Finite Group Databasebeta

← #22613610

Subgroups — #22613610

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×#14556569C211yesmaximal, characteristic
2C2×#14556549C211yesmaximal, characteristic
3#17988521C211yesmaximal, characteristic, complemented
4#17988520C211yesmaximal, characteristic, complemented
5#17988508C211yesmaximal, characteristic, complemented
6#17988491C211yesmaximal, characteristic, complemented
7#17988483C211yesmaximal, characteristic, complemented
8#17988472C211yesmaximal, characteristic, complemented
9#17988469C211yesmaximal, characteristic, complemented
10#17988461C211yesmaximal, characteristic
11#17988461C211yesmaximal, characteristic
12#17988449C211yesmaximal, characteristic
13#17988446C211yesmaximal, characteristic
14#95×D73C211yesmaximal, characteristic
15#400×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20#14556569—24no—
21#14556549—24no—
22C2×C4⋊Dic73C2211yescharacteristic
23C2×C4⋊Dic73C2211yescharacteristic
24C2×C4⋊Dic73C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×#11924007C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
36C2×C4×Dic73C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C2×C4⋊C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48#95×C73C2211yescharacteristic
49#95×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C2×Dic146—22no—
55C2×Dic146—22no—
56C2×Dic146—41no—
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C2×C4×D73—22no—
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×D73Q814yescomplemented
73C4⋊Dic73—22no—
74C4⋊Dic73—22no—
75C4⋊Dic73—22no—
76#11924007—22no—
77#11924007—22no—
78#11924007—22no—
79#11924007—41no—
80#11924007—41no—
81#11924007—41no—
82#11924005—22no—
83#11924005—22no—
84#11924005—22no—
85#11924005D414yes—
86C4×Dic73—22no—
87C4×Dic73—22no—
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C4⋊C4×C73—22no—
96C4⋊C4×C73—22no—
97C23×C73C2411yescharacteristic
98C22×D73—21no—
99C22×D73—21no—
100C22×D73—21no—
101C22×D73—21no—
102C22×D73C2×D412yes—
103C22×D73C2×Q812yes—
104C22×D73#4112yes—
105C2×C4×C73—21no—
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—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73C2×D412yes—
125C2×C4×C73C2×Q812yes—
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×Dic73C2×D412yes—
144C2×Dic73C2×Q812yes—
145C2×Dic73#4112yes—
146C2×Dic73#4112yes—
147C4×D73—28no—
148C4×D73—44no—
149C4×D73—44no—
150Dic146—44no—
151C22×C73C22×D411yescharacteristic
152C22×C73C22×Q811yescharacteristic
153C22×C73C2×#4111yescharacteristic
154C22×C73C2×#4111yescharacteristic
155C22×C73C2×#4111yescharacteristic
156C22×C73H(5,𝔽2)11yescharacteristic
157C22×C732−1+411yescharacteristic
158C2×D73—22no—
159C2×D73—22no—
160C2×D73—22no—
161C2×D73—22no—
162C2×D73—22no—
163C2×D73—22no—
164C2×D73C22⋊Q814yes—
165C4×C73—22no—
166C4×C73—22no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73—41no—
171C4×C73—41no—
172Dic73—22no—
173Dic73—22no—
174Dic73—22no—
175Dic73—22no—
176Dic73—41no—
177Dic73—41no—
178Dic73—41no—
179C2×C73C2×C22⋊Q811yescharacteristic
180C2×C73#53311yescharacteristic
181C2×C73#54411yescharacteristic
182C2×C73#54611yescharacteristic
183C2×C73#54711yescharacteristic
184C2×C73#55111yescharacteristic
185C2×C73#55211yescharacteristic
186D73—24no—
187#2438—731nomaximal, Sylow
188C73#243811yescharacteristic, complemented, Sylow
189C2×C22⋊Q8—731no—
190C2×#117—731no—
191#400D7311yescharacteristic, complemented
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×#95—731no—
204C22×Q8—731no—
205C23×C4—731no—
206C23×C4—731no—
207C23×C4—731no—
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⋊C4C2×D7311yescharacteristic
220C2×C4⋊C4C2×D7311yescharacteristic
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#95C2×D7311yescharacteristic
237#95C2×D7311yescharacteristic
238#95C2×D7311yescharacteristic
239#95C2×D7311yescharacteristic
240#95C2×D7311yescharacteristic
241C24—731no—
242C2×Q8—2921no—
243C2×Q8—1462no—
244C2×Q8—1462no—
245C22×C4—2921no—
246C22×C4—2921no—
247C22×C4—731no—
248C22×C4—731no—
249C22×C4—731no—
250C22×C4—731no—
251C22×C4—734no—
252C22×C4—731no—
253C22×C4—731no—
254C22×C4—731no—
255C22×C4—1462no—
256C22×C4—1462no—
257C22×C4—1462no—
258C22×C4—1462no—
259C22×C4—1462no—
260C22×C4—1462no—
261C22×C4C22×D7311yescharacteristic
262C22×C4C22×D7311yescharacteristic
263C22×C4C22×D7311yescharacteristic
264C22×C4C22×D7311yescharacteristic
265C22×C4C22×D7311yescharacteristic
266C22×C4C22×D7311yescharacteristic
267C22×C4C22×D7311yescharacteristic
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—2921no—
271C4⋊C4—2921no—
272C4⋊C4—2921no—
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—732no—
286C23—732no—
287C23—732no—
288C23—1461no—
289C23—1461no—
290C23—1461no—
291C23—1461no—
292C23C23×D7311yescharacteristic
293Q8—2924no—
294C2×C4—21no—
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—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—2924no—
314C2×C4—2924no—
315C2×C4—732no—
316C2×C4—732no—
317C2×C4—732no—
318C2×C4—732no—
319C2×C4—1468no—
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×C4—1461no—
336C2×C4—1461no—
337C2×C4D4×D7312yes—
338C2×C4Q8×D7312yes—
339C22—734no—
340C22—1462no—
341C22—1462no—
342C22—1462no—
343C22—1462no—
344C22—1462no—
345C22—1462no—
346C22C2×D4×D7311yescharacteristic
347C22C2×Q8×D7311yescharacteristic
348C22#41×D7311yescharacteristic
349C22#41×D7311yescharacteristic
350C22#41×D7311yescharacteristic
351C22#1455663711yescharacteristic
352C22#1455663811yescharacteristic
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—2921no—
361C4—2921no—
362C4—2921no—
363C4—1462no—
364C4—1462no—
365C4—1462no—
366C4—1462no—
367C2—1464no—
368C2C22⋊Q8×D7311yescharacteristic
369C2#1798914311yescharacteristic
370C2#1798921711yescharacteristic
371C2#1798923011yescharacteristic
372C2#1798923511yescharacteristic
373C2#1798926211yescharacteristic
374C2#1798927311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2438
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #17988521C2semidirect
4. #17988520C2semidirect
5. #17988508C2semidirect
6. #17988491C2semidirect
7. #17988483C2semidirect
8. #17988472C2semidirect
9. #17988469C2semidirect
15. #400×C73C2semidirect
72. C2×C4×D73Q8semidirect
188. C73#2438semidirect
191. #400D73semidirect