Finite Group Databasebeta

← #22619402

Subgroups — #22619402

Order 9344.

484 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C2×#14556624C211yesmaximal, characteristic, complemented
2C2×#14556621C211yesmaximal, characteristic, complemented
3#17989133C211yesmaximal, characteristic
4C2×#14556556C211yesmaximal, characteristic, complemented
5#17988812C212yesmaximal, complemented
6#17988808C212yesmaximal, complemented
7#17988796C212yesmaximal, complemented
8#17988786C212yesmaximal, complemented
9#17988610C211yesmaximal, characteristic, complemented
10#17988586C211yesmaximal, characteristic, complemented
11#417×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C22×Dic146C2211yescharacteristic
14#14556624—24no—
15#14556621—24no—
16C2×Dic292C2212yes—
17C2×#11924018C2212yes—
18C2×#11924017C2212yes—
19C2×#11924016C2212yes—
20C2×#11924012C2211yescharacteristic
21#14556589C2211yescharacteristic
22#14556587C2211yescharacteristic
23#14556580C2211yescharacteristic
24#14556578C2211yescharacteristic
25#14556563—21no—
26#14556563—21no—
27#14556556—21no—
28#14556556—21no—
29#14556556C2212yes—
30#14556556C2212yes—
31C4×C22⋊D73—21no—
32C4×C22⋊D73—21no—
33C2×#11924007—21no—
34C2×C4×Dic73—21no—
35C2×C4×Dic73C2211yescharacteristic
36#14556520C2212yes—
37#14556520C2212yes—
38#14556514C2212yes—
39#14556511C2212yes—
40C2×#41×C73C2211yescharacteristic
41C2×M16×C73C2211yescharacteristic
42C2×C4⋊C4×C73C2211yescharacteristic
43#103×C73C2212yes—
44#102×C73C2212yes—
45#11924028—22no—
46#11924028—22no—
47C2×Dic146—21no—
48C2×Dic146—22no—
49C2×Dic146D414yescomplemented
50C2×Dic146C2311yescharacteristic
51C2×Dic146C2312yes—
52C2×D292C2311yescharacteristic
53C2×C22⋊D73—21no—
54C2×C22⋊D73—21no—
55C2×C22⋊D73—21no—
56C22×Dic73—21no—
57C22×Dic73D411yescharacteristic
58C22×Dic73D411yescharacteristic
59C2×C4×D73—21no—
60Dic292—24no—
61#11924018—24no—
62#11924017—24no—
63#11924016—24no—
64#11924012—22no—
65C2×#10596831C2312yes—
66#11924007—22no—
67#11924007—22no—
68#11924007—21no—
69#11924007—21no—
70C22⋊Dic73—21no—
71C22⋊Dic73—21no—
72#11924005—21no—
73#11924005—21no—
74C4×Dic73—22no—
75C4×Dic73—22no—
76C4×Dic73D411yescharacteristic
77C4×Dic73D411yescharacteristic
78C4×Dic73C2311yescharacteristic
79C4×Dic73C2311yescharacteristic
80#41×C73—22no—
81#41×C73—22no—
82C2×Q8×C73C2311yescharacteristic
83C2×D4×C73—21no—
84C2×D4×C73C2311yescharacteristic
85C22×C4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73C2311yescharacteristic
88M16×C73—22no—
89C2×C8×C73C2312yes—
90C4⋊C4×C73—21no—
91C4⋊C4×C73C2312yes—
92C23×C73—21no—
93C23×C73C2×D411yescharacteristic
94C22×D73—21no—
95Q8×C73—21no—
96Q8×C73—21no—
97D4×C73—21no—
98D4×C73—21no—
99D4×C73—42no—
100C2×C4×C73—22no—
101C2×C4×C73—21no—
102C2×C4×C73—42no—
103C2×C4×C73—42no—
104C2×C4×C73C2×D411yescharacteristic
105C2×C4×C73C2×D412yes—
106C2×C4×C73#4112yes—
107C2×C4×C73C2411yescharacteristic
108C22⋊D73—42no—
109C22⋊D73—42no—
110C22⋊D73—42no—
111C2×Dic73—24no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73—21no—
115C2×Dic73—41no—
116C2×Dic73C2×D411yescharacteristic
117C2×Dic73C2×D411yescharacteristic
118C2×Dic73C2×D411yescharacteristic
119C2×Dic73C2×D411yescharacteristic
120D292—21no—
121D292—21no—
122C4×D73—42no—
123Dic146—24no—
124Dic146—22no—
125Dic146—21no—
126Dic146—21no—
127Dic146C2×D414yes—
128C8×C73—22no—
129#10596831—22no—
130C22×C73—21no—
131C22×C73—21no—
132C22×C73—41no—
133C22×C73—41no—
134C22×C73—41no—
135C22×C73#12112yes—
136C22×C73C22×D411yescharacteristic
137C2×D73—41no—
138C2×D73—41no—
139C2×D73—41no—
140C4×C73—41no—
141C4×C73—42no—
142C4×C73#12112yes—
143C4×C73C22×D411yescharacteristic
144C4×C73C2×#4111yescharacteristic
145Dic73—24no—
146Dic73—21no—
147Dic73—21no—
148Dic73—21no—
149Dic73—41no—
150Dic73#13712yescomplemented
151C2×C73—22no—
152C2×C73—81no—
153C2×C73C2×#12111yescharacteristic
154C2×C73C2×#13711yescharacteristic
155C2×C73#57511yescharacteristic
156D73—81no—
157#3037—731nomaximal, Sylow
158C73#303711yescharacteristic, complemented, Sylow
159C2×#137—731no—
160C2×#137—731no—
161#532—731no—
162C2×C4×Q8—731no—
163#464—732no—
164#464—732no—
165#462—732no—
166#460—732no—
167#423—731no—
168#417—731no—
169#417D7311yescharacteristic, complemented
170C2×#41—731no—
171C2×#41C2×D7311yescharacteristic
172C22×Q8—731no—
173#137—1464no—
174#137—1464no—
175C2×Q16—732no—
176C2×Q16—732no—
177C2×SD16—732no—
178C2×SD16—732no—
179C2×M16—731no—
180C2×M16C2×D7311yescharacteristic
181C4⋊Q8—731no—
182#127—731no—
183#124—731no—
184#124—731no—
185#121—1461no—
186#121—1461no—
187C4×Q8—732no—
188C4×Q8—732no—
189C4×Q8—1461no—
190C4×Q8—1461no—
191C4×D4—1461no—
192C4×D4—1461no—
193C2×C4⋊C4—1461no—
194C2×C4⋊C4C2×D7311yescharacteristic
195C2×C42—731no—
196C2×C42—1461no—
197C4⋊C8—732no—
198C4⋊C8—732no—
199#103—732no—
200#103C2×D7312yes—
201#102—732no—
202#102C2×D7312yes—
203#41—22no—
204#41—22no—
205#41—1462no—
206#41—1462no—
207C2×Q8—734no—
208C2×Q8—732no—
209C2×Q8—731no—
210C2×Q8—1461no—
211C2×Q8—1462no—
212C2×Q8C22×D7311yescharacteristic
213C2×D4—21no—
214C2×D4—731no—
215C2×D4—1461no—
216C2×D4—1461no—
217C2×D4—1461no—
218C2×D4C22×D7311yescharacteristic
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—731no—
222C22×C4—731no—
223C22×C4—1461no—
224C22×C4—1461no—
225C22×C4C22×D7311yescharacteristic
226Q16—1464no—
227Q16—1464no—
228SD16—1464no—
229SD16—1464no—
230M16—22no—
231M16—1462no—
232C2×C8—732no—
233C2×C8C22×D7312yes—
234C4⋊C4—21no—
235C4⋊C4—1462no—
236C4⋊C4—1462no—
237C4⋊C4—1461no—
238C4⋊C4—1461no—
239C4⋊C4C22×D7312yes—
240C22⋊C4—1461no—
241C22⋊C4—1461no—
242C22⋊C4—1461no—
243C22⋊C4—1461no—
244C42—731no—
245C42—731no—
246C42—731no—
247C42—731no—
248C42—1462no—
249C42—1462no—
250C23—21no—
251C23—1461no—
252C23D4×D7311yescharacteristic
253Q8—21no—
254Q8—21no—
255Q8—734no—
256Q8—1461no—
257Q8—1461no—
258Q8—1464no—
259Q8—1462no—
260D4—21no—
261D4—21no—
262D4—42no—
263D4—2922no—
264D4—2922no—
265D4—2922no—
266D4—1461no—
267D4—1461no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—2922no—
273C2×C4—2921no—
274C2×C4—731no—
275C2×C4—731no—
276C2×C4—731no—
277C2×C4—731no—
278C2×C4—1461no—
279C2×C4—1462no—
280C2×C4—1464no—
281C2×C4—1462no—
282C2×C4D4×D7311yescharacteristic
283C2×C4D4×D7312yes—
284C2×C4#1192402812yes—
285C2×C4C23×D7311yescharacteristic
286C8—22no—
287C8—1462no—
288C22—21no—
289C22—21no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—2921no—
294C22—2921no—
295C22—2921no—
296C22#1455656412yes—
297C22C2×D4×D7311yescharacteristic
298C4—42no—
299C4—41no—
300C4—2921no—
301C4—732no—
302C4—1461no—
303C4—1461no—
304C4—1461no—
305C4—1464no—
306C4#1455656412yes—
307C4C2×D4×D7311yescharacteristic
308C4C2×#1192402811yescharacteristic
309C2—22no—
310C2—81no—
311C2—5841no—
312C2C2×#1455656411yescharacteristic
313C2#137×D7311yescharacteristic
314C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#417×C73C2
socleC22×C73C22×D4
hypercenter#417D73
hypocenterC73#3037
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#14556624C2semidirect
2. C2×#14556621C2semidirect
4. C2×#14556556C2semidirect
5. #17988812C2semidirect
6. #17988808C2semidirect
7. #17988796C2semidirect
8. #17988786C2semidirect
9. #17988610C2semidirect
10. #17988586C2semidirect
11. #417×C73C2semidirect
49. C2×Dic146D4semidirect
150. Dic73#137semidirect
158. C73#3037semidirect
169. #417D73semidirect