Finite Group Databasebeta

← #22613607

Subgroups — #22613607

Order 9344.

528 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556570C211yesmaximal, characteristic
2C2×#14556550C211yesmaximal, characteristic
3#17988529C211yesmaximal, characteristic, complemented
4#17988521C211yesmaximal, characteristic, complemented
5#17988519C211yesmaximal, characteristic, complemented
6#17988508C211yesmaximal, characteristic, complemented
7#17988491C211yesmaximal, characteristic, complemented
8#17988484C211yesmaximal, characteristic, complemented
9#17988474C211yesmaximal, characteristic, complemented
10#17988470C211yesmaximal, characteristic, complemented
11#17988460C211yesmaximal, characteristic
12#17988460C211yesmaximal, characteristic
13#17988450C211yesmaximal, characteristic
14#17988447C211yesmaximal, characteristic
15C2×#95×C73C211yesmaximal, characteristic
16C22×Dic146C2211yescharacteristic
17#14556570—24no—
18#14556550—24no—
19C2×C4⋊Dic73C2211yescharacteristic
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×C4⋊Dic73C2211yescharacteristic
23C2×C4⋊Dic73C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×C22⋊Dic73C2211yescharacteristic
34C2×C4×Dic73C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C23×C4×C73C2211yescharacteristic
47C23×C4×C73C2211yescharacteristic
48C23×C4×C73C2211yescharacteristic
49#95×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C2×Dic146—22no—
54C2×Dic146—22no—
55C2×Dic146—41no—
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C4⋊Dic73—22no—
65C4⋊Dic73—22no—
66C4⋊Dic73—22no—
67C4⋊Dic73—22no—
68C4⋊Dic73—41no—
69#11924007—22no—
70#11924007—22no—
71#11924007—22no—
72#11924007—22no—
73#11924007—41no—
74#11924007—41no—
75C22⋊Dic73—22no—
76C22⋊Dic73—22no—
77C22⋊Dic73—22no—
78C22⋊Dic73D414yes—
79C4×Dic73—22no—
80C4×Dic73—22no—
81C24×C73C2311yescharacteristic
82C22×C4×C73—22no—
83C22×C4×C73—22no—
84C22×C4×C73—22no—
85C22×C4×C73—22no—
86C22×C4×C73—22no—
87C22×C4×C73—22no—
88C22×C4×C73—41no—
89C22×C4×C73—41no—
90C22×C4×C73Q814yescomplemented
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96C22×C4×C73C2311yescharacteristic
97C23×C73—21no—
98C23×C73—21no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73C2×D412yes—
102C23×C73C2×Q812yes—
103C23×C73#4112yes—
104C23×C73C2411yescharacteristic
105C2×C4×C73—28no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
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—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—44no—
121C2×C4×C73—44no—
122C2×C4×C73C2×Q812yes—
123C2×C4×C73C2×Q812yes—
124C2×C4×C73#4112yes—
125C2×C4×C73#4112yes—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73C2×D412yes—
149C2×Dic73C2×D412yes—
150Dic146—44no—
151C22×C73—22no—
152C22×C73—22no—
153C22×C73—22no—
154C22×C73—22no—
155C22×C73—22no—
156C22×C73—22no—
157C22×C73C22⋊Q814yes—
158C22×C73C22×D411yescharacteristic
159C22×C73C22×Q811yescharacteristic
160C22×C73C2×#4111yescharacteristic
161C22×C73C2×#4111yescharacteristic
162C22×C73C2×#4111yescharacteristic
163C22×C73H(5,𝔽2)11yescharacteristic
164C22×C732−1+411yescharacteristic
165C4×C73—22no—
166C4×C73—22no—
167C4×C73—22no—
168C4×C73—22no—
169C4×C73—41no—
170C4×C73—41no—
171Dic73—22no—
172Dic73—22no—
173Dic73—41no—
174Dic73—41no—
175Dic73—41no—
176Dic73—41no—
177Dic73—41no—
178Dic73—41no—
179C2×C73—24no—
180C2×C73C2×C22⋊Q811yescharacteristic
181C2×C73#53311yescharacteristic
182C2×C73#54411yescharacteristic
183C2×C73#54611yescharacteristic
184C2×C73#54711yescharacteristic
185C2×C73#55111yescharacteristic
186C2×C73#55211yescharacteristic
187#2438—731nomaximal, Sylow
188C73#243811yescharacteristic, complemented, Sylow
189C2×C22⋊Q8—731no—
190C2×#117—731no—
191#400—731no—
192#398—731no—
193#398—731no—
194#395—731no—
195#391—731no—
196#389—731no—
197#387—731no—
198#387—731no—
199#385—731no—
200#385—731no—
201#381—731no—
202#380—731no—
203C2×#95D7311yescharacteristic
204C22×Q8—731no—
205C23×C4C2×D7311yescharacteristic
206C23×C4C2×D7311yescharacteristic
207C23×C4C2×D7311yescharacteristic
208C22⋊Q8—1464no—
209#117—1464no—
210C2×C4⋊C4—731no—
211C2×C4⋊C4—731no—
212C2×C4⋊C4—731no—
213C2×C4⋊C4—731no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4—731no—
217C2×C4⋊C4—731no—
218C2×C4⋊C4—731no—
219C2×C4⋊C4—731no—
220C2×C4⋊C4—731no—
221C2×C22⋊C4—731no—
222C2×C22⋊C4—731no—
223C2×C22⋊C4—731no—
224C2×C22⋊C4—731no—
225C2×C42—731no—
226C2×C42—731no—
227#95—731no—
228#95—731no—
229#95—731no—
230#95—731no—
231#95—731no—
232#95—731no—
233#95—731no—
234#95—731no—
235#95—731no—
236#95—731no—
237#95C2×D7311yescharacteristic
238#95C2×D7311yescharacteristic
239#95C2×D7311yescharacteristic
240#95C2×D7311yescharacteristic
241C24C22×D7311yescharacteristic
242C2×Q8—2921no—
243C2×Q8—1462no—
244C2×Q8—1462no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—731no—
254C22×C4—731no—
255C22×C4—731no—
256C22×C4—731no—
257C22×C4—731no—
258C22×C4—731no—
259C22×C4—731no—
260C22×C4—731no—
261C22×C4Dic14614yescomplemented
262C22×C4C22×D7311yescharacteristic
263C22×C4C22×D7311yescharacteristic
264C22×C4C22×D7311yescharacteristic
265C22×C4C22×D7311yescharacteristic
266C22×C4C22×D7311yescharacteristic
267C22×C4C22×D7311yescharacteristic
268C4⋊C4—2921no—
269C4⋊C4—2921no—
270C4⋊C4—2921no—
271C4⋊C4—1462no—
272C4⋊C4—1462no—
273C4⋊C4—1462no—
274C4⋊C4—1462no—
275C4⋊C4—1462no—
276C4⋊C4—1462no—
277C4⋊C4—1462no—
278C4⋊C4—1462no—
279C22⋊C4—734no—
280C22⋊C4—1462no—
281C22⋊C4—1462no—
282C22⋊C4—1462no—
283C42—1462no—
284C42—1462no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23D4×D7312yes—
290C23C2×Dic14612yes—
291C23#1192402712yes—
292C23C23×D7311yescharacteristic
293Q8—2924no—
294C2×C4—28no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—732no—
312C2×C4—732no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4—1461no—
324C2×C4—1461no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4C2×Dic14612yes—
336C2×C4C2×Dic14612yes—
337C2×C4#1192402812yes—
338C2×C4#1192402812yes—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22#1455656814yes—
346C22C2×D4×D7311yescharacteristic
347C22C22×Dic14611yescharacteristic
348C22C2×#1192402711yescharacteristic
349C22C2×#1192402811yescharacteristic
350C22C2×#1192402811yescharacteristic
351C22#1455663611yescharacteristic
352C22#1455663911yescharacteristic
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—2921no—
360C4—2921no—
361C4—2921no—
362C4—2921no—
363C4—2921no—
364C4—2921no—
365C4—1462no—
366C4—1462no—
367C2—24no—
368C2C2×#1455656811yescharacteristic
369C2#1798914411yescharacteristic
370C2#1798921811yescharacteristic
371C2#1798922711yescharacteristic
372C2#1798923811yescharacteristic
373C2#1798926311yescharacteristic
374C2#1798927211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#95×C73C2
hypercenterC2×#95D73
hypocenterC73#2438
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #17988529C2semidirect
4. #17988521C2semidirect
5. #17988519C2semidirect
6. #17988508C2semidirect
7. #17988491C2semidirect
8. #17988484C2semidirect
9. #17988474C2semidirect
10. #17988470C2semidirect
90. C22×C4×C73Q8semidirect
188. C73#2438semidirect
261. C22×C4Dic146semidirect