Finite Group Databasebeta

← #34070235

Subgroups — #34070235

Order 19328.

638 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752771C211yesmaximal, characteristic, complemented
2C2×#18012709C211yesmaximal, characteristic, complemented
3C2×#18012707C211yesmaximal, characteristic, complemented
4C2×#18012653C211yesmaximal, characteristic, complemented
5#23752067C211yesmaximal, characteristic, complemented
6#23751978C211yesmaximal, characteristic, complemented
7C2×#99×C151C211yesmaximal, characteristic, complemented
8C24×D151C2211yescharacteristic
9C22×D604—21no—
10C22×C22⋊D151—21no—
11C22×C22⋊D151C2211yescharacteristic
12#18012722—21no—
13#18012720—21no—
14#18012711—22no—
15#18012709—22no—
16#18012709—22no—
17#18012708—21no—
18#18012707—21no—
19#18012707—22no—
20#18012707—22no—
21C2×C22⋊Dic151C2211yescharacteristic
22C2×C22⋊Dic151C2211yescharacteristic
23C2×(C2×D151)⋊C4—21no—
24C2×(C2×D151)⋊C4—21no—
25C2×(C2×D151)⋊C4—22no—
26#18012653—22no—
27C22×D4×C151C2211yescharacteristic
28C2×C22⋊C4×C151C2211yescharacteristic
29C2×C22⋊C4×C151C2211yescharacteristic
30#99×C151—22no—
31C23×D151—21no—
32C23×D151—21no—
33C23×D151—21no—
34C23×D151—21no—
35C23×D151—21no—
36C23×D151—21no—
37C23×D151—44no—
38C23×D151D412yescomplemented
39C23×D151D411yescharacteristic, complemented
40C2×D604—24no—
41C2×D604—44no—
42C2×C22⋊D151—24no—
43C2×C22⋊D151—22no—
44C2×C22⋊D151—21no—
45C2×C22⋊D151—21no—
46C2×C22⋊D151—21no—
47C2×C22⋊D151—21no—
48C2×C22⋊D151—21no—
49C2×C22⋊D151—21no—
50C2×C22⋊D151—44no—
51C22×Dic151—21no—
52C22×Dic151D411yescharacteristic, complemented
53C22×Dic151D412yescomplemented
54Dic151⋊C4—22no—
55C22⋊Dic151—22no—
56C22⋊Dic151—21no—
57C22⋊Dic151—21no—
58C22⋊Dic151—21no—
59C22⋊Dic151D412yescomplemented
60(C2×D151)⋊C4—24no—
61(C2×D151)⋊C4—24no—
62(C2×D151)⋊C4—22no—
63(C2×D151)⋊C4—44no—
64C24×C151D411yescharacteristic, complemented
65C24×C151C2311yescharacteristic
66C2×D4×C151—21no—
67C2×D4×C151—21no—
68C2×D4×C151—21no—
69C2×D4×C151—21no—
70C2×D4×C151—21no—
71C2×D4×C151—21no—
72C22×C4×C151—21no—
73C22×C4×C151—21no—
74C22×C4×C151D411yescharacteristic, complemented
75C22⋊C4×C151—21no—
76C22⋊C4×C151—21no—
77C22⋊C4×C151—21no—
78C22⋊C4×C151D412yescomplemented
79C22×D151—24no—
80C22×D151—24no—
81C22×D151—24no—
82C22×D151—22no—
83C22×D151—22no—
84C22×D151—22no—
85C22×D151—21no—
86C22×D151—21no—
87C22×D151—21no—
88C22×D151—44no—
89C22×D151—44no—
90C22×D151—44no—
91C22×D151—44no—
92C22×D151—42no—
93C22×D151—42no—
94C22×D151—42no—
95C22×D151—41no—
96C22×D151—41no—
97C22×D151—41no—
98C22×D151—41no—
99C22×D151—42no—
100D604—48no—
101C22⋊D151—48no—
102C22⋊D151—41no—
103C22⋊D151—41no—
104C22⋊D151—41no—
105C22⋊D151—41no—
106C22⋊D151—82no—
107C2×Dic151—21no—
108C2×Dic151—22no—
109C2×Dic151—22no—
110C2×Dic151—21no—
111C2×Dic151—21no—
112C2×Dic151—42no—
113C2×Dic151—42no—
114C23×C151—21no—
115C23×C151—21no—
116C23×C151—21no—
117C23×C151—42no—
118C23×C151—42no—
119C23×C151C2×D411yescharacteristic
120C23×C151C2×D411yescharacteristic
121C23×C151C2×D411yescharacteristic
122C23×C151C2×D411yescharacteristic
123C23×C151C2×D411yescharacteristic
124C23×C151C2×D411yescharacteristic
125C23×C151#4111yescharacteristic
126D4×C151—41no—
127D4×C151—41no—
128D4×C151—41no—
129D4×C151—41no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—22no—
133C2×C4×C151—21no—
134C2×C4×C151—42no—
135C2×C4×C151—42no—
136C2×C4×C151—41no—
137C22×C151—22no—
138C22×C151—22no—
139C22×C151—22no—
140C22×C151—41no—
141C22×C151—41no—
142C22×C151—41no—
143C22×C151—41no—
144C22×C151—42no—
145C22×C151—41no—
146C22×C151—42no—
147C22×C151—81no—
148C22×C151#12011yescharacteristic
149C22×C151#12011yescharacteristic
150C22×C151#12011yescharacteristic
151C22×C151#12111yescharacteristic
152C22×C151#12111yescharacteristic
153C22×C151#12111yescharacteristic
154C22×C151#12711yescharacteristic
155C2×D151—24no—
156C2×D151—24no—
157C2×D151—24no—
158C2×D151—42no—
159C2×D151—42no—
160C2×D151—44no—
161C2×D151—42no—
162C2×D151—44no—
163C2×D151—44no—
164C2×D151—42no—
165C2×D151—44no—
166C2×D151—42no—
167C2×D151—41no—
168C2×D151—42no—
169C2×D151—81no—
170C4×C151—42no—
171C4×C151—41no—
172C4×C151—81no—
173Dic151—42no—
174Dic151—41no—
175Dic151—42no—
176C2×C151—21no—
177C2×C151—21no—
178C2×C151—21no—
179C2×C151—21no—
180C2×C151—21no—
181C2×C151—21no—
182C2×C151—81no—
183C2×C151#39211yescharacteristic
184C2×C151B(4,𝔽2)12yes—
185D151—44no—
186D151—81no—
187C151#202111yescharacteristic, complemented, Sylow
188#2021—1511nomaximal, Sylow
189#534—1511no—
190C2×#120—1511no—
191C2×#120—1511no—
192C2×#99—1511no—
193C2×#99D15111yescharacteristic, complemented
194#379—1511no—
195#342—1511no—
196C25—1511no—
197C22×D4—3021no—
198C22×D4—3021no—
199C22×D4—1511no—
200C22×D4C2×D15111yescharacteristic
201#123—3021no—
202#123—3021no—
203#121—3022no—
204#120—3022no—
205#120—3022no—
206#120—3021no—
207#120—3021no—
208#120—3022no—
209#120—3022no—
210C2×C22⋊C4—3021no—
211C2×C22⋊C4—3021no—
212C2×C22⋊C4—3022no—
213C2×C22⋊C4—1511no—
214C2×C22⋊C4—1511no—
215C2×C22⋊C4C2×D15111yescharacteristic
216C2×C22⋊C4C2×D15111yescharacteristic
217#99—22no—
218#99—3022no—
219C24—3021no—
220C24—3021no—
221C24—3021no—
222C24—3021no—
223C24—3021no—
224C24—3021no—
225C24—6044no—
226C24—1512no—
227C24—1511no—
228C24D60411yescharacteristic, complemented
229C24C22×D15111yescharacteristic
230C2×D4—21no—
231C2×D4—21no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—3024no—
237C2×D4—3024no—
238C2×D4—3021no—
239C2×D4—3021no—
240C2×D4—3021no—
241C2×D4—3021no—
242C2×D4—3021no—
243C2×D4—3021no—
244C2×D4—3022no—
245C2×D4—6044no—
246C2×D4—6044no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—3021no—
250C22×C4—1511no—
251C22×C4—1512no—
252C22×C4D60411yescharacteristic, complemented
253C4⋊C4—3022no—
254C22⋊C4—21no—
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4—3024no—
258C22⋊C4—3024no—
259C22⋊C4—3022no—
260C22⋊C4—3022no—
261C22⋊C4—3021no—
262C22⋊C4—3021no—
263C22⋊C4—3021no—
264C22⋊C4—6044no—
265C22⋊C4—1512no—
266C22⋊C4C22⋊D15112yescomplemented
267C23—21no—
268C23—21no—
269C23—21no—
270C23—42no—
271C23—42no—
272C23—3024no—
273C23—3024no—
274C23—3024no—
275C23—3022no—
276C23—3022no—
277C23—3022no—
278C23—3021no—
279C23—3021no—
280C23—3021no—
281C23—6042no—
282C23—6042no—
283C23—6042no—
284C23—6042no—
285C23—6044no—
286C23—6044no—
287C23—6044no—
288C23—6044no—
289C23—6041no—
290C23—6041no—
291C23—6041no—
292C23—6041no—
293C23D4×D15111yescharacteristic
294C23D4×D15111yescharacteristic
295C23D4×D15111yescharacteristic
296C23D4×D15111yescharacteristic
297C23C2×C22⋊D15111yescharacteristic
298C23C2×D60411yescharacteristic
299C23#1455900411yescharacteristic
300D4—41no—
301D4—41no—
302D4—41no—
303D4—41no—
304D4—6048no—
305D4—6048no—
306D4—6041no—
307D4—6041no—
308D4—6041no—
309D4—6041no—
310D4—12082no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—3021no—
319C2×C4—3022no—
320C2×C4—3022no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—6042no—
324C2×C4—6042no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—42no—
333C22—41no—
334C22—42no—
335C22—81no—
336C22—3024no—
337C22—3024no—
338C22—3024no—
339C22—6042no—
340C22—6044no—
341C22—6042no—
342C22—6044no—
343C22—6042no—
344C22—6044no—
345C22—6042no—
346C22—6042no—
347C22—6044no—
348C22—6041no—
349C22—6042no—
350C22—12081no—
351C22#1801270711yescharacteristic
352C22#1801270911yescharacteristic
353C22#1801270911yescharacteristic
354C22#1801271211yescharacteristic
355C22#1801271211yescharacteristic
356C22#1801271311yescharacteristic
357C22#1801273511yescharacteristic
358C4—42no—
359C4—41no—
360C4—81no—
361C4—6042no—
362C4—6041no—
363C4—6042no—
364C2—21no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—81no—
371C2—6044no—
372C2—12081no—
373C2#2375212111yescharacteristic
374C2#2375240012yes—
subgroupG/H
centerC22#18012709
commutator, cosocleC24×C151C23
FrattiniC24C22×D151
FittingC2×#99×C151C2
socleC22×C151#120
hypercenterC2×#99D151
hypocenterC151#2021
LCSG ▷ C24×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. #23752771C2semidirect
2. C2×#18012709C2semidirect
3. C2×#18012707C2semidirect
4. C2×#18012653C2semidirect
5. #23752067C2semidirect
6. #23751978C2semidirect
7. C2×#99×C151C2semidirect
38. C23×D151D4semidirect
39. C23×D151D4semidirect
52. C22×Dic151D4semidirect
53. C22×Dic151D4semidirect
59. C22⋊Dic151D4semidirect
64. C24×C151D4semidirect
74. C22×C4×C151D4semidirect
78. C22⋊C4×C151D4semidirect
187. C151#2021semidirect
193. C2×#99D151semidirect
228. C24D604semidirect
252. C22×C4D604semidirect
266. C22⋊C4C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237527712
C2×#180127092
C2×#180127072
C2×#180126532
#237520672
#237519782
C2×#99×C1512
#2021151