Finite Group Databasebeta

← #22617869

Subgroups — #22617869

Order 9344.

470 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17988505C211yesmaximal, characteristic, complemented
2#17988504C211yesmaximal, characteristic, complemented
3#17988503C211yesmaximal, characteristic, complemented
4#17988502C211yesmaximal, characteristic, complemented
5#17988496C211yesmaximal, characteristic
6#17988487C211yesmaximal, characteristic, complemented
7#17988487C211yesmaximal, characteristic, complemented
8#17988482C211yesmaximal, characteristic, complemented
9#17988479C211yesmaximal, characteristic, complemented
10#17988476C211yesmaximal, characteristic, complemented
11#17988476C211yesmaximal, characteristic, complemented
12#17988476C211yesmaximal, characteristic, complemented
13#17988475C211yesmaximal, characteristic, complemented
14#17988472C211yesmaximal, characteristic, complemented
15#397×C73C211yesmaximal, characteristic, complemented
16C22×D292C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C2×C4⋊Dic73C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×C22⋊Dic73C2211yescharacteristic
25C2×C22⋊Dic73C2211yescharacteristic
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×C4×Dic73C2211yescharacteristic
37C2×C4×Dic73C2211yescharacteristic
38C2×C4×Dic73C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44C2×C4⋊C4×C73C2211yescharacteristic
45C2×C22⋊C4×C73C2211yescharacteristic
46C2×C22⋊C4×C73C2211yescharacteristic
47C2×C22⋊C4×C73C2211yescharacteristic
48#95×C73C2211yescharacteristic
49#95×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51C23×D73C2311yescharacteristic
52C23×D73C2311yescharacteristic
53C2×D292—41no—
54C2×D292—41no—
55C2×D292—41no—
56C2×C22⋊D73—22no—
57C2×C22⋊D73—22no—
58C2×C22⋊D73—41no—
59C2×C22⋊D73—41no—
60C2×C22⋊D73—41no—
61C2×C22⋊D73—41no—
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C4⋊Dic73—22no—
69#11924007—22no—
70#11924007—41no—
71#11924007—41no—
72#11924007—41no—
73C22⋊Dic73—22no—
74C22⋊Dic73—41no—
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—
84#11924005—41no—
85C4×Dic73—41no—
86C4×Dic73—41no—
87C4×Dic73—41no—
88C24×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C4⋊C4×C73—41no—
96C22⋊C4×C73—41no—
97C22⋊C4×C73—41no—
98C22⋊C4×C73—41no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73C2411yescharacteristic
107C22×D73—21no—
108C22×D73—21no—
109C22×D73—21no—
110C22×D73—21no—
111C22×D73—21no—
112C22×D73—21no—
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—21no—
118C22×D73—21no—
119C22×D73—21no—
120C22×D73—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×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C22⋊D73—44no—
140C22⋊D73—44no—
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—21no—
155C2×Dic73—21no—
156C2×Dic73#4112yes—
157C2×Dic73#4112yes—
158C2×Dic73#4112yes—
159D292—44no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73C2×#4111yescharacteristic
168C22×C73C2×#4111yescharacteristic
169C22×C73C2×#4111yescharacteristic
170C22×C73H(5,𝔽2)11yescharacteristic
171C22×C73H(5,𝔽2)11yescharacteristic
172C22×C73H(5,𝔽2)11yescharacteristic
173C22×C73H(5,𝔽2)11yescharacteristic
174C2×D73—41no—
175C2×D73—41no—
176C2×D73—41no—
177C2×D73—41no—
178C2×D73—41no—
179C2×D73—41no—
180C2×D73—41no—
181C2×D73—41no—
182C2×D73—41no—
183C2×D73—41no—
184C2×D73—41no—
185C2×D73—41no—
186C2×D73—41no—
187C2×D73—41no—
188C4×C73—41no—
189C4×C73—41no—
190C4×C73—41no—
191C4×C73—41no—
192C4×C73—41no—
193C4×C73—41no—
194Dic73—22no—
195Dic73—22no—
196Dic73—22no—
197Dic73—41no—
198Dic73—41no—
199Dic73—41no—
200C2×C73—81no—
201C2×C73#53811yescharacteristic
202C2×C73#53811yescharacteristic
203C2×C73#54011yescharacteristic
204C2×C73#55311yescharacteristic
205C2×C73#55511yescharacteristic
206C2×C73#55911yescharacteristic
207C2×C73#56011yescharacteristic
208D73—81no—
209D73—81no—
210#2803—731nomaximal, Sylow
211C73#280311yescharacteristic, complemented, Sylow
212#397D7311yescharacteristic, complemented
213#394—731no—
214#394—731no—
215#394—731no—
216#394—731no—
217#392—731no—
218#390—731no—
219#390—731no—
220#389—731no—
221#388—731no—
222#388—731no—
223#388—731no—
224#388—731no—
225#388—731no—
226#387—731no—
227C22×D4—731no—
228C22×D4—731no—
229C22×D4—731no—
230C2×C4⋊C4—731no—
231C2×C4⋊C4—731no—
232C2×C4⋊C4—731no—
233C2×C4⋊C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4C2×D7311yescharacteristic
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×C22⋊C4—731no—
243C2×C22⋊C4—731no—
244C2×C22⋊C4—731no—
245C2×C22⋊C4—731no—
246C2×C22⋊C4—731no—
247C2×C22⋊C4—731no—
248C2×C22⋊C4C2×D7311yescharacteristic
249C2×C22⋊C4C2×D7311yescharacteristic
250C2×C22⋊C4C2×D7311yescharacteristic
251C2×C42—731no—
252C2×C42—731no—
253C2×C42—731no—
254#95—731no—
255#95—731no—
256#95—731no—
257#95—731no—
258#95—731no—
259#95C2×D7311yescharacteristic
260#95C2×D7311yescharacteristic
261#95C2×D7311yescharacteristic
262C24—731no—
263C24—731no—
264C24C22×D7311yescharacteristic
265C2×D4—2921no—
266C2×D4—2921no—
267C2×D4—2921no—
268C2×D4—2921no—
269C2×D4—2921no—
270C2×D4—2921no—
271C2×D4—2921no—
272C2×D4—1462no—
273C2×D4—1462no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—731no—
280C22×C4C22×D7311yescharacteristic
281C22×C4C22×D7311yescharacteristic
282C22×C4C22×D7311yescharacteristic
283C22×C4C22×D7311yescharacteristic
284C22×C4C22×D7311yescharacteristic
285C22×C4C22×D7311yescharacteristic
286C4⋊C4—41no—
287C4⋊C4—2921no—
288C4⋊C4—2921no—
289C4⋊C4—2921no—
290C4⋊C4—1462no—
291C4⋊C4—1462no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—2921no—
296C22⋊C4—2921no—
297C22⋊C4—2921no—
298C22⋊C4—2921no—
299C22⋊C4—2921no—
300C22⋊C4—2921no—
301C22⋊C4—2921no—
302C22⋊C4—1462no—
303C22⋊C4—1462no—
304C22⋊C4—1462no—
305C22⋊C4—1462no—
306C22⋊C4—1462no—
307C42—2921no—
308C42—2921no—
309C42—2921no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—1461no—
318C23—1461no—
319C23—1461no—
320C23—1461no—
321C23—1461no—
322C23—1461no—
323C23—1461no—
324C23—1461no—
325C23—1461no—
326C23—1461no—
327C23—1461no—
328C23—1461no—
329C23—1461no—
330C23—1461no—
331C23C23×D7311yescharacteristic
332D4—2924no—
333D4—2924no—
334D4—2924no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—732no—
354C2×C4—732no—
355C2×C4—732no—
356C2×C4—1461no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4—1461no—
363C2×C4—1461no—
364C2×C4—1461no—
365C2×C4—1461no—
366C2×C4—1461no—
367C2×C4—1461no—
368C2×C4—1461no—
369C2×C4—1461no—
370C2×C4—1461no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—2921no—
379C22—2921no—
380C22—2921no—
381C22—2921no—
382C22—2921no—
383C22—2921no—
384C22—2921no—
385C22—2921no—
386C22—2921no—
387C22—2921no—
388C22—2921no—
389C22—2921no—
390C22—2921no—
391C22—2921no—
392C22#41×D7311yescharacteristic
393C22#41×D7311yescharacteristic
394C22#41×D7311yescharacteristic
395C22#1455663611yescharacteristic
396C22#1455663611yescharacteristic
397C22#1455663711yescharacteristic
398C22#1455663711yescharacteristic
399C4—41no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—2921no—
406C4—2921no—
407C4—2921no—
408C4—1462no—
409C4—1462no—
410C4—1462no—
411C2—81no—
412C2—5841no—
413C2—5841no—
414C2#1798917311yescharacteristic
415C2#1798917611yescharacteristic
416C2#1798918911yescharacteristic
417C2#1798928811yescharacteristic
418C2#1798929911yescharacteristic
419C2#1798932111yescharacteristic
420C2#1798932511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#397×C73C2
hypercenter#397D73
hypocenterC73#2803
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #17988505C2semidirect
2. #17988504C2semidirect
3. #17988503C2semidirect
4. #17988502C2semidirect
6. #17988487C2semidirect
7. #17988487C2semidirect
8. #17988482C2semidirect
9. #17988479C2semidirect
10. #17988476C2semidirect
11. #17988476C2semidirect
12. #17988476C2semidirect
13. #17988475C2semidirect
14. #17988472C2semidirect
15. #397×C73C2semidirect
211. C73#2803semidirect
212. #397D73semidirect