Finite Group Databasebeta

← #34005259

Subgroups — #34005259

Order 18688.

514 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 114 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#22625787C211yesmaximal, characteristic
2#22625787C211yesmaximal, characteristic
3#22624809C212yesmaximal, complemented
4#22624809C212yesmaximal, complemented
5#22612333C211yesmaximal, characteristic
6C2×#14556658C2212yes—
7C2×#14556658C2212yes—
8C2×C22⋊#10596833—21no—
9C2×C22⋊#10596833—21no—
10#17989453—21no—
11#17989453—21no—
12C2×#14556547—21no—
13C22×C4×Dic73C2211yescharacteristic
14#17988456C2211yescharacteristic
15#17988456C2211yescharacteristic
16#17988451—21no—
17#17988447C411yescharacteristic
18#17988445—21no—
19C4⋊C4×Dic73C411yescharacteristic
20C4⋊C4×Dic73C411yescharacteristic
21#17988438—21no—
22#380×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25#14556658—24no—
26#14556658—24no—
27C22⋊#10596833—42no—
28C22⋊#10596833—42no—
29C23×Dic73D411yescharacteristic
30C23×Dic73D411yescharacteristic
31#14556547—42no—
32#14556547—42no—
33C2×C4⋊Dic73C2×C411yescharacteristic
34C2×C4⋊Dic73C2×C411yescharacteristic
35C2×#11924007—21no—
36C2×#11924007—21no—
37C2×#11924007—21no—
38C2×#11924007—21no—
39C2×C22⋊Dic73—21no—
40C2×C4×Dic73—24no—
41C2×C4×Dic73—21no—
42C2×C4×Dic73—21no—
43C2×C4×Dic73C2×C411yescharacteristic
44C2×C4×Dic73D411yescharacteristic
45C2×C4×Dic73D411yescharacteristic
46C2×C4×Dic73C2311yescharacteristic
47#14556498—21no—
48#14556498—21no—
49#14556498—21no—
50C23×C4×C73C2×C411yescharacteristic
51C2×C4⋊C4×C73C2×C411yescharacteristic
52C2×C4⋊C4×C73C2×C411yescharacteristic
53C2×C22⋊C4×C73—21no—
54#95×C73—21no—
55C2×#10596833—42no—
56C2×#10596833—42no—
57C2×#10596833—42no—
58C2×#10596833—42no—
59C2×#10596833—42no—
60C2×#10596833—42no—
61C22×Dic73—22no—
62C22×Dic73—22no—
63C22×Dic73—22no—
64C22×Dic73—22no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C22×Dic73C22⋊C411yescharacteristic
70C22×Dic73C22⋊C411yescharacteristic
71C22×Dic73D812yes—
72C22×Dic73SD1612yes—
73C22×Dic73C2×D411yescharacteristic
74C22×Dic73C2×D411yescharacteristic
75C4⋊Dic73—41no—
76C4⋊Dic73—41no—
77#11924007—41no—
78#11924007—41no—
79#11924007—41no—
80#11924007—41no—
81#11924007—42no—
82#11924007—41no—
83#11924007—41no—
84C22⋊Dic73—42no—
85C4×Dic73—22no—
86C4×Dic73—22no—
87C4×Dic73—22no—
88C4×Dic73—42no—
89C4×Dic73—42no—
90C4×Dic73#4114yes—
91C24×C73C22⋊C411yescharacteristic
92C22×C4×C73—22no—
93C22×C4×C73—21no—
94C22×C4×C73—21no—
95C22×C4×C73—41no—
96C22×C4×C73—41no—
97C22×C4×C73C22⋊C411yescharacteristic
98C22×C4×C73C22×C411yescharacteristic
99C4⋊C4×C73—41no—
100C4⋊C4×C73—41no—
101C22⋊C4×C73—42no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73#10212yes—
109C23×C73C2×C22⋊C411yescharacteristic
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—44no—
116C2×C4×C73—41no—
117C2×C4×C73—41no—
118C2×C4×C73—41no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73#11712yes—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—24no—
126C2×Dic73—24no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—42no—
131C2×Dic73—42no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73#10212yes—
139C2×Dic73#12312yes—
140C2×Dic73#12312yes—
141C2×Dic73C2×D811yescharacteristic
142C2×Dic73C2×SD1611yescharacteristic
143C2×Dic73#13512yes—
144C2×Dic73AGL(1,ℤ/8)11yescharacteristic
145C2×Dic73#13712yes—
146C2×Dic73#13711yescharacteristic
147#10596833—82no—
148#10596833—82no—
149C22×C73—22no—
150C22×C73—22no—
151C22×C73—22no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73#38111yescharacteristic
157C22×C73#41311yescharacteristic
158C22×C73#41311yescharacteristic
159C22×C73C2×#10211yescharacteristic
160C22×C73#41611yescharacteristic
161C22×C73#41711yescharacteristic
162C22×C73#41911yescharacteristic
163C4×C73—22no—
164C4×C73—41no—
165C4×C73—81no—
166C4×C73—81no—
167Dic73—22no—
168Dic73—41no—
169Dic73—81no—
170Dic73—81no—
171Dic73#48012yes—
172Dic73#48212yes—
173Dic73#48312yes—
174Dic73#48512yes—
175#8726—731nomaximal, Sylow
176C2×C73—42no—
177C2×C73#154011yescharacteristic
178C2×C73#154711yescharacteristic
179C2×C73#155411yescharacteristic
180C2×C73#155911yescharacteristic
181C2×C73#182211yescharacteristic
182C2×C73#182311yescharacteristic
183C2×C73#182511yescharacteristic
184#2285—731no—
185#1797—731no—
186#1797—731no—
187#1296—732no—
188#1296—732no—
189C73#872611yescharacteristic, complemented, Sylow
190C2×#117—1461no—
191C22×C42—731no—
192C2×C4⋊C8—732no—
193C2×C4⋊C8—732no—
194C2×C22⋊C8—1461no—
195C2×C22⋊C8—1461no—
196#384—731no—
197#384—731no—
198#382—1461no—
199#380—731no—
200#380—1461no—
201#380#6440811yescharacteristic
202C4×C4⋊C4—731no—
203C4×C4⋊C4—731no—
204C4×C4⋊C4—1461no—
205#336—1461no—
206#336—1461no—
207C23×C4—731no—
208C23×C4—731no—
209C23×C4C2×#6440811yescharacteristic
210C22×C8—1462no—
211C22×C8—1462no—
212#117—2922no—
213#117—2922no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4—1461no—
217C2×C4⋊C4—1461no—
218C2×C4⋊C4—1461no—
219C2×C4⋊C4—1461no—
220C2×C4⋊C4C2×#6440811yescharacteristic
221C2×C4⋊C4C2×#6440811yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—1461no—
224C2×C42—731no—
225C2×C42—731no—
226C2×C42—731no—
227C2×C42—731no—
228C2×C42—1461no—
229C2×C42—1461no—
230C2×C42—1464no—
231C4⋊C8—1464no—
232C4⋊C8—1464no—
233C22⋊C8—2922no—
234C22⋊C8—2922no—
235#95—21no—
236#95—1461no—
237#95—1461no—
238#95—1461no—
239C24C22⋊#6440811yescharacteristic
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—731no—
246C22×C4—731no—
247C22×C4—732no—
248C22×C4—732no—
249C22×C4—731no—
250C22×C4—731no—
251C22×C4—1461no—
252C22×C4—1461no—
253C22×C4—1461no—
254C22×C4—1462no—
255C22×C4—1462no—
256C22×C4—1461no—
257C22×C4—1462no—
258C22×C4—1462no—
259C22×C4C22⋊#6440811yescharacteristic
260C22×C4C22×#6440811yescharacteristic
261C2×C8—2922no—
262C2×C8—2922no—
263C2×C8—2922no—
264C2×C8—2922no—
265C2×C8—2922no—
266C2×C8—2922no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—2921no—
270C4⋊C4—2921no—
271C4⋊C4—2922no—
272C4⋊C4—2921no—
273C4⋊C4—2921no—
274C4⋊C4—2921no—
275C4⋊C4—2921no—
276C4⋊C4—2921no—
277C4⋊C4—2921no—
278C22⋊C4—42no—
279C22⋊C4—2922no—
280C42—2922no—
281C42—2922no—
282C42—734no—
283C42—1462no—
284C42—1462no—
285C42—1462no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23#1455665312yes—
293C23C2×C22⋊#6440811yescharacteristic
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—44no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—2922no—
307C2×C4—2922no—
308C2×C4—2921no—
309C2×C4—2921no—
310C2×C4—2921no—
311C2×C4—2921no—
312C2×C4—2921no—
313C2×C4—2921no—
314C2×C4—732no—
315C2×C4—732no—
316C2×C4—731no—
317C2×C4—731no—
318C2×C4—732no—
319C2×C4—731no—
320C2×C4—731no—
321C2×C4—732no—
322C2×C4—732no—
323C2×C4—1461no—
324C2×C4—1461no—
325C2×C4—1461no—
326C2×C4—1464no—
327C2×C4—1464no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4#1455667012yes—
331C8—5842no—
332C8—5842no—
333C22—22no—
334C22—22no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1798953011yescharacteristic
341C22#1798957411yescharacteristic
342C22#1798957411yescharacteristic
343C22C2×#1455665311yescharacteristic
344C22#1798957711yescharacteristic
345C22#1798957811yescharacteristic
346C22#1798958011yescharacteristic
347C4—22no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—2921no—
352C4—5841no—
353C4—5841no—
354C4—732no—
355C4—732no—
356C4—732no—
357C4—732no—
358C4—1462no—
359C2—42no—
360C2#2262542911yescharacteristic
361C2#2262544311yescharacteristic
362C2#2262545711yescharacteristic
363C2#2262546711yescharacteristic
364C2#2262583311yescharacteristic
365C2#2262583411yescharacteristic
366C2#2262583611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#380×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#380#64408
hypocenterC73#8726
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #22624809C2semidirect
4. #22624809C2semidirect
189. C73#8726semidirect

Maximal subgroups

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

subgroupindex
#226257872
#226248092
#226123332
#872673