Finite Group Databasebeta

← #22620123

Subgroups — #22620123

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#17989190C211yesmaximal, characteristic, complemented
2#17989070C211yesmaximal, characteristic, complemented
3#17988903C211yesmaximal, characteristic, complemented
4#17988901C211yesmaximal, characteristic, complemented
5#17988896C211yesmaximal, characteristic, complemented
6#17988885C211yesmaximal, characteristic, complemented
7#17988785C211yesmaximal, characteristic, complemented
8#17988780C211yesmaximal, characteristic, complemented
9#17988732C211yesmaximal, characteristic, complemented
10#17988696C211yesmaximal, characteristic, complemented
11#17988688C211yesmaximal, characteristic, complemented
12#17988672C211yesmaximal, characteristic, complemented
13D8×Dic73C211yesmaximal, characteristic, complemented
14#17988645C211yesmaximal, characteristic, complemented
15#449×C73C211yesmaximal, characteristic, complemented
16C2×#11924015C2211yescharacteristic
17C2×#11924013C2211yescharacteristic
18#14556587C2211yescharacteristic
19#14556582C2211yescharacteristic
20#14556575—21no—
21#14556573—21no—
22#14556565C2211yescharacteristic
23#14556563—21no—
24#14556562—21no—
25Q8×Dic73C2211yescharacteristic
26Q8×Dic73C2211yescharacteristic
27D4×Dic73—21no—
28D4×Dic73—21no—
29D4×Dic73C2211yescharacteristic
30D4×Dic73C2211yescharacteristic
31D4×Dic73C2211yescharacteristic
32#14556553C2211yescharacteristic
33#14556550—21no—
34#14556550C2211yescharacteristic
35C2×C4⋊Dic73—21no—
36C2×C4⋊Dic73C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556525C2211yescharacteristic
39#14556522C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C2×D8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59C2×D292C2311yescharacteristic
60C2×C22⋊D73—21no—
61C2×C22⋊D73—21no—
62C2×C22⋊D73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C2×C4×D73—21no—
68#11924015—22no—
69#11924013—22no—
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73D411yescharacteristic
77C4⋊Dic73D411yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82C22⋊Dic73—21no—
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85C22⋊Dic73D411yescharacteristic
86C22⋊Dic73D411yescharacteristic
87#11924005—21no—
88#11924005—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73C2311yescharacteristic
92C4×Dic73C2311yescharacteristic
93#41×C73—22no—
94#41×C73—22no—
95C2×Q8×C73C2311yescharacteristic
96C2×D4×C73—21no—
97C2×D4×C73—21no—
98C2×D4×C73C2311yescharacteristic
99C2×D4×C73C2311yescharacteristic
100C22×C4×C73—21no—
101C22×C4×C73C2311yescharacteristic
102SD16×C73—22no—
103D8×C73—22no—
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C22⋊C4×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73C2×D411yescharacteristic
111C22×D73—21no—
112Q8×C73—21no—
113Q8×C73#4112yes—
114D4×C73—24no—
115D4×C73—21no—
116D4×C73—21no—
117D4×C73—21no—
118D4×C73—81no—
119D4×C73#4112yes—
120C2×C4×C73—24no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2411yescharacteristic
127C22⋊D73—81no—
128C22⋊D73—81no—
129C22⋊D73—81no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—81no—
134C2×Dic73—81no—
135C2×Dic73—81no—
136C2×Dic73—81no—
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139C2×Dic73C2×D411yescharacteristic
140C2×Dic73C2×D411yescharacteristic
141D292—21no—
142D292—21no—
143C4×D73—81no—
144C8×C73—21no—
145C8×C73—21no—
146#10596831—21no—
147#10596831—21no—
148C22×C73—21no—
149C22×C73—22no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73C22×D411yescharacteristic
158C2×D73—41no—
159C2×D73—41no—
160C2×D73—41no—
161C4×C73—21no—
162C4×C73—22no—
163C4×C73—41no—
164C4×C73C2×#4111yescharacteristic
165C4×C73C2×#4111yescharacteristic
166Dic73—21no—
167Dic73—21no—
168Dic73—21no—
169Dic73—21no—
170Dic73—41no—
171Dic73—41no—
172Dic73—41no—
173C2×C73—41no—
174C2×C73—42no—
175C2×C73—81no—
176C2×C73#52511yescharacteristic
177C2×C73#57611yescharacteristic
178C2×C73#57711yescharacteristic
179D73—81no—
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#459—731no—
190#449—731no—
191#449D7311yescharacteristic, complemented
192#442—731no—
193#440—731no—
194C4×SD16—731no—
195C4×D8—731no—
196#433—731no—
197C2×#41C2×D7311yescharacteristic
198C2×SD16—731no—
199C2×SD16C2×D7311yescharacteristic
200C2×D8—731no—
201C2×D8C2×D7311yescharacteristic
202#127—731no—
203#125—731no—
204#123—1461no—
205#123—1461no—
206#121—731no—
207#121—1461no—
208#121—1461no—
209#121C2×D7311yescharacteristic
210C4×Q8—731no—
211C4×Q8—731no—
212C4×D4—731no—
213C4×D4—731no—
214C4×D4—731no—
215C4×D4—731no—
216C4×D4—1461no—
217C4×D4—1461no—
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⋊C8—731no—
228#103—731no—
229#103C2×D7311yescharacteristic
230#102—731no—
231#102—731no—
232#102—731no—
233#102—731no—
234#102—731no—
235#102C2×D7311yescharacteristic
236C22⋊C8—731no—
237C22⋊C8C2×D7311yescharacteristic
238#97—731no—
239C4×C8—731no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D7311yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—731no—
246C2×D4—1461no—
247C2×D4—1461no—
248C2×D4—1461no—
249C2×D4C22×D7311yescharacteristic
250C2×D4C22×D7311yescharacteristic
251C22×C4—21no—
252C22×C4—1461no—
253C22×C4—1461no—
254C22×C4—1461no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4C22×D7311yescharacteristic
258SD16—22no—
259SD16—1462no—
260D8—22no—
261D8—1462no—
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—731no—
287C42—1461no—
288C42—1461no—
289C23—21no—
290C23—21no—
291C23—1461no—
292C23D4×D7311yescharacteristic
293Q8—21no—
294Q8#1192402712yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—5841no—
301D4—5841no—
302D4—5841no—
303D4—1461no—
304D4—1461no—
305D4#1192402712yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—5841no—
312C2×C4—5841no—
313C2×C4—5841no—
314C2×C4—5841no—
315C2×C4—5841no—
316C2×C4—731no—
317C2×C4—731no—
318C2×C4—731no—
319C2×C4—731no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4D4×D7311yescharacteristic
324C2×C4C23×D7311yescharacteristic
325C8—21no—
326C8—21no—
327C8—1461no—
328C8—1461no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—2921no—
339C22—2921no—
340C22—2921no—
341C22C2×D4×D7311yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—2921no—
346C4—2921no—
347C4—2921no—
348C4—1461no—
349C4—1461no—
350C4—1461no—
351C4—1461no—
352C4C2×#1192402711yescharacteristic
353C4C2×#1192402711yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—5841no—
358C2#1798909311yescharacteristic
359C2#1798938911yescharacteristic
360C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#449×C73C2
socleC22×C73C22×D4
hypercenter#449D73
hypocenterC73#3119
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #17989190C2semidirect
2. #17989070C2semidirect
3. #17988903C2semidirect
4. #17988901C2semidirect
5. #17988896C2semidirect
6. #17988885C2semidirect
7. #17988785C2semidirect
8. #17988780C2semidirect
9. #17988732C2semidirect
10. #17988696C2semidirect
11. #17988688C2semidirect
12. #17988672C2semidirect
13. D8×Dic73C2semidirect
14. #17988645C2semidirect
15. #449×C73C2semidirect
181. C73#3119semidirect
191. #449D73semidirect