Finite Group Databasebeta

← #32975212

Subgroups — #32975212

Order 18688.

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

normal subgroups only

This group has 410 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
1#22616962C211yesmaximal, characteristic
2#22611475C211yesmaximal, characteristic
3#22611408C211yesmaximal, characteristic
4#22607756C211yesmaximal, characteristic
5#22607754C211yesmaximal, characteristic
6#22607753C211yesmaximal, characteristic
7C73×#2084C211yesmaximal, characteristic
8C2×#14556590—21no—
9C2×#14556522—21no—
10C2×#14556522—21no—
11C2×#14556514—21no—
12#17988520—21no—
13#17988508—21no—
14#17988507—21no—
15#17988493C2211yescharacteristic
16#17988485C2211yescharacteristic
17#17988473—21no—
18#17988470—21no—
19#17988349—21no—
20#17988342C2211yescharacteristic
21#17988342C2211yescharacteristic
22C2×#106×C73—21no—
23#389×C73C2211yescharacteristic
24#384×C73C2211yescharacteristic
25#340×C73—21no—
26#336×C73C2211yescharacteristic
27C22×Dic146—21no—
28C22×Dic146D411yescharacteristic
29C22×#10596831—21no—
30C22×#10596831—21no—
31#14556590—42no—
32#14556590—42no—
33C2×C4⋊Dic73—21no—
34C2×C4⋊Dic73D411yescharacteristic
35C2×C4⋊Dic73D411yescharacteristic
36C2×C4⋊Dic73D411yescharacteristic
37C2×#11924007—21no—
38C2×#11924007—21no—
39C2×#11924007—21no—
40C2×C4×Dic73—21no—
41#14556522—42no—
42#14556522—42no—
43#14556514—42no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49#14556498—21no—
50C22×C8×C73—21no—
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73—21no—
53C2×C4⋊C4×C73—21no—
54C2×C4⋊C4×C73—21no—
55C2×C4⋊C4×C73D411yescharacteristic
56C2×C4⋊C4×C73D411yescharacteristic
57C2×C42×C73C2311yescharacteristic
58#106×C73—42no—
59#95×C73—21no—
60C2×Dic146—21no—
61C2×Dic146—41no—
62C2×Dic146—41no—
63C2×Dic146—42no—
64C2×Dic146—81no—
65C2×Dic146—81no—
66C2×Dic146SD1612yes—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C22×Dic73—21no—
71C2×#10596831—22no—
72C2×#10596831—22no—
73C2×#10596831—41no—
74C2×#10596831—41no—
75C2×#10596831—41no—
76C2×#10596831—41no—
77C4⋊Dic73—21no—
78C4⋊Dic73—42no—
79C4⋊Dic73—41no—
80C4⋊Dic73—41no—
81C4⋊Dic73SD1612yes—
82#11924007—42no—
83#11924007—41no—
84#11924007—41no—
85#11924007—81no—
86C4×Dic73—42no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—41no—
90C22×C4×C73C2×D411yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92C22×C4×C73C2×D411yescharacteristic
93C2×C8×C73—22no—
94C2×C8×C73—41no—
95C2×C8×C73—41no—
96C4⋊C4×C73—21no—
97C4⋊C4×C73—41no—
98C4⋊C4×C73—41no—
99C4⋊C4×C73—41no—
100C4⋊C4×C73—41no—
101C4⋊C4×C73—41no—
102C4⋊C4×C73—41no—
103C4⋊C4×C73—41no—
104C4⋊C4×C73—41no—
105C4⋊C4×C73—41no—
106C4⋊C4×C73SD1612yes—
107C42×C73—41no—
108C23×C73#12011yescharacteristic
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—22no—
116C2×C4×C73—41no—
117C2×C4×C73—41no—
118C2×C4×C73—41no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—81no—
122C2×C4×C73—81no—
123C2×C4×C73—81no—
124C2×C4×C73C2×SD1611yescharacteristic
125C2×C4×C73C2×SD1611yescharacteristic
126C2×C4×C73C2×SD1611yescharacteristic
127C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C73#13711yescharacteristic
129C2×C4×C73#13711yescharacteristic
130C2×Dic73—22no—
131C2×Dic73—22no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—41no—
142Dic146—42no—
143Dic146—81no—
144Dic146—84no—
145C8×C73—42no—
146#10596831—42no—
147#10596831—42no—
148C22×C73#44811yescharacteristic
149C22×C73#44811yescharacteristic
150C22×C73#45011yescharacteristic
151C22×C73#45311yescharacteristic
152C22×C73#45611yescharacteristic
153C22×C73#45611yescharacteristic
154C22×C73#45811yescharacteristic
155C4×C73—21no—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—42no—
162C4×C73—81no—
163C4×C73—161no—
164Dic73—42no—
165Dic73—42no—
166Dic73—81no—
167Dic73—81no—
168#7817—731nomaximal, Sylow
169C2×C73#161111yescharacteristic
170C2×C73#161111yescharacteristic
171C2×C73#161311yescharacteristic
172C2×C73#162311yescharacteristic
173C2×C73#165111yescharacteristic
174C2×C73#165111yescharacteristic
175C2×C73#166011yescharacteristic
176#2734—731no—
177#2096—731no—
178#2084—731no—
179#2084D7311yescharacteristic
180#1272—731no—
181#1271—731no—
182#1271—731no—
183C73#781711yescharacteristic, complemented, Sylow
184C2×C4⋊Q8—1461no—
185C2×#106—21no—
186C2×#106—1461no—
187C2×#106—1461no—
188C2×#103—1461no—
189#398—1461no—
190#395—1461no—
191#395—1461no—
192#391—731no—
193#389—731no—
194#389C2×D7311yescharacteristic
195#387—1461no—
196#387—1461no—
197#384C2×D7311yescharacteristic
198#340—21no—
199#340—1461no—
200#336—731no—
201#336—731no—
202#336C2×D7311yescharacteristic
203C22×Q8—731no—
204C22×Q8—1461no—
205C22×C8—21no—
206C22×C8—1461no—
207C22×C8—1461no—
208C4⋊Q8—2922no—
209C4⋊Q8—2922no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4—731no—
217C2×C4⋊C4—1461no—
218C2×C4⋊C4—1461no—
219C2×C4⋊C4—1461no—
220C2×C4⋊C4—1461no—
221C2×C4⋊C4C22⋊D7311yescharacteristic
222C2×C4⋊C4C22⋊D7311yescharacteristic
223C2×C42—1461no—
224C2×C42C22×D7311yescharacteristic
225#106—42no—
226#106—2922no—
227#106—2922no—
228#103—2922no—
229#95—21no—
230#95—1461no—
231#95—1461no—
232#95—1461no—
233#95—1461no—
234#95—1461no—
235#95—1461no—
236C2×Q8—2921no—
237C2×Q8—2921no—
238C2×Q8—2922no—
239C2×Q8—5841no—
240C2×Q8—5841no—
241C2×Q8—732no—
242C2×Q8—1461no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—1461no—
247C22×C4—1461no—
248C22×C4—1461no—
249C22×C4—1461no—
250C22×C4D4×D7311yescharacteristic
251C22×C4D4×D7311yescharacteristic
252C22×C4C2×C22⋊D7311yescharacteristic
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—2921no—
257C2×C8—2921no—
258C2×C8—2921no—
259C2×C8—2921no—
260C2×C8—1462no—
261C2×C8—1462no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—2921no—
273C4⋊C4—2921no—
274C4⋊C4—2922no—
275C4⋊C4—2922no—
276C4⋊C4—2921no—
277C4⋊C4—2921no—
278C4⋊C4—5841no—
279C4⋊C4—732no—
280C4⋊C4—1461no—
281C4⋊C4#1192401612yes—
282C42—41no—
283C42—2922no—
284C23#1455655911yescharacteristic
285Q8—2922no—
286Q8—5841no—
287Q8—5844no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—2921no—
304C2×C4—2921no—
305C2×C4—2921no—
306C2×C4—2921no—
307C2×C4—2921no—
308C2×C4—2921no—
309C2×C4—2921no—
310C2×C4—2921no—
311C2×C4—2921no—
312C2×C4—2921no—
313C2×C4—1462no—
314C2×C4—1462no—
315C2×C4SD16×D7311yescharacteristic
316C2×C4SD16×D7311yescharacteristic
317C2×C4C2×#1192401611yescharacteristic
318C2×C4#1455661811yescharacteristic
319C2×C4#1455662011yescharacteristic
320C2×C4#1455662111yescharacteristic
321C8—42no—
322C8—2922no—
323C8—2922no—
324C22#1798872411yescharacteristic
325C22#1798872511yescharacteristic
326C22#1798873611yescharacteristic
327C22#1798875311yescharacteristic
328C22#1798876811yescharacteristic
329C22#1798876911yescharacteristic
330C22#1798877611yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—81no—
339C4—161no—
340C4—2922no—
341C4—2922no—
342C4—5841no—
343C4—5841no—
344C2#2260893711yescharacteristic
345C2#2260893811yescharacteristic
346C2#2260894911yescharacteristic
347C2#2260900811yescharacteristic
348C2#2260919111yescharacteristic
349C2#2260919211yescharacteristic
350C2#2260924111yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2084C2
socle, prime radicalC23×C73#120
hypercenter#2084D73
hypocenterC73#7817
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
183. C73#7817semidirect

Maximal subgroups

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

subgroupindex
#226169622
#226114752
#226114082
#226077562
#226077542
#226077532
C73×#20842
#781773