Finite Group Databasebeta

← #22616628

Subgroups — #22616628

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×#14556576C211yesmaximal, characteristic
2#17988520C211yesmaximal, characteristic, complemented
3#17988513C211yesmaximal, characteristic, complemented
4#17988509C211yesmaximal, characteristic, complemented
5#17988509C211yesmaximal, characteristic, complemented
6#17988509C211yesmaximal, characteristic, complemented
7#17988504C211yesmaximal, characteristic
8#17988489C211yesmaximal, characteristic
9#17988486C211yesmaximal, characteristic, complemented
10#17988477C211yesmaximal, characteristic, complemented
11#17988477C211yesmaximal, characteristic, complemented
12#17988471C211yesmaximal, characteristic, complemented
13#17988458C211yesmaximal, characteristic, complemented
14#17988444C211yesmaximal, characteristic, complemented
15C2×#125×C73C211yesmaximal, characteristic, complemented
16C22×D292C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18#14556576—24no—
19C2×C4⋊Dic73C2211yescharacteristic
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×C4×Dic73C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#125×C73—24no—
46C2×C4⋊C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C4⋊C4×C73C2211yescharacteristic
50C2×C4⋊C4×C73C2211yescharacteristic
51C2×C4⋊C4×C73C2211yescharacteristic
52C2×C42×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C23×D73C2311yescharacteristic
55C2×D292—22no—
56C2×D292—22no—
57C2×D292—41no—
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C2×C4×D73—22no—
65C2×C4×D73—22no—
66C2×C4×D73—41no—
67C4⋊Dic73—41no—
68C4⋊Dic73—41no—
69C4⋊Dic73—41no—
70#11924007—22no—
71#11924007—22no—
72#11924007—41no—
73#11924005—22no—
74#11924005—22no—
75#11924005—22no—
76#11924005—22no—
77#11924005—22no—
78#11924005—22no—
79#11924005—41no—
80#11924005—41no—
81#11924005—41no—
82#11924005—41no—
83#11924005—41no—
84C4×Dic73—41no—
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C4⋊C4×C73—22no—
93C4⋊C4×C73—22no—
94C4⋊C4×C73—22no—
95C4⋊C4×C73—22no—
96C4⋊C4×C73—22no—
97C4⋊C4×C73D414yes—
98C42×C73—22no—
99C23×C73C2411yescharacteristic
100C22×D73—21no—
101C22×D73—21no—
102C22×D73—21no—
103C22×D73—21no—
104C22×D73—21no—
105C22×D73—21no—
106C22×D73—21no—
107C22×D73—21no—
108C22×D73—21no—
109C22×D73—21no—
110C22×D73—21no—
111C22×D73—21no—
112C22×D73—21no—
113C22×D73#4112yes—
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—21no—
131C2×C4×C73C2×D412yes—
132C2×C4×C73C2×D412yes—
133C2×C4×C73C2×D412yes—
134C2×C4×C73#4112yes—
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—
153D292—44no—
154C4×D73—44no—
155C22×C73C22×D411yescharacteristic
156C22×C73C2×#4111yescharacteristic
157C22×C73C2×#4111yescharacteristic
158C22×C73H(5,𝔽2)11yescharacteristic
159C22×C73H(5,𝔽2)11yescharacteristic
160C22×C732−1+411yescharacteristic
161C22×C732−1+411yescharacteristic
162C2×D73—22no—
163C2×D73—22no—
164C2×D73—22no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C2×D73—41no—
172C2×D73—41no—
173C2×D73—41no—
174C2×D73—41no—
175C2×D73—41no—
176C4×C73—22no—
177C4×C73—22no—
178C4×C73—22no—
179C4×C73—22no—
180C4×C73—41no—
181C4×C73—41no—
182C4×C73—41no—
183Dic73—41no—
184Dic73—41no—
185Dic73—41no—
186Dic73—41no—
187Dic73—41no—
188Dic73—41no—
189C2×C73#53711yescharacteristic
190C2×C73#53911yescharacteristic
191C2×C73#54011yescharacteristic
192C2×C73#54611yescharacteristic
193C2×C73#54811yescharacteristic
194C2×C73#55211yescharacteristic
195C2×C73#56311yescharacteristic
196D73—42no—
197D73—81no—
198#2707—731nomaximal, Sylow
199C73#270711yescharacteristic, complemented, Sylow
200C2×#125D7311yescharacteristic, complemented
201C2×#123—731no—
202#398—731no—
203#397—731no—
204#396—731no—
205#396—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×D4—731no—
216C23×C4—731no—
217#125—24no—
218#123—1464no—
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⋊C4C2×D7311yescharacteristic
226C2×C4⋊C4C2×D7311yescharacteristic
227C2×C4⋊C4C2×D7311yescharacteristic
228C2×C4⋊C4C2×D7311yescharacteristic
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⋊C4—731no—
240C2×C22⋊C4—731no—
241C2×C22⋊C4—731no—
242C2×C42—731no—
243C2×C42C2×D7311yescharacteristic
244#95—731no—
245#95—731no—
246#95—731no—
247#95—731no—
248#95—731no—
249#95—731no—
250#95—731no—
251#95—731no—
252C24—731no—
253C24—731no—
254C2×D4—2921no—
255C2×D4—1462no—
256C2×D4—1462no—
257C22×C4—2921no—
258C22×C4—731no—
259C22×C4—731no—
260C22×C4—731no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4—731no—
264C22×C4—1462no—
265C22×C4—1462no—
266C22×C4C22×D7311yescharacteristic
267C22×C4C22×D7311yescharacteristic
268C22×C4C22×D7311yescharacteristic
269C22×C4C22×D7311yescharacteristic
270C22×C4C22×D7311yescharacteristic
271C22×C4C22×D7311yescharacteristic
272C22×C4C22×D7311yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—2921no—
279C4⋊C4—2921no—
280C4⋊C4—2921no—
281C4⋊C4—2921no—
282C4⋊C4—1462no—
283C4⋊C4—1462no—
284C4⋊C4C22⋊D7314yes—
285C22⋊C4—2921no—
286C22⋊C4—2921no—
287C22⋊C4—2921no—
288C22⋊C4—2921no—
289C22⋊C4—2921no—
290C22⋊C4—1462no—
291C22⋊C4—1462no—
292C22⋊C4—1462no—
293C22⋊C4—1462no—
294C22⋊C4—1462no—
295C22⋊C4—1462no—
296C42—22no—
297C42—2921no—
298C23—732no—
299C23—1461no—
300C23—1461no—
301C23—1461no—
302C23—1461no—
303C23—1461no—
304C23—1461no—
305C23—1461no—
306C23—1461no—
307C23—1461no—
308C23—1461no—
309C23—1461no—
310C23—1461no—
311C23—1461no—
312C23C23×D7311yescharacteristic
313D4—2924no—
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—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—2924no—
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×C4C2×C22⋊D7312yes—
351C2×C4C2×C22⋊D7312yes—
352C2×C4C2×C22⋊D7312yes—
353C2×C4#1192402912yes—
354C22—2921no—
355C22—2921no—
356C22—2921no—
357C22—2921no—
358C22—2921no—
359C22—2921no—
360C22—2921no—
361C22—2921no—
362C22—2921no—
363C22—2921no—
364C22—2921no—
365C22—1462no—
366C22—1462no—
367C22—1462no—
368C22C22×C22⋊D7311yescharacteristic
369C22#41×D7311yescharacteristic
370C22C2×#1192402911yescharacteristic
371C22#1455663711yescharacteristic
372C22#1455663711yescharacteristic
373C22#1455663811yescharacteristic
374C22#1455663911yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—2921no—
383C4—2921no—
384C4—2921no—
385C4—2921no—
386C4—2921no—
387C4—2921no—
388C2—2922no—
389C2—5841no—
390C2#1798916511yescharacteristic
391C2#1798918511yescharacteristic
392C2#1798919311yescharacteristic
393C2#1798922511yescharacteristic
394C2#1798924811yescharacteristic
395C2#1798927511yescharacteristic
396C2#1798934111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#125×C73C2
hypercenterC2×#125D73
hypocenterC73#2707
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #17988520C2semidirect
3. #17988513C2semidirect
4. #17988509C2semidirect
5. #17988509C2semidirect
6. #17988509C2semidirect
9. #17988486C2semidirect
10. #17988477C2semidirect
11. #17988477C2semidirect
12. #17988471C2semidirect
13. #17988458C2semidirect
14. #17988444C2semidirect
15. C2×#125×C73C2semidirect
199. C73#2707semidirect
200. C2×#125D73semidirect