Finite Group Databasebeta

← #22620611

Subgroups — #22620611

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#17989206C211yesmaximal, characteristic, complemented
2#17989191C211yesmaximal, characteristic, complemented
3#17988996C211yesmaximal, characteristic, complemented
4#17988941C211yesmaximal, characteristic, complemented
5#17988933C211yesmaximal, characteristic, complemented
6#17988837C211yesmaximal, characteristic, complemented
7#17988830C211yesmaximal, characteristic, complemented
8#17988820C211yesmaximal, characteristic, complemented
9#17988813C211yesmaximal, characteristic, complemented
10#17988699C211yesmaximal, characteristic, complemented
11#17988688C211yesmaximal, characteristic, complemented
12SD16×Dic73C211yesmaximal, characteristic, complemented
13D8×Dic73C211yesmaximal, characteristic, complemented
14#17988544C211yesmaximal, characteristic, complemented
15#496×C73C211yesmaximal, characteristic, complemented
16C2×#11924011C2211yescharacteristic
17C2×C8×D73C2211yescharacteristic
18#14556591C2211yescharacteristic
19#14556584—21no—
20#14556583C2211yescharacteristic
21#14556577—21no—
22#14556575—21no—
23#14556572—21no—
24#14556572—21no—
25#14556568—21no—
26#14556567C2211yescharacteristic
27#14556563—21no—
28#14556563—21no—
29#14556562C2211yescharacteristic
30#14556562C2211yescharacteristic
31#14556562C2211yescharacteristic
32Q8×Dic73C2211yescharacteristic
33D4×Dic73C2211yescharacteristic
34D4×Dic73C2211yescharacteristic
35D4×Dic73C2211yescharacteristic
36#14556548C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556525C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556523C2211yescharacteristic
41#14556515C2211yescharacteristic
42#14556515C2211yescharacteristic
43#14556512C2211yescharacteristic
44#14556512C2211yescharacteristic
45#14556512C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556501C2211yescharacteristic
50C4×#10596831C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C2×D8×C73C2211yescharacteristic
55C2×D8×C73C2211yescharacteristic
56#127×C73C2211yescharacteristic
57#124×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×C22⋊D73—21no—
61C2×C22⋊D73—21no—
62C2×C22⋊D73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C2×C4×D73C2311yescharacteristic
67#11924011—22no—
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C8×D73—22no—
71C4⋊Dic73—21no—
72C4⋊Dic73—21no—
73C4⋊Dic73C2311yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80#11924007D411yescharacteristic
81#11924007D411yescharacteristic
82C22⋊Dic73—21no—
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88#11924005—21no—
89#11924005D411yescharacteristic
90#11924005D411yescharacteristic
91C4×Dic73—21no—
92C4×Dic73C2311yescharacteristic
93C2×Q8×C73C2311yescharacteristic
94C2×D4×C73—21no—
95C2×D4×C73—21no—
96C2×D4×C73C2311yescharacteristic
97C2×D4×C73C2311yescharacteristic
98C2×D4×C73C2311yescharacteristic
99SD16×C73—22no—
100SD16×C73—22no—
101D8×C73—22no—
102D8×C73—22no—
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C22×D73C2×D411yescharacteristic
112Q8×C73—21no—
113Q8×C73—21no—
114D4×C73—21no—
115D4×C73—21no—
116D4×C73—21no—
117D4×C73—21no—
118D4×C73—21no—
119D4×C73—21no—
120D4×C73—81no—
121D4×C73—81no—
122C2×C4×C73—21no—
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2411yescharacteristic
126C22⋊D73—81no—
127C22⋊D73—81no—
128C22⋊D73—81no—
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—
141Dic146—81no—
142C8×C73#4112yes—
143C8×C73#4112yes—
144#10596831—21no—
145#10596831—21no—
146C22×C73—41no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73C22×D411yescharacteristic
156C2×D73—21no—
157C2×D73—21no—
158C2×D73—21no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—41no—
162C4×C73C2×#4111yescharacteristic
163C4×C73C2×#4111yescharacteristic
164Dic73—21no—
165Dic73—21no—
166Dic73—21no—
167Dic73—41no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171C2×C73—81no—
172C2×C73—81no—
173C2×C73—81no—
174C2×C73#53211yescharacteristic
175C2×C73#57611yescharacteristic
176C2×C73#57711yescharacteristic
177D73—41no—
178#3179—731nomaximal, Sylow
179C73#317911yescharacteristic, complemented, Sylow
180#542—731no—
181#540—731no—
182#501—731no—
183#496D7311yescharacteristic, complemented
184#488—731no—
185#486—731no—
186#469—731no—
187#468—731no—
188#466—731no—
189#465—731no—
190#442—731no—
191#440—731no—
192C4×SD16—731no—
193C4×D8—731no—
194#405—731no—
195C2×SD16C2×D7311yescharacteristic
196C2×SD16C2×D7311yescharacteristic
197C2×D8C2×D7311yescharacteristic
198C2×D8C2×D7311yescharacteristic
199C2×M16—731no—
200C22×C8—731no—
201C4⋊Q8—731no—
202#127C2×D7311yescharacteristic
203#126—1461no—
204#125—731no—
205#124—1461no—
206#124C2×D7311yescharacteristic
207#123—1461no—
208#123—1461no—
209#123—1461no—
210C22⋊Q8—731no—
211C22⋊Q8—1461no—
212#121—731no—
213#121—731no—
214#121—731no—
215#121—1461no—
216#121—1461no—
217C4×Q8—731no—
218C4×D4—731no—
219C4×D4—731no—
220C4×D4—731no—
221#117—731no—
222#107—731no—
223#107—731no—
224#106—731no—
225#106—731no—
226#103—731no—
227#103—731no—
228#102—731no—
229#102—731no—
230#102—731no—
231#102—731no—
232#102—731no—
233#102—731no—
234#97—731no—
235#97C2×D7311yescharacteristic
236C4×C8—731no—
237C4×C8—731no—
238C2×Q8—1461no—
239C2×Q8C22×D7311yescharacteristic
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—1461no—
243C2×D4—1461no—
244C2×D4—1461no—
245C2×D4C22×D7311yescharacteristic
246C2×D4C22×D7311yescharacteristic
247C2×D4C22×D7311yescharacteristic
248C22×C4—731no—
249C22×C4—1461no—
250C22×C4—1461no—
251C22×C4—1461no—
252SD16—22no—
253SD16—22no—
254D8—22no—
255D8—22no—
256M16—1462no—
257C2×C8—731no—
258C2×C8—731no—
259C2×C8—1462no—
260C2×C8C22×D7311yescharacteristic
261C2×C8C22×D7311yescharacteristic
262C4⋊C4—731no—
263C4⋊C4—731no—
264C4⋊C4—731no—
265C4⋊C4—731no—
266C4⋊C4—731no—
267C4⋊C4—731no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
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—1461no—
286C42C22×D7311yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—731no—
291Q8—21no—
292Q8—21no—
293Q8—5841no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—5841no—
303D4—5841no—
304D4—5841no—
305C2×C4—21no—
306C2×C4—5841no—
307C2×C4—5841no—
308C2×C4—5841no—
309C2×C4—731no—
310C2×C4—731no—
311C2×C4—731no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4D4×D7311yescharacteristic
319C2×C4D4×D7311yescharacteristic
320C2×C4C23×D7311yescharacteristic
321C8—1461no—
322C8—1461no—
323C8#1192402712yes—
324C8#1192402712yes—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—1461no—
335C22—1461no—
336C22—1461no—
337C22C2×D4×D7311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—2921no—
342C4—2921no—
343C4—2921no—
344C4—2921no—
345C4—1461no—
346C4—1461no—
347C4—1461no—
348C4C2×#1192402711yescharacteristic
349C4C2×#1192402711yescharacteristic
350C2—81no—
351C2—81no—
352C2—81no—
353C2—2921no—
354C2#1798913511yescharacteristic
355C2#1798939111yescharacteristic
356C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#496×C73C2
socleC22×C73C22×D4
hypercenter#496D73
hypocenterC73#3179
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #17989206C2semidirect
2. #17989191C2semidirect
3. #17988996C2semidirect
4. #17988941C2semidirect
5. #17988933C2semidirect
6. #17988837C2semidirect
7. #17988830C2semidirect
8. #17988820C2semidirect
9. #17988813C2semidirect
10. #17988699C2semidirect
11. #17988688C2semidirect
12. SD16×Dic73C2semidirect
13. D8×Dic73C2semidirect
14. #17988544C2semidirect
15. #496×C73C2semidirect
179. C73#3179semidirect
183. #496D73semidirect