Finite Group Databasebeta

← #32981589

Subgroups — #32981589

Order 18688.

626 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618241C211yesmaximal, characteristic
2#22609693C211yesmaximal, characteristic
3C2×#17988328C212yesmaximal, complemented
4#22607813C212yesmaximal, complemented
5C22×#97×C73C211yesmaximal, characteristic
6C2×#14556583C2211yescharacteristic
7C2×C22⋊#10596831—21no—
8C2×#14556502C2212yes—
9#17988485C411yescharacteristic
10#17988485C411yescharacteristic
11#17988471—21no—
12#17988471—21no—
13#17988460—21no—
14#17988460—21no—
15#17988453C2211yescharacteristic
16#17988447C411yescharacteristic
17#17988447C411yescharacteristic
18#17988342—21no—
19#17988328—24no—
20C23×C8×C73—21no—
21C22×C42×C73C2211yescharacteristic
22C2×#97×C73—21no—
23C2×#97×C73—24no—
24C2×#97×C73C2212yes—
25C22×#10596831—22no—
26#14556583—22no—
27#14556583—22no—
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×C4⋊Dic73C2×C411yescharacteristic
30C2×C4⋊Dic73C2×C411yescharacteristic
31C2×C4⋊Dic73C2×C411yescharacteristic
32C2×#11924007—21no—
33C2×#11924007—21no—
34C2×#11924007—21no—
35C2×#11924007—21no—
36C2×C22⋊Dic73—21no—
37C2×C22⋊Dic73—21no—
38C22⋊#10596831—24no—
39#14556502—22no—
40#14556502—22no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47C23×C4×C73C2×C411yescharacteristic
48C23×C4×C73D411yescharacteristic
49C23×C4×C73D411yescharacteristic
50C22×C8×C73—24no—
51C22×C8×C73—24no—
52C22×C8×C73—24no—
53C22×C8×C73—22no—
54C2×C42×C73—22no—
55C2×C42×C73—22no—
56C2×C42×C73C2×C411yescharacteristic
57C2×C42×C73D411yescharacteristic
58C2×C42×C73D411yescharacteristic
59C2×C42×C73C2311yescharacteristic
60#97×C73—24no—
61#97×C73—22no—
62#97×C73D414yes—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C2×#10596831—24no—
68C2×#10596831—42no—
69C2×#10596831—42no—
70C4⋊Dic73—22no—
71C4⋊Dic73—22no—
72C4⋊Dic73—41no—
73C4⋊Dic73—41no—
74#11924007—42no—
75#11924007—42no—
76#11924007—41no—
77#11924007—42no—
78#11924007—41no—
79C22⋊Dic73—42no—
80C22⋊Dic73—42no—
81C24×C73C22⋊C411yescharacteristic
82C22×C4×C73—22no—
83C22×C4×C73—22no—
84C22×C4×C73—21no—
85C22×C4×C73—21no—
86C22×C4×C73—22no—
87C22×C4×C73—22no—
88C22×C4×C73—22no—
89C22×C4×C73—22no—
90C22×C4×C73—41no—
91C22×C4×C73—41no—
92C22×C4×C73C22⋊C411yescharacteristic
93C22×C4×C73C22⋊C411yescharacteristic
94C22×C4×C73C22⋊C411yescharacteristic
95C22×C4×C73C22×C411yescharacteristic
96C22×C4×C73C2×D411yescharacteristic
97C22×C4×C73C2×D411yescharacteristic
98C2×C8×C73—216no—
99C2×C8×C73—24no—
100C2×C8×C73—24no—
101C2×C8×C73—24no—
102C42×C73—22no—
103C42×C73—21no—
104C42×C73—22no—
105C42×C73—21no—
106C42×C73C2×D412yes—
107C42×C73#4112yes—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—21no—
112C23×C73#10112yes—
113C23×C73#10412yes—
114C23×C73#10412yes—
115C23×C73C2×C22⋊C411yescharacteristic
116C2×C4×C73—24no—
117C2×C4×C73—24no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—44no—
133C2×C4×C73—44no—
134C2×C4×C73#10412yes—
135C2×C4×C73C4×D412yes—
136C2×C4×C73#12011yescharacteristic
137C2×C4×C73#12112yes—
138C2×C4×C73#12311yescharacteristic
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—41no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145C2×Dic73—41no—
146C2×Dic73—41no—
147C2×Dic73—41no—
148C2×Dic73—41no—
149C2×Dic73—41no—
150C2×Dic73—41no—
151C8×C73—28no—
152#10596831—44no—
153C22×C73—22no—
154C22×C73—22no—
155C22×C73—22no—
156C22×C73—22no—
157C22×C73—22no—
158C22×C73—22no—
159C22×C73#33014yescomplemented
160C22×C73#38611yescharacteristic
161C22×C73C2×#10111yescharacteristic
162C22×C73#41311yescharacteristic
163C22×C73C2×#10411yescharacteristic
164C22×C73C2×#10411yescharacteristic
165C22×C73C2×#10411yescharacteristic
166C22×C73#42111yescharacteristic
167C4×C73—22no—
168C4×C73—21no—
169C4×C73—22no—
170C4×C73—21no—
171C4×C73—22no—
172C4×C73—41no—
173C4×C73—41no—
174Dic73—81no—
175Dic73—81no—
176Dic73—81no—
177Dic73—81no—
178#9121—731nomaximal, Sylow
179C2×C73—24no—
180C2×C73C2×#33011yescharacteristic
181C2×C73#152411yescharacteristic
182C2×C73#153111yescharacteristic
183C2×C73#153211yescharacteristic
184C2×C73#187111yescharacteristic
185C2×C73#189611yescharacteristic
186C2×C73#190111yescharacteristic
187C22×#97D7311yescharacteristic
188#2851—731no—
189#1749—731no—
190C2×#330—732no—
191#1295—732no—
192C73#912111yescharacteristic, complemented, Sylow
193C23×C8—21no—
194C2×#125—731no—
195C22×C42C2×D7311yescharacteristic
196C2×C22⋊C8—1461no—
197C2×#97—21no—
198C2×#97—24no—
199C2×#97—732no—
200C2×#97C2×D7312yes—
201#389—731no—
202#389—731no—
203#387—1461no—
204#387—1461no—
205#385—1461no—
206#385—1461no—
207#382—731no—
208#380—731no—
209#380—731no—
210#336—1461no—
211#330—1464no—
212C23×C4C4×D7311yescharacteristic
213C23×C4D29211yescharacteristic
214C23×C4C22⋊D7311yescharacteristic
215C22×C8—24no—
216C22×C8—24no—
217C22×C8—24no—
218C22×C8—22no—
219C22×C8—1462no—
220#125—1462no—
221#125—1462no—
222C2×C4⋊C4—731no—
223C2×C4⋊C4—731no—
224C2×C4⋊C4—731no—
225C2×C4⋊C4—731no—
226C2×C4⋊C4—1461no—
227C2×C4⋊C4—1461no—
228C2×C4⋊C4—1461no—
229C2×C4⋊C4—1461no—
230C2×C22⋊C4—1461no—
231C2×C22⋊C4—1461no—
232C2×C42—22no—
233C2×C42—22no—
234C2×C42C4×D7311yescharacteristic
235C2×C42D29211yescharacteristic
236C2×C42C22⋊D7311yescharacteristic
237C2×C42C22×D7311yescharacteristic
238C22⋊C8—1464no—
239#97—24no—
240#97—22no—
241#97—1462no—
242#97—1462no—
243#97C22⋊D7314yes—
244#95—1461no—
245#95—1461no—
246#95—1461no—
247#95—1461no—
248#95—1461no—
249#95—1461no—
250C24#1192400511yescharacteristic
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—1461no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4#1192400511yescharacteristic
266C22×C4#1192400511yescharacteristic
267C22×C4#1192400511yescharacteristic
268C22×C4C2×C4×D7311yescharacteristic
269C22×C4C2×C22⋊D7311yescharacteristic
270C22×C4C2×D29211yescharacteristic
271C2×C8—216no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—24no—
275C2×C8—2922no—
276C2×C8—2922no—
277C2×C8—1464no—
278C4⋊C4—2921no—
279C4⋊C4—2921no—
280C4⋊C4—2922no—
281C4⋊C4—2922no—
282C4⋊C4—2921no—
283C4⋊C4—2922no—
284C4⋊C4—2921no—
285C4⋊C4—1462no—
286C4⋊C4—1462no—
287C22⋊C4—2922no—
288C22⋊C4—2922no—
289C42—22no—
290C42—21no—
291C42—22no—
292C42—21no—
293C42C2×C22⋊D7312yes—
294C42#1192402812yes—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23#1455650912yes—
300C23#1455651712yes—
301C23#1455651912yes—
302C23C2×#1192400511yescharacteristic
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—2921no—
322C2×C4—2921no—
323C2×C4—2921no—
324C2×C4—2921no—
325C2×C4—2921no—
326C2×C4—2921no—
327C2×C4—2921no—
328C2×C4—2921no—
329C2×C4—2921no—
330C2×C4—2921no—
331C2×C4—2921no—
332C2×C4—2921no—
333C2×C4#1455651912yes—
334C2×C4C4×C22⋊D7312yes—
335C2×C4#1455656011yescharacteristic
336C2×C4#1455656512yes—
337C2×C4#1455657411yescharacteristic
338C8—28no—
339C8—2924no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22#1798832814yescomplemented
347C22#1798846611yescharacteristic
348C22C2×#1455650911yescharacteristic
349C22#1798856911yescharacteristic
350C22C2×#1455651711yescharacteristic
351C22C2×#1455651911yescharacteristic
352C22C2×#1455651911yescharacteristic
353C22#1798860311yescharacteristic
354C4—22no—
355C4—21no—
356C4—22no—
357C4—21no—
358C4—22no—
359C4—41no—
360C4—41no—
361C4—5841no—
362C4—5841no—
363C4—5841no—
364C4—5841no—
365C2—24no—
366C2C2×#1798832811yescharacteristic
367C2#2260851711yescharacteristic
368C2#2260854511yescharacteristic
369C2#2260854911yescharacteristic
370C2#2261023311yescharacteristic
371C2#2261037411yescharacteristic
372C2#2261039911yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC22×#97×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C42×C73C23
hypercenterC22×#97D73
hypocenterC73#9121
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#97

Complements

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

NH ≅ G/Ntype
3. C2×#17988328C2semidirect
4. #22607813C2semidirect
159. C22×C73#330semidirect
192. C73#9121semidirect
346. C22#17988328semidirect

Maximal subgroups

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

subgroupindex
#226182412
#226096932
C2×#179883282
#226078132
C22×#97×C732
#912173