Finite Group Databasebeta

← #34013955

Subgroups — #34013955

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#22626173C212yesmaximal, complemented
3#22626160C212yesmaximal, complemented
4#22626154C211yesmaximal, characteristic, complemented
5#22618628C211yesmaximal, characteristic
6C2×#14556665C2212yes—
7C2×#14556665C2212yes—
8#17989509—22no—
9#17989485—24no—
10#17989482—24no—
11#17989480—22no—
12C2×#14556598C2211yescharacteristic
13C22×C8×D73C2211yescharacteristic
14#17989094C411yescharacteristic
15#17988661—22no—
16#17988650—22no—
17#17988613C411yescharacteristic
18#17988550C411yescharacteristic
19#17988545C2211yescharacteristic
20#408×C73C411yescharacteristic
21#14556665—22no—
22#14556665—22no—
23#14556665—22no—
24#14556665—22no—
25C2×#11924031—22no—
26C2×#11924031D414yescomplemented
27C22×C4×D73C2×C411yescharacteristic
28#14556598—22no—
29#14556598—22no—
30C2×#11924012—21no—
31C2×#11924012C2×C411yescharacteristic
32C22×#10596831—21no—
33C22×#10596831C2311yescharacteristic
34C2×C8×D73—21no—
35C2×C8×D73—21no—
36C2×C8×D73—22no—
37C2×C8×D73—22no—
38#14556572—21no—
39#14556567—21no—
40#14556562—21no—
41#14556559—21no—
42C4×C22⋊D73—22no—
43#14556550C2×C411yescharacteristic
44#14556520—22no—
45#14556503—22no—
46#14556501D412yes—
47C8×Dic73D412yes—
48C2×#41×C73C2×C411yescharacteristic
49C2×M16×C73C2×C411yescharacteristic
50C22×C8×C73C2×C411yescharacteristic
51C22⋊C8×C73—22no—
52#11924031—24no—
53#11924031—42no—
54C23×D73M1611yescharacteristic
55C2×C22⋊D73—22no—
56C22×Dic73M1611yescharacteristic
57C2×C4×D73—21no—
58C2×C4×D73—22no—
59C2×C4×D73—21no—
60C2×C4×D73—22no—
61#11924012—22no—
62#11924012—42no—
63C2×#10596831—21no—
64C2×#10596831—41no—
65C2×#10596831—41no—
66C2×#10596831C2×D411yescharacteristic
67C2×#10596831C2×D412yes—
68C2×#10596831C2×D411yescharacteristic
69C2×#10596831#4112yes—
70C8×D73—42no—
71C8×D73—41no—
72C8×D73—41no—
73C4⋊Dic73—21no—
74#11924007—22no—
75C22⋊Dic73—22no—
76C22⋊Dic73—21no—
77#11924005—22no—
78C4×Dic73C22⋊C412yes—
79#41×C73—22no—
80#41×C73—22no—
81C2×Q8×C73M1611yescharacteristic
82C2×D4×C73—21no—
83C2×D4×C73M1611yescharacteristic
84C22×C4×C73—21no—
85C22×C4×C73C22×C411yescharacteristic
86M16×C73—22no—
87C2×C8×C73—21no—
88C2×C8×C73—22no—
89C2×C8×C73C22⋊C412yes—
90C23×C73—21no—
91C23×C73C2×M1611yescharacteristic
92C22×D73—21no—
93C22×D73—22no—
94C22×D73—42no—
95Q8×C73—22no—
96D4×C73—22no—
97D4×C73—42no—
98C2×C4×C73—21no—
99C2×C4×C73—41no—
100C2×C4×C73—41no—
101C2×C4×C73C2×C22⋊C411yescharacteristic
102C2×C4×C73C4×D412yes—
103C2×C4×C73C2×M1611yescharacteristic
104C2×C4×C73#13112yes—
105C22⋊D73—44no—
106C2×Dic73—22no—
107C2×Dic73—21no—
108C2×Dic73—22no—
109C4×D73—41no—
110C4×D73—41no—
111C4×D73—42no—
112C8×C73—22no—
113C8×C73—41no—
114#10596831—41no—
115#10596831#12112yes—
116#10596831#12411yescharacteristic
117#10596831#12711yescharacteristic
118C22×C73—41no—
119C22×C73—42no—
120C22×C73—41no—
121C22×C73#40711yescharacteristic
122C22×C73#43512yes—
123C2×D73—22no—
124C2×D73—24no—
125C2×D73—41no—
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—81no—
138C2×C73#195511yescharacteristic
139D73—42no—
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#6440811yescharacteristic
155#407—731no—
156#405—731no—
157#364—1462no—
158#350—1464no—
159C22⋊C16—1464no—
160#347—1462no—
161C2×#41C2×#6440811yescharacteristic
162C23×C4—731no—
163#131—1462no—
164#131—1462no—
165C2×M16—731no—
166C2×M16—1461no—
167C2×M16C2×#6440811yescharacteristic
168C22×C8—731no—
169C22×C8—1462no—
170C22×C8—1462no—
171C22×C8—1461no—
172C22×C8—1461no—
173C22×C8—1461no—
174C22×C8C2×#6440811yescharacteristic
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—731no—
193#41—22no—
194#41—22no—
195C2×Q8#1192403811yescharacteristic
196C2×D4—21no—
197C2×D4—1462no—
198C2×D4#1192403811yescharacteristic
199C22×C4—21no—
200C22×C4—731no—
201C22×C4—1461no—
202C22×C4—1462no—
203C22×C4—1461no—
204C22×C4—1462no—
205C22×C4C22×#6440811yescharacteristic
206M16—22no—
207M16—2922no—
208M16—1462no—
209C2×C8—21no—
210C2×C8—22no—
211C2×C8—2921no—
212C2×C8—2922no—
213C2×C8—2921no—
214C2×C8—2921no—
215C2×C8—2921no—
216C2×C8—731no—
217C2×C8—731no—
218C2×C8—732no—
219C2×C8—732no—
220C2×C8—1461no—
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—2922no—
232C23—1461no—
233C23—1462no—
234C23D73⋊M1611yescharacteristic
235Q8—22no—
236D4—22no—
237D4—42no—
238D4—2924no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—2921no—
243C2×C4—2921no—
244C2×C4—2922no—
245C2×C4—1462no—
246C2×C4—1461no—
247C2×C4—1462no—
248C2×C4C2×C22⋊#6440811yescharacteristic
249C2×C4D4×#6440812yes—
250C2×C4C2×#1192403811yescharacteristic
251C2×C4#1455667812yes—
252C8—22no—
253C8—41no—
254C8—2921no—
255C8—731no—
256C8—732no—
257C8—731no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22—2921no—
262C22—2922no—
263C22—2921no—
264C22—1462no—
265C22—1464no—
266C22#1798955811yescharacteristic
267C22#1798961912yes—
268C4—41no—
269C4—2922no—
270C4—2921no—
271C4#1798953911yescharacteristic
272C4#1798956011yescharacteristic
273C4#1798961612yes—
274C2—21no—
275C2—22no—
276C2—81no—
277C2—2922no—
278C2#2262605611yescharacteristic
subgroupG/H
centerC4#17989539
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#408×C73C4
socleC2×C73#1955
prime radical#17989094C4
cosocleC22×#10596831C23
hypercenter#408#64408
hypocenterC73#13200
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #22626272C2semidirect
2. #22626173C2semidirect
3. #22626160C2semidirect
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
#226261732
#226261602
#226261542
#226186282
#1320073