Finite Group Databasebeta

← #22620646

Subgroups — #22620646

Order 9344.

402 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989141C211yesmaximal, characteristic, complemented
2#17989134C211yesmaximal, characteristic
3#17988991C211yesmaximal, characteristic, complemented
4#17988958C211yesmaximal, characteristic, complemented
5#17988936C211yesmaximal, characteristic, complemented
6#17988932C211yesmaximal, characteristic, complemented
7#17988836C211yesmaximal, characteristic, complemented
8#17988834C211yesmaximal, characteristic, complemented
9#17988832C211yesmaximal, characteristic, complemented
10#17988830C211yesmaximal, characteristic, complemented
11#17988689C211yesmaximal, characteristic, complemented
12#17988687C211yesmaximal, characteristic, complemented
13#17988685C211yesmaximal, characteristic, complemented
14#17988539C211yesmaximal, characteristic, complemented
15#440×C73C211yesmaximal, characteristic, complemented
16C2×#11924028—21no—
17C2×#11924017C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21C2×#11924011C2211yescharacteristic
22#14556590C2211yescharacteristic
23#14556590C2211yescharacteristic
24#14556589C2211yescharacteristic
25#14556587C2211yescharacteristic
26#14556581—21no—
27#14556577—21no—
28#14556571C2211yescharacteristic
29#14556569—21no—
30#14556567C2211yescharacteristic
31#14556566C2211yescharacteristic
32#14556564—21no—
33#14556562C2211yescharacteristic
34C4×Dic146—21no—
35C4×Dic146C2211yescharacteristic
36C4×D292C2211yescharacteristic
37C4×C22⋊D73—21no—
38#14556548—21no—
39C42×D73C2211yescharacteristic
40#14556525C2211yescharacteristic
41#14556524C2211yescharacteristic
42#14556524C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556502C2211yescharacteristic
50C8×Dic73C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59#11924028—44no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63C2×D292—21no—
64C2×D292C2311yescharacteristic
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73D411yescharacteristic
70C2×C4×D73D411yescharacteristic
71C2×C4×D73C2311yescharacteristic
72#11924017—22no—
73#11924016—22no—
74#11924015—22no—
75#11924011—22no—
76#11924011—22no—
77C2×#10596831C2311yescharacteristic
78C2×#10596831C2311yescharacteristic
79C4⋊Dic73—21no—
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88C22⋊Dic73—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93C4×Dic73—21no—
94C4×Dic73D411yescharacteristic
95C4×Dic73D411yescharacteristic
96C4×Dic73C2311yescharacteristic
97C2×Q8×C73C2311yescharacteristic
98C2×D4×C73C2311yescharacteristic
99C22×C4×C73—21no—
100SD16×C73—22no—
101C2×C8×C73C2311yescharacteristic
102C2×C8×C73C2311yescharacteristic
103C4⋊C4×C73—21no—
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C22⋊C4×C73—21no—
107C42×C73—21no—
108C42×C73C2311yescharacteristic
109C23×C73—21no—
110C22×D73—21no—
111C22×D73C2×D411yescharacteristic
112Q8×C73—21no—
113Q8×C73—21no—
114D4×C73—21no—
115D4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—42no—
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2×D411yescharacteristic
122C2×C4×C73C2411yescharacteristic
123C22⋊D73—42no—
124C22⋊D73—42no—
125C22⋊D73—42no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131C2×Dic73C2×D411yescharacteristic
132D292—21no—
133D292—21no—
134D292—42no—
135C4×D73—21no—
136C4×D73—21no—
137C4×D73—22no—
138C4×D73—22no—
139C4×D73—42no—
140Dic146—21no—
141Dic146—21no—
142Dic146—42no—
143Dic146—42no—
144C8×C73—21no—
145C8×C73#4112yescomplemented
146#10596831—21no—
147#10596831#4112yescomplemented
148C22×C73—41no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73C22×D411yescharacteristic
152C2×D73—21no—
153C2×D73—21no—
154C2×D73—21no—
155C2×D73—41no—
156C2×D73—41no—
157C2×D73—41no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73C2×#4111yescharacteristic
164C4×C73C2×#4111yescharacteristic
165Dic73—21no—
166Dic73—41no—
167Dic73—41no—
168Dic73—41no—
169Dic73AGL(1,ℤ/8)12yes—
170Dic73#13712yes—
171C2×C73—81no—
172C2×C73#53211yescharacteristic
173C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C73C2×#13711yescharacteristic
175D73—41no—
176D73—81no—
177#3182—731nomaximal, Sylow
178C73#318211yescharacteristic, complemented, Sylow
179#533—731no—
180#532—731no—
181#500—731no—
182#492—731no—
183#487—731no—
184#486—731no—
185#468—731no—
186#468—731no—
187#468—731no—
188#468—731no—
189#440—731no—
190#440—731no—
191#440—731no—
192#440D7311yescharacteristic, complemented
193C4×M16—731no—
194C2×#41—1461no—
195C2×SD16—731no—
196C2×SD16—731no—
197C2×SD16—731no—
198C2×SD16C2×D7311yescharacteristic
199C2×M16—731no—
200C2×M16—731no—
201C4⋊Q8—731no—
202C4⋊Q8—731no—
203C4⋊Q8—731no—
204#127—731no—
205#125—1461no—
206#124—1461no—
207C22⋊Q8—731no—
208C22⋊Q8—731no—
209C22⋊Q8—1461no—
210#121—731no—
211#121—731no—
212#121—1461no—
213C4×Q8—731no—
214C4×Q8—1461no—
215C4×Q8C2×D7311yescharacteristic
216C4×D4—731no—
217C4×D4—1461no—
218C4×D4C2×D7311yescharacteristic
219#117—1461no—
220C2×C42—731no—
221#107—731no—
222#107—731no—
223#107—731no—
224#107C2×D7311yescharacteristic
225#103—731no—
226#103—731no—
227#103—731no—
228#103C2×D7311yescharacteristic
229#102—731no—
230#102—731no—
231#102—731no—
232#102C2×D7311yescharacteristic
233#97—731no—
234#97C2×D7311yescharacteristic
235C4×C8—731no—
236C4×C8—731no—
237#41—2924no—
238C2×Q8—731no—
239C2×Q8—1461no—
240C2×Q8—1461no—
241C2×Q8C22×D7311yescharacteristic
242C2×D4—731no—
243C2×D4—1461no—
244C2×D4—1461no—
245C2×D4—1461no—
246C2×D4—1461no—
247C2×D4C22×D7311yescharacteristic
248C22×C4—21no—
249C22×C4—731no—
250C22×C4—731no—
251C22×C4—731no—
252C22×C4—1461no—
253SD16—22no—
254SD16—1462no—
255SD16—1462no—
256SD16—1462no—
257M16—1462no—
258M16—1462no—
259C2×C8—731no—
260C2×C8—731no—
261C2×C8C22×D7311yescharacteristic
262C2×C8C22×D7311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—731no—
265C4⋊C4—731no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4C22×D7311yescharacteristic
274C4⋊C4C22×D7311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—1461no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C42—21no—
282C42—731no—
283C42—731no—
284C42—731no—
285C42—1461no—
286C42C22×D7311yescharacteristic
287C23—21no—
288C23—731no—
289C23—1461no—
290Q8—21no—
291Q8—21no—
292Q8—2922no—
293Q8—2922no—
294Q8—1461no—
295Q8—1461no—
296D4—21no—
297D4—21no—
298D4—2922no—
299D4—2922no—
300D4—2922no—
301D4—2922no—
302D4—1461no—
303D4—1461no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—2922no—
309C2×C4—731no—
310C2×C4—731no—
311C2×C4—731no—
312C2×C4—1462no—
313C2×C4—1462no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4D4×D7311yescharacteristic
320C2×C4D4×D7311yescharacteristic
321C2×C4C23×D7311yescharacteristic
322C8—21no—
323C8—732no—
324C8—1461no—
325C8#1192402812yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—2921no—
330C22—2921no—
331C22—2921no—
332C22—1461no—
333C22—1461no—
334C22—1461no—
335C22C2×D4×D7311yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—2921no—
342C4—2921no—
343C4—2921no—
344C4—732no—
345C4—732no—
346C4—1461no—
347C4#41×D7311yescharacteristic
348C4C2×#1192402811yescharacteristic
349C2—81no—
350C2—2921no—
351C2—5841no—
352C2#1798913411yescharacteristic
353C2AGL(1,ℤ/8)×D7311yescharacteristic
354C2#137×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#440×C73C2
socleC22×C73C22×D4
hypercenter#440D73
hypocenterC73#3182
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #17989141C2semidirect
3. #17988991C2semidirect
4. #17988958C2semidirect
5. #17988936C2semidirect
6. #17988932C2semidirect
7. #17988836C2semidirect
8. #17988834C2semidirect
9. #17988832C2semidirect
10. #17988830C2semidirect
11. #17988689C2semidirect
12. #17988687C2semidirect
13. #17988685C2semidirect
14. #17988539C2semidirect
15. #440×C73C2semidirect
145. C8×C73#41semidirect
147. #10596831#41semidirect
178. C73#3182semidirect
192. #440D73semidirect
325. C8#11924028semidirect