Finite Group Databasebeta

← #32987302

Subgroups — #32987302

Order 18688.

484 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 97 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×#17988997C211yesmaximal, characteristic
2C2×#17988957C211yesmaximal, characteristic
3#22610903C211yesmaximal, characteristic
4C2×#17988329C211yesmaximal, characteristic
5C2×#17988329C211yesmaximal, characteristic
6#22607812C211yesmaximal, characteristic
7C73×#2822C211yesmaximal, characteristic
8C2×#14556591C2211yescharacteristic
9#17988997—22no—
10#17988997—22no—
11#17988957—22no—
12#17988957—22no—
13C2×#14556524—21no—
14C2×#14556522—21no—
15C2×#14556514—21no—
16C2×#14556514—21no—
17C2×#14556502C2211yescharacteristic
18C2×#14556502C2211yescharacteristic
19C2×#14556502C2211yescharacteristic
20#17988349—22no—
21#17988329—22no—
22#17988329—22no—
23C2×#125×C73C2211yescharacteristic
24C2×#125×C73C2211yescharacteristic
25#400×C73—21no—
26#400×C73—21no—
27#398×C73—22no—
28#398×C73—21no—
29#398×C73—21no—
30#382×C73C2211yescharacteristic
31C22×Dic146—21no—
32C22×#10596831—21no—
33C22×#10596831—21no—
34C22×#10596831—21no—
35#14556591—21no—
36#14556591—21no—
37#14556591—21no—
38#14556591D412yes—
39C2×C4⋊Dic73—21no—
40C2×C4⋊Dic73—21no—
41#14556524—24no—
42#14556522—24no—
43#14556514—24no—
44#14556514—24no—
45#14556502—21no—
46#14556502—21no—
47#14556502—21no—
48#14556502—21no—
49#14556502D412yes—
50#14556502D412yes—
51#125×C73—21no—
52#125×C73—21no—
53#125×C73—21no—
54#125×C73—21no—
55#125×C73—21no—
56#125×C73—21no—
57#125×C73—21no—
58#125×C73—21no—
59C2×C4⋊C4×C73—21no—
60C2×C4⋊C4×C73—21no—
61C2×C4⋊C4×C73—21no—
62C2×C4⋊C4×C73—21no—
63C2×C4⋊C4×C73—22no—
64C2×C4⋊C4×C73D411yescharacteristic
65C2×C4⋊C4×C73D411yescharacteristic
66C2×C4⋊C4×C73D411yescharacteristic
67C2×C4⋊C4×C73D411yescharacteristic
68C2×C4⋊C4×C73D412yes—
69C2×C42×C73C2311yescharacteristic
70#95×C73—22no—
71#95×C73—22no—
72#95×C73—22no—
73#95×C73—21no—
74#95×C73—21no—
75C2×Dic146—22no—
76C2×Dic146—44no—
77C2×Dic146—41no—
78C22×Dic73—41no—
79C2×#10596831—24no—
80C2×#10596831—22no—
81C2×#10596831—22no—
82C2×#10596831—22no—
83C2×#10596831—42no—
84C2×#10596831—41no—
85C2×#10596831—41no—
86C4⋊Dic73—22no—
87C4⋊Dic73—22no—
88C4⋊Dic73—41no—
89C4⋊Dic73—41no—
90C22×C4×C73—22no—
91C22×C4×C73—21no—
92C22×C4×C73—21no—
93C22×C4×C73—21no—
94C22×C4×C73—21no—
95C22×C4×C73C2×D411yescharacteristic
96C22×C4×C73C2×D411yescharacteristic
97C22×C4×C73C2×D411yescharacteristic
98C4⋊C4×C73—21no—
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73—21no—
102C4⋊C4×C73—21no—
103C4⋊C4×C73—21no—
104C4⋊C4×C73—21no—
105C4⋊C4×C73—21no—
106C4⋊C4×C73—42no—
107C4⋊C4×C73—41no—
108C4⋊C4×C73—41no—
109C4⋊C4×C73—41no—
110C4⋊C4×C73—41no—
111C4⋊C4×C73—41no—
112C4⋊C4×C73—41no—
113C4⋊C4×C73—41no—
114C4⋊C4×C73—41no—
115C4⋊C4×C73—82no—
116C42×C73C2×D411yescharacteristic
117C42×C73C2×D411yescharacteristic
118C42×C73C2×D411yescharacteristic
119C42×C73#4111yescharacteristic
120C23×C73#12011yescharacteristic
121C2×C4×C73—22no—
122C2×C4×C73—21no—
123C2×C4×C73—22no—
124C2×C4×C73—21no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73—41no—
128C2×C4×C73—41no—
129C2×C4×C73—42no—
130C2×C4×C73—42no—
131C2×C4×C73—42no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73—42no—
135C2×C4×C73—42no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73#12011yescharacteristic
139C2×C4×C73#12011yescharacteristic
140C2×C4×C73#12111yescharacteristic
141C2×C4×C73#12111yescharacteristic
142C2×C4×C73#12111yescharacteristic
143C2×C4×C73#12711yescharacteristic
144C2×Dic73—42no—
145C2×Dic73—82no—
146Dic146—44no—
147Dic146—82no—
148#10596831—24no—
149#10596831—42no—
150#10596831—42no—
151C22×C73#39211yescharacteristic
152C22×C73#45412yes—
153C22×C73#45511yescharacteristic
154C22×C73#45611yescharacteristic
155C22×C73#45612yes—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—21no—
162C4×C73—82no—
163C4×C73—81no—
164C4×C73—81no—
165C4×C73—81no—
166C4×C73—81no—
167Dic73—82no—
168#10084—731nomaximal, Sylow
169C2×C73#166312yes—
170C2×C73#166412yes—
171C2×C73#200311yescharacteristic
172C2×C73#200511yescharacteristic
173C2×C73#200711yescharacteristic
174C2×#501—731no—
175C2×#491—731no—
176#2822D7311yescharacteristic
177#1993—731no—
178C2×#330—731no—
179C2×#330—731no—
180#1295—731no—
181C73#1008411yescharacteristic, complemented, Sylow
182C2×C4⋊Q8—731no—
183C2×#125C2×D7311yescharacteristic
184C2×#125C2×D7311yescharacteristic
185#501—1462no—
186#501—1462no—
187#491—1462no—
188#491—1462no—
189C2×#107—1461no—
190C2×#106—1461no—
191C2×#103—1461no—
192C2×#103—1461no—
193C2×#97—731no—
194C2×#97—731no—
195C2×#97—731no—
196#400—21no—
197#400—21no—
198#398—22no—
199#398—21no—
200#398—21no—
201#382C2×D7311yescharacteristic
202#340—1462no—
203#330—1462no—
204#330—1462no—
205C22×Q8—1461no—
206C22×C8—1461no—
207C22×C8—1461no—
208C22×C8—1461no—
209C4⋊Q8—732no—
210C4⋊Q8—1461no—
211C4⋊Q8—1461no—
212C4⋊Q8—1461no—
213#125—21no—
214#125—21no—
215#125—21no—
216#125—21no—
217#125—21no—
218#125—21no—
219#125—21no—
220#125—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—1461no—
227C2×C4⋊C4—1461no—
228C2×C4⋊C4C22⋊D7311yescharacteristic
229C2×C4⋊C4C22⋊D7311yescharacteristic
230C2×C4⋊C4C22⋊D7311yescharacteristic
231C2×C4⋊C4C22⋊D7311yescharacteristic
232C2×C4⋊C4C22⋊D7312yes—
233C2×C42C22×D7311yescharacteristic
234#107—1464no—
235#106—1464no—
236#103—1464no—
237#103—1464no—
238#97—732no—
239#97—732no—
240#97—1461no—
241#97—1461no—
242#97—1461no—
243#97—1461no—
244#95—22no—
245#95—22no—
246#95—22no—
247#95—21no—
248#95—21no—
249C2×Q8—2924no—
250C2×Q8—2921no—
251C2×Q8—1462no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—2921no—
258C22×C4C2×C22⋊D7311yescharacteristic
259C22×C4C2×C22⋊D7311yescharacteristic
260C22×C4C2×C22⋊D7311yescharacteristic
261C2×C8—2922no—
262C2×C8—2921no—
263C2×C8—2921no—
264C2×C8—1462no—
265C2×C8—1462no—
266C2×C8—1464no—
267C2×C8—1462no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—82no—
286C4⋊C4—2921no—
287C4⋊C4—2921no—
288C4⋊C4—1462no—
289C4⋊C4—1462no—
290C42D4×D7311yescharacteristic
291C42D4×D7311yescharacteristic
292C42D4×D7311yescharacteristic
293C42#1192402711yescharacteristic
294C23#1455656011yescharacteristic
295Q8—2924no—
296Q8—5842no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—2922no—
315C2×C4—5842no—
316C2×C4#1455655911yescharacteristic
317C2×C4#1455655911yescharacteristic
318C2×C4#1455656211yescharacteristic
319C2×C4#1455656311yescharacteristic
320C2×C4#1455656311yescharacteristic
321C2×C4#1455658711yescharacteristic
322C8—2922no—
323C8—2922no—
324C8—1464no—
325C22#1798849511yescharacteristic
326C22#1798876012yes—
327C22#1798876511yescharacteristic
328C22#1798877012yes—
329C22#1798877011yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4—82no—
341C4—5842no—
342C2#2260925912yes—
343C2#2260926512yes—
344C2#2261095111yescharacteristic
345C2#2261096511yescharacteristic
346C2#2261097811yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2822C2
socle, prime radicalC23×C73#120
hypercenter#2822D73
hypocenterC73#10084
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
181. C73#10084semidirect

Maximal subgroups

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

subgroupindex
C2×#179889972
C2×#179889572
#226109032
C2×#179883292
#226078122
C73×#28222
#1008473