Finite Group Databasebeta

← #32983978

Subgroups — #32983978

Order 18688.

478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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#22614214C211yesmaximal, characteristic
2#22610014C211yesmaximal, characteristic
3#22608260C212yesmaximal
4#22607840C212yesmaximal
5C73×#2921C211yesmaximal, characteristic
6C22×#11924007C2211yescharacteristic
7#17988551C2212yes—
8#17988525—21no—
9#17988518—21no—
10#17988471—21no—
11#17988471—21no—
12#17988459C411yescharacteristic
13#17988459C411yescharacteristic
14#17988450C2211yescharacteristic
15#17988448C411yescharacteristic
16#17988448C411yescharacteristic
17#17988356—21no—
18#17988356—21no—
19#17988312—24no—
20C2×#117×C73C2211yescharacteristic
21#433×C73—24no—
22#423×C73—21no—
23#407×C73C2212yes—
24C4×M16×C73—21no—
25C23×Dic73C2×C411yescharacteristic
26C23×Dic73C2×C411yescharacteristic
27C2×#11924012—22no—
28C2×#11924007—21no—
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×#11924007—22no—
33C2×#11924007—22no—
34C2×C22⋊Dic73C2×C411yescharacteristic
35C2×C22⋊Dic73C2×C411yescharacteristic
36C22⋊#10596831—22no—
37C22⋊#10596831—22no—
38#14556498—21no—
39#14556498—21no—
40#14556498—21no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46C23×C4×C73C2311yescharacteristic
47C2×M16×C73—22no—
48#117×C73—22no—
49#117×C73—22no—
50C2×C4⋊C4×C73D411yescharacteristic
51C2×C4⋊C4×C73D411yescharacteristic
52C2×C22⋊C4×C73C2×C411yescharacteristic
53C2×C22⋊C4×C73C2×C411yescharacteristic
54C2×C42×C73D411yescharacteristic
55C2×C42×C73D411yescharacteristic
56C4⋊C8×C73—24no—
57C22⋊C8×C73—22no—
58C22⋊C8×C73D414yes—
59#97×C73—22no—
60C4×C8×C73—22no—
61C22×Dic73—21no—
62C22×Dic73—22no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C22×Dic73—22no—
67C22×Dic73—42no—
68C22×Dic73—41no—
69C22×Dic73—41no—
70#11924012—42no—
71#11924012—42no—
72C2×#10596831—42no—
73#11924007—42no—
74#11924007—42no—
75#11924007—41no—
76#11924007—42no—
77#11924007—41no—
78C22⋊Dic73—41no—
79C22⋊Dic73—41no—
80C24×C73C22×C411yescharacteristic
81C22×C4×C73—41no—
82C22×C4×C73—41no—
83C22×C4×C73C22⋊C411yescharacteristic
84C22×C4×C73C22⋊C411yescharacteristic
85C22×C4×C73C22⋊C411yescharacteristic
86C22×C4×C73C22⋊C411yescharacteristic
87C22×C4×C73C2×D411yescharacteristic
88C22×C4×C73C2×D412yes—
89C22×C4×C73C2×D411yescharacteristic
90C22×C4×C73#4112yes—
91M16×C73—42no—
92M16×C73—42no—
93C2×C8×C73—24no—
94C4⋊C4×C73—22no—
95C4⋊C4×C73—22no—
96C22⋊C4×C73—22no—
97C22⋊C4×C73—22no—
98C42×C73—21no—
99C42×C73—21no—
100C42×C73—21no—
101C42×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—41no—
105C23×C73—41no—
106C23×C73C2×C22⋊C411yescharacteristic
107C23×C73C4×D412yes—
108C2×C4×C73—21no—
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—21no—
116C2×C4×C73—42no—
117C2×C4×C73—42no—
118C2×C4×C73—41no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73#12011yescharacteristic
123C2×C4×C73#12112yes—
124C2×C4×C73#12311yescharacteristic
125C2×Dic73—22no—
126C2×Dic73—24no—
127C2×Dic73—41no—
128C2×Dic73—42no—
129C2×Dic73—41no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—82no—
140C8×C73—44no—
141#10596831—82no—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73—22no—
145C22×C73—22no—
146C22×C73—22no—
147C22×C73—42no—
148C22×C73—42no—
149C22×C73#38611yescharacteristic
150C22×C73#41011yescharacteristic
151C22×C73#41011yescharacteristic
152C4×C73—22no—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—41no—
156C4×C73—41no—
157C4×C73—41no—
158C4×C73—41no—
159Dic73—42no—
160Dic73—81no—
161Dic73—81no—
162Dic73—81no—
163#9514—731nomaximal, Sylow
164C2×C73—21no—
165C2×C73—21no—
166C2×C73—42no—
167C2×C73#189111yescharacteristic
168C2×C73#189911yescharacteristic
169C2×C73#191511yescharacteristic
170#2921D7311yescharacteristic
171#2484—731no—
172#1822—731no—
173#1463—732no—
174#1306—732no—
175C73#951411yescharacteristic, complemented, Sylow
176C2×#117C2×D7311yescharacteristic
177C22×C4⋊C4—731no—
178#433—24no—
179#423—21no—
180#407—732no—
181#407C2×D7312yes—
182C4×M16—21no—
183#400—1461no—
184#398—1461no—
185#387—1461no—
186#387—1461no—
187#385—731no—
188#385—731no—
189#381—731no—
190#381—731no—
191#381—731no—
192#343—1461no—
193#343—1461no—
194#324—1464no—
195C23×C4—731no—
196C23×C4—731no—
197C23×C4C22×D7311yescharacteristic
198C2×M16—22no—
199C2×M16—1462no—
200#117—22no—
201#117—22no—
202C2×C4⋊C4—1461no—
203C2×C4⋊C4—1461no—
204C2×C4⋊C4—1462no—
205C2×C4⋊C4—1461no—
206C2×C4⋊C4—1461no—
207C2×C4⋊C4—1462no—
208C2×C4⋊C4D29211yescharacteristic
209C2×C4⋊C4D29211yescharacteristic
210C2×C22⋊C4—731no—
211C2×C22⋊C4—731no—
212C2×C22⋊C4C4×D7311yescharacteristic
213C2×C22⋊C4C4×D7311yescharacteristic
214C2×C42C22⋊D7311yescharacteristic
215C2×C42C22⋊D7311yescharacteristic
216C4⋊C8—24no—
217C22⋊C8—22no—
218C22⋊C8—1462no—
219C22⋊C8—1462no—
220C22⋊C8C22⋊D7314yes—
221#97—22no—
222C4×C8—22no—
223#95—1461no—
224#95—1461no—
225#95—1461no—
226#95—1461no—
227#95—1461no—
228#95—1461no—
229#95—1461no—
230#95—1461no—
231C24C2×C4×D7311yescharacteristic
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—2922no—
235C22×C4—2921no—
236C22×C4—2921no—
237C22×C4—1461no—
238C22×C4—1461no—
239C22×C4—1461no—
240C22×C4—1461no—
241C22×C4—1462no—
242C22×C4—1462no—
243C22×C4#1192400511yescharacteristic
244C22×C4#1192400511yescharacteristic
245C22×C4#1192400511yescharacteristic
246C22×C4#1192400511yescharacteristic
247C22×C4C2×C22⋊D7311yescharacteristic
248C22×C4C2×C22⋊D7312yes—
249C22×C4C2×D29211yescharacteristic
250C22×C4#1192402812yes—
251M16—42no—
252M16—42no—
253M16—2922no—
254M16—2922no—
255C2×C8—24no—
256C2×C8—2922no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—2922no—
260C4⋊C4—2922no—
261C4⋊C4—2921no—
262C4⋊C4—2922no—
263C4⋊C4—2921no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—2921no—
267C22⋊C4—2921no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23C2×#1192400511yescharacteristic
277C23C4×C22⋊D7312yes—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—2921no—
293C2×C4—2922no—
294C2×C4—2921no—
295C2×C4—2921no—
296C2×C4—2921no—
297C2×C4—2921no—
298C2×C4—2921no—
299C2×C4—2921no—
300C2×C4—2921no—
301C2×C4—2921no—
302C2×C4—2921no—
303C2×C4—2921no—
304C2×C4—5842no—
305C2×C4—1462no—
306C2×C4—1464no—
307C2×C4#1455656011yescharacteristic
308C2×C4#1455656512yes—
309C2×C4#1455657411yescharacteristic
310C8—44no—
311C8—5842no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—42no—
318C22—42no—
319C22#1798846611yescharacteristic
320C22#1798856011yescharacteristic
321C22#1798856011yescharacteristic
322C4—21no—
323C4—22no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—2922no—
330C4—5841no—
331C4—5841no—
332C4—5841no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#2261034911yescharacteristic
337C2#2261038911yescharacteristic
338C2#2261048311yescharacteristic
subgroupG/H
centerC22#17988466
commutator, prime radicalC24×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#2921C2
socleC22×C73#386
cosocleC23×C4×C73C23
hypercenter#2921D73
hypocenterC73#9514
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2921

Complements

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

NH ≅ G/Ntype
175. C73#9514semidirect

Maximal subgroups

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

subgroupindex
#226142142
#226100142
#226082602
#226078402
C73×#29212
#951473