Finite Group Databasebeta

← #32978748

Subgroups — #32978748

Order 18688.

456 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556583C211yesmaximal, characteristic
2#22609784C211yesmaximal, characteristic
3C2×#17988328C212yesmaximal
4#22607813C212yesmaximal
5C73×#1767C211yesmaximal, characteristic
6C2×#14556583C2211yescharacteristic
7C2×C4⋊#10596831—21no—
8C2×#14556502C2212yes—
9#17988485C411yescharacteristic
10#17988485C411yescharacteristic
11#17988471—21no—
12#17988471—21no—
13#17988453C2211yescharacteristic
14C4×#11924007—21no—
15C4×#11924007—21no—
16C4×C4⋊Dic73C411yescharacteristic
17C4×C4⋊Dic73C411yescharacteristic
18#17988342—21no—
19#17988328—24no—
20C2×C4⋊C8×C73—21no—
21C2×#97×C73C2212yes—
22C43×C73C2211yescharacteristic
23#336×C73—21no—
24C22×#10596831—22no—
25#14556583—21no—
26#14556583—21no—
27#14556583D412yes—
28#14556583Q812yes—
29C2×C4⋊Dic73C2×C411yescharacteristic
30C2×C4⋊Dic73C2×C411yescharacteristic
31C2×C4⋊Dic73C2×C411yescharacteristic
32C2×C4⋊Dic73C2×C411yescharacteristic
33C2×#11924007—21no—
34C2×#11924007—21no—
35C2×#11924007—21no—
36C2×#11924007—21no—
37C2×C4×Dic73—21no—
38C2×C4×Dic73—21no—
39C4⋊#10596831—24no—
40#14556502—22no—
41#14556502—22no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48C22×C8×C73—22no—
49C2×C42×C73C2×C411yescharacteristic
50C2×C42×C73C2×C411yescharacteristic
51C2×C42×C73D411yescharacteristic
52C2×C42×C73D411yescharacteristic
53C2×C42×C73D411yescharacteristic
54C2×C42×C73D411yescharacteristic
55C2×C42×C73C2311yescharacteristic
56C4⋊C8×C73—24no—
57#97×C73—22no—
58#97×C73—22no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C2×#10596831—24no—
64C2×#10596831—42no—
65C2×#10596831—42no—
66C4⋊Dic73—21no—
67C4⋊Dic73—21no—
68C4⋊Dic73—41no—
69C4⋊Dic73—41no—
70C4⋊Dic73C4⋊C412yes—
71C4⋊Dic73C4⋊C412yes—
72#11924007—22no—
73#11924007—22no—
74#11924007—22no—
75#11924007—22no—
76#11924007—42no—
77#11924007—42no—
78C4×Dic73—42no—
79C4×Dic73—42no—
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22⋊C411yescharacteristic
82C22×C4×C73C22⋊C411yescharacteristic
83C22×C4×C73C22⋊C411yescharacteristic
84C22×C4×C73C22×C411yescharacteristic
85C22×C4×C73C2×D411yescharacteristic
86C22×C4×C73C2×D411yescharacteristic
87C2×C8×C73—24no—
88C2×C8×C73—42no—
89C2×C8×C73—42no—
90C42×C73—22no—
91C42×C73—22no—
92C42×C73—22no—
93C42×C73—41no—
94C42×C73—41no—
95C42×C73—41no—
96C42×C73C2×D411yescharacteristic
97C42×C73C2×Q811yescharacteristic
98C42×C73#4111yescharacteristic
99C42×C73#4111yescharacteristic
100C23×C73C2×C22⋊C411yescharacteristic
101C2×C4×C73—21no—
102C2×C4×C73—21no—
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—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73#10112yes—
117C2×C4×C73#10412yes—
118C2×C4×C73#10412yes—
119C2×C4×C73C2×C4⋊C411yescharacteristic
120C2×C4×C73#11711yescharacteristic
121C2×C4×C73#12111yescharacteristic
122C2×C4×C73#12111yescharacteristic
123C2×C4×C73C22⋊Q811yescharacteristic
124C2×C4×C73C22⋊Q811yescharacteristic
125C2×Dic73—22no—
126C2×Dic73—22no—
127C2×Dic73—41no—
128C2×Dic73—41no—
129C2×Dic73—41no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C8×C73—44no—
138#10596831—44no—
139C22×C73#38011yescharacteristic
140C22×C73C2×#10111yescharacteristic
141C22×C73#41311yescharacteristic
142C22×C73C2×#10411yescharacteristic
143C22×C73C2×#10411yescharacteristic
144C22×C73#42111yescharacteristic
145C22×C73#42111yescharacteristic
146C4×C73—21no—
147C4×C73—21no—
148C4×C73—21no—
149C4×C73—21no—
150C4×C73—21no—
151C4×C73—21no—
152C4×C73—41no—
153C4×C73—41no—
154C4×C73—41no—
155C4×C73#33014yescomplemented
156Dic73—42no—
157Dic73—42no—
158Dic73—81no—
159Dic73—81no—
160#8580—731nomaximal, Sylow
161C2×C73C2×#33011yescharacteristic
162C2×C73#152911yescharacteristic
163C2×C73#152911yescharacteristic
164C2×C73#153711yescharacteristic
165C2×C73#180111yescharacteristic
166C2×C73#180611yescharacteristic
167C2×C73#180611yescharacteristic
168C4×#125—731no—
169#1767—731no—
170#1767D7311yescharacteristic
171C2×#330—732no—
172#1295—732no—
173C73#858011yescharacteristic, complemented, Sylow
174C2×#125—731no—
175C2×C4⋊C8—21no—
176C2×C4⋊C8—1461no—
177C2×#97—732no—
178C2×#97C2×D7312yes—
179#389—731no—
180#389—731no—
181#387—1461no—
182#387—1461no—
183#382—731no—
184C4×C4⋊C4—731no—
185C4×C4⋊C4—731no—
186C4×C4⋊C4—1461no—
187C4×C4⋊C4—1461no—
188C43C2×D7311yescharacteristic
189#336—21no—
190#336—1461no—
191#330—1464no—
192C22×C8—22no—
193C22×C8—1462no—
194#125—732no—
195#125—732no—
196#125—1461no—
197#125—1461no—
198C2×C4⋊C4—731no—
199C2×C4⋊C4—731no—
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×C42—1461no—
207C2×C42—1461no—
208C2×C42C4×D7311yescharacteristic
209C2×C42C4×D7311yescharacteristic
210C2×C42D29211yescharacteristic
211C2×C42D29211yescharacteristic
212C2×C42C22⋊D7311yescharacteristic
213C2×C42C22⋊D7311yescharacteristic
214C2×C42C22×D7311yescharacteristic
215C4⋊C8—24no—
216C4⋊C8—1464no—
217#97—22no—
218#97—22no—
219#97—1462no—
220#97—1462no—
221#95—1461no—
222#95—1461no—
223#95—1461no—
224#95—1461no—
225#95—1461no—
226#95—1461no—
227C22×C4—1461no—
228C22×C4—1461no—
229C22×C4—1461no—
230C22×C4—1461no—
231C22×C4#1192400511yescharacteristic
232C22×C4#1192400511yescharacteristic
233C22×C4#1192400511yescharacteristic
234C22×C4#1192400511yescharacteristic
235C22×C4C2×C4×D7311yescharacteristic
236C22×C4C2×C22⋊D7311yescharacteristic
237C22×C4C2×D29211yescharacteristic
238C2×C8—24no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—2922no—
242C2×C8—2922no—
243C2×C8—1464no—
244C4⋊C4—2921no—
245C4⋊C4—2921no—
246C4⋊C4—2922no—
247C4⋊C4—2922no—
248C4⋊C4—732no—
249C4⋊C4—732no—
250C4⋊C4—1461no—
251C4⋊C4—1461no—
252C4⋊C4—1462no—
253C4⋊C4—1462no—
254C4⋊C4—1462no—
255C4⋊C4—1462no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42—2922no—
263C42—2922no—
264C42D4×D7311yescharacteristic
265C42Q8×D7311yescharacteristic
266C42#1192402711yescharacteristic
267C42#1192402911yescharacteristic
268C23C2×#1192400511yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—2921no—
285C2×C4—2921no—
286C2×C4—2921no—
287C2×C4—2921no—
288C2×C4—2921no—
289C2×C4—2921no—
290C2×C4—2921no—
291C2×C4—2921no—
292C2×C4—2921no—
293C2×C4—2921no—
294C2×C4—1462no—
295C2×C4—1462no—
296C2×C4#1455650912yes—
297C2×C4#1455651712yes—
298C2×C4#1455651912yes—
299C2×C4C4⋊C4×D7311yescharacteristic
300C2×C4#1455654911yescharacteristic
301C2×C4#1455656211yescharacteristic
302C2×C4#1455656611yescharacteristic
303C2×C4#1455656711yescharacteristic
304C2×C4#1455657111yescharacteristic
305C8—44no—
306C8—2924no—
307C22#1798844411yescharacteristic
308C22C2×#1455650911yescharacteristic
309C22#1798856911yescharacteristic
310C22C2×#1455651711yescharacteristic
311C22C2×#1455651911yescharacteristic
312C22#1798860311yescharacteristic
313C22#1798860511yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—2922no—
324C4—2922no—
325C4—5841no—
326C4—5841no—
327C4#1798832814yescomplemented
328C2C2×#1798832811yescharacteristic
329C2#2260853611yescharacteristic
330C2#2260853911yescharacteristic
331C2#2260856811yescharacteristic
332C2#2260992411yescharacteristic
333C2#2260994811yescharacteristic
334C2#2260995211yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1767C2
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenter#1767D73
hypocenterC73#8580
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
155. C4×C73#330semidirect
173. C73#8580semidirect
327. C4#17988328semidirect

Maximal subgroups

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

subgroupindex
C4×#145565832
#226097842
C2×#179883282
#226078132
C73×#17672
#858073