Finite Group Databasebeta

← #22616447

Subgroups — #22616447

Order 9344.

490 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556582C211yesmaximal, characteristic, complemented
2#17988523C211yesmaximal, characteristic, complemented
3#17988523C211yesmaximal, characteristic, complemented
4#17988517C211yesmaximal, characteristic, complemented
5#17988512C211yesmaximal, characteristic, complemented
6#17988510C211yesmaximal, characteristic, complemented
7#17988501C211yesmaximal, characteristic
8#17988490C211yesmaximal, characteristic
9#17988482C211yesmaximal, characteristic, complemented
10#17988475C211yesmaximal, characteristic, complemented
11#17988475C211yesmaximal, characteristic, complemented
12#17988473C211yesmaximal, characteristic, complemented
13#17988460C211yesmaximal, characteristic, complemented
14#17988447C211yesmaximal, characteristic, complemented
15C2×#123×C73C211yesmaximal, characteristic
16#14556582—24no—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2211yescharacteristic
19C2×C4⋊Dic73C2211yescharacteristic
20C2×C4⋊Dic73C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×C22⋊Dic73C2211yescharacteristic
34C2×C22⋊Dic73C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
36C2×C4×Dic73C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45C22×D4×C73C2211yescharacteristic
46C23×C4×C73C2211yescharacteristic
47#123×C73—24no—
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C4⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73C2211yescharacteristic
53C22×Dic73C2311yescharacteristic
54C22×Dic73C2311yescharacteristic
55C22×Dic73C2311yescharacteristic
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C4⋊Dic73—22no—
62C4⋊Dic73—22no—
63C4⋊Dic73—22no—
64C4⋊Dic73—41no—
65#11924007—22no—
66#11924007—22no—
67#11924007—22no—
68#11924007—41no—
69#11924007—41no—
70#11924007—41no—
71C22⋊Dic73—22no—
72C22⋊Dic73—22no—
73C22⋊Dic73—22no—
74C22⋊Dic73—41no—
75C22⋊Dic73—41no—
76C22⋊Dic73—41no—
77C22⋊Dic73—41no—
78C22⋊Dic73—41no—
79C4×Dic73—22no—
80C4×Dic73—41no—
81C24×C73C2311yescharacteristic
82C24×C73C2311yescharacteristic
83C2×D4×C73—22no—
84C2×D4×C73—22no—
85C2×D4×C73—41no—
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
94C4⋊C4×C73—22no—
95C4⋊C4×C73D414yes—
96C22⋊C4×C73—22no—
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—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—21no—
112C23×C73#4112yes—
113C23×C73C2411yescharacteristic
114D4×C73—44no—
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—44no—
128C2×C4×C73C2×D412yes—
129C2×C4×C73C2×D412yes—
130C2×C4×C73C2×D412yes—
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×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—21no—
151C2×Dic73—21no—
152C2×Dic73—21no—
153C2×Dic73—21no—
154C2×Dic73#4112yes—
155C22×C73—22no—
156C22×C73—22no—
157C22×C73—22no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73C22×D411yescharacteristic
170C22×C73C2×#4111yescharacteristic
171C22×C73C2×#4111yescharacteristic
172C22×C73H(5,𝔽2)11yescharacteristic
173C22×C73H(5,𝔽2)11yescharacteristic
174C22×C732−1+411yescharacteristic
175C22×C732−1+411yescharacteristic
176C4×C73—22no—
177C4×C73—22no—
178C4×C73—22no—
179C4×C73—41no—
180C4×C73—41no—
181Dic73—22no—
182Dic73—41no—
183Dic73—41no—
184Dic73—41no—
185Dic73—41no—
186Dic73—41no—
187Dic73—41no—
188Dic73—41no—
189C2×C73—42no—
190C2×C73—81no—
191C2×C73#53611yescharacteristic
192C2×C73#53911yescharacteristic
193C2×C73#53911yescharacteristic
194C2×C73#54611yescharacteristic
195C2×C73#55011yescharacteristic
196C2×C73#55211yescharacteristic
197C2×C73#56211yescharacteristic
198#2694—731nomaximal, Sylow
199C73#269411yescharacteristic, complemented, Sylow
200C2×#125—731no—
201C2×#123D7311yescharacteristic
202#399—731no—
203#399—731no—
204#398—731no—
205#397—731no—
206#396—731no—
207#394—731no—
208#390—731no—
209#389—731no—
210#388—731no—
211#388—731no—
212#387—731no—
213#385—731no—
214#380—731no—
215C22×D4C2×D7311yescharacteristic
216C23×C4C2×D7311yescharacteristic
217#125—1464no—
218#123—24no—
219C2×C4⋊C4—731no—
220C2×C4⋊C4—731no—
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⋊C4—731no—
229C2×C4⋊C4C2×D7311yescharacteristic
230C2×C4⋊C4C2×D7311yescharacteristic
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⋊C4—731no—
239C2×C22⋊C4C2×D7311yescharacteristic
240C2×C22⋊C4C2×D7311yescharacteristic
241C2×C22⋊C4C2×D7311yescharacteristic
242C2×C42—731no—
243C2×C42—731no—
244#95—731no—
245#95—731no—
246#95—731no—
247#95—731no—
248#95—731no—
249#95—731no—
250#95—731no—
251#95—731no—
252C24C22×D7311yescharacteristic
253C24C22×D7311yescharacteristic
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—41no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—731no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4—731no—
264C22×C4—731no—
265C22×C4—731no—
266C22×C4—731no—
267C22×C4—731no—
268C22×C4C22×D7311yescharacteristic
269C22×C4C22×D7311yescharacteristic
270C22×C4C22×D7311yescharacteristic
271C22×C4C22×D7311yescharacteristic
272C22×C4C22×D7311yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—2921no—
275C4⋊C4—2921no—
276C4⋊C4—2921no—
277C4⋊C4—2921no—
278C4⋊C4—1462no—
279C4⋊C4—1462no—
280C4⋊C4—1462no—
281C4⋊C4—1462no—
282C4⋊C4—1462no—
283C4⋊C4—1462no—
284C4⋊C4C22⋊D7314yes—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—2921no—
289C22⋊C4—2921no—
290C22⋊C4—2921no—
291C22⋊C4—2921no—
292C22⋊C4—2921no—
293C22⋊C4—1462no—
294C22⋊C4—1462no—
295C22⋊C4—1462no—
296C42—2921no—
297C42—1462no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23#1192402712yes—
312C23C23×D7311yescharacteristic
313D4—44no—
314C2×C4—21no—
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—44no—
327C2×C4—732no—
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×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×C4C2×C22⋊D7312yes—
352C2×C4C2×C22⋊D7312yes—
353C2×C4C2×C22⋊D7312yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22C22×C22⋊D7311yescharacteristic
369C22#41×D7311yescharacteristic
370C22C2×#1192402711yescharacteristic
371C22#1455663611yescharacteristic
372C22#1455663711yescharacteristic
373C22#1455663811yescharacteristic
374C22#1455663811yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—2921no—
381C4—2921no—
382C4—2921no—
383C4—2921no—
384C4—2921no—
385C4—2921no—
386C4—2921no—
387C4—1462no—
388C2—42no—
389C2—81no—
390C2#1798915811yescharacteristic
391C2#1798918011yescharacteristic
392C2#1798918111yescharacteristic
393C2#1798923111yescharacteristic
394C2#1798925611yescharacteristic
395C2#1798927411yescharacteristic
396C2#1798933411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#123×C73C2
hypercenterC2×#123D73
hypocenterC73#2694
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#14556582C2semidirect
2. #17988523C2semidirect
3. #17988523C2semidirect
4. #17988517C2semidirect
5. #17988512C2semidirect
6. #17988510C2semidirect
9. #17988482C2semidirect
10. #17988475C2semidirect
11. #17988475C2semidirect
12. #17988473C2semidirect
13. #17988460C2semidirect
14. #17988447C2semidirect
199. C73#2694semidirect