Finite Group Databasebeta

← #37576078

Subgroups — #37576078

Order 24448.

666 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259307C211yesmaximal, characteristic, complemented
2C2×#20259307C211yesmaximal, characteristic, complemented
3C2×#20259297C211yesmaximal, characteristic
4C2×C4×D764C211yesmaximal, characteristic, complemented
5#27132596C211yesmaximal, characteristic, complemented
6#27132589C211yesmaximal, characteristic, complemented
7#27132585C211yesmaximal, characteristic, complemented
8#27132580C211yesmaximal, characteristic, complemented
9#27132554C211yesmaximal, characteristic, complemented
10#27132541C211yesmaximal, characteristic, complemented
11#27132541C211yesmaximal, characteristic, complemented
12#27132534C211yesmaximal, characteristic, complemented
13#27132522C211yesmaximal, characteristic, complemented
14#95×D191C211yesmaximal, characteristic, complemented
15#389×C191C211yesmaximal, characteristic, complemented
16C22×D764C2211yescharacteristic
17C22×D764C2211yescharacteristic
18C22×D764C2211yescharacteristic
19C22×C4×D191C2211yescharacteristic
20C22×C4×D191C2211yescharacteristic
21C22×C4×D191C2211yescharacteristic
22C22×C4×D191C2211yescharacteristic
23#20259307—24no—
24#20259307—24no—
25#20259297—24no—
26C4×D764—24no—
27C2×C4⋊Dic191C2211yescharacteristic
28C2×Dic191⋊C4C2211yescharacteristic
29C2×Dic191⋊C4C2211yescharacteristic
30C2×Dic191⋊C4C2211yescharacteristic
31C2×(C2×D191)⋊C4C2211yescharacteristic
32C2×(C2×D191)⋊C4C2211yescharacteristic
33C2×(C2×D191)⋊C4C2211yescharacteristic
34C2×(C2×D191)⋊C4C2211yescharacteristic
35C2×(C2×D191)⋊C4C2211yescharacteristic
36C2×(C2×D191)⋊C4C2211yescharacteristic
37C2×(C2×D191)⋊C4C2211yescharacteristic
38C2×(C2×D191)⋊C4C2211yescharacteristic
39C2×(C2×D191)⋊C4C2211yescharacteristic
40C2×(C2×D191)⋊C4C2211yescharacteristic
41C2×(C2×D191)⋊C4C2211yescharacteristic
42C191⋊#95C2211yescharacteristic
43C191⋊#95C2211yescharacteristic
44C191⋊#95C2211yescharacteristic
45C191⋊#95C2211yescharacteristic
46C191⋊#95C2211yescharacteristic
47C191⋊#95C2211yescharacteristic
48C2×C4⋊C4×C191C2211yescharacteristic
49C2×C4⋊C4×C191C2211yescharacteristic
50C2×C4⋊C4×C191C2211yescharacteristic
51C2×C4⋊C4×C191C2211yescharacteristic
52C2×C42×C191C2211yescharacteristic
53#95×C191C2211yescharacteristic
54#95×C191C2211yescharacteristic
55C23×D191C2311yescharacteristic
56C23×D191C2311yescharacteristic
57C23×D191C2311yescharacteristic
58C2×D764—22no—
59C2×D764—22no—
60C2×D764—22no—
61C2×D764—22no—
62C2×D764—22no—
63C2×D764—22no—
64C2×D764—22no—
65C2×D764—41no—
66C2×D764D414yes—
67C22×Dic191C2311yescharacteristic
68C22×Dic191C2311yescharacteristic
69C22×Dic191C2311yescharacteristic
70C22×Dic191C2311yescharacteristic
71C22×Dic191C2311yescharacteristic
72C2×C4×D191—22no—
73C2×C4×D191—22no—
74C2×C4×D191—22no—
75C2×C4×D191—22no—
76C2×C4×D191—22no—
77C2×C4×D191—22no—
78C2×C4×D191—22no—
79C2×C4×D191—22no—
80C2×C4×D191—22no—
81C2×C4×D191—41no—
82C2×C4×D191—41no—
83C2×C4×D191—41no—
84C4⋊Dic191—22no—
85Dic191⋊C4—22no—
86Dic191⋊C4—22no—
87Dic191⋊C4—41no—
88(C2×D191)⋊C4—22no—
89(C2×D191)⋊C4—22no—
90(C2×D191)⋊C4—22no—
91(C2×D191)⋊C4—22no—
92(C2×D191)⋊C4—22no—
93(C2×D191)⋊C4—22no—
94(C2×D191)⋊C4—22no—
95(C2×D191)⋊C4—22no—
96(C2×D191)⋊C4—22no—
97(C2×D191)⋊C4—41no—
98(C2×D191)⋊C4D414yescomplemented
99C22×C4×C191C2311yescharacteristic
100C22×C4×C191C2311yescharacteristic
101C22×C4×C191C2311yescharacteristic
102C22×C4×C191C2311yescharacteristic
103C22×C4×C191C2311yescharacteristic
104C22×C4×C191C2311yescharacteristic
105C22×C4×C191C2311yescharacteristic
106C4⋊C4×C191—22no—
107C4⋊C4×C191—22no—
108C4⋊C4×C191—22no—
109C4⋊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—21no—
118C22×D191—21no—
119C22×D191—21no—
120C22×D191—21no—
121C22×D191—21no—
122C22×D191—21no—
123C22×D191—21no—
124C22×D191—21no—
125C22×D191—21no—
126C22×D191—21no—
127C22×D191—21no—
128C22×D191C2×D412yes—
129C22×D191C2×D412yes—
130C22×D191C2×D412yes—
131C22×D191#4112yes—
132D764—28no—
133D764—44no—
134D764—44no—
135C2×Dic191—21no—
136C2×Dic191—21no—
137C2×Dic191—21no—
138C2×Dic191—21no—
139C2×Dic191—21no—
140C2×Dic191—21no—
141C2×Dic191—21no—
142C2×Dic191—21no—
143C2×Dic191—21no—
144C2×Dic191—21no—
145C2×Dic191—21no—
146C2×Dic191—21no—
147C2×Dic191—21no—
148C2×Dic191—21no—
149C2×Dic191C2×D412yes—
150C4×D191—44no—
151C4×D191—44no—
152C4×D191—44no—
153C4×D191—44no—
154C23×C191C2411yescharacteristic
155C2×C4×C191—21no—
156C2×C4×C191—21no—
157C2×C4×C191—21no—
158C2×C4×C191—21no—
159C2×C4×C191—21no—
160C2×C4×C191—21no—
161C2×C4×C191—21no—
162C2×C4×C191—21no—
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—21no—
170C2×C4×C191—21no—
171C2×C4×C191—21no—
172C2×C4×C191C2×D412yes—
173C2×C4×C191C2×D412yes—
174C2×C4×C191#4112yes—
175C2×C4×C191#4112yes—
176C22×C191C22×D411yescharacteristic
177C22×C191C22×D411yescharacteristic
178C22×C191C2×#4111yescharacteristic
179C22×C191C2×#4111yescharacteristic
180C22×C191C2×#4111yescharacteristic
181C22×C191H(5,𝔽2)11yescharacteristic
182C22×C1912−1+411yescharacteristic
183C2×D191—22no—
184C2×D191—22no—
185C2×D191—22no—
186C2×D191—22no—
187C2×D191—22no—
188C2×D191—22no—
189C2×D191—22no—
190C2×D191—22no—
191C2×D191—22no—
192C2×D191—41no—
193C2×D191—41no—
194C2×D191—41no—
195C2×D191—41no—
196C2×D191—41no—
197C2×D191—41no—
198C2×D191—41no—
199C2×D191—41no—
200C2×D191—41no—
201C2×D191—41no—
202C2×D191—41no—
203C2×D191#12114yes—
204C4×C191—22no—
205C4×C191—22no—
206C4×C191—22no—
207C4×C191—22no—
208C4×C191—41no—
209C4×C191—41no—
210C4×C191—41no—
211Dic191—22no—
212Dic191—41no—
213Dic191—41no—
214Dic191—41no—
215Dic191—41no—
216C2×C191C2×#12111yescharacteristic
217C2×C191#52911yescharacteristic
218C2×C191#53911yescharacteristic
219C2×C191#54611yescharacteristic
220C2×C191#54611yescharacteristic
221C2×C191#54711yescharacteristic
222C2×C191#54711yescharacteristic
223D191—24no—
224D191—42no—
225D191—81no—
226C191#242511yescharacteristic, complemented, Sylow
227#2425—1911nomaximal, Sylow
228C2×#123—1911no—
229C2×#123—1911no—
230C2×#121—1911no—
231C2×C4×D4—1911no—
232#398—1911no—
233#397—1911no—
234#396—1911no—
235#394—1911no—
236#389D19111yescharacteristic, complemented
237#388—1911no—
238#386—1911no—
239#386—1911no—
240#385—1911no—
241#380—1911no—
242C2×#95—1911no—
243C22×D4—1911no—
244C22×D4—1911no—
245C22×D4—1911no—
246C23×C4—1911no—
247C23×C4—1911no—
248C23×C4—1911no—
249C23×C4—1911no—
250#123—3824no—
251#123—3824no—
252#121—3824no—
253C4×D4—3824no—
254C2×C4⋊C4—1911no—
255C2×C4⋊C4—1911no—
256C2×C4⋊C4—1911no—
257C2×C4⋊C4—1911no—
258C2×C4⋊C4C2×D19111yescharacteristic
259C2×C4⋊C4C2×D19111yescharacteristic
260C2×C4⋊C4C2×D19111yescharacteristic
261C2×C4⋊C4C2×D19111yescharacteristic
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⋊C4—1911no—
270C2×C22⋊C4—1911no—
271C2×C22⋊C4—1911no—
272C2×C22⋊C4—1911no—
273C2×C42C2×D19111yescharacteristic
274#95—1911no—
275#95—1911no—
276#95—1911no—
277#95—1911no—
278#95—1911no—
279#95—1911no—
280#95C2×D19111yescharacteristic
281#95C2×D19111yescharacteristic
282C24—1911no—
283C24—1911no—
284C24—1911no—
285C2×D4—3822no—
286C2×D4—3822no—
287C2×D4—3822no—
288C2×D4—3822no—
289C2×D4—3822no—
290C2×D4—3822no—
291C2×D4—3822no—
292C2×D4—1914no—
293C2×D4—7641no—
294C22×C4—3822no—
295C22×C4—3822no—
296C22×C4—3822no—
297C22×C4—3822no—
298C22×C4—3822no—
299C22×C4—3822no—
300C22×C4—3822no—
301C22×C4—3822no—
302C22×C4—3822no—
303C22×C4—1911no—
304C22×C4—1911no—
305C22×C4—1911no—
306C22×C4—1911no—
307C22×C4—1911no—
308C22×C4—7641no—
309C22×C4—7641no—
310C22×C4—7641no—
311C22×C4C22×D19111yescharacteristic
312C22×C4C22×D19111yescharacteristic
313C22×C4C22×D19111yescharacteristic
314C22×C4C22×D19111yescharacteristic
315C22×C4C22×D19111yescharacteristic
316C22×C4C22×D19111yescharacteristic
317C22×C4C22×D19111yescharacteristic
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—3822no—
323C4⋊C4—3822no—
324C4⋊C4—3822no—
325C4⋊C4—7641no—
326C22⋊C4—3822no—
327C22⋊C4—3822no—
328C22⋊C4—3822no—
329C22⋊C4—3822no—
330C22⋊C4—3822no—
331C22⋊C4—3822no—
332C22⋊C4—3822no—
333C22⋊C4—3822no—
334C22⋊C4—3822no—
335C22⋊C4—1914no—
336C22⋊C4—7641no—
337C42—22no—
338C23—3821no—
339C23—3821no—
340C23—3821no—
341C23—3821no—
342C23—3821no—
343C23—3821no—
344C23—3821no—
345C23—3821no—
346C23—3821no—
347C23—3821no—
348C23—3821no—
349C23—3821no—
350C23—3821no—
351C23—3821no—
352C23—3821no—
353C23—3821no—
354C23—3821no—
355C23—1912no—
356C23—1912no—
357C23—1912no—
358C23—1912no—
359C23C23×D19111yescharacteristic
360D4—3828no—
361D4—7644no—
362D4—7644no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
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—3821no—
393C2×C4—3821no—
394C2×C4—1912no—
395C2×C4—7644no—
396C2×C4—7644no—
397C2×C4—7644no—
398C2×C4—7644no—
399C2×C4D4×D19112yes—
400C2×C4D4×D19112yes—
401C2×C4#1569028712yes—
402C2×C4#1569028812yes—
403C22—3822no—
404C22—3822no—
405C22—3822no—
406C22—3822no—
407C22—3822no—
408C22—3822no—
409C22—3822no—
410C22—3822no—
411C22—3822no—
412C22—1914no—
413C22—7641no—
414C22—7641no—
415C22—7641no—
416C22—7641no—
417C22—7641no—
418C22—7641no—
419C22—7641no—
420C22—7641no—
421C22—7641no—
422C22—7641no—
423C22—7641no—
424C22C2×D4×D19111yescharacteristic
425C22C2×D4×D19111yescharacteristic
426C22#41×D19111yescharacteristic
427C22C2×#1569028711yescharacteristic
428C22C2×#1569028811yescharacteristic
429C22#2025936811yescharacteristic
430C22#2025937011yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—22no—
435C4—41no—
436C4—41no—
437C4—41no—
438C4—3822no—
439C4—7641no—
440C4—7641no—
441C4—7641no—
442C4—7641no—
443C2—3824no—
444C2—15281no—
445C2—7642no—
446C2#121×D19111yescharacteristic
447C2#2713320011yescharacteristic
448C2#2713326111yescharacteristic
449C2#2713330411yescharacteristic
450C2#2713330911yescharacteristic
451C2#2713331411yescharacteristic
452C2#2713331611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting#389×C191C2
prime radicalC2×#20259297C2
hypercenter#389D191
hypocenterC191#2425
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#20259307C2semidirect
2. C2×#20259307C2semidirect
4. C2×C4×D764C2semidirect
5. #27132596C2semidirect
6. #27132589C2semidirect
7. #27132585C2semidirect
8. #27132580C2semidirect
9. #27132554C2semidirect
10. #27132541C2semidirect
11. #27132541C2semidirect
12. #27132534C2semidirect
13. #27132522C2semidirect
14. #95×D191C2semidirect
15. #389×C191C2semidirect
98. (C2×D191)⋊C4D4semidirect
226. C191#2425semidirect
236. #389D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593072
C2×#202592972
C2×C4×D7642
#271325962
#271325892
#271325852
#271325802
#271325542
#271325412
#271325342
#271325222
#95×D1912
#389×C1912
#2425191