Finite Group Databasebeta

← #22614031

Subgroups — #22614031

Order 9344.

532 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556574C211yesmaximal, characteristic
2C2×#14556549C211yesmaximal, characteristic, complemented
3#17988529C211yesmaximal, characteristic, complemented
4#17988513C211yesmaximal, characteristic, complemented
5#17988510C211yesmaximal, characteristic, complemented
6#17988502C211yesmaximal, characteristic
7#17988482C211yesmaximal, characteristic, complemented
8#17988482C211yesmaximal, characteristic, complemented
9#17988480C211yesmaximal, characteristic, complemented
10#17988476C211yesmaximal, characteristic, complemented
11#17988472C211yesmaximal, characteristic, complemented
12#17988463C211yesmaximal, characteristic
13#17988461C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic73C211yesmaximal, characteristic, complemented
15#385×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18#14556574—24no—
19#14556549—24no—
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
36C2×C4×Dic73C2211yescharacteristic
37C2×C4×Dic73C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C23×C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C2×C22⋊D73—22no—
55C2×C22⋊D73—22no—
56C2×C22⋊D73—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—
67C4⋊Dic73—22no—
68C4⋊Dic73—22no—
69#11924007—22no—
70#11924007—22no—
71#11924007—22no—
72#11924007—22no—
73#11924007—41no—
74C22⋊Dic73—22no—
75C22⋊Dic73—22no—
76C22⋊Dic73—22no—
77#11924005—22no—
78#11924005—22no—
79#11924005—22no—
80#11924005—41no—
81#11924005D414yes—
82C4×Dic73—22no—
83C4×Dic73—22no—
84C4×Dic73—41no—
85C24×C73C2311yescharacteristic
86C22×C4×C73—22no—
87C22×C4×C73—22no—
88C22×C4×C73—41no—
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—41no—
97C22⋊C4×C73—22no—
98C22⋊C4×C73—22no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73#4112yes—
106C23×C73C2411yescharacteristic
107C22×D73—21no—
108C22×D73—21no—
109C22×D73—21no—
110C22×D73—21no—
111C22×D73—21no—
112C22×D73—21no—
113C22×D73C2×D412yes—
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×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—44no—
131C2×C4×C73C2×D412yes—
132C2×C4×C73#4112yes—
133C22⋊D73—44no—
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×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—21no—
151C2×Dic73—21no—
152C2×Dic73C2×D412yes—
153C2×Dic73#4112yes—
154C2×Dic73#4112yes—
155C4×D73—28no—
156C22×C73—22no—
157C22×C73—22no—
158C22×C73—22no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73C22×D411yescharacteristic
164C22×C73C2×#4111yescharacteristic
165C22×C73C2×#4111yescharacteristic
166C22×C73C2×#4111yescharacteristic
167C22×C73C2×#4111yescharacteristic
168C22×C73H(5,𝔽2)11yescharacteristic
169C22×C732−1+411yescharacteristic
170C2×D73—22no—
171C2×D73—22no—
172C2×D73—22no—
173C2×D73—41no—
174C2×D73—41no—
175C2×D73—41no—
176C2×D73—41no—
177C4×C73—22no—
178C4×C73—22no—
179C4×C73—41no—
180C4×C73—41no—
181C4×C73—41no—
182C4×C73—41no—
183Dic73—22no—
184Dic73—22no—
185Dic73—22no—
186Dic73—41no—
187Dic73—41no—
188Dic73—41no—
189Dic73—41no—
190C2×C73—42no—
191C2×C73#52511yescharacteristic
192C2×C73#52911yescharacteristic
193C2×C73#54211yescharacteristic
194C2×C73#54611yescharacteristic
195C2×C73#54711yescharacteristic
196C2×C73#55211yescharacteristic
197C2×C73#55311yescharacteristic
198D73—42no—
199#2470—731nomaximal, Sylow
200C73#247011yescharacteristic, complemented, Sylow
201C2×#123—731no—
202C2×#117—731no—
203#400—731no—
204#397—731no—
205#396—731no—
206#394—731no—
207#389—731no—
208#389—731no—
209#388—731no—
210#388—731no—
211#387—731no—
212#386—731no—
213#385—731no—
214#385D7311yescharacteristic, complemented
215C4×C22⋊C4—731no—
216C22×D4—731no—
217C23×C4—731no—
218C23×C4C2×D7311yescharacteristic
219#123—1464no—
220#117—1464no—
221C2×C4⋊C4—731no—
222C2×C4⋊C4—731no—
223C2×C4⋊C4—731no—
224C2×C4⋊C4—731no—
225C2×C4⋊C4—731no—
226C2×C4⋊C4—731no—
227C2×C4⋊C4—731no—
228C2×C4⋊C4C2×D7311yescharacteristic
229C2×C4⋊C4C2×D7311yescharacteristic
230C2×C22⋊C4—731no—
231C2×C22⋊C4—731no—
232C2×C22⋊C4—731no—
233C2×C22⋊C4—731no—
234C2×C22⋊C4—731no—
235C2×C22⋊C4—731no—
236C2×C22⋊C4—731no—
237C2×C22⋊C4—731no—
238C2×C22⋊C4C2×D7311yescharacteristic
239C2×C22⋊C4C2×D7311yescharacteristic
240C2×C42—731no—
241C2×C42—731no—
242C2×C42—731no—
243#95—731no—
244#95—731no—
245#95—731no—
246#95—731no—
247#95—731no—
248#95—731no—
249#95—731no—
250#95—731no—
251#95C2×D7311yescharacteristic
252#95C2×D7311yescharacteristic
253C24—731no—
254C24C22×D7311yescharacteristic
255C2×D4—2921no—
256C2×D4—1462no—
257C2×D4—1462no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4—731no—
264C22×C4—731no—
265C22×C4—731no—
266C22×C4—731no—
267C22×C4—731no—
268C22×C4—1462no—
269C22×C4—1462no—
270C22×C4—1462no—
271C22×C4C22×D7311yescharacteristic
272C22×C4C22×D7311yescharacteristic
273C22×C4C22×D7311yescharacteristic
274C22×C4C22×D7311yescharacteristic
275C22×C4C22×D7311yescharacteristic
276C22×C4C22×D7311yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—2921no—
280C4⋊C4—1462no—
281C4⋊C4—1462no—
282C4⋊C4—1462no—
283C4⋊C4—1462no—
284C4⋊C4—1462no—
285C4⋊C4—1462no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—2921no—
289C22⋊C4—734no—
290C22⋊C4—1462no—
291C22⋊C4—1462no—
292C22⋊C4—1462no—
293C22⋊C4—1462no—
294C22⋊C4—1462no—
295C22⋊C4—1462no—
296C42—2921no—
297C42—1462no—
298C42—1462no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—732no—
306C23—1461no—
307C23—1461no—
308C23—1461no—
309C23—1461no—
310C23—1461no—
311C23—1461no—
312C23#1192402712yes—
313C23C23×D7311yescharacteristic
314D4—2924no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—44no—
332C2×C4—732no—
333C2×C4—732no—
334C2×C4—732no—
335C2×C4—1468no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4D4×D7312yes—
355C2×C4#1192402812yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—2921no—
364C22—2921no—
365C22—2921no—
366C22—2921no—
367C22—1462no—
368C22—1462no—
369C22—1462no—
370C22C2×D4×D7311yescharacteristic
371C22#41×D7311yescharacteristic
372C22#41×D7311yescharacteristic
373C22C2×#1192402711yescharacteristic
374C22C2×#1192402811yescharacteristic
375C22#1455663611yescharacteristic
376C22#1455663911yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—2921no—
384C4—2921no—
385C4—2921no—
386C4—2921no—
387C4—1462no—
388C4—1462no—
389C4—1462no—
390C2—42no—
391C2—2922no—
392C2#1798909611yescharacteristic
393C2#1798911411yescharacteristic
394C2#1798920711yescharacteristic
395C2#1798922411yescharacteristic
396C2#1798923911yescharacteristic
397C2#1798927211yescharacteristic
398C2#1798928711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2470
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#14556549C2semidirect
3. #17988529C2semidirect
4. #17988513C2semidirect
5. #17988510C2semidirect
7. #17988482C2semidirect
8. #17988482C2semidirect
9. #17988480C2semidirect
10. #17988476C2semidirect
11. #17988472C2semidirect
13. #17988461C2semidirect
14. C4×C22⋊Dic73C2semidirect
15. #385×C73C2semidirect
200. C73#2470semidirect
214. #385D73semidirect