Finite Group Databasebeta

← #34009620

Subgroups — #34009620

Order 18688.

926 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 926 conjugacy classes of subgroups — too many to draw. Only its 172 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
1C2×#17989467C212yesmaximal
2C2×#17989467C212yesmaximal
3#22625594C212yesmaximal
4C22×#14556581C211yesmaximal, characteristic
5C22×#11924037C2214yes—
6#17989467—24no—
7#17989467—24no—
8#17989453—24no—
9C2×#14556581—24no—
10C2×#14556581—24no—
11C2×#14556581—24no—
12C22×C4⋊Dic73C411yescharacteristic
13C22×#11924007C411yescharacteristic
14C22×#11924007C411yescharacteristic
15C22×#11924007C2211yescharacteristic
16C22×#11924007C2211yescharacteristic
17C22×C4×Dic73C2211yescharacteristic
18C22×C4⋊C4×C73C411yescharacteristic
19C2×#11924037—24no—
20C2×#11924037—24no—
21C2×#11924037—24no—
22C2×#11924037—24no—
23C2×#11924037—24no—
24C2×#11924037Q818yes—
25C22×#10596833—24no—
26C23×Dic73C2×C411yescharacteristic
27C23×Dic73C2×C411yescharacteristic
28C23×Dic73C2×C411yescharacteristic
29C23×Dic73C2311yescharacteristic
30#14556581—232no—
31C2×C4⋊Dic73—22no—
32C2×C4⋊Dic73—22no—
33C2×C4⋊Dic73—22no—
34C2×#11924007—22no—
35C2×#11924007—22no—
36C2×#11924007—22no—
37C2×#11924007—22no—
38C2×#11924007—22no—
39C2×#11924007—22no—
40C2×#11924007—22no—
41C2×#11924007—22no—
42C2×#11924007—22no—
43C2×#11924007—22no—
44C2×#11924007D414yes—
45C2×#11924007D414yes—
46C2×C4×Dic73—22no—
47C2×C4×Dic73—22no—
48C2×C4×Dic73D414yes—
49C23×C4×C73C2×C411yescharacteristic
50C23×C4×C73C2×C411yescharacteristic
51C23×C4×C73C2×C411yescharacteristic
52C2×C4⋊C4×C73—22no—
53C2×C4⋊C4×C73—22no—
54C2×C4⋊C4×C73—22no—
55#11924037—28no—
56#11924037—28no—
57#11924037—44no—
58#11924037—44no—
59C2×#10596833—28no—
60C2×#10596833—44no—
61C2×#10596833—44no—
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73—42no—
69C22×Dic73—42no—
70C22×Dic73—42no—
71C22×Dic73C22⋊C412yes—
72C22×Dic73C22⋊C412yes—
73C22×Dic73C22⋊C412yes—
74C22×Dic73C2×D412yes—
75C22×Dic73C2×D412yes—
76C22×Dic73C2×D412yes—
77C22×Dic73C2×Q814yes—
78C22×Dic73#4114yes—
79C4⋊Dic73—28no—
80#11924007—28no—
81#11924007—28no—
82#11924007—28no—
83#11924007—28no—
84C4×Dic73—28no—
85C24×C73C22×C411yescharacteristic
86C22×C4×C73—21no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73—21no—
92C22×C4×C73—42no—
93C22×C4×C73—42no—
94C22×C4×C73—42no—
95C22×C4×C73C22⋊C412yes—
96C22×C4×C73C22⋊C412yes—
97C22×C4×C73C22⋊C412yes—
98C4⋊C4×C73—28no—
99C23×C73—22no—
100C23×C73—22no—
101C23×C73C2×C22⋊C411yescharacteristic
102C23×C73C2×C22⋊C411yescharacteristic
103C23×C73C2×C22⋊C411yescharacteristic
104C23×C73C4×Q814yes—
105C2×C4×C73—22no—
106C2×C4×C73—22no—
107C2×C4×C73—22no—
108C2×C4×C73—24no—
109C2×C4×C73—42no—
110C2×C4×C73—42no—
111C2×C4×C73—42no—
112C2×C4×C73—42no—
113C2×C4×C73—42no—
114C2×C4×C73—42no—
115C2×C4×C73—42no—
116C2×C4×C73—42no—
117C2×Dic73—22no—
118C2×Dic73—22no—
119C2×Dic73—22no—
120C2×Dic73—24no—
121C2×Dic73—42no—
122C2×Dic73—42no—
123C2×Dic73—42no—
124C2×Dic73—42no—
125C2×Dic73—42no—
126C2×Dic73—42no—
127C2×Dic73—42no—
128C2×Dic73—42no—
129C2×Dic73#12014yes—
130C2×Dic73C22⋊Q814yes—
131C2×Dic73C22⋊Q814yes—
132C2×Dic73C22⋊Q814yes—
133C2×Dic73#12412yes—
134C2×Dic73#12412yes—
135C2×Dic73#12412yes—
136C2×Dic73C4⋊Q812yes—
137C2×Dic73C4⋊Q812yes—
138C2×Dic73C4⋊Q812yes—
139#10596833—48no—
140C22×C73—28no—
141C22×C73—21no—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73#37911yescharacteristic
146C22×C73#39112yes—
147C22×C73#39112yes—
148C22×C73#39112yes—
149C22×C73#41312yes—
150C22×C73#41312yes—
151C4×C73—42no—
152C4×C73—42no—
153C4×C73—42no—
154Dic73—42no—
155Dic73—42no—
156Dic73—42no—
157Dic73#39314yes—
158Dic73#39514yes—
159#11383—731nomaximal, Sylow
160C2×C73—22no—
161C2×C73—22no—
162C2×C73#144611yescharacteristic
163C2×C73#178511yescharacteristic
164C2×C73#178511yescharacteristic
165C2×C73#199814yes—
166C22×#125—731no—
167C2×#343—732no—
168C2×#343—732no—
169#1728—732no—
170C73#1138311yescharacteristic, complemented, Sylow
171C22×M16—734no—
172C2×#125—1464no—
173C2×#125—1464no—
174C2×#125—1464no—
175C22×C4⋊C4—731no—
176C22×C4⋊C4—731no—
177C22×C4⋊C4—731no—
178C22×C4⋊C4—731no—
179C22×C4⋊C4—731no—
180C22×C4⋊C4#6440811yescharacteristic
181C22×C42—731no—
182#343—1464no—
183#343—1464no—
184#336—1464no—
185C23×C4—731no—
186C23×C4—731no—
187C23×C4—731no—
188C23×C4—731no—
189C23×C4C2×#6440811yescharacteristic
190C23×C4C2×#6440811yescharacteristic
191C23×C4C2×#6440811yescharacteristic
192C2×M16—738no—
193C2×M16—1464no—
194C2×M16—1464no—
195C2×M16—1464no—
196C2×M16—1464no—
197C2×M16—1464no—
198C22×C8—1464no—
199#125—14632no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—734no—
204C2×C4⋊C4—734no—
205C2×C4⋊C4—1462no—
206C2×C4⋊C4—1462no—
207C2×C4⋊C4—1462no—
208C2×C4⋊C4—1462no—
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×C42—734no—
219C2×C42—1462no—
220C2×C42—1462no—
221C24C22×#6440811yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—2922no—
232C22×C4—2922no—
233C22×C4—2922no—
234C22×C4—732no—
235C22×C4—732no—
236C22×C4—734no—
237C22×C4—734no—
238C22×C4—732no—
239C22×C4—732no—
240C22×C4—732no—
241C22×C4—732no—
242C22×C4—1461no—
243C22×C4—1461no—
244C22×C4—1461no—
245C22×C4—1461no—
246C22×C4—1461no—
247C22×C4—1461no—
248C22×C4C22⋊#6440812yes—
249C22×C4C22⋊#6440812yes—
250C22×C4C22⋊#6440812yes—
251M16—2924no—
252M16—2924no—
253M16—1468no—
254M16—1468no—
255C2×C8—2924no—
256C2×C8—2924no—
257C2×C8—1468no—
258C4⋊C4—28no—
259C4⋊C4—1468no—
260C4⋊C4—1468no—
261C4⋊C4—1468no—
262C4⋊C4—1468no—
263C4⋊C4—1468no—
264C42—1468no—
265C23—22no—
266C23—22no—
267C23C2×C22⋊#6440811yescharacteristic
268C23C2×C22⋊#6440811yescharacteristic
269C23C2×C22⋊#6440811yescharacteristic
270C23Q8×#6440814yes—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—2922no—
284C2×C4—2922no—
285C2×C4—2922no—
286C2×C4—2922no—
287C2×C4—2922no—
288C2×C4—2922no—
289C2×C4—2922no—
290C2×C4—2922no—
291C2×C4—734no—
292C2×C4—732no—
293C2×C4—734no—
294C2×C4—732no—
295C2×C4—732no—
296C2×C4—734no—
297C2×C4—734no—
298C2×C4—732no—
299C2×C4—732no—
300C2×C4—732no—
301C2×C4—1462no—
302C2×C4—1462no—
303C2×C4—1462no—
304C2×C4—1464no—
305C8—2928no—
306C22—28no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22#1798952811yescharacteristic
312C22(C2×#64408)⋊Q812yes—
313C22(C2×#64408)⋊Q812yes—
314C22(C2×#64408)⋊Q812yes—
315C22#1798957312yes—
316C22#1798957412yes—
317C4—42no—
318C4—42no—
319C4—42no—
320C4—2922no—
321C4—2922no—
322C4—2922no—
323C4—734no—
324C4—734no—
325C2—22no—
326C2—22no—
327C2#2262512111yescharacteristic
328C2#2262576711yescharacteristic
329C2#2262576811yescharacteristic
330C2#2262612514yes—
subgroupG/H
centerC23C2×C22⋊#64408
commutator, prime radicalC24×C73C22×C4
FrattiniC24C22×#64408
FittingC22×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
cosocleC23×Dic73C23
hypercenterC22×C4⋊C4#64408
hypocenterC73#11383
LCSG ▷ C24×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
170. C73#11383semidirect

Maximal subgroups

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

subgroupindex
C2×#179894672
#226255942
C22×#145565812
#1138373