Finite Group Databasebeta

← #34056415

Subgroups — #34056415

Order 19072.

494 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011932C211yesmaximal, characteristic, complemented
2#23750294C211yesmaximal, characteristic, complemented
3#23750274C211yesmaximal, characteristic, complemented
4#23749996C211yesmaximal, characteristic, complemented
5#23749854C211yesmaximal, characteristic, complemented
6#23749851C211yesmaximal, characteristic, complemented
7#23749833C211yesmaximal, characteristic, complemented
8#23749818C211yesmaximal, characteristic, complemented
9#23749787C211yesmaximal, characteristic, complemented
10#23749786C211yesmaximal, characteristic, complemented
11#23749770C211yesmaximal, characteristic, complemented
12#23749767C211yesmaximal, characteristic, complemented
13SD16×Dic149C211yesmaximal, characteristic, complemented
14C8×C22⋊D149C211yesmaximal, characteristic, complemented
15C2×#135×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18#18011932—24no—
19C2×#14558726C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558724C2211yescharacteristic
22C2×#14558723C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24C2×C8×D149C2211yescharacteristic
25#18011909C2211yescharacteristic
26#18011907—21no—
27#18011907C2211yescharacteristic
28#18011894—21no—
29#18011892—21no—
30#18011890C2211yescharacteristic
31#18011887C2211yescharacteristic
32#18011885—21no—
33#18011885C2211yescharacteristic
34#18011883—21no—
35#18011882—21no—
36#18011882C2211yescharacteristic
37Q8×Dic149C2211yescharacteristic
38D4×Dic149C2211yescharacteristic
39C4×C22⋊D149—21no—
40C4×C22⋊D149C2211yescharacteristic
41C2×#14558715—21no—
42#18011843C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011832C2211yescharacteristic
50C22⋊#11924746C2211yescharacteristic
51#18011823C2211yescharacteristic
52C8×Dic149C2211yescharacteristic
53C2×#41×C149C2211yescharacteristic
54C2×#41×C149C2211yescharacteristic
55#135×C149—24no—
56C2×Q16×C149C2211yescharacteristic
57C2×SD16×C149C2211yescharacteristic
58C2×SD16×C149C2211yescharacteristic
59C2×D8×C149C2211yescharacteristic
60C22×C8×C149C2211yescharacteristic
61#14558737—22no—
62#14558737—41no—
63#14558735—22no—
64#14558735—41no—
65C2×Dic298C2311yescharacteristic
66C2×D596—21no—
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C2×C22⋊D149D411yescharacteristic
74C22×Dic149—21no—
75C22×Dic149—21no—
76C2×C4×D149—21no—
77C2×C4×D149C2311yescharacteristic
78#14558726—22no—
79#14558725—22no—
80#14558724—41no—
81#14558723—41no—
82#14558721—22no—
83C2×#11924746C2311yescharacteristic
84C2×#11924746C2311yescharacteristic
85C8×D149—22no—
86C4⋊Dic149—21no—
87C4⋊Dic149C2311yescharacteristic
88C4⋊Dic149C2311yescharacteristic
89#14558715—21no—
90#14558715—21no—
91#14558715—21no—
92#14558715—21no—
93#14558715D411yescharacteristic
94C22⋊Dic149—21no—
95C22⋊Dic149—21no—
96C22⋊Dic149—21no—
97C22⋊Dic149D411yescharacteristic
98#14558713—21no—
99#14558713—21no—
100#14558713D411yescharacteristic
101C4×Dic149—21no—
102C4×Dic149C2311yescharacteristic
103#41×C149—22no—
104#41×C149—22no—
105#41×C149—41no—
106#41×C149—41no—
107C2×Q8×C149C2311yescharacteristic
108C2×Q8×C149C2311yescharacteristic
109C2×D4×C149—21no—
110C2×D4×C149—21no—
111C2×D4×C149C2311yescharacteristic
112C2×D4×C149C2311yescharacteristic
113C22×C4×C149—21no—
114C22×C4×C149—21no—
115C22×C4×C149C2311yescharacteristic
116Q16×C149—22no—
117SD16×C149—22no—
118SD16×C149D414yescomplemented
119D8×C149—22no—
120C2×C8×C149—22no—
121C2×C8×C149C2311yescharacteristic
122C2×C8×C149C2311yescharacteristic
123C22×D149—21no—
124C22×D149C2×D411yescharacteristic
125Dic298—21no—
126Dic298—21no—
127D596—21no—
128D596—21no—
129D596—42no—
130C22⋊D149—22no—
131C22⋊D149—42no—
132C22⋊D149—42no—
133C22⋊D149—81no—
134C22⋊D149—81no—
135C22⋊D149—81no—
136C2×Dic149—21no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C2×Dic149—42no—
140C2×Dic149—42no—
141C2×Dic149C2×D411yescharacteristic
142C2×Dic149C2×D411yescharacteristic
143C2×Dic149C2×D411yescharacteristic
144C4×D149—21no—
145C4×D149—21no—
146C4×D149—42no—
147#11924746—21no—
148#11924746—21no—
149C23×C149—21no—
150C23×C149—21no—
151C23×C149C2×D411yescharacteristic
152Q8×C149—21no—
153Q8×C149—21no—
154Q8×C149—21no—
155Q8×C149C2×D412yes—
156D4×C149—21no—
157D4×C149—21no—
158D4×C149—21no—
159D4×C149—42no—
160D4×C149—42no—
161D4×C149C2×D412yes—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—42no—
167C2×C4×C149—42no—
168C2×C4×C149C2×D411yescharacteristic
169C2×C4×C149C2411yescharacteristic
170C8×C149—21no—
171C8×C149C2×D412yes—
172C22×C149—21no—
173C22×C149—22no—
174C22×C149—21no—
175C22×C149—21no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149—41no—
179C22×C149—41no—
180C22×C149—41no—
181C22×C149C22×D411yescharacteristic
182C2×D149—21no—
183C2×D149—21no—
184C2×D149—21no—
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—41no—
188C4×C149—21no—
189C4×C149—22no—
190C4×C149—41no—
191C4×C149C22×D411yescharacteristic
192C4×C149H(5,𝔽2)11yescharacteristic
193Dic149—21no—
194Dic149—21no—
195Dic149—41no—
196Dic149—41no—
197Dic149—41no—
198Dic149#13512yescomplemented
199C2×C149—41no—
200C2×C149—42no—
201C2×C149—81no—
202C2×C149D4211yescharacteristic
203C2×C149C2×#13511yescharacteristic
204C2×C149#57711yescharacteristic
205D149—41no—
206D149—81no—
207C149#328411yescharacteristic, complemented, Sylow
208#3284—1491nomaximal, Sylow
209C2×#135—1491no—
210C2×#135D14911yescharacteristic, complemented
211#550—1491no—
212#547—1491no—
213#492—1491no—
214#465—1491no—
215#465—1491no—
216#462—1491no—
217#459—1491no—
218#452—1491no—
219#452—1491no—
220#449—1491no—
221#449—1491no—
222C4×SD16—1491no—
223C8×D4—1491no—
224C2×#41—1491no—
225C2×#41—1491no—
226C2×#41C2×D14911yescharacteristic
227C2×#41C2×D14911yescharacteristic
228#135—24no—
229#135—2984no—
230C2×Q16—1491no—
231C2×Q16C2×D14911yescharacteristic
232C2×SD16—1491no—
233C2×SD16—1491no—
234C2×SD16—1491no—
235C2×SD16C2×D14911yescharacteristic
236C2×SD16C2×D14911yescharacteristic
237C2×D8—1491no—
238C2×D8C2×D14911yescharacteristic
239C22×C8—1491no—
240C22×C8C2×D14911yescharacteristic
241C4⋊Q8—1491no—
242#127—2981no—
243#127—1491no—
244#123—2981no—
245#123—2981no—
246C22⋊Q8—1491no—
247C22⋊Q8—1491no—
248#121—2981no—
249#121—2981no—
250#121—2981no—
251#121—1491no—
252#121—1491no—
253C4×Q8—1491no—
254C4×D4—2981no—
255C4×D4—1491no—
256C4×D4—1491no—
257C2×C4⋊C4—2981no—
258#106—1491no—
259C4⋊C8—1491no—
260#103—1491no—
261#103—1491no—
262#103—1491no—
263#102—1491no—
264#102—1491no—
265#102—1491no—
266C22⋊C8—1491no—
267C22⋊C8—1491no—
268C4×C8—1491no—
269#41—22no—
270#41—22no—
271#41—41no—
272#41—41no—
273#41—2982no—
274#41—2982no—
275#41—5961no—
276#41—5961no—
277C2×Q8—1491no—
278C2×Q8C22×D14911yescharacteristic
279C2×Q8C22×D14911yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—2981no—
283C2×D4—2981no—
284C2×D4—2981no—
285C2×D4—2981no—
286C2×D4—2981no—
287C2×D4—2981no—
288C2×D4—1491no—
289C2×D4—1491no—
290C2×D4C22×D14911yescharacteristic
291C2×D4C22×D14911yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—2981no—
295C22×C4—2981no—
296C22×C4—2981no—
297C22×C4—1491no—
298C22×C4C22×D14911yescharacteristic
299Q16—22no—
300Q16—2982no—
301SD16—22no—
302SD16—2982no—
303SD16—5961no—
304SD16—5961no—
305SD16C22⋊D14914yescomplemented
306D8—22no—
307D8—2982no—
308C2×C8—22no—
309C2×C8—2982no—
310C2×C8—1491no—
311C2×C8—1491no—
312C2×C8C22×D14911yescharacteristic
313C2×C8C22×D14911yescharacteristic
314C4⋊C4—2981no—
315C4⋊C4—2981no—
316C4⋊C4—2981no—
317C4⋊C4—2981no—
318C4⋊C4—2981no—
319C4⋊C4—1491no—
320C4⋊C4—1491no—
321C4⋊C4—1491no—
322C22⋊C4—2981no—
323C22⋊C4—2981no—
324C22⋊C4—2981no—
325C22⋊C4—2981no—
326C22⋊C4—2981no—
327C22⋊C4—1491no—
328C22⋊C4—1491no—
329C42—2981no—
330C42—1491no—
331C23—21no—
332C23—21no—
333C23—2981no—
334C23—1491no—
335C23D4×D14911yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—2981no—
340Q8—2981no—
341Q8C2×C22⋊D14912yes—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—42no—
347D4—2982no—
348D4—2981no—
349D4—2981no—
350D4—5962no—
351D4—5962no—
352D4—5962no—
353D4—11921no—
354D4—11921no—
355D4—11921no—
356D4C2×C22⋊D14912yes—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—2981no—
364C2×C4—2981no—
365C2×C4—2981no—
366C2×C4—2981no—
367C2×C4—2981no—
368C2×C4—5962no—
369C2×C4—5962no—
370C2×C4—5962no—
371C2×C4—1491no—
372C2×C4—1491no—
373C2×C4—1491no—
374C2×C4D4×D14911yescharacteristic
375C2×C4C23×D14911yescharacteristic
376C8—21no—
377C8—2981no—
378C8—2981no—
379C8C2×C22⋊D14912yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—2981no—
390C22—2981no—
391C22—2981no—
392C22—5961no—
393C22—5961no—
394C22—5961no—
395C22C2×D4×D14911yescharacteristic
396C4—21no—
397C4—22no—
398C4—41no—
399C4—2981no—
400C4—2981no—
401C4—5961no—
402C4—5961no—
403C4—5961no—
404C4—1492no—
405C4C22×C22⋊D14911yescharacteristic
406C4#1801195611yescharacteristic
407C2—41no—
408C2—42no—
409C2—81no—
410C2—5961no—
411C2—11921no—
412C2D4×C22⋊D14911yescharacteristic
413C2#135×D14911yescharacteristic
414C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#135×C149C2
socleC22×C149C22×D4
hypercenterC2×#135D149
hypocenterC149#3284
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#18011932C2semidirect
2. #23750294C2semidirect
3. #23750274C2semidirect
4. #23749996C2semidirect
5. #23749854C2semidirect
6. #23749851C2semidirect
7. #23749833C2semidirect
8. #23749818C2semidirect
9. #23749787C2semidirect
10. #23749786C2semidirect
11. #23749770C2semidirect
12. #23749767C2semidirect
13. SD16×Dic149C2semidirect
14. C8×C22⋊D149C2semidirect
15. C2×#135×C149C2semidirect
118. SD16×C149D4semidirect
198. Dic149#135semidirect
207. C149#3284semidirect
210. C2×#135D149semidirect
305. SD16C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119322
#237502942
#237502742
#237499962
#237498542
#237498512
#237498332
#237498182
#237497872
#237497862
#237497702
#237497672
SD16×Dic1492
C8×C22⋊D1492
C2×#135×C1492
#3284149