Finite Group Databasebeta

← #34013953

Subgroups — #34013953

Order 18688.

438 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 94 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#22626272C211yesmaximal, characteristic, complemented
2#22626175C212yesmaximal, complemented
3#22626158C212yesmaximal, complemented
4#22626154C211yesmaximal, characteristic, complemented
5#22618621C211yesmaximal, characteristic
6C2×#14556665C2212yes—
7C2×#14556665C2212yes—
8#17989509—22no—
9#17989486—24no—
10C22⋊#11924031—24no—
11#17989480—22no—
12C2×#14556599C2211yescharacteristic
13C23×#10596831C2211yescharacteristic
14#17989098C411yescharacteristic
15#17988655—22no—
16#17988650—22no—
17#17988615C411yescharacteristic
18#17988555C411yescharacteristic
19#17988545C2211yescharacteristic
20#407×C73C411yescharacteristic
21#14556665—22no—
22#14556665—22no—
23#14556665—22no—
24#14556665—22no—
25C2×#11924031—22no—
26C2×#11924031D414yescomplemented
27C2×#11924028C2×C411yescharacteristic
28#14556599—22no—
29#14556599—22no—
30C2×#11924011—21no—
31C22×#10596831—21no—
32C22×#10596831—21no—
33C22×#10596831—22no—
34C22×#10596831—22no—
35C22×#10596831C2×C411yescharacteristic
36C22×#10596831C2311yescharacteristic
37C2×C8×D73—21no—
38#14556574—21no—
39#14556570—21no—
40#14556565—21no—
41#14556560—21no—
42C4×C22⋊D73—22no—
43#14556550C2×C411yescharacteristic
44#14556520—22no—
45#14556503—22no—
46#14556501D412yes—
47C8×Dic73D412yes—
48C23×C4×C73C2×C411yescharacteristic
49C2×M16×C73C2×C411yescharacteristic
50C2×M16×C73C2×C411yescharacteristic
51C22⋊C8×C73—22no—
52#11924031—24no—
53#11924031—42no—
54#11924028—22no—
55#11924028—22no—
56C2×Dic146M1611yescharacteristic
57C2×D292M1611yescharacteristic
58C2×C22⋊D73—22no—
59C2×C22⋊D73—21no—
60C2×C4×D73—21no—
61#11924011—42no—
62C2×#10596831—21no—
63C2×#10596831—22no—
64C2×#10596831—42no—
65C2×#10596831—41no—
66C2×#10596831—41no—
67C2×#10596831C2×D411yescharacteristic
68C2×#10596831C2×D412yes—
69C2×#10596831C2×D411yescharacteristic
70C2×#10596831#4112yes—
71C8×D73—41no—
72C8×D73—41no—
73C4⋊Dic73—21no—
74#11924007—22no—
75C22⋊Dic73—22no—
76C22⋊Dic73—21no—
77#11924005—22no—
78C4×Dic73C22⋊C412yes—
79C24×C73M1611yescharacteristic
80C22×C4×C73—21no—
81C22×C4×C73—22no—
82C22×C4×C73—21no—
83C22×C4×C73—22no—
84C22×C4×C73M1611yescharacteristic
85C22×C4×C73C22×C411yescharacteristic
86M16×C73—22no—
87M16×C73—22no—
88C2×C8×C73—21no—
89C2×C8×C73C22⋊C412yes—
90C23×C73—21no—
91C23×C73—22no—
92C23×C73—42no—
93C23×C73C2×M1611yescharacteristic
94C22×D73—21no—
95C2×C4×C73—21no—
96C2×C4×C73—22no—
97C2×C4×C73—41no—
98C2×C4×C73—41no—
99C2×C4×C73—42no—
100C2×C4×C73C2×C22⋊C411yescharacteristic
101C2×C4×C73C4×D412yes—
102C2×C4×C73C2×M1611yescharacteristic
103C2×C4×C73#13112yes—
104C22⋊D73—44no—
105C22⋊D73—42no—
106C2×Dic73—22no—
107C2×Dic73—21no—
108D292—22no—
109C4×D73—41no—
110C4×D73—41no—
111Dic146—22no—
112C8×C73—22no—
113C8×C73—41no—
114#10596831—41no—
115#10596831#12112yes—
116#10596831#12411yescharacteristic
117#10596831#12711yescharacteristic
118C22×C73—22no—
119C22×C73—24no—
120C22×C73—41no—
121C22×C73—41no—
122C22×C73—42no—
123C22×C73—41no—
124C22×C73#40711yescharacteristic
125C22×C73#43512yes—
126C2×D73—42no—
127C2×D73—41no—
128C4×C73—41no—
129C4×C73#39011yescharacteristic
130C4×C73#40811yescharacteristic
131C4×C73#43512yes—
132Dic73—42no—
133Dic73—41no—
134#13200—731nomaximal, Sylow
135C2×C73—21no—
136C2×C73—22no—
137C2×C73—42no—
138C2×C73#195511yescharacteristic
139D73—81no—
140#2929—731no—
141#2153—731no—
142#2117—732no—
143#2112—732no—
144#2110—731no—
145C73#1320011yescharacteristic, complemented, Sylow
146C2×#131—731no—
147C23×C8—731no—
148#525—731no—
149C2×M32—732no—
150C2×M32—732no—
151#435—1462no—
152C8×D4—1462no—
153#424—731no—
154#408—731no—
155#407#6440811yescharacteristic
156#405—731no—
157#364—1462no—
158#350—1464no—
159C22⋊C16—1464no—
160#347—1462no—
161C2×#41—731no—
162C23×C4C2×#6440811yescharacteristic
163#131—1462no—
164#131—1462no—
165C2×M16—1461no—
166C2×M16C2×#6440811yescharacteristic
167C2×M16C2×#6440811yescharacteristic
168C22×C8—731no—
169C22×C8—731no—
170C22×C8—1461no—
171C22×C8—1462no—
172C22×C8—1462no—
173C22×C8—1461no—
174C22×C8—1461no—
175#123—1461no—
176C22⋊Q8—1461no—
177#121—1461no—
178#120—1461no—
179C4×D4—1462no—
180#117—731no—
181M32—1462no—
182M32—1462no—
183M32—1462no—
184M32—1462no—
185C2×C16—734no—
186C2×C16—1462no—
187C4⋊C8—1462no—
188C22⋊C8—22no—
189C22⋊C8—1462no—
190#97—732no—
191C4×C8—732no—
192C24#1192403811yescharacteristic
193#41—1462no—
194#41—1462no—
195C2×Q8—731no—
196C2×D4—731no—
197C2×D4—1462no—
198C2×D4—1461no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—1461no—
204C22×C4#1192403811yescharacteristic
205C22×C4C22×#6440811yescharacteristic
206M16—22no—
207M16—22no—
208M16—2922no—
209C2×C8—21no—
210C2×C8—2921no—
211C2×C8—2921no—
212C2×C8—2921no—
213C2×C8—2922no—
214C2×C8—2921no—
215C2×C8—731no—
216C2×C8—731no—
217C2×C8—732no—
218C2×C8—732no—
219C2×C8—1461no—
220C2×C8—1462no—
221C2×C8C22⋊#6440812yes—
222C4⋊C4—1462no—
223C4⋊C4—1461no—
224C22⋊C4—1462no—
225C22⋊C4—1462no—
226C22⋊C4—1461no—
227C42—732no—
228C16—2922no—
229C16—1464no—
230C23—21no—
231C23—22no—
232C23—42no—
233C23—1461no—
234C23C2×#1192403811yescharacteristic
235Q8—1462no—
236D4—2924no—
237D4—2922no—
238D4—1462no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—2921no—
245C2×C4—2921no—
246C2×C4—1462no—
247C2×C4—1461no—
248C2×C4C2×C22⋊#6440811yescharacteristic
249C2×C4D4×#6440812yes—
250C2×C4D73⋊M1611yescharacteristic
251C2×C4#1455667812yes—
252C8—22no—
253C8—41no—
254C8—2921no—
255C8—731no—
256C8—732no—
257C8—731no—
258C22—22no—
259C22—24no—
260C22—41no—
261C22—41no—
262C22—42no—
263C22—41no—
264C22—2922no—
265C22—2921no—
266C22#1798955811yescharacteristic
267C22#1798961612yes—
268C4—41no—
269C4—2922no—
270C4—2921no—
271C4#1798953911yescharacteristic
272C4#1798956011yescharacteristic
273C4#1798961912yes—
274C2—21no—
275C2—22no—
276C2—42no—
277C2—5841no—
278C2#2262605611yescharacteristic
subgroupG/H
centerC4#17989539
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#407×C73C4
socleC2×C73#1955
prime radical#17989098C4
cosocleC22×#10596831C23
hypercenter#407#64408
hypocenterC73#13200
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #22626272C2semidirect
2. #22626175C2semidirect
3. #22626158C2semidirect
4. #22626154C2semidirect
26. C2×#11924031D4semidirect
145. C73#13200semidirect

Maximal subgroups

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

subgroupindex
#226262722
#226261752
#226261582
#226261542
#226186212
#1320073