Finite Group Databasebeta

← #22622200

Subgroups — #22622200

Order 9344.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989272C211yesmaximal, characteristic, complemented
2#17989244C211yesmaximal, characteristic
3#17988940C211yesmaximal, characteristic, complemented
4#17988922C211yesmaximal, characteristic, complemented
5#17988910C211yesmaximal, characteristic, complemented
6#17988892C211yesmaximal, characteristic, complemented
7#17988845C211yesmaximal, characteristic, complemented
8#17988832C211yesmaximal, characteristic, complemented
9#17988808C211yesmaximal, characteristic, complemented
10#17988749C211yesmaximal, characteristic, complemented
11#17988744C211yesmaximal, characteristic, complemented
12#17988679C211yesmaximal, characteristic, complemented
13#17988663C211yesmaximal, characteristic, complemented
14#17988594C211yesmaximal, characteristic, complemented
15#417×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic
17C2×Dic292C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924016C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21#14556586—21no—
22#14556582C2211yescharacteristic
23#14556581—21no—
24#14556578—21no—
25#14556578C2211yescharacteristic
26#14556574—21no—
27#14556571C2211yescharacteristic
28#14556570—21no—
29#14556570C2211yescharacteristic
30#14556570C2211yescharacteristic
31#14556562—21no—
32#14556562C2211yescharacteristic
33Q8×Dic73C2211yescharacteristic
34#14556556C2211yescharacteristic
35C4×C22⋊D73—21no—
36C4×C22⋊D73C2211yescharacteristic
37#14556550—21no—
38#14556549C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556523C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C2×C4⋊C4×C73C2211yescharacteristic
55#103×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C2×Dic146C2311yescharacteristic
62Q8×D73—22no—
63Q8×D73—41no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73D411yescharacteristic
66C2×C4×D73—21no—
67C2×C4×D73C2311yescharacteristic
68Dic292—41no—
69#11924018—22no—
70#11924016—41no—
71#11924011—41no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007D411yescharacteristic
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73D411yescharacteristic
90#11924005—21no—
91#11924005—21no—
92#11924005D411yescharacteristic
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97#41×C73—22no—
98#41×C73—41no—
99C2×Q8×C73C2311yescharacteristic
100C2×D4×C73—21no—
101C2×D4×C73C2311yescharacteristic
102C22×C4×C73—21no—
103C22×C4×C73—21no—
104C22×C4×C73C2311yescharacteristic
105M16×C73—41no—
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C22×D73C2×D411yescharacteristic
114Q8×C73—21no—
115Q8×C73#4112yes—
116D4×C73—21no—
117D4×C73—21no—
118D4×C73—42no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—42no—
125C2×C4×C73—42no—
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2411yescharacteristic
128C22⋊D73—41no—
129C22⋊D73—42no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137C4×D73—21no—
138C4×D73—21no—
139C4×D73—42no—
140Dic146—21no—
141Dic146—21no—
142Dic146—21no—
143Dic146—21no—
144Dic146—42no—
145C8×C73—21no—
146C8×C73—21no—
147#10596831—21no—
148#10596831—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73C22×D411yescharacteristic
156C2×D73—21no—
157C2×D73—21no—
158C2×D73—21no—
159C4×C73—22no—
160C4×C73—21no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73C2×#4111yescharacteristic
164C4×C73H(5,𝔽2)11yescharacteristic
165Dic73—21no—
166Dic73—21no—
167Dic73—21no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171Dic73—41no—
172C2×C73—41no—
173C2×C73—81no—
174C2×C73#54611yescharacteristic
175C2×C73#57511yescharacteristic
176C2×C73#57811yescharacteristic
177D73—41no—
178#3327—731nomaximal, Sylow
179C73#332711yescharacteristic, complemented, Sylow
180#552—731no—
181#548—731no—
182#488—731no—
183#484—731no—
184#482—731no—
185#479—731no—
186#470—731no—
187#468—731no—
188#464—731no—
189#452—731no—
190#451—731no—
191C4×Q16—731no—
192#436—731no—
193#419—731no—
194#417D7311yescharacteristic, complemented
195C2×#41C2×D7311yescharacteristic
196C22×Q8—731no—
197C2×Q16—731no—
198C2×Q16—731no—
199C2×SD16—731no—
200C2×M16—731no—
201C2×M16C2×D7311yescharacteristic
202#126—1461no—
203#125—731no—
204#125—1461no—
205#124—731no—
206#124—1461no—
207#123—1461no—
208C22⋊Q8—731no—
209C22⋊Q8—731no—
210C22⋊Q8—731no—
211C22⋊Q8—1461no—
212#121—731no—
213#121—1461no—
214C4×Q8—731no—
215C4×Q8—731no—
216C4×D4—731no—
217C4×D4—1461no—
218#117—731no—
219#117—1461no—
220C2×C4⋊C4C2×D7311yescharacteristic
221#107—731no—
222#107—731no—
223#106—731no—
224C4⋊C8—731no—
225#103—731no—
226#103—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103C2×D7311yescharacteristic
231#103C2×D7311yescharacteristic
232#102—731no—
233#102C2×D7311yescharacteristic
234#102C2×D7311yescharacteristic
235C22⋊C8—731no—
236C22⋊C8—731no—
237C4×C8—731no—
238#41—22no—
239#41—41no—
240C2×Q8—2921no—
241C2×Q8—731no—
242C2×Q8—731no—
243C2×Q8—1461no—
244C2×Q8—1462no—
245C2×Q8C22×D7311yescharacteristic
246C2×D4—21no—
247C2×D4—731no—
248C2×D4—1461no—
249C2×D4C22×D7311yescharacteristic
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—731no—
253C22×C4—1461no—
254C22×C4C22×D7311yescharacteristic
255Q16—2921no—
256Q16—1462no—
257SD16—2921no—
258M16—41no—
259M16—2921no—
260C2×C8—731no—
261C2×C8—731no—
262C2×C8C22×D7311yescharacteristic
263C2×C8C22×D7311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—731no—
266C4⋊C4—731no—
267C4⋊C4—731no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4C22×D7311yescharacteristic
276C4⋊C4C22×D7311yescharacteristic
277C22⋊C4—731no—
278C22⋊C4—731no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C42—731no—
287C42—1461no—
288C42—1461no—
289C42—1461no—
290C23—21no—
291C23—731no—
292C23D4×D7311yescharacteristic
293Q8—21no—
294Q8—2922no—
295Q8—1461no—
296Q8—1461no—
297Q8—1461no—
298Q8—1461no—
299Q8#1192402812yes—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—2922no—
304D4—2921no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—2922no—
313C2×C4—731no—
314C2×C4—731no—
315C2×C4—731no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4D4×D7311yescharacteristic
323C2×C4C23×D7311yescharacteristic
324C8—21no—
325C8—21no—
326C8—1461no—
327C8—1461no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—1461no—
335C22—1461no—
336C22—1461no—
337C22C2×D4×D7311yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—2921no—
343C4—2921no—
344C4—2921no—
345C4—2921no—
346C4—1461no—
347C4—1461no—
348C4—1461no—
349C4C2×#1192402811yescharacteristic
350C4#1455663611yescharacteristic
351C2—41no—
352C2—81no—
353C2—2921no—
354C2#1798922711yescharacteristic
355C2#1798938311yescharacteristic
356C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#417×C73C2
socleC22×C73C22×D4
hypercenter#417D73
hypocenterC73#3327
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #17989272C2semidirect
3. #17988940C2semidirect
4. #17988922C2semidirect
5. #17988910C2semidirect
6. #17988892C2semidirect
7. #17988845C2semidirect
8. #17988832C2semidirect
9. #17988808C2semidirect
10. #17988749C2semidirect
11. #17988744C2semidirect
12. #17988679C2semidirect
13. #17988663C2semidirect
14. #17988594C2semidirect
15. #417×C73C2semidirect
179. C73#3327semidirect
194. #417D73semidirect