Finite Group Databasebeta

← #33004657

Subgroups — #33004657

Order 18688.

500 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 103 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#22615104C211yesmaximal, characteristic
2C4×#14556506C211yesmaximal, characteristic
3#22608055C214yesmaximal
4C73×#1799C211yesmaximal, characteristic
5C2×#14556591C411yescharacteristic, complemented
6C2×#14556506C2212yes—
7#17988499—21no—
8#17988499—21no—
9#17988490C2212yes—
10#17988452C412yescomplemented
11#17988447—21no—
12#17988447—21no—
13C4×C4⋊Dic73C411yescharacteristic, complemented
14C4×C22⋊Dic73—21no—
15#17988354—21no—
16C2×C4×D4×C73C2211yescharacteristic
17C2×#99×C73C2212yes—
18#380×C73—21no—
19#342×C73—21no—
20C22×Dic146—21no—
21#14556591—41no—
22#14556591—41no—
23C2×C4⋊Dic73—21no—
24C2×C4⋊Dic73—21no—
25C2×C4⋊Dic73C2×C412yes—
26C2×C22⋊Dic73—22no—
27C2×C22⋊Dic73—22no—
28C2×C22⋊Dic73—22no—
29C2×C4×Dic73—41no—
30C2×C4×Dic73C2×C412yes—
31#14556506—22no—
32#14556506Q814yescomplemented
33#14556498—21no—
34#14556498—22no—
35#14556498—22no—
36#14556498—41no—
37C22×D4×C73C2311yescharacteristic
38C23×C4×C73D411yescharacteristic
39C23×C4×C73D411yescharacteristic
40C4×D4×C73—41no—
41C4×D4×C73—41no—
42C2×C4⋊C4×C73—41no—
43C2×C4⋊C4×C73C2×C411yescharacteristic
44C2×C22⋊C4×C73—22no—
45C2×C22⋊C4×C73D411yescharacteristic
46C2×C22⋊C4×C73D411yescharacteristic
47C2×C42×C73C2×C411yescharacteristic
48#99×C73—24no—
49#95×C73—41no—
50C2×Dic146—42no—
51C2×Dic146—82no—
52C22×Dic73—22no—
53C22×Dic73—22no—
54C22×Dic73—42no—
55C4⋊Dic73—42no—
56C4⋊Dic73—41no—
57C4⋊Dic73—41no—
58C4⋊Dic73—42no—
59C22⋊Dic73—24no—
60C22⋊Dic73—42no—
61C22⋊Dic73—82no—
62C22⋊Dic73—82no—
63C4×Dic73—42no—
64C4×Dic73—82no—
65C24×C73C2×D411yescharacteristic
66C24×C73C2×D411yescharacteristic
67C2×D4×C73—41no—
68C2×D4×C73—41no—
69C2×D4×C73C2×Q812yes—
70C2×D4×C73#4112yes—
71C22×C4×C73—21no—
72C22×C4×C73—21no—
73C22×C4×C73—21no—
74C22×C4×C73—21no—
75C22×C4×C73—42no—
76C22×C4×C73—42no—
77C22×C4×C73—42no—
78C22×C4×C73C22⋊C411yescharacteristic
79C22×C4×C73C22⋊C411yescharacteristic
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22⋊C411yescharacteristic
82C22×C4×C73C22×C411yescharacteristic
83C4⋊C4×C73—41no—
84C4⋊C4×C73—82no—
85C22⋊C4×C73—41no—
86C22⋊C4×C73—41no—
87C22⋊C4×C73—42no—
88C22⋊C4×C73—42no—
89C42×C73—21no—
90C42×C73—21no—
91C23×C73—21no—
92C23×C73—21no—
93C23×C73—21no—
94C23×C73—21no—
95C23×C73—41no—
96C23×C73—41no—
97C23×C73—41no—
98C23×C73—41no—
99C23×C73C2×C22⋊C411yescharacteristic
100C23×C73C22⋊Q812yes—
101C23×C73#12411yescharacteristic
102C23×C73C4⋊Q811yescharacteristic
103D4×C73—42no—
104D4×C73—42no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—22no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—42no—
112C2×C4×C73—42no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—41no—
116C2×C4×C73—81no—
117C2×C4×C73—81no—
118C2×C4×C73—82no—
119C2×C4×C73—82no—
120C2×C4×C73—82no—
121C2×C4×C73#9911yescharacteristic
122C2×C4×C73#9911yescharacteristic
123C2×C4×C73C4×Q812yes—
124C2×Dic73—44no—
125C2×Dic73—42no—
126C2×Dic73—42no—
127C2×Dic73—42no—
128C2×Dic73—42no—
129C2×Dic73—42no—
130C2×Dic73—42no—
131C2×Dic73—82no—
132C2×Dic73—82no—
133Dic146—84no—
134C22×C73—21no—
135C22×C73—21no—
136C22×C73—22no—
137C22×C73—21no—
138C22×C73—21no—
139C22×C73—42no—
140C22×C73—41no—
141C22×C73—41no—
142C22×C73—41no—
143C22×C73—41no—
144C22×C73—41no—
145C22×C73—41no—
146C22×C73—81no—
147C22×C73—81no—
148C22×C73#39111yescharacteristic
149C22×C73C2×#9911yescharacteristic
150C22×C73#41011yescharacteristic
151C4×C73—21no—
152C4×C73—22no—
153C4×C73—41no—
154C4×C73—41no—
155C4×C73—41no—
156C4×C73—162no—
157C4×C73#35412yes—
158Dic73—82no—
159Dic73—84no—
160Dic73—82no—
161#13299—731nomaximal, Sylow
162C2×C73—21no—
163C2×C73—21no—
164C2×C73—42no—
165C2×C73—41no—
166C2×C73—41no—
167C2×C73#199611yescharacteristic
168C2×C73C2×#35411yescharacteristic
169C2×C73#212811yescharacteristic
170#2563—731no—
171#1799D7311yescharacteristic
172C4×#99—731no—
173#1393—734no—
174C73#1329911yescharacteristic, complemented, Sylow
175C2×C4⋊Q8—731no—
176C2×C4×D4C2×D7311yescharacteristic
177C2×#99—732no—
178C2×#99C2×D7312yes—
179#393—1461no—
180#393—1461no—
181#390—732no—
182#382—732no—
183#380—21no—
184#380—1461no—
185#380—1461no—
186C4×C4⋊C4—731no—
187C4×C22⋊C4—1461no—
188#342—21no—
189#342—1461no—
190C22×Q8—1461no—
191C22×D4C22×D7311yescharacteristic
192C23×C4D29211yescharacteristic
193C23×C4C22⋊D7311yescharacteristic
194C4⋊Q8—2921no—
195C4⋊Q8—2921no—
196C4×D4—41no—
197C4×D4—41no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4—732no—
200C2×C4⋊C4—1461no—
201C2×C4⋊C4—1461no—
202C2×C4⋊C4C4×D7311yescharacteristic
203C2×C22⋊C4—22no—
204C2×C22⋊C4—1462no—
205C2×C22⋊C4—1462no—
206C2×C22⋊C4—1462no—
207C2×C22⋊C4D29211yescharacteristic
208C2×C22⋊C4C22⋊D7311yescharacteristic
209C2×C42—2921no—
210C2×C42—732no—
211C2×C42C4×D7311yescharacteristic
212#99—24no—
213#99—734no—
214#99—1462no—
215#95—41no—
216#95—2921no—
217#95—1461no—
218#95—1462no—
219#95—1462no—
220C24C2×C22⋊D7311yescharacteristic
221C24C2×D29211yescharacteristic
222C2×Q8—2922no—
223C2×Q8—5842no—
224C2×D4—41no—
225C2×D4—41no—
226C2×D4Q8×D7312yes—
227C2×D4#1192402712yes—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—2922no—
236C22×C4—1462no—
237C22×C4—1462no—
238C22×C4#1192400511yescharacteristic
239C22×C4#1192400511yescharacteristic
240C22×C4#1192400511yescharacteristic
241C22×C4#1192400511yescharacteristic
242C22×C4C2×C4×D7311yescharacteristic
243C4⋊C4—41no—
244C4⋊C4—82no—
245C4⋊C4—2922no—
246C4⋊C4—2922no—
247C4⋊C4—2921no—
248C4⋊C4—2921no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—2922no—
254C22⋊C4—5842no—
255C22⋊C4—5842no—
256C22⋊C4—1464no—
257C42—21no—
258C42—21no—
259C42—2922no—
260C42—5842no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23C2×#1192400511yescharacteristic
270C23#1455657112yes—
271C23#1455657811yescharacteristic
272C23#1455658911yescharacteristic
273Q8—5844no—
274D4—42no—
275D4—42no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4—82no—
292C2×C4—2924no—
293C2×C4—2922no—
294C2×C4—2922no—
295C2×C4—2922no—
296C2×C4—2922no—
297C2×C4—2922no—
298C2×C4—2922no—
299C2×C4—5842no—
300C2×C4—5842no—
301C2×C4#1455650511yescharacteristic
302C2×C4#1455650511yescharacteristic
303C2×C4#1455655612yes—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—21no—
309C22—42no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22—81no—
318C22#1798849211yescharacteristic
319C22C2×#1455650511yescharacteristic
320C22#1798856011yescharacteristic
321C4—21no—
322C4—22no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—162no—
327C4—5842no—
328C4—5844no—
329C4—5842no—
330C4#1798838112yes—
331C2—21no—
332C2—21no—
333C2—41no—
334C2—42no—
335C2—41no—
336C2#2261091511yescharacteristic
337C2C2×#1798838111yescharacteristic
338C2#2261160211yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC22×D4C22×D73
FittingC73×#1799C2
socleC22×C73C2×#99
prime radical, cosocleC22×D4×C73C23
hypercenter#1799D73
hypocenterC73#13299
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
5. C2×#14556591C4semidirect
10. #17988452C4semidirect
13. C4×C4⋊Dic73C4semidirect
32. #14556506Q8semidirect
174. C73#13299semidirect

Maximal subgroups

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

subgroupindex
#226151042
C4×#145565062
#226080552
C73×#17992
#1329973