Finite Group Databasebeta

← #34001423

Subgroups — #34001423

Order 18688.

482 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 102 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#22625859C211yesmaximal, characteristic, complemented
2#22625847C211yesmaximal, characteristic, complemented
3#22624750C212yesmaximal, complemented
4#22624747C212yesmaximal
5#22612393C211yesmaximal, characteristic
6C2×#14556658—21no—
7#17989453—21no—
8#17989453—21no—
9#17989453—21no—
10#17989453C2212yes—
11#17989453C2212yes—
12C2×D4×Dic73C411yescharacteristic
13C2×#14556547—21no—
14#17988490C2211yescharacteristic
15#17988485C411yescharacteristic
16#17988483C2211yescharacteristic
17#17988481—21no—
18#17988475—21no—
19C4⋊C4×Dic73C411yescharacteristic
20C22⋊C4×Dic73—21no—
21C42×Dic73C2211yescharacteristic
22#390×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25#14556658—42no—
26C23×Dic73—21no—
27D4×Dic73—22no—
28D4×Dic73C814yescomplemented
29#14556547—44no—
30C2×C4⋊Dic73C2×C411yescharacteristic
31C2×C4⋊Dic73C2×C411yescharacteristic
32C2×#11924007—21no—
33C2×#11924007—21no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73—21no—
36C2×C22⋊Dic73—21no—
37C2×C4×Dic73—21no—
38C2×C4×Dic73C2×C411yescharacteristic
39C2×C4×Dic73D411yescharacteristic
40C2×C4×Dic73D411yescharacteristic
41C2×C4×Dic73D411yescharacteristic
42C2×C4×Dic73D411yescharacteristic
43C2×C4×Dic73C2311yescharacteristic
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47C22×D4×C73C2×C411yescharacteristic
48C2×C4⋊C4×C73C2×C411yescharacteristic
49C2×C22⋊C4×C73—21no—
50C2×C22⋊C4×C73—21no—
51C2×C42×C73C2×C411yescharacteristic
52C2×#10596833—42no—
53C2×#10596833—42no—
54C2×#10596833—42no—
55C2×#10596833—42no—
56C2×#10596833—42no—
57C2×#10596833—42no—
58C22×Dic73—21no—
59C22×Dic73—24no—
60C22×Dic73—21no—
61C22×Dic73—42no—
62C22×Dic73—42no—
63C22×Dic73C22⋊C411yescharacteristic
64C22×Dic73C22⋊C411yescharacteristic
65C22×Dic73C2×D411yescharacteristic
66C22×Dic73C2×D411yescharacteristic
67C4⋊Dic73—21no—
68C4⋊Dic73—41no—
69C4⋊Dic73C2×C812yes—
70#11924007—42no—
71#11924007—42no—
72C22⋊Dic73—24no—
73C22⋊Dic73—41no—
74C22⋊Dic73—42no—
75C22⋊Dic73—41no—
76C4×Dic73—22no—
77C4×Dic73—21no—
78C4×Dic73—21no—
79C4×Dic73—41no—
80C4×Dic73—41no—
81C4×Dic73—41no—
82C4×Dic73—42no—
83C4×Dic73C2×C812yes—
84C4×Dic73M1612yes—
85C24×C73—21no—
86C2×D4×C73—21no—
87C2×D4×C73—41no—
88C2×D4×C73—41no—
89C2×D4×C73C2×C812yes—
90C22×C4×C73—21no—
91C22×C4×C73C22⋊C411yescharacteristic
92C22×C4×C73C22⋊C411yescharacteristic
93C22×C4×C73C22×C411yescharacteristic
94C4⋊C4×C73—41no—
95C22⋊C4×C73—42no—
96C22⋊C4×C73—42no—
97C42×C73—41no—
98C23×C73—22no—
99C23×C73—41no—
100C23×C73—41no—
101C23×C73—41no—
102C23×C73—41no—
103C23×C73—41no—
104C23×C73—41no—
105C23×C73C2×C22⋊C411yescharacteristic
106D4×C73—42no—
107D4×C73—42no—
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—41no—
117C2×C4×C73—41no—
118C2×C4×C73—41no—
119C2×C4×C73C22×C811yescharacteristic
120C2×C4×C73C2×M1611yescharacteristic
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—22no—
130C2×Dic73—48no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73C22⋊C812yes—
137C2×Dic73C22⋊C812yes—
138C2×Dic73AGL(1,ℤ/8)11yescharacteristic
139C2×Dic73AGL(1,ℤ/8)12yes—
140C2×Dic73#13711yescharacteristic
141#10596833—82no—
142#10596833—82no—
143C22×C73—42no—
144C22×C73—42no—
145C22×C73—42no—
146C22×C73—81no—
147C22×C73—81no—
148C22×C73—81no—
149C22×C73—81no—
150C22×C73C2×C22⋊C811yescharacteristic
151C22×C73#41011yescharacteristic
152C22×C73#41311yescharacteristic
153C22×C73#41711yescharacteristic
154C22×C73#41811yescharacteristic
155C22×C73#42111yescharacteristic
156C22×C73#42111yescharacteristic
157C4×C73—21no—
158C4×C73—21no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73—81no—
162Dic73—22no—
163Dic73—22no—
164Dic73—21no—
165Dic73—21no—
166Dic73—22no—
167Dic73—42no—
168Dic73—81no—
169#7594—731nomaximal, Sylow
170C2×C73—82no—
171C2×C73#145811yescharacteristic
172C2×C73#147711yescharacteristic
173C2×C73#147811yescharacteristic
174C2×C73#151211yescharacteristic
175C2×C73#151411yescharacteristic
176C2×C73#153511yescharacteristic
177C2×C73#155711yescharacteristic
178#2293—731no—
179#1839—731no—
180#1831—731no—
181#1271—732no—
182#1270—732no—
183C73#759411yescharacteristic, complemented, Sylow
184C2×C4×D4—731no—
185C2×#117—1461no—
186C2×C4⋊C8—1461no—
187#390—731no—
188#390#6440811yescharacteristic
189#389—731no—
190#389—731no—
191#388—1461no—
192#388—1461no—
193C4×C4⋊C4—731no—
194C4×C22⋊C4—1461no—
195C43—731no—
196#336—732no—
197#336—732no—
198#336—1461no—
199#336—1461no—
200#336—1461no—
201C22×D4C2×#6440811yescharacteristic
202C23×C4—1461no—
203C22×C8—1462no—
204C22×C8—1462no—
205C4×D4—734no—
206C4×D4—1462no—
207#117—2924no—
208C2×C4⋊C4—731no—
209C2×C4⋊C4—731no—
210C2×C4⋊C4—1461no—
211C2×C4⋊C4—1461no—
212C2×C4⋊C4C2×#6440811yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—1461no—
216C2×C22⋊C4—1461no—
217C2×C22⋊C4—1461no—
218C2×C42—731no—
219C2×C42—731no—
220C2×C42—731no—
221C2×C42—731no—
222C2×C42—731no—
223C2×C42—731no—
224C2×C42—1461no—
225C2×C42C2×#6440811yescharacteristic
226C4⋊C8—2922no—
227#95—1461no—
228#95—1461no—
229#95—1461no—
230C24—21no—
231C2×D4—21no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4#1192403612yes—
235C22×C4—21no—
236C22×C4—2922no—
237C22×C4—2922no—
238C22×C4—731no—
239C22×C4—731no—
240C22×C4—731no—
241C22×C4—731no—
242C22×C4—1461no—
243C22×C4—1464no—
244C22×C4—1461no—
245C22×C4C22⋊#6440811yescharacteristic
246C22×C4C22⋊#6440811yescharacteristic
247C22×C4C22×#6440811yescharacteristic
248C2×C8—2922no—
249C2×C8—2922no—
250C2×C8—2922no—
251C2×C8—2922no—
252C2×C8—2922no—
253C2×C8—2922no—
254C4⋊C4—41no—
255C4⋊C4—2921no—
256C4⋊C4—2922no—
257C4⋊C4—2922no—
258C4⋊C4—732no—
259C4⋊C4—1461no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—2921no—
263C22⋊C4—2921no—
264C22⋊C4—2922no—
265C22⋊C4—1464no—
266C42—41no—
267C42—2921no—
268C42—2921no—
269C42—2921no—
270C42—2922no—
271C42—732no—
272C42—732no—
273C42—1461no—
274C42—1461no—
275C42—1462no—
276C23—22no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23C2×C22⋊#6440811yescharacteristic
284D4—42no—
285D4—42no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—2921no—
298C2×C4—2921no—
299C2×C4—2928no—
300C2×C4—2921no—
301C2×C4—2921no—
302C2×C4—2921no—
303C2×C4—732no—
304C2×C4—732no—
305C2×C4—731no—
306C2×C4—731no—
307C2×C4—732no—
308C2×C4—1462no—
309C2×C4—1461no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4C2×#1192403611yescharacteristic
318C2×C4D73⋊M1611yescharacteristic
319C8—5842no—
320C8—5842no—
321C22—42no—
322C22—42no—
323C22—42no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22#1798955511yescharacteristic
329C22#1798956711yescharacteristic
330C22#1798957411yescharacteristic
331C22#1798957811yescharacteristic
332C22#1798957911yescharacteristic
333C22#1798958411yescharacteristic
334C22#1798958511yescharacteristic
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—2922no—
341C4—5841no—
342C4—1461no—
343C4—1461no—
344C4—1462no—
345C4—1462no—
346C4—1462no—
347C2—82no—
348C2#2262516311yescharacteristic
349C2#2262522711yescharacteristic
350C2#2262523111yescharacteristic
351C2#2262534311yescharacteristic
352C2#2262535111yescharacteristic
353C2#2262541611yescharacteristic
354C2#2262546311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
Fitting#390×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC22×D4×C73C2×C4
cosocleC2×C4×Dic73C23
hypercenter#390#64408
hypocenterC73#7594
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #22625859C2semidirect
2. #22625847C2semidirect
3. #22624750C2semidirect
28. D4×Dic73C8semidirect
183. C73#7594semidirect

Maximal subgroups

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

subgroupindex
#226258592
#226258472
#226247502
#226247472
#226123932
#759473