Finite Group Databasebeta

← #34052812

Subgroups — #34052812

Order 19072.

508 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23749566C211yesmaximal, characteristic, complemented
2#23749552C211yesmaximal, characteristic, complemented
3#23749543C211yesmaximal, characteristic, complemented
4#23749543C211yesmaximal, characteristic, complemented
5#23749542C211yesmaximal, characteristic, complemented
6#23749541C211yesmaximal, characteristic, complemented
7#23749540C211yesmaximal, characteristic, complemented
8#23749535C211yesmaximal, characteristic, complemented
9#23749534C211yesmaximal, characteristic, complemented
10#23749534C211yesmaximal, characteristic, complemented
11#23749534C211yesmaximal, characteristic, complemented
12#23749525C211yesmaximal, characteristic, complemented
13#23749517C211yesmaximal, characteristic, complemented
14#23749515C211yesmaximal, characteristic, complemented
15#397×C149C211yesmaximal, characteristic, complemented
16C22×D596C2211yescharacteristic
17C22×D596C2211yescharacteristic
18C22×D596C2211yescharacteristic
19C22×C22⋊D149C2211yescharacteristic
20C22×C22⋊D149C2211yescharacteristic
21C22×C22⋊D149C2211yescharacteristic
22C2×C4⋊Dic149C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×C22⋊Dic149C2211yescharacteristic
26C2×#14558713C2211yescharacteristic
27C2×#14558713C2211yescharacteristic
28C2×#14558713C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×#14558713C2211yescharacteristic
36C2×#14558713C2211yescharacteristic
37C2×#14558713C2211yescharacteristic
38C2×C4×Dic149C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44C2×C4⋊C4×C149C2211yescharacteristic
45C2×C22⋊C4×C149C2211yescharacteristic
46C2×C22⋊C4×C149C2211yescharacteristic
47C2×C22⋊C4×C149C2211yescharacteristic
48#95×C149C2211yescharacteristic
49#95×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51C23×D149C2311yescharacteristic
52C23×D149C2311yescharacteristic
53C23×D149C2311yescharacteristic
54C2×D596—41no—
55C2×D596—41no—
56C2×D596—41no—
57C2×D596—41no—
58C2×D596—41no—
59C2×D596—41no—
60C2×D596—41no—
61C2×D596—41no—
62C2×D596—41no—
63C2×C22⋊D149—22no—
64C2×C22⋊D149—41no—
65C2×C22⋊D149—41no—
66C2×C22⋊D149—41no—
67C2×C22⋊D149—41no—
68C2×C22⋊D149—41no—
69C2×C22⋊D149—41no—
70C2×C22⋊D149—41no—
71C2×C22⋊D149—41no—
72C22×Dic149C2311yescharacteristic
73C22×Dic149C2311yescharacteristic
74C22×Dic149C2311yescharacteristic
75C22×Dic149C2311yescharacteristic
76C22×Dic149C2311yescharacteristic
77C4⋊Dic149—41no—
78#14558715—41no—
79#14558715—41no—
80C22⋊Dic149—41no—
81#14558713—22no—
82#14558713—22no—
83#14558713—41no—
84#14558713—41no—
85#14558713—41no—
86#14558713—41no—
87#14558713—41no—
88#14558713—41no—
89#14558713—41no—
90#14558713—41no—
91#14558713—41no—
92#14558713—41no—
93C4×Dic149—41no—
94C24×C149C2311yescharacteristic
95C22×C4×C149C2311yescharacteristic
96C22×C4×C149C2311yescharacteristic
97C22×C4×C149C2311yescharacteristic
98C22×C4×C149C2311yescharacteristic
99C22×C4×C149C2311yescharacteristic
100C22×C4×C149C2311yescharacteristic
101C4⋊C4×C149—41no—
102C22⋊C4×C149—41no—
103C22⋊C4×C149—41no—
104C22⋊C4×C149—41no—
105C22×D149—21no—
106C22×D149—21no—
107C22×D149—21no—
108C22×D149—21no—
109C22×D149—21no—
110C22×D149—21no—
111C22×D149—21no—
112C22×D149—21no—
113C22×D149—21no—
114C22×D149—21no—
115C22×D149—21no—
116C22×D149—21no—
117C22×D149—21no—
118C22×D149—21no—
119C22×D149—21no—
120C22×D149—21no—
121C22×D149—21no—
122C22×D149—21no—
123C22×D149—21no—
124C22×D149—21no—
125C22×D149—21no—
126D596—44no—
127D596—44no—
128D596—44no—
129C22⋊D149—44no—
130C22⋊D149—44no—
131C22⋊D149—44no—
132C2×Dic149—21no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C2×Dic149—21no—
140C2×Dic149—21no—
141C2×Dic149—21no—
142C2×Dic149—21no—
143C2×Dic149—21no—
144C2×Dic149—21no—
145C2×Dic149—21no—
146C2×Dic149#4112yes—
147C23×C149—21no—
148C23×C149—21no—
149C23×C149—21no—
150C23×C149—21no—
151C23×C149—21no—
152C23×C149—21no—
153C23×C149—21no—
154C23×C149C2411yescharacteristic
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149—21no—
158C2×C4×C149—21no—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—21no—
167C2×C4×C149—21no—
168C2×C4×C149—21no—
169C2×C4×C149—21no—
170C2×C4×C149—21no—
171C2×C4×C149—21no—
172C2×C4×C149—21no—
173C22×C149—41no—
174C22×C149—41no—
175C22×C149—41no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149—41no—
179C22×C149—41no—
180C22×C149C2×#4111yescharacteristic
181C22×C149H(5,𝔽2)11yescharacteristic
182C22×C149H(5,𝔽2)11yescharacteristic
183C22×C149H(5,𝔽2)11yescharacteristic
184C22×C149H(5,𝔽2)11yescharacteristic
185C22×C149H(5,𝔽2)11yescharacteristic
186C22×C149H(5,𝔽2)11yescharacteristic
187C2×D149—41no—
188C2×D149—41no—
189C2×D149—41no—
190C2×D149—41no—
191C2×D149—41no—
192C2×D149—41no—
193C2×D149—41no—
194C2×D149—41no—
195C2×D149—41no—
196C2×D149—41no—
197C2×D149—41no—
198C2×D149—41no—
199C2×D149—41no—
200C2×D149—41no—
201C2×D149—41no—
202C2×D149—41no—
203C2×D149—41no—
204C2×D149—41no—
205C2×D149—41no—
206C2×D149—41no—
207C2×D149—41no—
208C4×C149—41no—
209C4×C149—41no—
210C4×C149—41no—
211C4×C149—41no—
212C4×C149—41no—
213C4×C149—41no—
214Dic149—22no—
215Dic149—41no—
216Dic149—41no—
217Dic149—41no—
218Dic149—41no—
219C2×C149—81no—
220C2×C149#53811yescharacteristic
221C2×C149#54011yescharacteristic
222C2×C149#54011yescharacteristic
223C2×C149#56011yescharacteristic
224C2×C149#56011yescharacteristic
225C2×C149#56011yescharacteristic
226C2×C149H(3,𝔽4)11yescharacteristic
227D149—81no—
228D149—81no—
229D149—81no—
230C149#282811yescharacteristic, complemented, Sylow
231#2828—1491nomaximal, Sylow
232#400—1491no—
233#397—1491no—
234#397D14911yescharacteristic, complemented
235#394—1491no—
236#394—1491no—
237#394—1491no—
238#394—1491no—
239#394—1491no—
240#392—1491no—
241#392—1491no—
242#392—1491no—
243#392—1491no—
244#390—1491no—
245#388—1491no—
246#388—1491no—
247C22×D4—1491no—
248C22×D4—1491no—
249C22×D4—1491no—
250C22×D4—1491no—
251C22×D4—1491no—
252C22×D4—1491no—
253C2×C4⋊C4—1491no—
254C2×C4⋊C4—1491no—
255C2×C4⋊C4—1491no—
256C2×C4⋊C4C2×D14911yescharacteristic
257C2×C22⋊C4—1491no—
258C2×C22⋊C4—1491no—
259C2×C22⋊C4—1491no—
260C2×C22⋊C4—1491no—
261C2×C22⋊C4—1491no—
262C2×C22⋊C4—1491no—
263C2×C22⋊C4—1491no—
264C2×C22⋊C4—1491no—
265C2×C22⋊C4—1491no—
266C2×C22⋊C4—1491no—
267C2×C22⋊C4—1491no—
268C2×C22⋊C4—1491no—
269C2×C22⋊C4—1491no—
270C2×C22⋊C4C2×D14911yescharacteristic
271C2×C22⋊C4C2×D14911yescharacteristic
272C2×C22⋊C4C2×D14911yescharacteristic
273C2×C42—1491no—
274#95—1491no—
275#95—1491no—
276#95—1491no—
277#95—1491no—
278#95—1491no—
279#95C2×D14911yescharacteristic
280#95C2×D14911yescharacteristic
281#95C2×D14911yescharacteristic
282C24—1491no—
283C24—1491no—
284C24—1491no—
285C24C22×D14911yescharacteristic
286C2×D4—2982no—
287C2×D4—5961no—
288C2×D4—5961no—
289C2×D4—5961no—
290C2×D4—5961no—
291C2×D4—5961no—
292C2×D4—5961no—
293C2×D4—5961no—
294C2×D4—5961no—
295C2×D4—5961no—
296C2×D4—5961no—
297C2×D4—5961no—
298C2×D4—5961no—
299C2×D4—5961no—
300C2×D4—5961no—
301C2×D4—5961no—
302C2×D4—5961no—
303C2×D4—5961no—
304C22×C4—1491no—
305C22×C4—1491no—
306C22×C4—1491no—
307C22×C4—1491no—
308C22×C4—1491no—
309C22×C4C22×D14911yescharacteristic
310C22×C4C22×D14911yescharacteristic
311C22×C4C22×D14911yescharacteristic
312C22×C4C22×D14911yescharacteristic
313C22×C4C22×D14911yescharacteristic
314C22×C4C22×D14911yescharacteristic
315C4⋊C4—41no—
316C4⋊C4—5961no—
317C4⋊C4—5961no—
318C4⋊C4—5961no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—2982no—
323C22⋊C4—2982no—
324C22⋊C4—5961no—
325C22⋊C4—5961no—
326C22⋊C4—5961no—
327C22⋊C4—5961no—
328C22⋊C4—5961no—
329C22⋊C4—5961no—
330C22⋊C4—5961no—
331C22⋊C4—5961no—
332C22⋊C4—5961no—
333C22⋊C4—5961no—
334C22⋊C4—5961no—
335C42—5961no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—2981no—
344C23—2981no—
345C23—2981no—
346C23—2981no—
347C23—2981no—
348C23—2981no—
349C23—2981no—
350C23—2981no—
351C23—2981no—
352C23—2981no—
353C23—2981no—
354C23—2981no—
355C23—2981no—
356C23—2981no—
357C23—2981no—
358C23—2981no—
359C23—2981no—
360C23—2981no—
361C23—2981no—
362C23—2981no—
363C23—2981no—
364C23C23×D14911yescharacteristic
365D4—5964no—
366D4—5964no—
367D4—5964no—
368D4—5964no—
369D4—5964no—
370D4—5964no—
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—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—2981no—
390C2×C4—2981no—
391C2×C4—2981no—
392C2×C4—2981no—
393C2×C4—2981no—
394C2×C4—2981no—
395C2×C4—2981no—
396C2×C4—2981no—
397C2×C4—2981no—
398C2×C4—2981no—
399C2×C4—2981no—
400C2×C4—2981no—
401C2×C4—2981no—
402C2×C4—2981no—
403C2×C4—1492no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—5961no—
412C22—5961no—
413C22—5961no—
414C22—5961no—
415C22—5961no—
416C22—5961no—
417C22—5961no—
418C22—5961no—
419C22—5961no—
420C22—5961no—
421C22—5961no—
422C22—5961no—
423C22—5961no—
424C22—5961no—
425C22—5961no—
426C22—5961no—
427C22—5961no—
428C22—5961no—
429C22—5961no—
430C22—5961no—
431C22—5961no—
432C22#41×D14911yescharacteristic
433C22#1801195611yescharacteristic
434C22#1801195611yescharacteristic
435C22#1801195711yescharacteristic
436C22#1801195711yescharacteristic
437C22#1801195711yescharacteristic
438C22#1801195711yescharacteristic
439C4—41no—
440C4—41no—
441C4—41no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—2982no—
446C4—5961no—
447C4—5961no—
448C4—5961no—
449C4—5961no—
450C2—81no—
451C2—11921no—
452C2—11921no—
453C2—11921no—
454C2#2375021411yescharacteristic
455C2#2375022711yescharacteristic
456C2#2375022711yescharacteristic
457C2#2375036311yescharacteristic
458C2#2375036511yescharacteristic
459C2#2375036611yescharacteristic
460C2#2375036711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#397×C149C2
hypercenter#397D149
hypocenterC149#2828
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #23749566C2semidirect
2. #23749552C2semidirect
3. #23749543C2semidirect
4. #23749543C2semidirect
5. #23749542C2semidirect
6. #23749541C2semidirect
7. #23749540C2semidirect
8. #23749535C2semidirect
9. #23749534C2semidirect
10. #23749534C2semidirect
11. #23749534C2semidirect
12. #23749525C2semidirect
13. #23749517C2semidirect
14. #23749515C2semidirect
15. #397×C149C2semidirect
230. C149#2828semidirect
234. #397D149semidirect

Maximal subgroups

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

subgroupindex
#237495662
#237495522
#237495432
#237495422
#237495412
#237495402
#237495352
#237495342
#237495252
#237495172
#237495152
#397×C1492
#2828149