Finite Group Databasebeta

← #32995386

Subgroups — #32995386

Order 18688.

446 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 87 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#22612334C211yesmaximal, characteristic
2#22608265C211yesmaximal, characteristic
3#22607876C212yesmaximal, complemented
4#22607874C212yesmaximal, complemented
5C73×#1464C211yesmaximal, characteristic
6C2×#14556550C411yescharacteristic
7C22×C4×Dic73C411yescharacteristic
8#17988644—21no—
9#17988456C411yescharacteristic
10#17988456C2211yescharacteristic
11#17988452C411yescharacteristic
12#17988452C2211yescharacteristic
13#17988445—21no—
14#17988445—21no—
15C4×#11924007—21no—
16C4×#11924007—21no—
17#17988313C2212yes—
18#17988311—21no—
19C2×#117×C73C2211yescharacteristic
20#432×C73—21no—
21#324×C73C2212yes—
22#323×C73—21no—
23C23×Dic73—21no—
24#14556550—41no—
25#14556550—41no—
26C2×C4⋊Dic73C2×C411yescharacteristic
27C2×C4⋊Dic73C2×C411yescharacteristic
28C2×#11924007—21no—
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×C22⋊Dic73—21no—
33C2×C4×Dic73—22no—
34C2×C4×Dic73—22no—
35C2×C4×Dic73—21no—
36C2×C4×Dic73—21no—
37C2×C4×Dic73C2×C411yescharacteristic
38C2×C4×Dic73C2×C411yescharacteristic
39C4⋊#10596831—41no—
40C22⋊#10596831—22no—
41#14556502—41no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46C23×C4×C73C2×C411yescharacteristic
47#117×C73—41no—
48#117×C73—41no—
49C2×C4⋊C4×C73C2×C411yescharacteristic
50C2×C4⋊C4×C73C2311yescharacteristic
51C2×C22⋊C4×C73D411yescharacteristic
52C2×C22⋊C4×C73D411yescharacteristic
53C2×C42×C73D411yescharacteristic
54C2×C42×C73D411yescharacteristic
55C4⋊C8×C73—41no—
56C22⋊C8×C73—22no—
57#97×C73—41no—
58C22×Dic73—21no—
59C22×Dic73—24no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73—42no—
64C22×Dic73—42no—
65C2×#10596831—42no—
66C4⋊Dic73—41no—
67C4⋊Dic73—41no—
68#11924007—42no—
69#11924007—42no—
70#11924007—42no—
71#11924007—42no—
72C22⋊Dic73—42no—
73C4×Dic73—24no—
74C4×Dic73—21no—
75C4×Dic73—21no—
76C4×Dic73—41no—
77C4×Dic73—41no—
78C4×Dic73M1612yes—
79C4×Dic73M1612yes—
80C24×C73C22⋊C411yescharacteristic
81C22×C4×C73—22no—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—21no—
86C22×C4×C73C22⋊C411yescharacteristic
87C22×C4×C73C22⋊C411yescharacteristic
88C22×C4×C73C22⋊C411yescharacteristic
89C22×C4×C73C22×C411yescharacteristic
90C22×C4×C73C2×D411yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92C2×C8×C73—42no—
93C4⋊C4×C73—41no—
94C4⋊C4×C73—41no—
95C22⋊C4×C73—41no—
96C22⋊C4×C73—41no—
97C42×C73—21no—
98C42×C73—21no—
99C42×C73—21no—
100C42×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—41no—
104C23×C73—41no—
105C23×C73#10112yes—
106C23×C73C2×C22⋊C411yescharacteristic
107C2×C4×C73—22no—
108C2×C4×C73—22no—
109C2×C4×C73—22no—
110C2×C4×C73—22no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73#9911yescharacteristic
124C2×C4×C73#9911yescharacteristic
125C2×C4×C73C2×M1611yescharacteristic
126C2×C4×C73C2×M1611yescharacteristic
127C2×Dic73—22no—
128C2×Dic73—22no—
129C2×Dic73—22no—
130C2×Dic73—22no—
131C2×Dic73—48no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C8×C73—82no—
141#10596831—82no—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73—22no—
145C22×C73—42no—
146C22×C73—42no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73#40711yescharacteristic
150C22×C73C2×#9911yescharacteristic
151C22×C73C2×#10111yescharacteristic
152C4×C73—21no—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—21no—
156C4×C73—41no—
157C4×C73—41no—
158C4×C73—41no—
159C4×C73—41no—
160Dic73—24no—
161Dic73—42no—
162Dic73—81no—
163Dic73—81no—
164#11513—731nomaximal, Sylow
165C2×C73—21no—
166C2×C73—21no—
167C2×C73—42no—
168C2×C73#146311yescharacteristic
169C2×C73#212611yescharacteristic
170C2×C73#213211yescharacteristic
171#2285—731no—
172#1464—731no—
173#1464D7311yescharacteristic
174#1325—732no—
175#1324—732no—
176C73#1151311yescharacteristic, complemented, Sylow
177C2×#117—731no—
178C2×#117C2×D7311yescharacteristic
179C22×C42—731no—
180#432—21no—
181#432—1461no—
182#384—731no—
183#384—731no—
184#382—731no—
185#382—731no—
186#380—1461no—
187#380—1461no—
188C4×C4⋊C4—1461no—
189C4×C4⋊C4—1461no—
190#324—732no—
191#324C2×D7312yes—
192#323—21no—
193#323—1461no—
194C23×C4—1461no—
195C23×C4C4×D7311yescharacteristic
196#117—41no—
197#117—41no—
198#117—2921no—
199#117—2921no—
200C2×C4⋊C4—731no—
201C2×C4⋊C4—731no—
202C2×C4⋊C4—1461no—
203C2×C4⋊C4—1461no—
204C2×C4⋊C4—1461no—
205C2×C4⋊C4—1461no—
206C2×C4⋊C4C4×D7311yescharacteristic
207C2×C4⋊C4C22×D7311yescharacteristic
208C2×C22⋊C4—1461no—
209C2×C22⋊C4D29211yescharacteristic
210C2×C22⋊C4C22⋊D7311yescharacteristic
211C2×C42—731no—
212C2×C42—731no—
213C2×C42—1461no—
214C2×C42—1462no—
215C2×C42—1462no—
216C2×C42—1461no—
217C2×C42D29211yescharacteristic
218C2×C42C22⋊D7311yescharacteristic
219C4⋊C8—41no—
220C4⋊C8—2921no—
221C22⋊C8—22no—
222C22⋊C8—1462no—
223#97—41no—
224#97—2921no—
225#95—1461no—
226#95—1461no—
227#95—1461no—
228#95—1461no—
229C24#1192400511yescharacteristic
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—2922no—
236C22×C4—2922no—
237C22×C4—1461no—
238C22×C4—1461no—
239C22×C4—1464no—
240C22×C4—1461no—
241C22×C4—1461no—
242C22×C4#1192400511yescharacteristic
243C22×C4#1192400511yescharacteristic
244C22×C4#1192400511yescharacteristic
245C22×C4C2×C4×D7311yescharacteristic
246C22×C4C2×C22⋊D7311yescharacteristic
247C22×C4C2×D29211yescharacteristic
248C2×C8—42no—
249C2×C8—2922no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—2921no—
253C4⋊C4—2921no—
254C4⋊C4—2922no—
255C4⋊C4—2922no—
256C4⋊C4—2922no—
257C4⋊C4—2922no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—2922no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—2921no—
266C42—2921no—
267C42—732no—
268C42—732no—
269C42—1464no—
270C42—1461no—
271C42—1461no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23#1455650912yes—
277C23C2×#1192400511yescharacteristic
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—2921no—
295C2×C4—2921no—
296C2×C4—2928no—
297C2×C4—2921no—
298C2×C4—2921no—
299C2×C4—2921no—
300C2×C4—2921no—
301C2×C4—2921no—
302C2×C4—2921no—
303C2×C4—1462no—
304C2×C4—1462no—
305C2×C4—1462no—
306C2×C4—1462no—
307C2×C4#1455650511yescharacteristic
308C2×C4#1455650511yescharacteristic
309C2×C4M16×D7311yescharacteristic
310C2×C4M16×D7311yescharacteristic
311C8—82no—
312C8—5842no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—42no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22#1798855011yescharacteristic
321C22C2×#1455650511yescharacteristic
322C22C2×#1455650911yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2922no—
332C4—5841no—
333C4—5841no—
334C4—1464no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#2260826011yescharacteristic
339C2#2261159411yescharacteristic
340C2#2261161411yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1464C2
socleC22×C73C2×#99
prime radicalC24×C73C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1464D73
hypocenterC73#11513
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #22607876C2semidirect
4. #22607874C2semidirect
176. C73#11513semidirect

Maximal subgroups

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

subgroupindex
#226123342
#226082652
#226078762
#226078742
C73×#14642
#1151373