Finite Group Databasebeta

← #32978626

Subgroups — #32978626

Order 18688.

778 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C22×#14556581C211yesmaximal, characteristic
2#22610011C211yesmaximal, characteristic
3#22608260C212yesmaximal
4#22608260C212yesmaximal
5C73×#1821C211yesmaximal, characteristic
6C2×#14556581—24no—
7C2×#14556581—24no—
8C2×#14556581—22no—
9C2×#14556581—22no—
10C22×C4⋊Dic73C411yescharacteristic
11C22×#11924007C411yescharacteristic
12C22×#11924007C411yescharacteristic
13C22×#11924007C2211yescharacteristic
14C22×#11924007C2211yescharacteristic
15C22×C4×Dic73C411yescharacteristic
16#17988551C2212yes—
17#17988356—22no—
18#17988312—24no—
19#17988312—24no—
20C22×C4⋊C4×C73C2211yescharacteristic
21#407×C73C2212yes—
22#343×C73—22no—
23C23×Dic73C2×C411yescharacteristic
24C23×Dic73C2×C411yescharacteristic
25C23×Dic73C2×C411yescharacteristic
26C23×Dic73C2×C411yescharacteristic
27C2×#11924012—22no—
28#14556581—216no—
29#14556581—216no—
30C2×C4⋊Dic73—22no—
31C2×C4⋊Dic73—22no—
32C2×C4⋊Dic73—22no—
33C2×#11924007—22no—
34C2×#11924007—22no—
35C2×#11924007—22no—
36C2×#11924007—22no—
37C2×#11924007—22no—
38C2×#11924007—22no—
39C2×#11924007—22no—
40C2×#11924007—22no—
41C2×#11924007—21no—
42C2×#11924007—21no—
43C2×#11924007—21no—
44C2×#11924007—21no—
45C2×#11924007D414yes—
46C2×#11924007D414yes—
47C2×C4×Dic73—22no—
48C2×C4×Dic73—22no—
49C2×C4×Dic73—22no—
50C22⋊#10596831—22no—
51C22⋊#10596831—22no—
52C23×C4×C73C2×C411yescharacteristic
53C23×C4×C73C2×C411yescharacteristic
54C23×C4×C73C2311yescharacteristic
55C2×M16×C73—22no—
56C2×C4⋊C4×C73—22no—
57C2×C4⋊C4×C73—22no—
58C2×C4⋊C4×C73D412yes—
59C2×C4⋊C4×C73D412yes—
60C22⋊C8×C73—22no—
61C22⋊C8×C73—22no—
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73—24no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C22×Dic73—21no—
71C22×Dic73—42no—
72C22×Dic73—42no—
73C22×Dic73—42no—
74C22×Dic73C22⋊C412yes—
75C22×Dic73C22⋊C412yes—
76C22×Dic73C22⋊C412yes—
77C22×Dic73C22⋊C412yes—
78#11924012—44no—
79C2×#10596831—42no—
80C4⋊Dic73—28no—
81#11924007—28no—
82#11924007—28no—
83#11924007—24no—
84#11924007—24no—
85#11924007—24no—
86#11924007—24no—
87C4×Dic73—28no—
88C24×C73C22×C411yescharacteristic
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73—21no—
92C22×C4×C73—21no—
93C22×C4×C73—42no—
94C22×C4×C73—42no—
95C22×C4×C73—42no—
96C22×C4×C73C22⋊C412yes—
97C22×C4×C73C22⋊C412yes—
98C22×C4×C73C2×D412yes—
99C22×C4×C73C2×D412yes—
100C22×C4×C73C2×D411yescharacteristic
101C22×C4×C73C2×D411yescharacteristic
102M16×C73—44no—
103C2×C8×C73—42no—
104C4⋊C4×C73—24no—
105C4⋊C4×C73—24no—
106C23×C73—22no—
107C23×C73—22no—
108C23×C73—22no—
109C23×C73C2×C22⋊C411yescharacteristic
110C23×C73C2×C22⋊C411yescharacteristic
111C23×C73C2×C22⋊C411yescharacteristic
112C2×C4×C73—22no—
113C2×C4×C73—22no—
114C2×C4×C73—22no—
115C2×C4×C73—22no—
116C2×C4×C73—42no—
117C2×C4×C73—42no—
118C2×C4×C73—42no—
119C2×C4×C73—42no—
120C2×C4×C73—42no—
121C2×C4×C73—42no—
122C2×C4×C73—42no—
123C2×C4×C73—42no—
124C2×C4×C73#12012yes—
125C2×C4×C73#12012yes—
126C2×Dic73—24no—
127C2×Dic73—24no—
128C2×Dic73—22no—
129C2×Dic73—22no—
130C2×Dic73—22no—
131C2×Dic73—22no—
132C2×Dic73—22no—
133C2×Dic73—24no—
134C2×Dic73—42no—
135C2×Dic73—42no—
136C2×Dic73—42no—
137C2×Dic73—42no—
138C2×Dic73—42no—
139C2×Dic73—42no—
140C2×Dic73—42no—
141C2×Dic73—42no—
142C2×Dic73#10114yes—
143C8×C73—82no—
144#10596831—82no—
145C22×C73—28no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73#37911yescharacteristic
153C22×C73#41012yes—
154C22×C73C2×#10112yes—
155C22×C73#41312yes—
156C4×C73—22no—
157C4×C73—22no—
158C4×C73—42no—
159C4×C73—42no—
160Dic73—24no—
161Dic73—42no—
162Dic73—42no—
163Dic73—42no—
164#8554—731nomaximal, Sylow
165C2×C73—22no—
166C2×C73—22no—
167C2×C73—22no—
168C2×C73#178211yescharacteristic
169C2×C73#178411yescharacteristic
170C2×C73#178511yescharacteristic
171C22×#125—731no—
172#1821—731no—
173#1821D7311yescharacteristic
174#1463—732no—
175#1463—732no—
176C73#855411yescharacteristic, complemented, Sylow
177C2×#125—1464no—
178C2×#125—1464no—
179C2×#125—1462no—
180C2×#125—1462no—
181C22×C4⋊C4—731no—
182C22×C4⋊C4—731no—
183C22×C4⋊C4—731no—
184C22×C4⋊C4—731no—
185C22×C4⋊C4—731no—
186C22×C4⋊C4C2×D7311yescharacteristic
187C22×C42—731no—
188#407—732no—
189#407C2×D7312yes—
190#343—22no—
191#343—1462no—
192#324—1464no—
193#324—1464no—
194C23×C4—731no—
195C23×C4—731no—
196C23×C4—731no—
197C23×C4—731no—
198C23×C4C4×D7311yescharacteristic
199C23×C4C4×D7311yescharacteristic
200C23×C4C22×D7311yescharacteristic
201C2×M16—22no—
202C2×M16—1462no—
203#125—14616no—
204#125—14616no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—734no—
208C2×C4⋊C4—734no—
209C2×C4⋊C4—1462no—
210C2×C4⋊C4—1462no—
211C2×C4⋊C4—1462no—
212C2×C4⋊C4—1462no—
213C2×C4⋊C4—1462no—
214C2×C4⋊C4—1462no—
215C2×C4⋊C4—1462no—
216C2×C4⋊C4—1462no—
217C2×C4⋊C4—1462no—
218C2×C4⋊C4—1462no—
219C2×C4⋊C4—1462no—
220C2×C4⋊C4—1461no—
221C2×C4⋊C4—1461no—
222C2×C4⋊C4—1461no—
223C2×C4⋊C4—1461no—
224C2×C4⋊C4D29212yes—
225C2×C4⋊C4C22⋊D7312yes—
226C2×C42—1462no—
227C2×C42—1462no—
228C2×C42—1462no—
229C22⋊C8—22no—
230C22⋊C8—22no—
231C22⋊C8—1462no—
232C22⋊C8—1462no—
233C24C2×C4×D7311yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—2922no—
242C22×C4—2922no—
243C22×C4—2922no—
244C22×C4—732no—
245C22×C4—732no—
246C22×C4—732no—
247C22×C4—732no—
248C22×C4—1461no—
249C22×C4—1461no—
250C22×C4—1461no—
251C22×C4—1461no—
252C22×C4—1461no—
253C22×C4—1461no—
254C22×C4—1464no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4#1192400512yes—
258C22×C4#1192400512yes—
259C22×C4D4×D7312yes—
260C22×C4D4×D7312yes—
261C22×C4C2×C22⋊D7311yescharacteristic
262C22×C4C2×D29211yescharacteristic
263M16—44no—
264M16—2924no—
265C2×C8—42no—
266C2×C8—2922no—
267C4⋊C4—24no—
268C4⋊C4—24no—
269C4⋊C4—1468no—
270C4⋊C4—1468no—
271C4⋊C4—1468no—
272C4⋊C4—1464no—
273C4⋊C4—1464no—
274C4⋊C4—1464no—
275C4⋊C4—1464no—
276C42—1468no—
277C23—22no—
278C23—22no—
279C23—22no—
280C23C22⋊C4×D7311yescharacteristic
281C23C22⋊C4×D7311yescharacteristic
282C23C2×#1192400511yescharacteristic
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—2922no—
296C2×C4—2922no—
297C2×C4—2922no—
298C2×C4—2922no—
299C2×C4—2922no—
300C2×C4—2922no—
301C2×C4—2922no—
302C2×C4—2922no—
303C2×C4—734no—
304C2×C4—1462no—
305C2×C4—1462no—
306C2×C4—1462no—
307C2×C4—1464no—
308C2×C4—1464no—
309C2×C4—1464no—
310C2×C4—1462no—
311C2×C4—1462no—
312C2×C4#1455655912yes—
313C2×C4#1455656112yes—
314C8—82no—
315C8—5842no—
316C22—28no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22#1798844211yescharacteristic
324C22#1798856012yes—
325C22#101×D7312yes—
326C22#1798856812yes—
327C4—22no—
328C4—22no—
329C4—42no—
330C4—42no—
331C4—2922no—
332C4—2922no—
333C4—2922no—
334C4—1464no—
335C2—22no—
336C2—22no—
337C2—22no—
338C2#2260984811yescharacteristic
339C2#2260985311yescharacteristic
340C2#2260985611yescharacteristic
subgroupG/H
centerC22#17988442
commutator, prime radicalC24×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1821C2
socleC22×C73#379
cosocleC23×C4×C73C23
hypercenter#1821D73
hypocenterC73#8554
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
176. C73#8554semidirect

Maximal subgroups

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

subgroupindex
C22×#145565812
#226100112
#226082602
C73×#18212
#855473