Finite Group Databasebeta

← #34001660

Subgroups — #34001660

Order 18688.

482 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 100 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#22625787C211yesmaximal, characteristic
2C4×C22⋊#10596833C211yesmaximal, characteristic
3#22624752C212yesmaximal, complemented
4#22624749C212yesmaximal, complemented
5#22618271C211yesmaximal, characteristic
6C2×#14556658—21no—
7C2×C22⋊#10596833—21no—
8C2×C22⋊#10596833—21no—
9C2×C4×#10596833—21no—
10#17989453C2212yes—
11#17989453C2212yes—
12C2×#14556570C411yescharacteristic
13C22×C4×Dic73C2211yescharacteristic
14#17988492C411yescharacteristic
15#17988492C2211yescharacteristic
16#17988486C411yescharacteristic
17#17988486C2211yescharacteristic
18#17988472—21no—
19#17988472—21no—
20#17988462—21no—
21#17988448—21no—
22#380×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25#14556658—42no—
26C22⋊#10596833—24no—
27C22⋊#10596833—42no—
28C4×#10596833—42no—
29C22×Dic146C2×C411yescharacteristic
30C23×Dic73D411yescharacteristic
31C23×Dic73D411yescharacteristic
32#14556570—42no—
33C2×C4⋊Dic73—21no—
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73C2×C411yescharacteristic
36C2×#11924007—21no—
37C2×C22⋊Dic73—21no—
38C2×C4×Dic73—42no—
39C2×C4×Dic73C2×C411yescharacteristic
40C2×C4×Dic73D411yescharacteristic
41C2×C4×Dic73D411yescharacteristic
42C2×C4×Dic73C2311yescharacteristic
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49C23×C4×C73C2×C411yescharacteristic
50C2×C4⋊C4×C73C2×C411yescharacteristic
51C2×C4⋊C4×C73C2×C411yescharacteristic
52C2×C22⋊C4×C73—21no—
53#95×C73—21no—
54C2×#10596833—24no—
55C2×#10596833—42no—
56C2×#10596833—42no—
57C2×#10596833—42no—
58C2×#10596833—42no—
59C2×#10596833—42no—
60C2×Dic146—22no—
61C2×Dic146—41no—
62C2×Dic146—41no—
63C22×Dic73—22no—
64C22×Dic73—22no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—41no—
68C22×Dic73—41no—
69C22×Dic73—41no—
70C22×Dic73C22⋊C411yescharacteristic
71C22×Dic73C22⋊C411yescharacteristic
72C22×Dic73SD1612yes—
73C22×Dic73Q1612yes—
74C22×Dic73C2×D411yescharacteristic
75C22×Dic73C2×D411yescharacteristic
76C4⋊Dic73—42no—
77C4⋊Dic73—42no—
78C4⋊Dic73—41no—
79#11924007—42no—
80C22⋊Dic73—42no—
81C4×Dic73—22no—
82C4×Dic73—22no—
83C4×Dic73—41no—
84C4×Dic73—41no—
85C24×C73C22⋊C411yescharacteristic
86C22×C4×C73—22no—
87C22×C4×C73—22no—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—41no—
91C22×C4×C73C22⋊C411yescharacteristic
92C22×C4×C73C22×C411yescharacteristic
93C4⋊C4×C73—22no—
94C4⋊C4×C73—41no—
95C22⋊C4×C73—42no—
96C23×C73—21no—
97C23×C73—21no—
98C23×C73—21no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73#10312yes—
103C23×C73C2×C22⋊C411yescharacteristic
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—44no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73#9912yes—
116C2×C4×C73#13112yes—
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—42no—
126C2×Dic73—42no—
127C2×Dic73—44no—
128C2×Dic73—41no—
129C2×Dic73—41no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73#10312yes—
135C2×Dic73#10412yes—
136C2×Dic73C2×SD1611yescharacteristic
137C2×Dic73C2×Q1611yescharacteristic
138C2×Dic73#13512yes—
139Dic146—82no—
140#10596833—44no—
141#10596833—82no—
142C22×C73—22no—
143C22×C73—22no—
144C22×C73—22no—
145C22×C73—41no—
146C22×C73—41no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73#40811yescharacteristic
150C22×C73C2×#9911yescharacteristic
151C22×C73#41311yescharacteristic
152C22×C73C2×#10311yescharacteristic
153C22×C73#41611yescharacteristic
154C22×C73C2×#10411yescharacteristic
155C22×C73#42111yescharacteristic
156C4×C73—22no—
157C4×C73—22no—
158C4×C73—81no—
159C4×C73—81no—
160Dic73—22no—
161Dic73—22no—
162Dic73—21no—
163Dic73—22no—
164Dic73—21no—
165Dic73—81no—
166Dic73—81no—
167#7661—731nomaximal, Sylow
168C2×C73—42no—
169C2×C73#146811yescharacteristic
170C2×C73#148211yescharacteristic
171C2×C73#149311yescharacteristic
172C2×C73#150111yescharacteristic
173C2×C73#152011yescharacteristic
174C2×C73#152911yescharacteristic
175C2×C73#154211yescharacteristic
176#2855—731no—
177#1797—731no—
178C4×C22⋊C8—731no—
179#1272—732no—
180#1271—732no—
181C73#766111yescharacteristic, complemented, Sylow
182C2×C22⋊Q8—731no—
183C22×C42—731no—
184C2×C4⋊C8—1461no—
185C2×C22⋊C8—1461no—
186C2×C22⋊C8—1461no—
187C2×C4×C8—1461no—
188#391—731no—
189#391—731no—
190#389—731no—
191#389—731no—
192#387—1461no—
193#387—1461no—
194#385—1461no—
195#381—1461no—
196#380#6440811yescharacteristic
197#336—732no—
198#336—732no—
199C22×Q8—731no—
200C23×C4—731no—
201C23×C4—731no—
202C23×C4C2×#6440811yescharacteristic
203C22×C8—1462no—
204C22×C8—1462no—
205C22⋊Q8—2922no—
206C2×C4⋊C4—731no—
207C2×C4⋊C4—1461no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4—1461no—
210C2×C4⋊C4C2×#6440811yescharacteristic
211C2×C4⋊C4C2×#6440811yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—1461no—
214C2×C42—2922no—
215C2×C42—731no—
216C2×C42—731no—
217C2×C42—731no—
218C2×C42—731no—
219C4⋊C8—2922no—
220C22⋊C8—2922no—
221C22⋊C8—1464no—
222C4×C8—2922no—
223#95—21no—
224#95—1461no—
225#95—1461no—
226#95—1461no—
227#95—1461no—
228#95—1461no—
229#95—1461no—
230C24C22⋊#6440811yescharacteristic
231C2×Q8—2921no—
232C2×Q8—2921no—
233C2×Q8—1462no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—2921no—
240C22×C4—2921no—
241C22×C4—2921no—
242C22×C4—732no—
243C22×C4—732no—
244C22×C4—731no—
245C22×C4—731no—
246C22×C4—731no—
247C22×C4—731no—
248C22×C4—1461no—
249C22×C4—1461no—
250C22×C4—1462no—
251C22×C4—1462no—
252C22×C4C22⋊#6440811yescharacteristic
253C22×C4C22×#6440811yescharacteristic
254C2×C8—2922no—
255C2×C8—2922no—
256C2×C8—2922no—
257C2×C8—2922no—
258C2×C8—2922no—
259C2×C8—1464no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—2921no—
263C4⋊C4—2922no—
264C4⋊C4—2922no—
265C4⋊C4—2922no—
266C22⋊C4—42no—
267C22⋊C4—2922no—
268C42—2921no—
269C42—2921no—
270C42—1462no—
271C42—1462no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23#1455665412yes—
279C23C2×C22⋊#6440811yescharacteristic
280Q8—5842no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—44no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—2921no—
293C2×C4—2921no—
294C2×C4—2921no—
295C2×C4—2921no—
296C2×C4—2921no—
297C2×C4—2921no—
298C2×C4—2922no—
299C2×C4—2922no—
300C2×C4—2924no—
301C2×C4—731no—
302C2×C4—732no—
303C2×C4—731no—
304C2×C4—732no—
305C2×C4—732no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4#1455665012yes—
315C2×C4#1455667812yes—
316C8—2924no—
317C8—5842no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22#1798956011yescharacteristic
326C22C2×#1455665011yescharacteristic
327C22#1798957411yescharacteristic
328C22C2×#1455665411yescharacteristic
329C22#1798957711yescharacteristic
330C22D73⋊#10411yescharacteristic
331C22#1798958511yescharacteristic
332C4—22no—
333C4—22no—
334C4—81no—
335C4—81no—
336C4—5841no—
337C4—5841no—
338C4—1462no—
339C4—1462no—
340C4—1461no—
341C4—1462no—
342C4—1461no—
343C2—42no—
344C2#2262519811yescharacteristic
345C2#2262524211yescharacteristic
346C2#2262527911yescharacteristic
347C2#2262530811yescharacteristic
348C2#2262537011yescharacteristic
349C2#2262539711yescharacteristic
350C2#2262543311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#380×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#380#64408
hypocenterC73#7661
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #22624752C2semidirect
4. #22624749C2semidirect
181. C73#7661semidirect

Maximal subgroups

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

subgroupindex
#226257872
C4×C22⋊#105968332
#226247522
#226247492
#226182712
#766173