Finite Group Databasebeta

← #22620127

Subgroups — #22620127

Order 9344.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989191C211yesmaximal, characteristic, complemented
2#17989066C211yesmaximal, characteristic, complemented
3#17988904C211yesmaximal, characteristic, complemented
4#17988899C211yesmaximal, characteristic, complemented
5#17988895C211yesmaximal, characteristic, complemented
6#17988887C211yesmaximal, characteristic, complemented
7#17988784C211yesmaximal, characteristic, complemented
8#17988729C211yesmaximal, characteristic, complemented
9#17988729C211yesmaximal, characteristic, complemented
10#17988699C211yesmaximal, characteristic, complemented
11#17988684C211yesmaximal, characteristic, complemented
12#17988678C211yesmaximal, characteristic, complemented
13D8×Dic73C211yesmaximal, characteristic, complemented
14#17988647C211yesmaximal, characteristic, complemented
15#459×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×#11924016C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19#14556583C2211yescharacteristic
20#14556572—21no—
21#14556572—21no—
22#14556563—21no—
23#14556563—21no—
24#14556562C2211yescharacteristic
25#14556562C2211yescharacteristic
26C4×Dic146C2211yescharacteristic
27#14556556C2211yescharacteristic
28D4×Dic73C2211yescharacteristic
29D4×Dic73C2211yescharacteristic
30D4×Dic73C2211yescharacteristic
31C4×C22⋊D73—21no—
32#14556551—21no—
33#14556548C2211yescharacteristic
34#14556547—21no—
35C2×#11924007—21no—
36C4⋊C4×D73C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556512C2211yescharacteristic
45#14556512C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×D8×C73C2211yescharacteristic
53C2×D8×C73C2211yescharacteristic
54#127×C73C2211yescharacteristic
55C4×D4×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924027—22no—
60#11924027—22no—
61C2×Dic146C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C2×C4×D73—21no—
70C2×C4×D73C2311yescharacteristic
71#11924016—22no—
72#11924016—22no—
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007D411yescharacteristic
84#11924007D411yescharacteristic
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90#11924005D411yescharacteristic
91#11924005D411yescharacteristic
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73C2311yescharacteristic
95C2×D4×C73—21no—
96C2×D4×C73—21no—
97C2×D4×C73C2311yescharacteristic
98C2×D4×C73C2311yescharacteristic
99C2×D4×C73C2311yescharacteristic
100C22×C4×C73—21no—
101D8×C73—22no—
102D8×C73—22no—
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C22⋊C4×C73—21no—
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C22×D73C2×D411yescharacteristic
112D4×C73—21no—
113D4×C73—21no—
114D4×C73—21no—
115D4×C73—21no—
116D4×C73—21no—
117D4×C73—81no—
118D4×C73—81no—
119D4×C73#4112yes—
120C2×C4×C73—21no—
121C2×C4×C73—81no—
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2411yescharacteristic
125C22⋊D73—24no—
126C22⋊D73—81no—
127C22⋊D73—81no—
128C2×Dic73—24no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—81no—
134C2×Dic73—81no—
135C2×Dic73—81no—
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139C4×D73—21no—
140C4×D73—21no—
141C4×D73—81no—
142Dic146—21no—
143Dic146#4112yes—
144C8×C73—21no—
145C8×C73—21no—
146#10596831—21no—
147#10596831—21no—
148C22×C73—22no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73C22×D411yescharacteristic
158C2×D73—21no—
159C2×D73—21no—
160C2×D73—21no—
161C4×C73—21no—
162C4×C73—21no—
163C4×C73—41no—
164C4×C73C2×#4111yescharacteristic
165C4×C73C2×#4111yescharacteristic
166Dic73—22no—
167Dic73—21no—
168Dic73—21no—
169Dic73—21no—
170Dic73—41no—
171Dic73—41no—
172Dic73—41no—
173C2×C73—42no—
174C2×C73—81no—
175C2×C73—81no—
176C2×C73#52511yescharacteristic
177C2×C73#57611yescharacteristic
178C2×C73#57711yescharacteristic
179D73—41no—
180#3119—731nomaximal, Sylow
181C73#311911yescharacteristic, complemented, Sylow
182#540—731no—
183#520—731no—
184#481—731no—
185#480—731no—
186#479—731no—
187#478—731no—
188#460—731no—
189#459D7311yescharacteristic, complemented
190#449—731no—
191#449—731no—
192#442—731no—
193#440—731no—
194C4×SD16—731no—
195C4×D8—731no—
196#433—731no—
197C2×#41—731no—
198C2×SD16—731no—
199C2×SD16—731no—
200C2×D8C2×D7311yescharacteristic
201C2×D8C2×D7311yescharacteristic
202#127C2×D7311yescharacteristic
203#125—731no—
204#123—1461no—
205#123—1461no—
206#121—731no—
207#121—731no—
208#121—1461no—
209#121—1461no—
210C4×Q8—731no—
211C4×Q8—731no—
212C4×D4—731no—
213C4×D4—731no—
214C4×D4—731no—
215C4×D4—1461no—
216C4×D4—1461no—
217C4×D4C2×D7311yescharacteristic
218#117—731no—
219#117—1461no—
220C2×C4⋊C4—731no—
221C2×C4⋊C4—1461no—
222#107—731no—
223#107—731no—
224#106—731no—
225#106—731no—
226C4⋊C8—731no—
227C4⋊C8C2×D7311yescharacteristic
228#103—731no—
229#103—731no—
230#102—731no—
231#102—731no—
232#102—731no—
233#102—731no—
234#102C2×D7311yescharacteristic
235#102C2×D7311yescharacteristic
236C22⋊C8—731no—
237C22⋊C8—731no—
238#97—731no—
239C4×C8—731no—
240#41—1462no—
241#41—1462no—
242C2×Q8—731no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—1461no—
246C2×D4—1461no—
247C2×D4—1461no—
248C2×D4C22×D7311yescharacteristic
249C2×D4C22×D7311yescharacteristic
250C2×D4C22×D7311yescharacteristic
251C22×C4—21no—
252C22×C4—731no—
253C22×C4—1461no—
254C22×C4—1461no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4—1461no—
258SD16—1462no—
259SD16—1462no—
260D8—22no—
261D8—22no—
262C2×C8—731no—
263C2×C8—731no—
264C2×C8C22×D7311yescharacteristic
265C2×C8C22×D7311yescharacteristic
266C4⋊C4—731no—
267C4⋊C4—731no—
268C4⋊C4—731no—
269C4⋊C4—731no—
270C4⋊C4—731no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4C22×D7311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—731no—
279C22⋊C4—731no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C42—731no—
286C42—1461no—
287C42—1461no—
288C42C22×D7311yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292C23—731no—
293Q8—732no—
294Q8—1461no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—5841no—
303D4—5841no—
304D4—1464no—
305D4#1192402712yes—
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—5841no—
309C2×C4—5841no—
310C2×C4—5841no—
311C2×C4—5841no—
312C2×C4—731no—
313C2×C4—731no—
314C2×C4—731no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1464no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4D4×D7311yescharacteristic
323C2×C4D4×D7311yescharacteristic
324C2×C4C23×D7311yescharacteristic
325C8—21no—
326C8—21no—
327C8—1461no—
328C8—1461no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—1461no—
339C22—1461no—
340C22—1461no—
341C22C2×D4×D7311yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—2921no—
346C4—2921no—
347C4—2921no—
348C4—1461no—
349C4—1461no—
350C4—1461no—
351C4—1462no—
352C4#41×D7311yescharacteristic
353C4C2×#1192402711yescharacteristic
354C2—42no—
355C2—81no—
356C2—81no—
357C2—2921no—
358C2#1798909711yescharacteristic
359C2#1798938811yescharacteristic
360C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#459×C73C2
socleC22×C73C22×D4
hypercenter#459D73
hypocenterC73#3119
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #17989191C2semidirect
2. #17989066C2semidirect
3. #17988904C2semidirect
4. #17988899C2semidirect
5. #17988895C2semidirect
6. #17988887C2semidirect
7. #17988784C2semidirect
8. #17988729C2semidirect
9. #17988729C2semidirect
10. #17988699C2semidirect
11. #17988684C2semidirect
12. #17988678C2semidirect
13. D8×Dic73C2semidirect
14. #17988647C2semidirect
15. #459×C73C2semidirect
181. C73#3119semidirect
189. #459D73semidirect