Finite Group Databasebeta

← #34001349

Subgroups — #34001349

Order 18688.

604 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 146 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#22625785C211yesmaximal, characteristic
2C4×C22⋊#10596833C211yesmaximal, characteristic
3#22624750C214yesmaximal, complemented
4C2×#17988483C211yesmaximal, characteristic
5C2×C4⋊#10596833—21no—
6C2×C22⋊#10596833—21no—
7C2×C22⋊#10596833—21no—
8C2×C4×#10596833—21no—
9#17989453C2212yes—
10#17989453C2212yes—
11C22×C4⋊Dic73C411yescharacteristic
12C22×#11924007—21no—
13C22×C4×Dic73C2211yescharacteristic
14#17988483—21no—
15#17988483—21no—
16#17988483C412yes—
17#17988483C2212yes—
18C2×#14556498—21no—
19C22×C4⋊C4×C73C411yescharacteristic
20C22×#10596833—22no—
21C22×#10596833—22no—
22C4⋊#10596833—42no—
23C22⋊#10596833—24no—
24C22⋊#10596833—42no—
25C4×#10596833—42no—
26C23×Dic73—21no—
27C23×Dic73D411yescharacteristic
28C23×Dic73D411yescharacteristic
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73—22no—
31C2×C4⋊Dic73C814yescomplemented
32C2×C4⋊Dic73C2×C412yes—
33C2×#11924007—22no—
34C2×#11924007—22no—
35C2×#11924007—42no—
36C2×#11924007—42no—
37C2×C4×Dic73—42no—
38C2×C4×Dic73C2×C411yescharacteristic
39C2×C4×Dic73D411yescharacteristic
40C2×C4×Dic73D411yescharacteristic
41C2×C4×Dic73C2311yescharacteristic
42#14556498—22no—
43#14556498—22no—
44C23×C4×C73—21no—
45C23×C4×C73C2×C411yescharacteristic
46C2×C4⋊C4×C73—21no—
47C2×C4⋊C4×C73—42no—
48C2×C4⋊C4×C73C2×C412yes—
49C2×#10596833—24no—
50C2×#10596833—42no—
51C2×#10596833—42no—
52C2×#10596833—42no—
53C2×#10596833—42no—
54C2×#10596833—42no—
55C22×Dic73—24no—
56C22×Dic73—22no—
57C22×Dic73—22no—
58C22×Dic73—22no—
59C22×Dic73—41no—
60C22×Dic73—41no—
61C22×Dic73—41no—
62C22×Dic73—42no—
63C22×Dic73—42no—
64C22×Dic73C22⋊C411yescharacteristic
65C22×Dic73C22⋊C411yescharacteristic
66C22×Dic73D812yes—
67C22×Dic73SD1612yes—
68C22×Dic73C2×D411yescharacteristic
69C22×Dic73C2×D411yescharacteristic
70C4⋊Dic73—24no—
71C4⋊Dic73—22no—
72C4⋊Dic73C2×C814yes—
73#11924007—44no—
74#11924007—42no—
75#11924007—42no—
76C4×Dic73—22no—
77C4×Dic73—22no—
78C4×Dic73—41no—
79C4×Dic73—41no—
80C24×C73C22⋊C411yescharacteristic
81C22×C4×C73—22no—
82C22×C4×C73—22no—
83C22×C4×C73—22no—
84C22×C4×C73—42no—
85C22×C4×C73—42no—
86C22×C4×C73—42no—
87C22×C4×C73C22⋊C411yescharacteristic
88C22×C4×C73C2×C812yes—
89C22×C4×C73M1612yes—
90C22×C4×C73C22×C411yescharacteristic
91C4⋊C4×C73—42no—
92C4⋊C4×C73—42no—
93C23×C73—21no—
94C23×C73—21no—
95C23×C73—21no—
96C23×C73—21no—
97C23×C73C22⋊C812yes—
98C23×C73#10212yes—
99C23×C73#10412yes—
100C23×C73C2×C22⋊C411yescharacteristic
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73—24no—
104C2×C4×C73—24no—
105C2×C4×C73—42no—
106C2×C4×C73—42no—
107C2×C4×C73—42no—
108C2×C4×C73—84no—
109C2×C4×C73C22⋊C812yes—
110C2×C4×C73#9912yes—
111C2×C4×C73#10112yes—
112C2×C4×C73C22×C811yescharacteristic
113C2×C4×C73C2×M1611yescharacteristic
114C2×Dic73—21no—
115C2×Dic73—21no—
116C2×Dic73—21no—
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—24no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—42no—
125C2×Dic73—42no—
126C2×Dic73—44no—
127C2×Dic73—48no—
128C2×Dic73—42no—
129C2×Dic73—42no—
130C2×Dic73#10212yes—
131C2×Dic73C2×D811yescharacteristic
132C2×Dic73C2×SD1611yescharacteristic
133C2×Dic73#13712yes—
134#10596833—44no—
135#10596833—82no—
136C22×C73—22no—
137C22×C73—22no—
138C22×C73—22no—
139C22×C73—22no—
140C22×C73—22no—
141C22×C73—22no—
142C22×C73D4⋊C814yes—
143C22×C73C2×C22⋊C811yescharacteristic
144C22×C73C2×#9911yescharacteristic
145C22×C73C2×#10111yescharacteristic
146C22×C73C2×#10211yescharacteristic
147C22×C73#41911yescharacteristic
148C22×C73C2×#10411yescharacteristic
149C22×C73#42111yescharacteristic
150C4×C73—21no—
151C4×C73—21no—
152C4×C73—82no—
153C4×C73#32414yes—
154Dic73—22no—
155Dic73—21no—
156Dic73—22no—
157Dic73—21no—
158Dic73—44no—
159Dic73—41no—
160#7573—731nomaximal, Sylow
161C2×C73—24no—
162C2×C73C2×#32411yescharacteristic
163C2×C73C2×D4⋊C811yescharacteristic
164C2×C73#147911yescharacteristic
165C2×C73#150811yescharacteristic
166C2×C73#151911yescharacteristic
167C2×C73#152811yescharacteristic
168C2×C73#154611yescharacteristic
169C2×#389—731no—
170#1797—731no—
171C4×C22⋊C8—731no—
172#1271—734no—
173C73#757311yescharacteristic, complemented, Sylow
174C22×C4⋊C4—731no—
175C22×C4⋊C4—1461no—
176C22×C4⋊C4#6440811yescharacteristic
177C22×C42—731no—
178C2×C4⋊C8—1461no—
179C2×C22⋊C8—1461no—
180C2×C22⋊C8—1461no—
181C2×C4×C8—1461no—
182#389—732no—
183#389—732no—
184#389—1461no—
185#389—1461no—
186C2×#95—1461no—
187#336—732no—
188#336—732no—
189C23×C4—21no—
190C23×C4—731no—
191C23×C4—731no—
192C23×C4—1461no—
193C23×C4C2×#6440811yescharacteristic
194C22×C8—1462no—
195C22×C8—1462no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—2922no—
199C2×C4⋊C4—2922no—
200C2×C4⋊C4—734no—
201C2×C4⋊C4—732no—
202C2×C4⋊C4—1462no—
203C2×C4⋊C4—1462no—
204C2×C4⋊C4—1461no—
205C2×C4⋊C4—1462no—
206C2×C4⋊C4C2×#6440812yes—
207C2×C42—2922no—
208C2×C42—731no—
209C2×C42—731no—
210C2×C42—731no—
211C2×C42—731no—
212C4⋊C8—2922no—
213C22⋊C8—2922no—
214C22⋊C8—1464no—
215C4×C8—2922no—
216#95—1462no—
217#95—1462no—
218C24C22⋊#6440811yescharacteristic
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—2922no—
226C22×C4—2922no—
227C22×C4—2921no—
228C22×C4—2921no—
229C22×C4—2921no—
230C22×C4—732no—
231C22×C4—732no—
232C22×C4—731no—
233C22×C4—731no—
234C22×C4—731no—
235C22×C4—731no—
236C22×C4—1462no—
237C22×C4—1464no—
238C22×C4—1462no—
239C22×C4—1462no—
240C22×C4C22⋊#6440811yescharacteristic
241C22×C4#1192403612yes—
242C22×C4#1192403812yes—
243C22×C4C22×#6440811yescharacteristic
244C2×C8—2922no—
245C2×C8—2922no—
246C2×C8—2922no—
247C2×C8—2922no—
248C2×C8—2922no—
249C2×C8—1464no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—2922no—
253C4⋊C4—2924no—
254C4⋊C4—2922no—
255C4⋊C4—734no—
256C4⋊C4—1462no—
257C4⋊C4—1464no—
258C42—2921no—
259C42—2921no—
260C42—1462no—
261C42—1462no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23#1455664812yes—
267C23#1455665312yes—
268C23#1455665612yes—
269C23C2×C22⋊#6440811yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—84no—
278C2×C4—2928no—
279C2×C4—2922no—
280C2×C4—2922no—
281C2×C4—2924no—
282C2×C4—2922no—
283C2×C4—2922no—
284C2×C4—731no—
285C2×C4—732no—
286C2×C4—731no—
287C2×C4—732no—
288C2×C4—1464no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4—1461no—
292C2×C4—1461no—
293C2×C4—1461no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4—1461no—
297C2×C4—1461no—
298C2×C4#1455664812yes—
299C2×C4#1455664912yes—
300C2×C4#1455665212yes—
301C2×C4C2×#1192403611yescharacteristic
302C2×C4C2×#1192403811yescharacteristic
303C8—2924no—
304C8—5842no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22#1798943514yes—
312C22C2×#1455664811yescharacteristic
313C22C2×#1455664911yescharacteristic
314C22C2×#1455665211yescharacteristic
315C22C2×#1455665311yescharacteristic
316C22#1798958011yescharacteristic
317C22C2×#1455665611yescharacteristic
318C22#1798958511yescharacteristic
319C4—21no—
320C4—21no—
321C4—82no—
322C4—2921no—
323C4—2924no—
324C4—1462no—
325C4—1461no—
326C4—1462no—
327C4—1461no—
328C4#1798943314yes—
329C2—24no—
330C2C2×#1798943311yescharacteristic
331C2C2×#1798943511yescharacteristic
332C2#2262523511yescharacteristic
333C2#2262533111yescharacteristic
334C2#2262536711yescharacteristic
335C2#2262539511yescharacteristic
336C2#2262544011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
FittingC22×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC22×C4⋊C4#64408
hypocenterC73#7573
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #22624750C2semidirect
31. C2×C4⋊Dic73C8semidirect
173. C73#7573semidirect

Maximal subgroups

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

subgroupindex
#226257852
C4×C22⋊#105968332
#226247502
C2×#179884832
#757373