Finite Group Databasebeta

← #32974420

Subgroups — #32974420

Order 18688.

396 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 97 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#22618317C211yesmaximal, characteristic
2#22609779C211yesmaximal, characteristic
3#22609678C211yesmaximal, characteristic
4#22607755C211yesmaximal, characteristic
5#22607754C211yesmaximal, characteristic
6#22607753C211yesmaximal, characteristic
7C73×#1271C211yesmaximal, characteristic
8C2×#14556520—21no—
9C2×#14556501—21no—
10C2×C8×Dic73—21no—
11#17988486C411yescharacteristic
12#17988485C2211yescharacteristic
13#17988483C411yescharacteristic
14#17988473—21no—
15#17988472—21no—
16#17988469—21no—
17#17988468—21no—
18#17988452C411yescharacteristic
19#17988452C411yescharacteristic
20C42×Dic73C2211yescharacteristic
21#17988342C2211yescharacteristic
22#17988342C2211yescharacteristic
23#17988341—21no—
24#389×C73C2211yescharacteristic
25#336×C73C2211yescharacteristic
26#336×C73C2211yescharacteristic
27C22×#10596831—21no—
28C22×#10596831—21no—
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73C2×C411yescharacteristic
31C2×C4⋊Dic73C2×C411yescharacteristic
32C2×#11924007—21no—
33C2×#11924007—21no—
34C2×C4×Dic73C2×C411yescharacteristic
35C2×C4×Dic73C2×C411yescharacteristic
36C2×C4×Dic73D411yescharacteristic
37C2×C4×Dic73D411yescharacteristic
38C2×C4×Dic73D411yescharacteristic
39C2×C4×Dic73D411yescharacteristic
40#14556520—24no—
41#14556501—24no—
42C8×Dic73—42no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49#14556498—21no—
50C22×C8×C73—21no—
51C22×C8×C73—21no—
52C2×C4⋊C4×C73—21no—
53C2×C4⋊C4×C73C2×C411yescharacteristic
54C2×C4⋊C4×C73C2×C411yescharacteristic
55C2×C42×C73C2311yescharacteristic
56#95×C73—21no—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73C22⋊C411yescharacteristic
60C22×Dic73C22⋊C411yescharacteristic
61C22×Dic73C22⋊C411yescharacteristic
62C22×Dic73C22⋊C411yescharacteristic
63C2×#10596831—22no—
64C2×#10596831—22no—
65C2×#10596831—41no—
66C2×#10596831—41no—
67C2×#10596831—41no—
68C2×#10596831—41no—
69C4⋊Dic73—21no—
70C4⋊Dic73—21no—
71C4⋊Dic73—42no—
72C4⋊Dic73—41no—
73#11924007—41no—
74#11924007—41no—
75#11924007—42no—
76C4×Dic73—21no—
77C4×Dic73—21no—
78C4×Dic73—21no—
79C4×Dic73—21no—
80C4×Dic73—21no—
81C4×Dic73—21no—
82C4×Dic73—22no—
83C4×Dic73—22no—
84C4×Dic73—22no—
85C22×C4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73C22×C411yescharacteristic
88C22×C4×C73C2×D411yescharacteristic
89C22×C4×C73C2×D411yescharacteristic
90C2×C8×C73—22no—
91C2×C8×C73—22no—
92C2×C8×C73—41no—
93C2×C8×C73—41no—
94C2×C8×C73—41no—
95C2×C8×C73—41no—
96C4⋊C4×C73—21no—
97C4⋊C4×C73—21no—
98C4⋊C4×C73—41no—
99C4⋊C4×C73—41no—
100C4⋊C4×C73—41no—
101C42×C73—41no—
102C23×C73C2×C22⋊C411yescharacteristic
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
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#13111yescharacteristic
116C2×C4×C73#13111yescharacteristic
117C2×C4×C73#13511yescharacteristic
118C2×C4×C73#13511yescharacteristic
119C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C73#13711yescharacteristic
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73#10112yes—
137C2×Dic73#10412yes—
138C2×Dic73#10412yes—
139C8×C73—42no—
140C8×C73—42no—
141#10596831—42no—
142#10596831—42no—
143C22×C73#40811yescharacteristic
144C22×C73#41011yescharacteristic
145C22×C73C2×#10111yescharacteristic
146C22×C73#41611yescharacteristic
147C22×C73#41711yescharacteristic
148C22×C73C2×#10411yescharacteristic
149C22×C73C2×#10411yescharacteristic
150C4×C73—21no—
151C4×C73—21no—
152C4×C73—21no—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—21no—
156C4×C73—81no—
157C4×C73—81no—
158Dic73—22no—
159Dic73—22no—
160Dic73—22no—
161Dic73—41no—
162Dic73—81no—
163Dic73—81no—
164#7677—731nomaximal, Sylow
165C2×C73#147011yescharacteristic
166C2×C73#148311yescharacteristic
167C2×C73#149411yescharacteristic
168C2×C73#150011yescharacteristic
169C2×C73#150911yescharacteristic
170C2×C73#152611yescharacteristic
171C2×C73#155211yescharacteristic
172#2864—731no—
173C4×C4⋊C8—731no—
174#1745—731no—
175#1271—731no—
176#1271—731no—
177#1271—731no—
178#1271D7311yescharacteristic
179C73#767711yescharacteristic, complemented, Sylow
180C2×C4⋊C8—1461no—
181C2×#97—1461no—
182C2×C4×C8—1461no—
183#389—731no—
184#389—731no—
185#389—731no—
186#389C2×D7311yescharacteristic
187#387—1461no—
188#387—1461no—
189#387—1461no—
190#387—1461no—
191#382—731no—
192#382—731no—
193C43—731no—
194#336—731no—
195#336—731no—
196#336—1461no—
197#336C2×D7311yescharacteristic
198#336C2×D7311yescharacteristic
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—1461no—
202C22×C8—1461no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—731no—
205C2×C4⋊C4—731no—
206C2×C4⋊C4—1461no—
207C2×C4⋊C4—1461no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4C4×D7311yescharacteristic
210C2×C4⋊C4C4×D7311yescharacteristic
211C2×C42—731no—
212C2×C42—731no—
213C2×C42—731no—
214C2×C42—731no—
215C2×C42—731no—
216C2×C42—731no—
217C2×C42C22×D7311yescharacteristic
218C4⋊C8—1464no—
219#97—1464no—
220C4×C8—2922no—
221#95—21no—
222#95—1461no—
223#95—1461no—
224#95—1461no—
225#95—1461no—
226#95—1461no—
227#95—1461no—
228#95—1461no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—731no—
232C22×C4—731no—
233C22×C4—731no—
234C22×C4—731no—
235C22×C4—1461no—
236C22×C4—1461no—
237C22×C4C2×C4×D7311yescharacteristic
238C22×C4D4×D7311yescharacteristic
239C22×C4D4×D7311yescharacteristic
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—2921no—
247C2×C8—2921no—
248C2×C8—2921no—
249C2×C8—2921no—
250C2×C8—1462no—
251C2×C8—1462no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—2921no—
258C4⋊C4—2922no—
259C4⋊C4—2922no—
260C4⋊C4—2921no—
261C4⋊C4—2921no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C42—41no—
265C42—1462no—
266C42—1462no—
267C42—1462no—
268C42—1461no—
269C42—1461no—
270C42—1461no—
271C42—1461no—
272C42—1461no—
273C42—1461no—
274C23C22⋊C4×D7311yescharacteristic
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—2921no—
288C2×C4—2921no—
289C2×C4—2921no—
290C2×C4—2921no—
291C2×C4—2921no—
292C2×C4—2921no—
293C2×C4—732no—
294C2×C4—732no—
295C2×C4—732no—
296C2×C4—1461no—
297C2×C4—1461no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4—1461no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4#1455659711yescharacteristic
306C2×C4#1455659911yescharacteristic
307C2×C4#1455661011yescharacteristic
308C2×C4#1455661211yescharacteristic
309C2×C4#1455661811yescharacteristic
310C2×C4#1455662311yescharacteristic
311C8—42no—
312C8—42no—
313C8—2922no—
314C8—2922no—
315C22#1798855211yescharacteristic
316C22#1798855911yescharacteristic
317C22#101×D7311yescharacteristic
318C22#1798858011yescharacteristic
319C22#1798858711yescharacteristic
320C22#104×D7311yescharacteristic
321C22#104×D7311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—81no—
329C4—81no—
330C4—2921no—
331C4—5841no—
332C4—5841no—
333C4—1462no—
334C4—1462no—
335C4—1462no—
336C2#2260828511yescharacteristic
337C2#2260834311yescharacteristic
338C2#2260838811yescharacteristic
339C2#2260841411yescharacteristic
340C2#2260845511yescharacteristic
341C2#2260852411yescharacteristic
342C2#2260862811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D73
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1271C2
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenter#1271D73
hypocenterC73#7677
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
179. C73#7677semidirect

Maximal subgroups

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

subgroupindex
#226183172
#226097792
#226096782
#226077552
#226077542
#226077532
C73×#12712
#767773