Finite Group Databasebeta

← #22620607

Subgroups — #22620607

Order 9344.

374 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#17989210C211yesmaximal, characteristic, complemented
2#17989190C211yesmaximal, characteristic, complemented
3#17988995C211yesmaximal, characteristic, complemented
4#17988973C211yesmaximal, characteristic, complemented
5#17988943C211yesmaximal, characteristic, complemented
6#17988932C211yesmaximal, characteristic, complemented
7#17988840C211yesmaximal, characteristic, complemented
8#17988821C211yesmaximal, characteristic, complemented
9#17988818C211yesmaximal, characteristic, complemented
10#17988696C211yesmaximal, characteristic, complemented
11#17988690C211yesmaximal, characteristic, complemented
12SD16×Dic73C211yesmaximal, characteristic, complemented
13#17988669C211yesmaximal, characteristic, complemented
14#17988545C211yesmaximal, characteristic, complemented
15#468×C73C211yesmaximal, characteristic, complemented
16C2×#11924015C2211yescharacteristic
17C2×D584C2211yescharacteristic
18C2×#11924013C2211yescharacteristic
19C22×#10596831C2211yescharacteristic
20#14556590C2211yescharacteristic
21#14556587C2211yescharacteristic
22#14556586—21no—
23#14556582C2211yescharacteristic
24#14556580C2211yescharacteristic
25#14556577—21no—
26#14556575—21no—
27#14556573—21no—
28#14556573—21no—
29#14556571—21no—
30#14556565C2211yescharacteristic
31#14556565C2211yescharacteristic
32#14556563—21no—
33#14556562—21no—
34Q8×Dic73C2211yescharacteristic
35D4×Dic73C2211yescharacteristic
36#14556553C2211yescharacteristic
37#14556553C2211yescharacteristic
38#14556550C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556523C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556515C2211yescharacteristic
43#14556513C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556512C2211yescharacteristic
46#14556511C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556501C2211yescharacteristic
49#14556501C2211yescharacteristic
50C8×Dic73C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×D292C2311yescharacteristic
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C22×Dic73—21no—
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69#11924015—22no—
70D584—22no—
71#11924013—22no—
72C2×#10596831—22no—
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77C4⋊Dic73D411yescharacteristic
78C4⋊Dic73D411yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83C22⋊Dic73—21no—
84C22⋊Dic73D411yescharacteristic
85C22⋊Dic73D411yescharacteristic
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92C4×Dic73—21no—
93C4×Dic73C2311yescharacteristic
94C4×Dic73C2311yescharacteristic
95C2×Q8×C73C2311yescharacteristic
96C2×D4×C73—21no—
97C2×D4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99SD16×C73—22no—
100M16×C73—22no—
101C2×C8×C73C2311yescharacteristic
102C2×C8×C73C2311yescharacteristic
103C4⋊C4×C73—21no—
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C22⋊C4×C73—21no—
107C22⋊C4×C73—21no—
108C23×C73—21no—
109C23×C73C2×D411yescharacteristic
110C22×D73—21no—
111C22×D73—21no—
112Q8×C73—21no—
113Q8×C73—21no—
114D4×C73—21no—
115D4×C73—21no—
116D4×C73—81no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2411yescharacteristic
124C22⋊D73—81no—
125C22⋊D73—81no—
126C22⋊D73—81no—
127C22⋊D73—81no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—81no—
131C2×Dic73C2×D411yescharacteristic
132C2×Dic73C2×D411yescharacteristic
133C2×Dic73C2×D411yescharacteristic
134C2×Dic73C2×D411yescharacteristic
135D292—21no—
136D292—21no—
137D292—21no—
138D292—21no—
139C4×D73—81no—
140C4×D73—81no—
141Dic146—81no—
142C8×C73—21no—
143C8×C73#4112yes—
144#10596831—21no—
145#10596831#4112yes—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73C22×D411yescharacteristic
153C2×D73—41no—
154C2×D73—41no—
155C2×D73—41no—
156C2×D73—41no—
157C2×D73—41no—
158C2×D73—41no—
159C4×C73—21no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73C2×#4111yescharacteristic
164C4×C73C2×#4111yescharacteristic
165Dic73—21no—
166Dic73—21no—
167Dic73—21no—
168Dic73—21no—
169Dic73—41no—
170Dic73—41no—
171C2×C73—41no—
172C2×C73—81no—
173C2×C73#53211yescharacteristic
174C2×C73#57611yescharacteristic
175C2×C73#57711yescharacteristic
176D73—81no—
177D73—81no—
178#3179—731nomaximal, Sylow
179C73#317911yescharacteristic, complemented, Sylow
180#542—731no—
181#540—731no—
182#501—731no—
183#496—731no—
184#488—731no—
185#486—731no—
186#469—731no—
187#468D7311yescharacteristic, complemented
188#466—731no—
189#465—731no—
190#442—731no—
191#440—731no—
192C4×SD16—731no—
193C4×D8—731no—
194#405—731no—
195C2×SD16—731no—
196C2×SD16C2×D7311yescharacteristic
197C2×D8—731no—
198C2×D8—731no—
199C2×M16C2×D7311yescharacteristic
200C22×C8—731no—
201C4⋊Q8—731no—
202#127—731no—
203#126—1461no—
204#125—731no—
205#124—731no—
206#124—1461no—
207#123—1461no—
208#123—1461no—
209#123—1461no—
210C22⋊Q8—1461no—
211C22⋊Q8C2×D7311yescharacteristic
212#121—731no—
213#121—731no—
214#121—1461no—
215#121—1461no—
216#121C2×D7311yescharacteristic
217C4×Q8—731no—
218C4×D4—731no—
219C4×D4—731no—
220C4×D4—731no—
221#117—731no—
222#107—731no—
223#107C2×D7311yescharacteristic
224#106—731no—
225#106—731no—
226#103—731no—
227#103C2×D7311yescharacteristic
228#102—731no—
229#102—731no—
230#102—731no—
231#102—731no—
232#102—731no—
233#102C2×D7311yescharacteristic
234#97—731no—
235#97—731no—
236C4×C8—731no—
237C4×C8—731no—
238C2×Q8—1461no—
239C2×Q8C22×D7311yescharacteristic
240C2×D4—21no—
241C2×D4—731no—
242C2×D4—731no—
243C2×D4—1461no—
244C2×D4—1461no—
245C2×D4—1461no—
246C2×D4—1461no—
247C2×D4C22×D7311yescharacteristic
248C22×C4—1461no—
249C22×C4—1461no—
250C22×C4—1461no—
251C22×C4C22×D7311yescharacteristic
252SD16—22no—
253SD16—1462no—
254D8—1462no—
255D8—1462no—
256M16—22no—
257C2×C8—731no—
258C2×C8—731no—
259C2×C8—1462no—
260C2×C8C22×D7311yescharacteristic
261C2×C8C22×D7311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—731no—
264C4⋊C4—731no—
265C4⋊C4—731no—
266C4⋊C4—731no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4C22×D7311yescharacteristic
272C4⋊C4C22×D7311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—731no—
276C22⋊C4—731no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C42—731no—
285C42—731no—
286C42—1461no—
287C23—21no—
288C23—1461no—
289C23—1461no—
290C23D4×D7311yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—5841no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—5841no—
298D4—5841no—
299D4—5841no—
300D4—5841no—
301D4—1461no—
302D4—1461no—
303D4—1461no—
304D4—1461no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—5841no—
311C2×C4—5841no—
312C2×C4—5841no—
313C2×C4—731no—
314C2×C4—731no—
315C2×C4—731no—
316C2×C4—731no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4D4×D7311yescharacteristic
320C2×C4C23×D7311yescharacteristic
321C8—21no—
322C8—732no—
323C8—1461no—
324C8#1192402712yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—2921no—
332C22—2921no—
333C22—2921no—
334C22—2921no—
335C22—2921no—
336C22—2921no—
337C22C2×D4×D7311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—2921no—
343C4—2921no—
344C4—1461no—
345C4—1461no—
346C4—1461no—
347C4—1461no—
348C4#41×D7311yescharacteristic
349C4C2×#1192402711yescharacteristic
350C2—41no—
351C2—81no—
352C2—5841no—
353C2—5841no—
354C2#1798913211yescharacteristic
355C2#1798939111yescharacteristic
356C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#468×C73C2
socleC22×C73C22×D4
hypercenter#468D73
hypocenterC73#3179
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #17989210C2semidirect
2. #17989190C2semidirect
3. #17988995C2semidirect
4. #17988973C2semidirect
5. #17988943C2semidirect
6. #17988932C2semidirect
7. #17988840C2semidirect
8. #17988821C2semidirect
9. #17988818C2semidirect
10. #17988696C2semidirect
11. #17988690C2semidirect
12. SD16×Dic73C2semidirect
13. #17988669C2semidirect
14. #17988545C2semidirect
15. #468×C73C2semidirect
179. C73#3179semidirect
187. #468D73semidirect