Finite Group Databasebeta

← #32974539

Subgroups — #32974539

Order 18688.

394 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 95 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#22618290C211yesmaximal, characteristic
2#22610073C211yesmaximal, characteristic
3#22609678C211yesmaximal, characteristic
4#22607755C211yesmaximal, characteristic
5#22607754C211yesmaximal, characteristic
6#22607753C211yesmaximal, characteristic
7C73×#1271C211yesmaximal, characteristic
8C2×#14556581—21no—
9C2×#14556501—21no—
10#17988486C411yescharacteristic
11#17988485C2211yescharacteristic
12#17988484—21no—
13#17988483C411yescharacteristic
14#17988482—21no—
15#17988456C411yescharacteristic
16#17988456C411yescharacteristic
17#17988451—21no—
18C42×Dic73C2211yescharacteristic
19#17988342C2211yescharacteristic
20#17988342C2211yescharacteristic
21#17988341—21no—
22#17988341—21no—
23#17988341—21no—
24#389×C73C2211yescharacteristic
25#336×C73C2211yescharacteristic
26#336×C73C2211yescharacteristic
27C22×#10596831—21no—
28C22×#10596831—21no—
29#14556581—42no—
30#14556581—42no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73C2×C411yescharacteristic
33C2×C4⋊Dic73C2×C411yescharacteristic
34C2×#11924007—21no—
35C2×#11924007—21no—
36C2×#11924007—21no—
37C2×#11924007—21no—
38C2×#11924007—21no—
39C2×#11924007—21no—
40C2×C4×Dic73C2×C411yescharacteristic
41C2×C4×Dic73C2×C411yescharacteristic
42C2×C4×Dic73D411yescharacteristic
43C2×C4×Dic73D411yescharacteristic
44C2×C4×Dic73D411yescharacteristic
45C2×C4×Dic73D411yescharacteristic
46#14556501—24no—
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—41no—
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—42no—
74#11924007—42no—
75#11924007—42no—
76#11924007—42no—
77#11924007—41no—
78#11924007—41no—
79#11924007—42no—
80C4×Dic73—21no—
81C4×Dic73—21no—
82C4×Dic73—21no—
83C4×Dic73—21no—
84C4×Dic73—21no—
85C4×Dic73—21no—
86C4×Dic73—22no—
87C4×Dic73—22no—
88C4×Dic73—41no—
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73C22×C411yescharacteristic
92C22×C4×C73C2×D411yescharacteristic
93C22×C4×C73C2×D411yescharacteristic
94C2×C8×C73—22no—
95C2×C8×C73—41no—
96C2×C8×C73—41no—
97C2×C8×C73—41no—
98C2×C8×C73—41no—
99C2×C8×C73—41no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73—21no—
102C4⋊C4×C73—41no—
103C4⋊C4×C73—41no—
104C4⋊C4×C73—41no—
105C42×C73—41no—
106C23×C73C2×C22⋊C411yescharacteristic
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—41no—
116C2×C4×C73—41no—
117C2×C4×C73—41no—
118C2×C4×C73—41no—
119C2×C4×C73#13111yescharacteristic
120C2×C4×C73#13111yescharacteristic
121C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C73#13711yescharacteristic
124C2×C4×C73#13711yescharacteristic
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73#10112yes—
142C2×Dic73#10412yes—
143C8×C73—42no—
144C8×C73—81no—
145#10596831—42no—
146#10596831—81no—
147C22×C73#40811yescharacteristic
148C22×C73#41011yescharacteristic
149C22×C73C2×#10111yescharacteristic
150C22×C73#41811yescharacteristic
151C22×C73#41911yescharacteristic
152C22×C73C2×#10411yescharacteristic
153C22×C73#42111yescharacteristic
154C4×C73—21no—
155C4×C73—21no—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—81no—
161C4×C73—81no—
162Dic73—22no—
163Dic73—22no—
164Dic73—41no—
165Dic73—41no—
166Dic73—81no—
167Dic73—81no—
168#7703—731nomaximal, Sylow
169C2×C73#147011yescharacteristic
170C2×C73#148411yescharacteristic
171C2×C73#149711yescharacteristic
172C2×C73#150611yescharacteristic
173C2×C73#151411yescharacteristic
174C2×C73#152811yescharacteristic
175C2×C73#155611yescharacteristic
176#2859—731no—
177#1839—731no—
178#1745—731no—
179#1271—731no—
180#1271—731no—
181#1271—731no—
182#1271D7311yescharacteristic
183C73#770311yescharacteristic, complemented, Sylow
184C2×#125—1461no—
185C2×#97—1461no—
186#389—731no—
187#389—731no—
188#389—731no—
189#389—1461no—
190#389—1461no—
191#389C2×D7311yescharacteristic
192#384—731no—
193#384—731no—
194#382—1461no—
195C43—731no—
196#336—731no—
197#336—731no—
198#336—1461no—
199#336—1461no—
200#336—1461no—
201#336C2×D7311yescharacteristic
202#336C2×D7311yescharacteristic
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—1461no—
206C22×C8—1461no—
207#125—2922no—
208#125—2922no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—731no—
211C2×C4⋊C4—731no—
212C2×C4⋊C4—1461no—
213C2×C4⋊C4—1461no—
214C2×C4⋊C4—1461no—
215C2×C4⋊C4—1461no—
216C2×C4⋊C4—1461no—
217C2×C4⋊C4—1461no—
218C2×C4⋊C4—1461no—
219C2×C4⋊C4C4×D7311yescharacteristic
220C2×C4⋊C4C4×D7311yescharacteristic
221C2×C42—731no—
222C2×C42—731no—
223C2×C42—731no—
224C2×C42—731no—
225C2×C42—731no—
226C2×C42—731no—
227C2×C42C22×D7311yescharacteristic
228#97—1464no—
229#95—21no—
230#95—1461no—
231#95—1461no—
232#95—1461no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—731no—
236C22×C4—731no—
237C22×C4—731no—
238C22×C4—731no—
239C22×C4—1461no—
240C22×C4—1461no—
241C22×C4C2×C4×D7311yescharacteristic
242C22×C4D4×D7311yescharacteristic
243C22×C4D4×D7311yescharacteristic
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—2921no—
251C2×C8—2921no—
252C2×C8—2921no—
253C2×C8—2921no—
254C2×C8—2921no—
255C2×C8—1462no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—2921no—
262C4⋊C4—2922no—
263C4⋊C4—2922no—
264C4⋊C4—2922no—
265C4⋊C4—2922no—
266C4⋊C4—2922no—
267C4⋊C4—2922no—
268C4⋊C4—2921no—
269C4⋊C4—2921no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C42—41no—
273C42—2921no—
274C42—1462no—
275C42—1462no—
276C42—1461no—
277C42—1461no—
278C42—1461no—
279C42—1461no—
280C42—1461no—
281C42—1461no—
282C23C22⋊C4×D7311yescharacteristic
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—2921no—
296C2×C4—2921no—
297C2×C4—2921no—
298C2×C4—2921no—
299C2×C4—2921no—
300C2×C4—2921no—
301C2×C4—732no—
302C2×C4—732no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4—1461no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4#1455659711yescharacteristic
314C2×C4#1455659911yescharacteristic
315C2×C4#1455661511yescharacteristic
316C2×C4#1455661811yescharacteristic
317C2×C4#1455662011yescharacteristic
318C2×C4#1455662311yescharacteristic
319C8—42no—
320C8—81no—
321C8—2922no—
322C8—5841no—
323C22#1798855211yescharacteristic
324C22#1798855911yescharacteristic
325C22#101×D7311yescharacteristic
326C22#1798859011yescharacteristic
327C22#1798859411yescharacteristic
328C22#104×D7311yescharacteristic
329C22#1798860211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—2921no—
339C4—2921no—
340C4—5841no—
341C4—5841no—
342C4—1462no—
343C4—1462no—
344C2#2260828511yescharacteristic
345C2#2260834611yescharacteristic
346C2#2260840211yescharacteristic
347C2#2260844111yescharacteristic
348C2#2260847611yescharacteristic
349C2#2260853111yescharacteristic
350C2#2260864611yescharacteristic
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#7703
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
183. C73#7703semidirect

Maximal subgroups

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

subgroupindex
#226182902
#226100732
#226096782
#226077552
#226077542
#226077532
C73×#12712
#770373