Finite Group Databasebeta

← #34034234

Subgroups — #34034234

Order 18688.

370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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#22627184C211yesmaximal, characteristic
2#22627127C212yesmaximal, complemented
3#22627102C211yesmaximal, characteristic
4#22627012C212yesmaximal, complemented
5#22625688C211yesmaximal, characteristic
6#17989708—22no—
7#17989708—22no—
8C2×#14556688C2211yescharacteristic
9#17989706C2212yes—
10C2×#14556687—22no—
11C2×#14556686C2211yescharacteristic
12#17989692—22no—
13#17989691—22no—
14C22⋊#11924040—22no—
15C2×#14556678C2211yescharacteristic
16#17989567C411yescharacteristic
17#17989553C2212yes—
18#17989470C412yes—
19#17988568C411yescharacteristic
20#14556688—22no—
21#14556688D412yes—
22#14556688D412yes—
23#14556687—24no—
24#14556687—22no—
25#14556686—22no—
26#14556686—22no—
27C2×#11924040—22no—
28C2×#11924040—22no—
29C2×#11924040—21no—
30C2×#11924040—21no—
31#14556678—22no—
32#14556678—22no—
33C2×#11924038C2×C411yescharacteristic
34C2×#11924037Q812yes—
35C2×#11924036C2311yescharacteristic
36C22×#10596833D412yes—
37#14556670C2×C412yes—
38#14556649—22no—
39#14556645—22no—
40C8×#64408—22no—
41C2×#11924027C2×C411yescharacteristic
42M16×D73C2×C412yes—
43#14556509C812yes—
44#14556508C811yescharacteristic
45#100×C73C811yescharacteristic
46#11924040—22no—
47#11924040—22no—
48#11924040—41no—
49#11924040—41no—
50#11924038—22no—
51#11924037—24no—
52#11924036C2×D412yes—
53#11924036#4112yes—
54C2×#10596833—22no—
55C2×#10596833—22no—
56C2×#10596833C4⋊C412yes—
57C2×#10596833C2×D411yescharacteristic
58C2×#10596833C2×Q811yescharacteristic
59C4⋊#64408—22no—
60C22⋊#64408—22no—
61C4×#64408—22no—
62#11924027—22no—
63#11924027—22no—
64C2×Dic146C2×C811yescharacteristic
65C2×C22⋊D73M1612yes—
66C22×Dic73C4⋊C412yes—
67C2×C4×D73C22×C411yescharacteristic
68#11924012C2×C812yes—
69#11924011—22no—
70C8×D73—22no—
71C2×D4×C73C2×C811yescharacteristic
72M16×C73C2×C812yes—
73C23×C73C4⋊C812yes—
74C22×D73C2×M1611yescharacteristic
75C2×#64408—42no—
76D4×C73—22no—
77C2×C4×C73C22×C811yescharacteristic
78C22⋊D73—24no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73C4⋊C812yes—
82C2×Dic73C2×C4⋊C411yescharacteristic
83C4×D73C4×D412yes—
84C4×D73#13112yes—
85Dic146—22no—
86#10596833—22no—
87#10596833#12011yescharacteristic
88#10596833C22⋊Q812yes—
89#10596833#12311yescharacteristic
90C8×C73—22no—
91#10596831—22no—
92C22×C73—22no—
93C22×C73—42no—
94C22×C73C2×C4⋊C811yescharacteristic
95C2×D73—41no—
96C2×D73#43512yes—
97#64408—82no—
98C4×C73C8×D412yes—
99Dic73—22no—
100Dic73#38511yescharacteristic
101Dic73#42411yescharacteristic
102#12916—731nomaximal, Sylow
103C2×C73—21no—
104C2×C73—42no—
105C2×C73#185011yescharacteristic
106D73—22no—
107#3407—731no—
108#2153—732no—
109#2113—731no—
110#1757—731no—
111#1379—732no—
112C73#1291611yescharacteristic, complemented, Sylow
113C2×#131—731no—
114#504—1462no—
115#504—1462no—
116C2×M32—732no—
117C2×M32—731no—
118C2×M32—1462no—
119C22×C16—731no—
120#413—731no—
121#410—731no—
122#405—732no—
123#364—1462no—
124#364—1462no—
125C22⋊C16—1462no—
126#344—732no—
127C2×#41—731no—
128#131—1462no—
129#131—1462no—
130C2×M16—732no—
131C2×M16—731no—
132C2×M16—732no—
133C22×C8—731no—
134C22×C8—732no—
135#117—732no—
136M32—732no—
137M32—732no—
138M32—1462no—
139M32—1462no—
140M32—1464no—
141C2×C16—1461no—
142C2×C16—1461no—
143C2×C16—1462no—
144C2×C16—1462no—
145C2×C16—1462no—
146C2×C16—1462no—
147#101—732no—
148#100—731no—
149#100#1059684211yescharacteristic
150#99—1462no—
151#97—1462no—
152C4×C8—1462no—
153#41—1462no—
154#41—1462no—
155C2×Q8—731no—
156C2×D4—732no—
157C2×D4C2×#1059684211yescharacteristic
158C22×C4—731no—
159C22×C4—732no—
160M16—732no—
161M16—1462no—
162M16—1464no—
163M16—1462no—
164M16C2×#1059684212yes—
165C2×C8—731no—
166C2×C8—731no—
167C2×C8—732no—
168C2×C8—732no—
169C2×C8—732no—
170C2×C8—1462no—
171C2×C8—1462no—
172C2×C8—1462no—
173C4⋊C4—1462no—
174C22⋊C4—1462no—
175C42—1462no—
176C16—2921no—
177C16—2921no—
178C16—1462no—
179C16—1462no—
180C23—731no—
181C23C4⋊#1059684212yes—
182Q8—1462no—
183D4—22no—
184D4—1464no—
185C2×C4—2922no—
186C2×C4—731no—
187C2×C4—732no—
188C2×C4—732no—
189C2×C4—732no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4C22×#1059684211yescharacteristic
193C8—22no—
194C8—731no—
195C8—731no—
196C8—732no—
197C8—1462no—
198C8—1462no—
199C22—22no—
200C22—42no—
201C22—2921no—
202C22—732no—
203C22C2×C4⋊#1059684211yescharacteristic
204C4—5842no—
205C4—731no—
206C4—731no—
207C4—1462no—
208C4D4×#1059684212yes—
209C2—21no—
210C2—42no—
211C2—1462no—
212C2#2262707611yescharacteristic
subgroupG/H
centerC2#22627076
commutatorC2×C4×C73C22×C8
FrattiniC2×C4C22×#10596842
Fitting#100×C73C8
socleC2×C73#1850
prime radicalC2×#11924027C2×C4
cosocleC2×#11924036C23
hypercenter#100#10596842
hypocenterC73#12916
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
2. #22627127C2semidirect
4. #22627012C2semidirect
112. C73#12916semidirect

Maximal subgroups

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

subgroupindex
#226271842
#226271272
#226271022
#226270122
#226256882
#1291673