic191C2211yescharacteristic
41C191⋊#95C2211yescharacteristic
42C191⋊#95C2211yescharacteristic
43C191⋊#95C2211yescharacteristic
44C191⋊#95C2211yescharacteristic
45C191⋊#95C2211yescharacteristic
46C191⋊#95C2211yescharacteristic
47C22×D4×C191C2211yescharacteristic
48C23×C4×C191C2211yescharacteristic
49C23×C4×C191C2211yescharacteristic
50C4×D4×C191—24no—
51C2×C4⋊C4×C191C2211yescharacteristic
52C2×C22⋊C4×C191C2211yescharacteristic
53C2×C22⋊C4×C191C2211yescharacteristic
54C2×C42×C191C2211yescharacteristic
55C23×D191C2311yescharacteristic
56C2×C22⋊D191—22no—
57C2×C22⋊D191—22no—
58C2×C22⋊D191—22no—
59C2×C22⋊D191—22no—
60C2×C22⋊D191—22no—
61C2×C22⋊D191—22no—
62C22×Dic191C2311yescharacteristic
63C22×Dic191C2311yescharacteristic
64C22×Dic191C2311yescharacteristic
65C22×Dic191C2311yescharacteristic
66C22×Dic191C2311yescharacteristic
67C22×Dic191C2311yescharacteristic
68C22×Dic191C2311yescharacteristic
69C2×C4×D191—22no—
70C2×C4×D191—22no—
71C2×C4×D191—22no—
72C4⋊Dic191—22no—
73C4⋊Dic191—22no—
74Dic191⋊C4—22no—
75Dic191⋊C4—22no—
76Dic191⋊C4—22no—
77Dic191⋊C4—22no—
78C22⋊Dic191—22no—
79C22⋊Dic191—22no—
80C22⋊Dic191—22no—
81C22⋊Dic191—22no—
82C22⋊Dic191—22no—
83C22⋊Dic191—22no—
84(C2×D191)⋊C4—22no—
85(C2×D191)⋊C4—22no—
86(C2×D191)⋊C4—22no—
87(C2×D191)⋊C4—22no—
88C4×Dic191—22no—
89C4×Dic191—22no—
90C4×Dic191D414yescomplemented
91C24×C191C2311yescharacteristic
92C24×C191C2311yescharacteristic
93C2×D4×C191—22no—
94C2×D4×C191—22no—
95C2×D4×C191—22no—
96C22×C4×C191—22no—
97C22×C4×C191—22no—
98C22×C4×C191—22no—
99C22×C4×C191—22no—
100C22×C4×C191—22no—
101C22×C4×C191D414yescomplemented
102C22×C4×C191C2311yescharacteristic
103C22×C4×C191C2311yescharacteristic
104C22×C4×C191C2311yescharacteristic
105C22×C4×C191C2311yescharacteristic
106C22×C4×C191C2311yescharacteristic
107C4⋊C4×C191—22no—
108C22⋊C4×C191—22no—
109C22⋊C4×C191—22no—
110C42×C191—22no—
111C22×D191—21no—
112C22×D191—21no—
113C22×D191—21no—
114C22×D191—21no—
115C22×D191—21no—
116C22×D191—21no—
117C22×D191#4112yes—
118C22⋊D191—28no—
119C22⋊D191—28no—
120C2×Dic191—21no—
121C2×Dic191—21no—
122C2×Dic191—21no—
123C2×Dic191—21no—
124C2×Dic191—21no—
125C2×Dic191—21no—
126C2×Dic191—21no—
127C2×Dic191—21no—
128C2×Dic191—21no—
129C2×Dic191—21no—
130C2×Dic191—21no—
131C2×Dic191—21no—
132C2×Dic191—21no—
133C2×Dic191—21no—
134C2×Dic191—21no—
135C2×Dic191—21no—
136C2×Dic191—21no—
137C2×Dic191—21no—
138C2×Dic191C2×D412yes—
139C2×Dic191C2×D412yes—
140C2×Dic191#4112yes—
141C4×D191—44no—
142C23×C191—21no—
143C23×C191—21no—
144C23×C191—21no—
145C23×C191—21no—
146C23×C191—21no—
147C23×C191—21no—
148C23×C191—21no—
149C23×C191—21no—
150C23×C191—21no—
151C23×C191—21no—
152C23×C191—21no—
153C23×C191—21no—
154C23×C191C2×D412yes—
155C23×C191#4112yes—
156C23×C191C2411yescharacteristic
157D4×C191—28no—
158C2×C4×C191—21no—
159C2×C4×C191—21no—
160C2×C4×C191—21no—
161C2×C4×C191—21no—
162C2×C4×C191—28no—
163C2×C4×C191—21no—
164C2×C4×C191—21no—
165C2×C4×C191—21no—
166C2×C4×C191—21no—
167C2×C4×C191—21no—
168C2×C4×C191—21no—
169C2×C4×C191—44no—
170C2×C4×C191C2×D412yes—
171C2×C4×C191C2×D412yes—
172C2×C4×C191C2×D412yes—
173C2×C4×C191#4112yes—
174C2×C4×C191#4112yes—
175C22×C191—22no—
176C22×C191—22no—
177C22×C191—22no—
178C22×C191—22no—
179C22×C191—22no—
180C22×C191—22no—
181C22×C191—41no—
182C22×C191—41no—
183C22×C191—41no—
184C22×C191—41no—
185C22×C191—41no—
186C22×C191—41no—
187C22×C191—41no—
188C22×C191—41no—
189C22×C191C22×D411yescharacteristic
190C22×C191C22×D411yescharacteristic
191C22×C191C2×#4111yescharacteristic
192C22×C191C2×#4111yescharacteristic
193C22×C191C2×#4111yescharacteristic
194C22×C191C2×#4111yescharacteristic
195C22×C191C2×#4111yescharacteristic
196C2×D191—22no—
197C2×D191—22no—
198C2×D191—22no—
199C2×D191—41no—
200C2×D191—41no—
201C2×D191—41no—
202C2×D191—41no—
203C4×C191—22no—
204C4×C191—22no—
205C4×C191—41no—
206C4×C191—41no—
207C4×C191#12114yes—
208Dic191—22no—
209Dic191—22no—
210Dic191—22no—
211Dic191—41no—
212Dic191—41no—
213Dic191—41no—
214Dic191—41no—
215C2×C191—42no—
216C2×C191—42no—
217C2×C191C2×#12111yescharacteristic
218C2×C191#52511yescharacteristic
219C2×C191#52511yescharacteristic
220C2×C191#52511yescharacteristic
221C2×C191#52911yescharacteristic
222C2×C191#52911yescharacteristic
223C2×C191#53211yescharacteristic
224D191—42no—
225C191#239211yescharacteristic, complemented, Sylow
226#2392—1911nomaximal, Sylow
227C2×C4×D4—1911no—
228C2×C4×D4—1911no—
229C2×C4×D4D19111yescharacteristic, complemented
230C2×#117—1911no—
231#398—1911no—
232#397—1911no—
233#396—1911no—
234#396—1911no—
235#394—1911no—
236#394—1911no—
237#394—1911no—
238#392—1911no—
239C4×C4⋊C4—1911no—
240C4×C22⋊C4—1911no—
241C4×C22⋊C4—1911no—
242C22×D4—1911no—
243C22×D4—1911no—
244C22×D4C2×D19111yescharacteristic
245C23×C4—1911no—
246C23×C4C2×D19111yescharacteristic
247C23×C4C2×D19111yescharacteristic
248C4×D4—24no—
249C4×D4—3824no—
250C4×D4—3824no—
251#117—3824no—
252C2×C4⋊C4—1911no—
253C2×C4⋊C4—1911no—
254C2×C4⋊C4—1911no—
255C2×C4⋊C4—1911no—
256C2×C4⋊C4—1911no—
257C2×C4⋊C4—1911no—
258C2×C4⋊C4C2×D19111yescharacteristic
259C2×C22⋊C4—1911no—
260C2×C22⋊C4—1911no—
261C2×C22⋊C4—1911no—
262C2×C22⋊C4—1911no—
263C2×C22⋊C4—1911no—
264C2×C22⋊C4—1911no—
265C2×C22⋊C4—1911no—
266C2×C22⋊C4—1911no—
267C2×C22⋊C4—1911no—
268C2×C22⋊C4—1911no—
269C2×C22⋊C4C2×D19111yescharacteristic
270C2×C22⋊C4C2×D19111yescharacteristic
271C2×C42—1911no—
272C2×C42—1911no—
273C2×C42—1911no—
274C2×C42C2×D19111yescharacteristic
275#95—1911no—
276#95—1911no—
277#95—1911no—
278#95—1911no—
279#95—1911no—
280#95—1911no—
281C24—1911no—
282C24C22×D19111yescharacteristic
283C24C22×D19111yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—3822no—
288C2×D4—3822no—
289C2×D4—3822no—
290C2×D4—3822no—
291C2×D4—3822no—
292C2×D4—3822no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—3822no—
299C22×C4—3822no—
300C22×C4—3822no—
301C22×C4—1911no—
302C22×C4—1911no—
303C22×C4—1911no—
304C22×C4—1911no—
305C22×C4—1911no—
306C22×C4—1911no—
307C22×C4—1911no—
308C22×C4C22⋊D19114yescomplemented
309C22×C4C22×D19111yescharacteristic
310C22×C4C22×D19111yescharacteristic
311C22×C4C22×D19111yescharacteristic
312C22×C4C22×D19111yescharacteristic
313C22×C4C22×D19111yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—3822no—
316C4⋊C4—3822no—
317C4⋊C4—3822no—
318C4⋊C4—3822no—
319C4⋊C4—3822no—
320C4⋊C4—3822no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—3822no—
324C22⋊C4—3822no—
325C22⋊C4—3822no—
326C22⋊C4—3822no—
327C22⋊C4—3822no—
328C22⋊C4—3822no—
329C22⋊C4—3822no—
330C22⋊C4—3822no—
331C22⋊C4—3822no—
332C22⋊C4—3822no—
333C42—22no—
334C42—3822no—
335C42—3822no—
336C42—1914no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—3821no—
350C23—3821no—
351C23—3821no—
352C23—3821no—
353C23—3821no—
354C23—3821no—
355C23—1912no—
356C23C2×C22⋊D19112yes—
357C23#1569028712yes—
358C23C23×D19111yescharacteristic
359D4—28no—
360D4—3828no—
361D4—3828no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—28no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—44no—
374C2×C4—3821no—
375C2×C4—3821no—
376C2×C4—3821no—
377C2×C4—3821no—
378C2×C4—3821no—
379C2×C4—3821no—
380C2×C4—3821no—
381C2×C4—3821no—
382C2×C4—3821no—
383C2×C4—3821no—
384C2×C4—3821no—
385C2×C4—3821no—
386C2×C4—3821no—
387C2×C4—3821no—
388C2×C4—3821no—
389C2×C4—3821no—
390C2×C4—3821no—
391C2×C4—3821no—
392C2×C4—1912no—
393C2×C4—1912no—
394C2×C4—1912no—
395C2×C4—7644no—
396C2×C4D4×D19112yes—
397C2×C4C2×C22⋊D19112yes—
398C2×C4C2×C22⋊D19112yes—
399C2×C4#1569028612yes—
400C2×C4#1569028712yes—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—3822no—
416C22—3822no—
417C22—3822no—
418C22—7641no—
419C22—7641no—
420C22—7641no—
421C22—7641no—
422C22C2×D4×D19111yescharacteristic
423C22C22×C22⋊D19111yescharacteristic
424C22#41×D19111yescharacteristic
425C22#41×D19111yescharacteristic
426C22C2×#1569028611yescharacteristic
427C22C2×#1569028711yescharacteristic
428C22C2×#1569028711yescharacteristic
429C4—22no—
430C4—22no—
431C4—41no—
432C4—41no—
433C4—3822no—
434C4—3822no—
435C4—3822no—
436C4—7641no—
437C4—7641no—
438C4—7641no—
439C4—7641no—
440C4#2025929414yes—
441C2—42no—
442C2—42no—
443C2—7642no—
444C2C2×#2025929411yescharacteristic
445C2#2713317011yescharacteristic
446C2#2713317211yescharacteristic
447C2#2713317411yescharacteristic
448C2#2713319311yescharacteristic
449C2#2713319511yescharacteristic
450C2#2713321011yescharacteristic
subgroupG/H
centerC22×C4C22×D191
commutator, socle, cosocleC23×C191C24
FrattiniC23C23×D191
FittingC2×C4×D4×C191C2
prime radical#27132571C2
hypercenterC2×C4×D4D191
hypocenterC191#2392
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D191C2semidirect
2. C2×C4×C22⋊D191C2semidirect
3. C2×#20259281C2semidirect
4. #27132596C2semidirect
5. #27132591C2semidirect
6. #27132586C2semidirect
7. #27132585C2semidirect
8. #27132579C2semidirect
9. #27132578C2semidirect
10. #27132577C2semidirect
12. C4×Dic191⋊C4C2semidirect
13. C4×(C2×D191)⋊C4C2semidirect
14. C4×C22⋊Dic191C2semidirect
15. C2×C4×D4×C191C2semidirect
90. C4×Dic191D4semidirect
101. C22×C4×C191D4semidirect
225. C191#2392semidirect
229. C2×C4×D4D191semidirect
308. C22×C4C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D1912
C2×#202592812
#271325962
#271325912
#271325862
#271325852
#271325792
#271325782
#271325772
#271325712
C4×Dic191⋊C42
C4×(C2×D191)⋊C42
C4×C22⋊Dic1912
C2×C4×D4×C1912
#2392191