Finite Group Databasebeta

← #34005244

Subgroups — #34005244

Order 18688.

482 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 94 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#22625658C211yesmaximal, characteristic
2#22625658C211yesmaximal, characteristic
3#22624807C212yesmaximal, complemented
4#22624807C212yesmaximal, complemented
5#22612327C211yesmaximal, characteristic
6C2×#14556648—21no—
7C2×#14556648—21no—
8C2×#14556646C2212yes—
9C2×#14556646C2212yes—
10#17989453—21no—
11#17989453—21no—
12C2×C42×D73C2211yescharacteristic
13#17988454—21no—
14#17988452C2211yescharacteristic
15#17988452C2211yescharacteristic
16#17988449—21no—
17#17988444C411yescharacteristic
18#17988444C411yescharacteristic
19C4×C4⋊Dic73C411yescharacteristic
20C4×#11924005—21no—
21#17988433—21no—
22C4×C4⋊C4×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25#14556648—24no—
26#14556648—24no—
27#14556646—24no—
28#14556646—24no—
29C22×C4×D73C2×C411yescharacteristic
30C22×C4×D73D411yescharacteristic
31C22×C4×D73D411yescharacteristic
32C2×C4⋊Dic73C2×C411yescharacteristic
33C2×C4⋊Dic73C2×C411yescharacteristic
34C2×#11924005—21no—
35C2×#11924005—21no—
36C2×C4×Dic73—21no—
37C2×C4×Dic73D411yescharacteristic
38C2×C4×Dic73D411yescharacteristic
39C2×C4×Dic73C2311yescharacteristic
40C42×D73—24no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48C2×C4⋊C4×C73C2×C411yescharacteristic
49C2×C4⋊C4×C73C2×C411yescharacteristic
50C2×C42×C73—21no—
51C2×C42×C73C2×C411yescharacteristic
52#95×C73—21no—
53C2×#10596833—24no—
54C2×#10596833—24no—
55C2×#10596833—42no—
56C2×#10596833—42no—
57C2×#10596833—42no—
58C2×#10596833—42no—
59C23×D73C22⋊C411yescharacteristic
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73C22⋊C411yescharacteristic
63C22×Dic73C2×D411yescharacteristic
64C22×Dic73C2×D411yescharacteristic
65C2×C4×D73—22no—
66C2×C4×D73—22no—
67C2×C4×D73—22no—
68C2×C4×D73—22no—
69C2×C4×D73—22no—
70C2×C4×D73—41no—
71C2×C4×D73—41no—
72C2×C4×D73—41no—
73C2×C4×D73—41no—
74C4⋊Dic73—41no—
75C4⋊Dic73—41no—
76#11924005—42no—
77#11924005—42no—
78C4×Dic73—22no—
79C4×Dic73—22no—
80C4×Dic73—42no—
81C4×Dic73#4114yes—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73C22⋊C411yescharacteristic
85C22×C4×C73C22⋊C411yescharacteristic
86C22×C4×C73C22×C411yescharacteristic
87C4⋊C4×C73—41no—
88C4⋊C4×C73—41no—
89C42×C73—22no—
90C42×C73—42no—
91C23×C73C2×C22⋊C411yescharacteristic
92C22×D73—21no—
93C22×D73—21no—
94C22×D73—21no—
95C22×D73—21no—
96C22×D73—21no—
97C22×D73—21no—
98C22×D73#10412yes—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—41no—
107C2×C4×C73—41no—
108C2×C4×C73—41no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73#10412yes—
113C2×C4×C73#11712yes—
114C2×Dic73—21no—
115C2×Dic73—21no—
116C2×Dic73—21no—
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—41no—
122C2×Dic73—41no—
123C2×Dic73—41no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73#12312yes—
128C2×Dic73#12312yes—
129C4×D73—44no—
130C4×D73—44no—
131C4×D73—44no—
132#10596833—44no—
133#10596833—44no—
134C22×C73#38111yescharacteristic
135C22×C73#41311yescharacteristic
136C22×C73#41311yescharacteristic
137C22×C73C2×#10411yescharacteristic
138C22×C73C2×#10411yescharacteristic
139C22×C73#42111yescharacteristic
140C22×C73#42111yescharacteristic
141C2×D73—22no—
142C2×D73—22no—
143C2×D73—22no—
144C2×D73—41no—
145C2×D73—41no—
146C2×D73—41no—
147C2×D73—41no—
148C4×C73—22no—
149C4×C73—22no—
150C4×C73—41no—
151C4×C73—81no—
152C4×C73—81no—
153Dic73—22no—
154Dic73—22no—
155Dic73—41no—
156Dic73—81no—
157Dic73—81no—
158#8720—731nomaximal, Sylow
159C2×C73#152411yescharacteristic
160C2×C73#152911yescharacteristic
161C2×C73#153211yescharacteristic
162C2×C73#153511yescharacteristic
163C2×C73#182211yescharacteristic
164C2×C73#182611yescharacteristic
165C2×C73#182611yescharacteristic
166D73—42no—
167#2283—731no—
168#1749—731no—
169#1749—731no—
170#1295—732no—
171#1295—732no—
172C73#872011yescharacteristic, complemented, Sylow
173C22×C42—731no—
174C2×C22⋊C8—1461no—
175C2×C22⋊C8—1461no—
176C2×#97—732no—
177C2×#97—732no—
178#383—1461no—
179#382—731no—
180#382—731no—
181#381—1461no—
182#380—731no—
183#380—731no—
184C4×C4⋊C4—731no—
185C4×C4⋊C4#6440811yescharacteristic
186C4×C22⋊C4—1461no—
187#376—1461no—
188#336—1461no—
189#336—1461no—
190C23×C4—731no—
191C23×C4—731no—
192C23×C4—731no—
193C22×C8—1462no—
194C22×C8—1462no—
195C2×C4⋊C4—731no—
196C2×C4⋊C4—731no—
197C2×C4⋊C4C2×#6440811yescharacteristic
198C2×C4⋊C4C2×#6440811yescharacteristic
199C2×C22⋊C4—1461no—
200C2×C22⋊C4—1461no—
201C2×C42—21no—
202C2×C42—731no—
203C2×C42—731no—
204C2×C42—731no—
205C2×C42—1464no—
206C2×C42—1461no—
207C2×C42C2×#6440811yescharacteristic
208C22⋊C8—1464no—
209C22⋊C8—1464no—
210#97—1464no—
211#97—1464no—
212#95—21no—
213#95—1461no—
214#95—1461no—
215#95—1461no—
216#95—1461no—
217#95—1461no—
218#95—1461no—
219#95—1461no—
220C24—731no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—2921no—
224C22×C4—2921no—
225C22×C4—2921no—
226C22×C4—2921no—
227C22×C4—731no—
228C22×C4—731no—
229C22×C4—731no—
230C22×C4—1462no—
231C22×C4—1462no—
232C22×C4—1462no—
233C22×C4—1461no—
234C22×C4—1461no—
235C22×C4—1462no—
236C22×C4—1462no—
237C22×C4C22⋊#6440811yescharacteristic
238C22×C4C22⋊#6440811yescharacteristic
239C22×C4C22×#6440811yescharacteristic
240C2×C8—2922no—
241C2×C8—2922no—
242C2×C8—2922no—
243C2×C8—2922no—
244C2×C8—1464no—
245C2×C8—1464no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—2921no—
249C4⋊C4—2921no—
250C22⋊C4—2922no—
251C22⋊C4—2922no—
252C42—22no—
253C42—42no—
254C42—2922no—
255C42—734no—
256C42—1462no—
257C42—1462no—
258C23—732no—
259C23—1461no—
260C23—1461no—
261C23—1461no—
262C23—1461no—
263C23—1461no—
264C23—1461no—
265C23C2×C22⋊#6440811yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—2924no—
280C2×C4—2924no—
281C2×C4—2924no—
282C2×C4—2921no—
283C2×C4—2921no—
284C2×C4—2921no—
285C2×C4—2921no—
286C2×C4—2921no—
287C2×C4—2921no—
288C2×C4—732no—
289C2×C4—732no—
290C2×C4—1461no—
291C2×C4—1461no—
292C2×C4—1461no—
293C2×C4—1461no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4—1461no—
297C2×C4#1455665612yes—
298C2×C4#1455667012yes—
299C8—2924no—
300C8—2924no—
301C22—2921no—
302C22—2921no—
303C22—2921no—
304C22—2921no—
305C22—1462no—
306C22—1462no—
307C22—1462no—
308C22#1798953011yescharacteristic
309C22#1798957311yescharacteristic
310C22#1798957311yescharacteristic
311C22D73⋊#10411yescharacteristic
312C22C2×#1455665611yescharacteristic
313C22#1798958411yescharacteristic
314C22#1798958511yescharacteristic
315C4—22no—
316C4—22no—
317C4—41no—
318C4—81no—
319C4—81no—
320C4—2921no—
321C4—5841no—
322C4—5841no—
323C4—1462no—
324C4—1462no—
325C2—2922no—
326C2#2262538311yescharacteristic
327C2#2262539811yescharacteristic
328C2#2262540611yescharacteristic
329C2#2262541511yescharacteristic
330C2#2262583211yescharacteristic
331C2#2262583811yescharacteristic
332C2#2262583911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC4×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC4×C4⋊C4#64408
hypocenterC73#8720
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #22624807C2semidirect
4. #22624807C2semidirect
172. C73#8720semidirect

Maximal subgroups

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

subgroupindex
#226256582
#226248072
#226123272
#872073