Finite Group Databasebeta

← #32996643

Subgroups — #32996643

Order 18688.

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

normal subgroups only

This group has 572 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
1C2×#17988512C211yesmaximal, characteristic
2#22608258C211yesmaximal, characteristic
3#22607930C214yesmaximal, complemented
4C73×#1819C211yesmaximal, characteristic
5C22×C4⋊Dic73C411yescharacteristic, complemented
6C22×C22⋊Dic73—21no—
7#17988551—21no—
8#17988512—21no—
9#17988512—21no—
10#17988512C412yescomplemented
11#17988512C2212yes—
12C2×#14556498—21no—
13C2×#14556498C411yescharacteristic, complemented
14#17988311—21no—
15#17988311C2212yes—
16C22×C22⋊C4×C73C2211yescharacteristic
17#379×C73—21no—
18#342×C73—21no—
19#342×C73C2212yes—
20C23×Dic73—21no—
21C23×Dic73—21no—
22C2×#11924012—41no—
23C2×C4⋊Dic73—21no—
24C2×C4⋊Dic73—41no—
25C2×C4⋊Dic73—41no—
26C2×C4⋊Dic73C2×C412yes—
27C2×C22⋊Dic73—22no—
28C2×C22⋊Dic73—22no—
29C2×C22⋊Dic73—44no—
30C22⋊#10596831—22no—
31C22⋊#10596831—41no—
32#14556498—22no—
33#14556498—21no—
34#14556498—22no—
35#14556498C2×C412yes—
36C25×C73D411yescharacteristic
37C23×C4×C73C2×C411yescharacteristic
38C23×C4×C73D411yescharacteristic
39C2×C22⋊C4×C73—22no—
40C2×C22⋊C4×C73—41no—
41C2×C22⋊C4×C73—41no—
42C2×C22⋊C4×C73—41no—
43C2×C22⋊C4×C73—41no—
44C2×C22⋊C4×C73C2×C411yescharacteristic
45C2×C22⋊C4×C73D411yescharacteristic
46C2×C22⋊C4×C73D411yescharacteristic
47C2×C22⋊C4×C73C2311yescharacteristic
48C22×Dic73—22no—
49C22×Dic73—22no—
50C22×Dic73—42no—
51C22×Dic73—42no—
52C22×Dic73—42no—
53C22×Dic73—42no—
54C22×Dic73—42no—
55C22×Dic73—41no—
56C22×Dic73—41no—
57#11924012—82no—
58C2×#10596831—42no—
59C4⋊Dic73—42no—
60C4⋊Dic73—42no—
61C22⋊Dic73—44no—
62C22⋊Dic73—44no—
63C24×C73—22no—
64C24×C73—21no—
65C24×C73—21no—
66C24×C73—41no—
67C24×C73—42no—
68C24×C73—42no—
69C24×C73C22⋊C411yescharacteristic
70C24×C73C22⋊C411yescharacteristic
71C24×C73C2×D411yescharacteristic
72C22×C4×C73—21no—
73C22×C4×C73—21no—
74C22×C4×C73—21no—
75C22×C4×C73—21no—
76C22×C4×C73—42no—
77C22×C4×C73—42no—
78C22×C4×C73—42no—
79C22×C4×C73C22⋊C411yescharacteristic
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22×C411yescharacteristic
82C22×C4×C73C2×D411yescharacteristic
83C22⋊C4×C73—41no—
84C22⋊C4×C73—41no—
85C22⋊C4×C73—41no—
86C22⋊C4×C73—41no—
87C22⋊C4×C73—42no—
88C22⋊C4×C73—42no—
89C22⋊C4×C73—82no—
90C22⋊C4×C73—82no—
91C23×C73—22no—
92C23×C73—22no—
93C23×C73—21no—
94C23×C73—21no—
95C23×C73—21no—
96C23×C73—21no—
97C23×C73—21no—
98C23×C73—21no—
99C23×C73—21no—
100C23×C73—42no—
101C23×C73—42no—
102C23×C73—41no—
103C23×C73—41no—
104C23×C73—41no—
105C23×C73—41no—
106C23×C73—48no—
107C23×C73—42no—
108C23×C73—42no—
109C23×C73—81no—
110C23×C73—81no—
111C23×C73—84no—
112C23×C73#9911yescharacteristic
113C23×C73#9911yescharacteristic
114C23×C73C2×C22⋊C411yescharacteristic
115C23×C73AGL(1,ℤ/8)12yes—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—42no—
121C2×C4×C73—42no—
122C2×C4×C73—42no—
123C2×C4×C73—41no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73—81no—
128C2×C4×C73—82no—
129C2×C4×C73—82no—
130C2×C4×C73—82no—
131C2×Dic73—42no—
132C2×Dic73—42no—
133C2×Dic73—42no—
134C2×Dic73—42no—
135C2×Dic73—42no—
136C2×Dic73—42no—
137C2×Dic73—84no—
138C2×Dic73—82no—
139C2×Dic73—82no—
140#10596831—82no—
141C22×C73—24no—
142C22×C73—24no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73—21no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—22no—
150C22×C73—42no—
151C22×C73—42no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—81no—
158C22×C73—84no—
159C22×C73—84no—
160C22×C73—81no—
161C22×C73#35212yes—
162C22×C73#35412yes—
163C22×C73C2×#9911yescharacteristic
164C22×C73#41811yescharacteristic
165C22×C73#42111yescharacteristic
166C4×C73—41no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73—162no—
171Dic73—82no—
172Dic73—82no—
173#11797—731nomaximal, Sylow
174C2×C73—21no—
175C2×C73—22no—
176C2×C73—22no—
177C2×C73—21no—
178C2×C73—42no—
179C2×C73—81no—
180C2×C73#151011yescharacteristic
181C2×C73C2×#35211yescharacteristic
182C2×C73C2×#35411yescharacteristic
183C2×#397—731no—
184#1819D7311yescharacteristic
185#1462—731no—
186#1344—734no—
187C73#1179711yescharacteristic, complemented, Sylow
188C22×C4⋊C4—731no—
189C22×C22⋊C4—1461no—
190C22×C22⋊C4C2×D7311yescharacteristic
191#407—1461no—
192#397—732no—
193#397—732no—
194#397—1461no—
195#397—1461no—
196#379—21no—
197C2×#95—731no—
198C2×#95—1461no—
199#342—21no—
200#342C2×D7312yes—
201#323—732no—
202#323—1461no—
203C25C22⋊D7311yescharacteristic
204C23×C4—1461no—
205C23×C4—1461no—
206C23×C4C4×D7311yescharacteristic
207C23×C4D29211yescharacteristic
208C2×M16—2921no—
209C2×C4⋊C4—2921no—
210C2×C4⋊C4—2921no—
211C2×C4⋊C4—732no—
212C2×C4⋊C4—1461no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—41no—
215C2×C22⋊C4—41no—
216C2×C22⋊C4—41no—
217C2×C22⋊C4—41no—
218C2×C22⋊C4—2924no—
219C2×C22⋊C4—1462no—
220C2×C22⋊C4—1462no—
221C2×C22⋊C4C4×D7311yescharacteristic
222C2×C22⋊C4D29211yescharacteristic
223C2×C22⋊C4C22⋊D7311yescharacteristic
224C2×C22⋊C4C22×D7311yescharacteristic
225C22⋊C8—2921no—
226C22⋊C8—1462no—
227#95—732no—
228#95—1461no—
229#95—1462no—
230#95—1462no—
231C24—22no—
232C24—21no—
233C24—21no—
234C24—41no—
235C24—42no—
236C24—42no—
237C24#1192400511yescharacteristic
238C24#1192400511yescharacteristic
239C24C2×C22⋊D7311yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—2922no—
248C22×C4—2922no—
249C22×C4—2922no—
250C22×C4—2922no—
251C22×C4—2922no—
252C22×C4—2921no—
253C22×C4—2921no—
254C22×C4—1462no—
255C22×C4—1462no—
256C22×C4#1192400511yescharacteristic
257C22×C4#1192400511yescharacteristic
258C22×C4C2×C4×D7311yescharacteristic
259C22×C4C2×D29211yescharacteristic
260M16—5842no—
261C2×C8—2922no—
262C4⋊C4—2922no—
263C4⋊C4—2922no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—82no—
271C22⋊C4—82no—
272C22⋊C4—2924no—
273C22⋊C4—2924no—
274C23—22no—
275C23—22no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—42no—
284C23—42no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—48no—
290C23—42no—
291C23—42no—
292C23—81no—
293C23—81no—
294C23—84no—
295C23#1455650511yescharacteristic
296C23#1455650511yescharacteristic
297C23C2×#1192400511yescharacteristic
298C23#1455661612yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4—2922no—
315C2×C4—2922no—
316C2×C4—2922no—
317C2×C4—2922no—
318C2×C4—2922no—
319C2×C4—2922no—
320C2×C4—5844no—
321C2×C4—5842no—
322C2×C4—5842no—
323C8—5842no—
324C22—24no—
325C22—24no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—81no—
341C22—84no—
342C22—84no—
343C22—81no—
344C22#1798837612yes—
345C22#1798838112yes—
346C22C2×#1455650511yescharacteristic
347C22#1798859111yescharacteristic
348C22#1798860511yescharacteristic
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—162no—
354C4—5842no—
355C4—5842no—
356C2—21no—
357C2—22no—
358C2—22no—
359C2—21no—
360C2—42no—
361C2—81no—
362C2#2260845911yescharacteristic
363C2C2×#1798837611yescharacteristic
364C2C2×#1798838111yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C22⋊C4C22×D73
FittingC73×#1819C2
socleC22×C73C2×#99
prime radicalC25×C73D4
cosocleC2×C22⋊C4×C73C23
hypercenter#1819D73
hypocenterC73#11797
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1819

Complements

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

NH ≅ G/Ntype
3. #22607930C2semidirect
5. C22×C4⋊Dic73C4semidirect
10. #17988512C4semidirect
13. C2×#14556498C4semidirect
187. C73#11797semidirect

Maximal subgroups

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

subgroupindex
C2×#179885122
#226082582
#226079302
C73×#18192
#1179773