Finite Group Databasebeta

← #34056444

Subgroups — #34056444

Order 19072.

504 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011932C211yesmaximal, characteristic, complemented
2C2×#18011931C211yesmaximal, characteristic, complemented
3#23750294C211yesmaximal, characteristic, complemented
4#23750293C211yesmaximal, characteristic, complemented
5#23750000C211yesmaximal, characteristic, complemented
6#23749860C211yesmaximal, characteristic, complemented
7#23749859C211yesmaximal, characteristic, complemented
8#23749824C211yesmaximal, characteristic, complemented
9#23749823C211yesmaximal, characteristic, complemented
10#23749773C211yesmaximal, characteristic, complemented
11#23749772C211yesmaximal, characteristic, complemented
12#23749767C211yesmaximal, characteristic, complemented
13#23749717C211yesmaximal, characteristic, complemented
14#23749688C211yesmaximal, characteristic, complemented
15#449×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558736C2211yescharacteristic
18C2×#14558735C2211yescharacteristic
19#18011932—24no—
20#18011931—24no—
21C2×#14558726C2211yescharacteristic
22C2×#14558725C2211yescharacteristic
23C2×#14558724C2211yescharacteristic
24C2×#14558723C2211yescharacteristic
25C2×D1192C2211yescharacteristic
26C2×#14558721C2211yescharacteristic
27C2×#14558721C2211yescharacteristic
28C22×#11924746C2211yescharacteristic
29C2×C8×D149C2211yescharacteristic
30#18011907—21no—
31#18011907—21no—
32#18011907C2211yescharacteristic
33#18011907C2211yescharacteristic
34#18011886C2211yescharacteristic
35#18011885—21no—
36#18011885C2211yescharacteristic
37#18011884—21no—
38#18011883—21no—
39#18011882—21no—
40#18011882C2211yescharacteristic
41Q8×Dic149C2211yescharacteristic
42#18011876C2211yescharacteristic
43C4×C22⋊D149—21no—
44C4×C22⋊D149C2211yescharacteristic
45#18011871—21no—
46#18011844C2211yescharacteristic
47#18011840C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011832C2211yescharacteristic
51#18011831C2211yescharacteristic
52#18011823C2211yescharacteristic
53C8×Dic149C2211yescharacteristic
54C2×#41×C149C2211yescharacteristic
55C2×SD16×C149C2211yescharacteristic
56C2×D8×C149C2211yescharacteristic
57#121×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59#102×C149C2211yescharacteristic
60C22⋊C8×C149C2211yescharacteristic
61#14558737—22no—
62#14558737—41no—
63#14558736—22no—
64#14558736—41no—
65#14558735—22no—
66#14558735—41no—
67C2×Dic298C2311yescharacteristic
68C2×D596—21no—
69C2×D596—21no—
70C2×D596C2311yescharacteristic
71C2×D596C2311yescharacteristic
72C2×C22⋊D149—21no—
73C2×C22⋊D149—21no—
74C2×C22⋊D149—21no—
75C2×C22⋊D149—21no—
76C2×C22⋊D149—21no—
77C2×C22⋊D149—21no—
78C2×C22⋊D149—21no—
79C2×C22⋊D149—21no—
80C2×C22⋊D149D411yescharacteristic
81C22×Dic149—21no—
82C2×C4×D149—21no—
83C2×C4×D149—21no—
84C2×C4×D149C2311yescharacteristic
85#14558726D414yescomplemented
86#14558725—22no—
87#14558724—22no—
88#14558723—22no—
89D1192—41no—
90#14558721—22no—
91#14558721—22no—
92C2×#11924746—22no—
93C2×#11924746C2311yescharacteristic
94C2×#11924746C2311yescharacteristic
95C8×D149—22no—
96C4⋊Dic149—21no—
97C4⋊Dic149C2311yescharacteristic
98#14558715—21no—
99#14558715D411yescharacteristic
100C22⋊Dic149—21no—
101C22⋊Dic149D411yescharacteristic
102#14558713—21no—
103#14558713—21no—
104#14558713D411yescharacteristic
105C4×Dic149—21no—
106C4×Dic149—21no—
107C4×Dic149C2311yescharacteristic
108#41×C149—22no—
109#41×C149—41no—
110C2×Q8×C149C2311yescharacteristic
111C2×D4×C149—21no—
112C2×D4×C149—21no—
113C2×D4×C149C2311yescharacteristic
114C2×D4×C149C2311yescharacteristic
115C22×C4×C149—21no—
116C22×C4×C149C2311yescharacteristic
117SD16×C149—22no—
118D8×C149—41no—
119C2×C8×C149C2311yescharacteristic
120C2×C8×C149C2311yescharacteristic
121C4⋊C4×C149C2311yescharacteristic
122C22⋊C4×C149—21no—
123C22×D149—21no—
124C22×D149—21no—
125C22×D149C2×D411yescharacteristic
126Dic298—21no—
127Dic298C2×D412yes—
128D596—21no—
129D596—21no—
130D596—21no—
131D596—21no—
132D596—42no—
133D596—81no—
134C22⋊D149—22no—
135C22⋊D149—42no—
136C22⋊D149—42no—
137C22⋊D149—42no—
138C22⋊D149—42no—
139C22⋊D149—81no—
140C22⋊D149—81no—
141C22⋊D149—81no—
142C22⋊D149—81no—
143C2×Dic149—21no—
144C2×Dic149—21no—
145C2×Dic149—42no—
146C2×Dic149C2×D411yescharacteristic
147C2×Dic149C2×D411yescharacteristic
148C2×Dic149C2×D411yescharacteristic
149C4×D149—21no—
150C4×D149—21no—
151C4×D149—42no—
152C4×D149—42no—
153#11924746—21no—
154#11924746C2×D412yes—
155C23×C149—21no—
156C23×C149—21no—
157C23×C149C2×D411yescharacteristic
158Q8×C149—21no—
159Q8×C149C2×D412yes—
160D4×C149—21no—
161D4×C149—21no—
162D4×C149—21no—
163D4×C149—21no—
164D4×C149—42no—
165D4×C149—81no—
166C2×C4×C149—21no—
167C2×C4×C149—21no—
168C2×C4×C149—21no—
169C2×C4×C149—21no—
170C2×C4×C149—42no—
171C2×C4×C149C2×D411yescharacteristic
172C2×C4×C149C2411yescharacteristic
173C8×C149—21no—
174C8×C149—21no—
175C22×C149—21no—
176C22×C149—21no—
177C22×C149—21no—
178C22×C149—41no—
179C22×C149—41no—
180C22×C149—41no—
181C22×C149—41no—
182C22×C149—41no—
183C22×C149—41no—
184C22×C149C22×D411yescharacteristic
185C2×D149—21no—
186C2×D149—21no—
187C2×D149—21no—
188C2×D149—41no—
189C2×D149—41no—
190C2×D149—41no—
191C2×D149—41no—
192C2×D149—41no—
193C2×D149—41no—
194C4×C149—21no—
195C4×C149—22no—
196C4×C149—41no—
197C4×C149C22×D411yescharacteristic
198C4×C149H(5,𝔽2)11yescharacteristic
199Dic149—21no—
200Dic149—22no—
201Dic149—21no—
202Dic149—41no—
203Dic149#13512yescomplemented
204C2×C149—41no—
205C2×C149—81no—
206C2×C149—81no—
207C2×C149D4211yescharacteristic
208C2×C149C2×#13511yescharacteristic
209C2×C149#57611yescharacteristic
210D149—41no—
211D149—81no—
212D149—81no—
213C149#328711yescharacteristic, complemented, Sylow
214#3287—1491nomaximal, Sylow
215C2×#135—1491no—
216C2×#135—1491no—
217#550—1491no—
218#550—1491no—
219#493—1491no—
220#466—1491no—
221#466—1491no—
222#460—1491no—
223#460—1491no—
224#449—1491no—
225#449—1491no—
226#449—1491no—
227#449D14911yescharacteristic, complemented
228C4×Q16—1491no—
229C8×D4—1491no—
230C2×#41—1491no—
231C2×#41—1491no—
232C2×#41—1491no—
233C2×#41C2×D14911yescharacteristic
234#135—2984no—
235#135—2984no—
236C2×Q16—1491no—
237C2×SD16—1491no—
238C2×SD16—1491no—
239C2×SD16—1491no—
240C2×SD16C2×D14911yescharacteristic
241C2×D8—1491no—
242C2×D8—1491no—
243C2×D8—1491no—
244C2×D8C2×D14911yescharacteristic
245C22×C8—1491no—
246C22×C8—1491no—
247#127—2981no—
248#127—2981no—
249#127—1491no—
250#127—1491no—
251#121—2981no—
252#121—2981no—
253#121—2981no—
254#121—2981no—
255#121—1491no—
256#121—1491no—
257#121—1491no—
258#121C2×D14911yescharacteristic
259C4×Q8—1491no—
260C4×Q8—1491no—
261C4×D4—2981no—
262C4×D4—2981no—
263C4×D4—1491no—
264#107—1491no—
265C4⋊C8—1491no—
266#103—1491no—
267#103C2×D14911yescharacteristic
268#102—1491no—
269#102—1491no—
270#102—1491no—
271#102C2×D14911yescharacteristic
272C22⋊C8—1491no—
273C22⋊C8C2×D14911yescharacteristic
274C4×C8—1491no—
275#41—22no—
276#41—41no—
277#41—2982no—
278#41—2982no—
279#41—2982no—
280#41—5961no—
281#41—5961no—
282#41—5961no—
283C2×Q8—1491no—
284C2×Q8C22×D14911yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—2981no—
288C2×D4—2981no—
289C2×D4—2981no—
290C2×D4—2981no—
291C2×D4—2981no—
292C2×D4—2981no—
293C2×D4—2981no—
294C2×D4—2981no—
295C2×D4—2981no—
296C2×D4—2981no—
297C2×D4—1491no—
298C2×D4—1491no—
299C2×D4—1491no—
300C2×D4C22×D14911yescharacteristic
301C2×D4C22×D14911yescharacteristic
302C22×C4—21no—
303C22×C4—2981no—
304C22×C4—2981no—
305C22×C4—2981no—
306C22×C4—1491no—
307C22×C4C22×D14911yescharacteristic
308Q16—1494no—
309SD16—22no—
310SD16—2982no—
311SD16—2982no—
312SD16—2982no—
313D8—41no—
314D8—2982no—
315D8—2982no—
316D8—5961no—
317C2×C8—2982no—
318C2×C8—2982no—
319C2×C8—1491no—
320C2×C8—1491no—
321C2×C8C22×D14911yescharacteristic
322C2×C8C22×D14911yescharacteristic
323C4⋊C4—2981no—
324C4⋊C4—2981no—
325C4⋊C4—1491no—
326C4⋊C4—1491no—
327C4⋊C4C22×D14911yescharacteristic
328C22⋊C4—21no—
329C22⋊C4—2981no—
330C22⋊C4—2981no—
331C22⋊C4—2981no—
332C22⋊C4—1491no—
333C22⋊C4—1491no—
334C42—2981no—
335C42—2981no—
336C42—1491no—
337C23—21no—
338C23—21no—
339C23—2981no—
340C23—2981no—
341C23—1491no—
342C23D4×D14911yescharacteristic
343Q8—21no—
344Q8—2981no—
345Q8—1492no—
346Q8D4×D14912yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—81no—
353D4—2982no—
354D4—2981no—
355D4—2981no—
356D4—2981no—
357D4—2981no—
358D4—5962no—
359D4—5962no—
360D4—5962no—
361D4—5962no—
362D4—5962no—
363D4—11921no—
364D4—11921no—
365D4—11921no—
366D4—11921no—
367D4—11921no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—42no—
373C2×C4—2981no—
374C2×C4—2981no—
375C2×C4—2981no—
376C2×C4—2981no—
377C2×C4—5962no—
378C2×C4—5962no—
379C2×C4—5962no—
380C2×C4—1491no—
381C2×C4—1491no—
382C2×C4—1491no—
383C2×C4D4×D14911yescharacteristic
384C2×C4C23×D14911yescharacteristic
385C8—21no—
386C8—21no—
387C8—2981no—
388C8—1492no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—2981no—
399C22—2981no—
400C22—2981no—
401C22—5961no—
402C22—5961no—
403C22—5961no—
404C22—5961no—
405C22—5961no—
406C22—5961no—
407C22C2×D4×D14911yescharacteristic
408C4—21no—
409C4—22no—
410C4—41no—
411C4—2981no—
412C4—2981no—
413C4—2982no—
414C4—5961no—
415C4—1492no—
416C4C2×D4×D14911yescharacteristic
417C4#1801195611yescharacteristic
418C2—41no—
419C2—81no—
420C2—81no—
421C2—5961no—
422C2—11921no—
423C2—11921no—
424C2#2375025711yescharacteristic
425C2#135×D14911yescharacteristic
426C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#449×C149C2
socleC22×C149C22×D4
hypercenter#449D149
hypocenterC149#3287
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#18011932C2semidirect
2. C2×#18011931C2semidirect
3. #23750294C2semidirect
4. #23750293C2semidirect
5. #23750000C2semidirect
6. #23749860C2semidirect
7. #23749859C2semidirect
8. #23749824C2semidirect
9. #23749823C2semidirect
10. #23749773C2semidirect
11. #23749772C2semidirect
12. #23749767C2semidirect
13. #23749717C2semidirect
14. #23749688C2semidirect
15. #449×C149C2semidirect
85. #14558726D4semidirect
203. Dic149#135semidirect
213. C149#3287semidirect
227. #449D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119322
C2×#180119312
#237502942
#237502932
#237500002
#237498602
#237498592
#237498242
#237498232
#237497732
#237497722
#237497672
#237497172
#237496882
#449×C1492
#3287149