Finite Group Databasebeta

← #33004297

Subgroups — #33004297

Order 18688.

552 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 107 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#22614923C211yesmaximal, characteristic
2C2×#17988381C214yesmaximal
3#22609919C211yesmaximal, characteristic
4C4×#99×C73C211yesmaximal, characteristic
5C2×#14556591C411yescharacteristic, complemented
6C2×#14556578C2212yes—
7C2×#14556506C2212yes—
8#17988512—21no—
9#17988512—21no—
10#17988492C412yescomplemented
11#17988447—21no—
12#17988447—21no—
13#17988447—21no—
14C4×C4⋊Dic73C411yescharacteristic, complemented
15#17988381—28no—
16#17988354—21no—
17C2×C4×D4×C73C2211yescharacteristic
18C2×#99×C73C2212yes—
19C4×C22⋊C4×C73—21no—
20#342×C73—21no—
21C22×Dic146C2×C412yes—
22#14556591—41no—
23#14556591—41no—
24#14556578—24no—
25#14556578—24no—
26C2×C4⋊Dic73—21no—
27C2×C4⋊Dic73—21no—
28C2×C4⋊Dic73—21no—
29C2×C4⋊Dic73—41no—
30C2×C22⋊Dic73—22no—
31C2×C22⋊Dic73—22no—
32C2×C22⋊Dic73—22no—
33C2×C4×Dic73C2×C412yes—
34#14556506—24no—
35#14556498—21no—
36#14556498—22no—
37#14556498—22no—
38#14556498—41no—
39C22×D4×C73C2311yescharacteristic
40C23×C4×C73D411yescharacteristic
41C23×C4×C73D411yescharacteristic
42C4×D4×C73—41no—
43C4×D4×C73—41no—
44C2×C4⋊C4×C73C2×C411yescharacteristic
45C2×C22⋊C4×C73—22no—
46C2×C22⋊C4×C73D411yescharacteristic
47C2×C22⋊C4×C73D411yescharacteristic
48C2×C42×C73—41no—
49C2×C42×C73C2×C411yescharacteristic
50#99×C73—22no—
51#99×C73D414yes—
52#95×C73—41no—
53C2×Dic146—24no—
54C2×Dic146—42no—
55C2×Dic146—42no—
56C22×Dic73—22no—
57C22×Dic73—22no—
58C22×Dic73—42no—
59C4⋊Dic73—42no—
60C4⋊Dic73—42no—
61C4⋊Dic73—41no—
62C4⋊Dic73—41no—
63C4⋊Dic73—82no—
64C22⋊Dic73—44no—
65C22⋊Dic73—42no—
66C22⋊Dic73—42no—
67C22⋊Dic73—42no—
68C22⋊Dic73—42no—
69C4×Dic73—24no—
70C24×C73C2×D411yescharacteristic
71C24×C73C2×D411yescharacteristic
72C2×D4×C73—41no—
73C2×D4×C73—41no—
74C2×D4×C73C2×D412yes—
75C2×D4×C73#4112yes—
76C22×C4×C73—21no—
77C22×C4×C73—21no—
78C22×C4×C73—21no—
79C22×C4×C73—21no—
80C22×C4×C73—42no—
81C22×C4×C73—42no—
82C22×C4×C73—42no—
83C22×C4×C73C22⋊C411yescharacteristic
84C22×C4×C73C22⋊C411yescharacteristic
85C22×C4×C73C22⋊C411yescharacteristic
86C22×C4×C73C22⋊C411yescharacteristic
87C22×C4×C73C22×C411yescharacteristic
88C4⋊C4×C73—41no—
89C22⋊C4×C73—24no—
90C22⋊C4×C73—41no—
91C22⋊C4×C73—41no—
92C22⋊C4×C73—42no—
93C42×C73—21no—
94C42×C73—21no—
95C42×C73—82no—
96C23×C73—21no—
97C23×C73—21no—
98C23×C73—21no—
99C23×C73—21no—
100C23×C73—41no—
101C23×C73—41no—
102C23×C73—41no—
103C23×C73—41no—
104C23×C73C2×C22⋊C411yescharacteristic
105C23×C73#12112yes—
106C23×C73#12411yescharacteristic
107C23×C73#12711yescharacteristic
108D4×C73—42no—
109D4×C73—42no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—22no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—42no—
117C2×C4×C73—42no—
118C2×C4×C73—41no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—44no—
122C2×C4×C73—81no—
123C2×C4×C73—81no—
124C2×C4×C73—82no—
125C2×C4×C73—82no—
126C2×C4×C73#9911yescharacteristic
127C2×C4×C73#9911yescharacteristic
128C2×C4×C73C4×D412yes—
129C2×Dic73—42no—
130C2×Dic73—42no—
131C2×Dic73—42no—
132C2×Dic73—42no—
133C2×Dic73—42no—
134C2×Dic73—42no—
135C2×Dic73—82no—
136C2×Dic73—82no—
137C2×Dic73—82no—
138Dic146—84no—
139C22×C73—21no—
140C22×C73—21no—
141C22×C73—21no—
142C22×C73—22no—
143C22×C73—21no—
144C22×C73—42no—
145C22×C73—41no—
146C22×C73—41no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—81no—
152C22×C73—81no—
153C22×C73#39011yescharacteristic
154C22×C73C2×#9911yescharacteristic
155C22×C73#41011yescharacteristic
156C4×C73—21no—
157C4×C73—22no—
158C4×C73—41no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73—84no—
162C4×C73#35412yescomplemented
163Dic73—82no—
164Dic73—82no—
165Dic73—162no—
166#13224—731nomaximal, Sylow
167C2×C73—21no—
168C2×C73—21no—
169C2×C73—41no—
170C2×C73—42no—
171C2×C73—41no—
172C2×C73#196411yescharacteristic
173C2×C73C2×#35411yescharacteristic
174C2×C73#212911yescharacteristic
175#2547—731no—
176C2×#354—734no—
177#1799—731no—
178C4×#99D7311yescharacteristic
179C73#1322411yescharacteristic, complemented, Sylow
180C2×C4⋊Q8—731no—
181C2×#124—732no—
182C2×C4×D4C2×D7311yescharacteristic
183C2×#99—732no—
184C2×#99C2×D7312yes—
185#397—1461no—
186#397—1461no—
187#391—732no—
188#380—1461no—
189#380—1461no—
190#380—1461no—
191C4×C4⋊C4—731no—
192C4×C22⋊C4—21no—
193#354—1468no—
194#342—21no—
195#342—1461no—
196C22×Q8—732no—
197C22×D4C22×D7311yescharacteristic
198C23×C4D29211yescharacteristic
199C23×C4C22⋊D7311yescharacteristic
200C4⋊Q8—2921no—
201C4⋊Q8—2921no—
202#124—1464no—
203#124—1464no—
204C4×D4—41no—
205C4×D4—41no—
206C2×C4⋊C4—2921no—
207C2×C4⋊C4—1461no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4—1461no—
210C2×C4⋊C4C4×D7311yescharacteristic
211C2×C22⋊C4—22no—
212C2×C22⋊C4—1462no—
213C2×C22⋊C4—1462no—
214C2×C22⋊C4—1462no—
215C2×C22⋊C4D29211yescharacteristic
216C2×C22⋊C4C22⋊D7311yescharacteristic
217C2×C42—41no—
218C2×C42—732no—
219C2×C42C4×D7311yescharacteristic
220#99—22no—
221#99—1464no—
222#99D29214yes—
223#95—41no—
224#95—2921no—
225#95—1461no—
226#95—1462no—
227#95—1462no—
228C24C2×C22⋊D7311yescharacteristic
229C24C2×D29211yescharacteristic
230C2×Q8—2922no—
231C2×Q8—2922no—
232C2×Q8—1464no—
233C2×D4—41no—
234C2×D4—41no—
235C2×D4C2×D29212yes—
236C2×D4#1192402812yes—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—2922no—
245C22×C4—1462no—
246C22×C4—1462no—
247C22×C4#1192400511yescharacteristic
248C22×C4#1192400511yescharacteristic
249C22×C4#1192400511yescharacteristic
250C22×C4#1192400511yescharacteristic
251C22×C4C2×C4×D7311yescharacteristic
252C4⋊C4—41no—
253C4⋊C4—2922no—
254C4⋊C4—2922no—
255C4⋊C4—2921no—
256C4⋊C4—2921no—
257C4⋊C4—5842no—
258C22⋊C4—24no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—42no—
262C22⋊C4—2924no—
263C22⋊C4—2922no—
264C22⋊C4—2922no—
265C22⋊C4—2922no—
266C22⋊C4—2922no—
267C42—21no—
268C42—21no—
269C42—82no—
270C42—1464no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23C2×#1192400511yescharacteristic
280C23#1455656512yes—
281C23#1455657911yescharacteristic
282C23#1455658811yescharacteristic
283Q8—5844no—
284D4—42no—
285D4—42no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—44no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—2922no—
303C2×C4—2922no—
304C2×C4—2922no—
305C2×C4—2922no—
306C2×C4—2922no—
307C2×C4—2922no—
308C2×C4—5842no—
309C2×C4—5842no—
310C2×C4—5842no—
311C2×C4#1455650511yescharacteristic
312C2×C4#1455650511yescharacteristic
313C2×C4C4×D29212yes—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22—81no—
328C22#1798848911yescharacteristic
329C22C2×#1455650511yescharacteristic
330C22#1798856011yescharacteristic
331C4—22no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—84no—
337C4—5842no—
338C4—5842no—
339C4—11682no—
340C4#1798838112yescomplemented
341C2—21no—
342C2—21no—
343C2—42no—
344C2—41no—
345C2—41no—
346C2#2261076711yescharacteristic
347C2C2×#1798838111yescharacteristic
348C2#2261160511yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC22×D4C22×D73
FittingC4×#99×C73C2
socleC22×C73C2×#99
prime radical, cosocleC22×D4×C73C23
hypercenterC4×#99D73
hypocenterC73#13224
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
5. C2×#14556591C4semidirect
10. #17988492C4semidirect
14. C4×C4⋊Dic73C4semidirect
162. C4×C73#354semidirect
179. C73#13224semidirect
340. C4#17988381semidirect

Maximal subgroups

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

subgroupindex
#226149232
C2×#179883812
#226099192
C4×#99×C732
#1322473