Finite Group Databasebeta

← C73×#13227 #32922631

Subgroups — C73×#13227 #32922631

Order 18688.

472 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C73×#2546C211yesmaximal, characteristic
2C2×#356×C73C214yesmaximal
3C73×#1801C211yesmaximal, characteristic
4C4×#101×C73C211yesmaximal, characteristic
5C2×C4⋊Q8×C73C411yescharacteristic
6C2×C4⋊Q8×C73C2212yes—
7C2×C4×Q8×C73C2211yescharacteristic
8#423×C73—21no—
9C2×#101×C73C2212yes—
10C2×#101×C73C2212yes—
11C4×M16×C73—21no—
12#398×C73—21no—
13#398×C73—21no—
14#391×C73C412yes—
15#389×C73—21no—
16#389×C73—21no—
17C4×C4⋊C4×C73C411yescharacteristic
18#356×C73—28no—
19#343×C73—21no—
20#343×C73—21no—
21C22×Q8×C73C2×C412yes—
22C22×Q8×C73C2311yescharacteristic
23C2×M16×C73—22no—
24C2×M16×C73—22no—
25C4⋊Q8×C73—24no—
26C4⋊Q8×C73—24no—
27C4⋊Q8×C73—41no—
28C4⋊Q8×C73—41no—
29C4×Q8×C73—41no—
30C4×Q8×C73—41no—
31C2×C4⋊C4×C73—21no—
32C2×C4⋊C4×C73—21no—
33C2×C4⋊C4×C73—21no—
34C2×C4⋊C4×C73—22no—
35C2×C4⋊C4×C73—22no—
36C2×C4⋊C4×C73C2×C411yescharacteristic
37C2×C4⋊C4×C73D411yescharacteristic
38C2×C4⋊C4×C73D411yescharacteristic
39C2×C42×C73C2×C412yes—
40C2×C42×C73C2×C411yescharacteristic
41C2×C42×C73D411yescharacteristic
42C2×C42×C73D411yescharacteristic
43C4⋊C8×C73—41no—
44C4⋊C8×C73—41no—
45#101×C73—22no—
46#101×C73—24no—
47#101×C73D414yes—
48#97×C73—41no—
49C4×C8×C73—41no—
50#95×C73—21no—
51#95×C73—22no—
52#95×C73—22no—
53C2×Q8×C73—24no—
54C2×Q8×C73—41no—
55C2×Q8×C73—41no—
56C2×Q8×C73—42no—
57C2×Q8×C73—42no—
58C2×Q8×C73C2×D412yes—
59C2×Q8×C73#4112yes—
60C22×C4×C73—22no—
61C22×C4×C73—22no—
62C22×C4×C73C22⋊C411yescharacteristic
63C22×C4×C73C22⋊C411yescharacteristic
64C22×C4×C73C22⋊C411yescharacteristic
65C22×C4×C73C22⋊C411yescharacteristic
66C22×C4×C73C22×C411yescharacteristic
67C22×C4×C73C2×D411yescharacteristic
68C22×C4×C73C2×D411yescharacteristic
69M16×C73—24no—
70M16×C73—42no—
71M16×C73—42no—
72M16×C73—42no—
73C2×C8×C73—42no—
74C2×C8×C73—42no—
75C4⋊C4×C73—24no—
76C4⋊C4×C73—41no—
77C4⋊C4×C73—41no—
78C4⋊C4×C73—41no—
79C4⋊C4×C73—42no—
80C4⋊C4×C73—41no—
81C4⋊C4×C73—41no—
82C4⋊C4×C73—44no—
83C4⋊C4×C73—42no—
84C4⋊C4×C73—42no—
85C42×C73—21no—
86C42×C73—21no—
87C42×C73—21no—
88C42×C73—21no—
89C42×C73—21no—
90C42×C73—21no—
91C42×C73—24no—
92C23×C73C2×C22⋊C411yescharacteristic
93Q8×C73—42no—
94Q8×C73—42no—
95Q8×C73—84no—
96C2×C4×C73—21no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—22no—
103C2×C4×C73—24no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—42no—
108C2×C4×C73—42no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—42no—
113C2×C4×C73—42no—
114C2×C4×C73—42no—
115C2×C4×C73#9911yescharacteristic
116C2×C4×C73#9911yescharacteristic
117C2×C4×C73C4×D412yes—
118C2×C4×C73#12112yes—
119C2×C4×C73#12411yescharacteristic
120C2×C4×C73#12711yescharacteristic
121C8×C73—44no—
122C8×C73—82no—
123C22×C73—21no—
124C22×C73—21no—
125C22×C73#39011yescharacteristic
126C22×C73C2×#9911yescharacteristic
127C22×C73#41011yescharacteristic
128C4×C73—21no—
129C4×C73—22no—
130C4×C73—21no—
131C4×C73—22no—
132C4×C73—21no—
133C4×C73—44no—
134C4×C73—41no—
135C4×C73—41no—
136C4×C73—41no—
137C4×C73—82no—
138C4×C73#35612yescomplemented
139#13227C7311yesmaximal, characteristic, direct product factor, Sylow
140C2×C73—21no—
141C2×C73—21no—
142C2×C73#196411yescharacteristic
143C2×C73C2×#35611yescharacteristic
144C2×C73#213511yescharacteristic
145#2546C2×C7311yescharacteristic
146C2×#356C2×C7314yes—
147#1801C2×C7311yescharacteristic
148C4×#101C2×C7311yescharacteristic
149C73#1322711yescharacteristic, direct product factor, Sylow
150C2×C4⋊Q8C4×C7311yescharacteristic
151C2×C4⋊Q8C22×C7312yes—
152C2×C4×Q8C22×C7311yescharacteristic
153#423—21no—
154C2×#101C22×C7312yes—
155C2×#101C22×C7312yes—
156C4×M16—21no—
157#398—21no—
158#398—21no—
159#391C4×C7312yes—
160#389—21no—
161#389—21no—
162C4×C4⋊C4C4×C7311yescharacteristic
163#356—28no—
164#343—21no—
165#343—21no—
166C22×Q8C2×C4×C7312yes—
167C22×Q8C23×C7311yescharacteristic
168C2×M16—22no—
169C2×M16—22no—
170C4⋊Q8—24no—
171C4⋊Q8—24no—
172C4⋊Q8—41no—
173C4⋊Q8—41no—
174C4×Q8—41no—
175C4×Q8—41no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4C2×C4×C7311yescharacteristic
182C2×C4⋊C4D4×C7311yescharacteristic
183C2×C4⋊C4D4×C7311yescharacteristic
184C2×C42C2×C4×C7312yes—
185C2×C42C2×C4×C7311yescharacteristic
186C2×C42D4×C7311yescharacteristic
187C2×C42D4×C7311yescharacteristic
188C4⋊C8—41no—
189C4⋊C8—41no—
190#101—22no—
191#101—24no—
192#101D4×C7314yes—
193#97—41no—
194C4×C8—41no—
195#95—21no—
196#95—22no—
197#95—22no—
198C2×Q8—24no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8—42no—
202C2×Q8—42no—
203C2×Q8C2×D4×C7312yes—
204C2×Q8#41×C7312yes—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4C22⋊C4×C7311yescharacteristic
208C22×C4C22⋊C4×C7311yescharacteristic
209C22×C4C22⋊C4×C7311yescharacteristic
210C22×C4C22⋊C4×C7311yescharacteristic
211C22×C4C22×C4×C7311yescharacteristic
212C22×C4C2×D4×C7311yescharacteristic
213C22×C4C2×D4×C7311yescharacteristic
214M16—24no—
215M16—42no—
216M16—42no—
217M16—42no—
218C2×C8—42no—
219C2×C8—42no—
220C4⋊C4—24no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—44no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—24no—
237C23C2×C22⋊C4×C7311yescharacteristic
238Q8—42no—
239Q8—42no—
240Q8—84no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4#99×C7311yescharacteristic
261C2×C4#99×C7311yescharacteristic
262C2×C4C4×D4×C7312yes—
263C2×C4#121×C7312yes—
264C2×C4#124×C7311yescharacteristic
265C2×C4#127×C7311yescharacteristic
266C8—44no—
267C8—82no—
268C22—21no—
269C22—21no—
270C22#390×C7311yescharacteristic
271C22C2×#99×C7311yescharacteristic
272C22#410×C7311yescharacteristic
273C4—22no—
274C4—21no—
275C4—22no—
276C4—21no—
277C4—21no—
278C4—44no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4—82no—
283C4#356×C7312yescomplemented
284C2—21no—
285C2—21no—
286C2C73×#196411yescharacteristic
287C2C2×#356×C7311yescharacteristic
288C2C73×#213511yescharacteristic
subgroupG/H
center, socleC22×C73C2×#99
commutatorC22×C4C22×C4×C73
Frattini, cosocleC22×Q8C23×C73
prime radicalC23×C73C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C22×C4×C73 ◁ C2×C4×Q8×C73 ◁ G

Complements

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

NH ≅ G/Ntype
138. C4×C73#356semidirect
139. #13227C73direct (N × H)
149. C73#13227direct (N × H)
283. C4#356×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#25462
C2×#356×C732
C73×#18012
C4×#101×C732
#1322773