Finite Group Databasebeta

← #22622412

Subgroups — #22622412

Order 9344.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989292C211yesmaximal, characteristic, complemented
2#17989285C211yesmaximal, characteristic
3#17988995C211yesmaximal, characteristic, complemented
4#17988930C211yesmaximal, characteristic, complemented
5#17988922C211yesmaximal, characteristic, complemented
6#17988905C211yesmaximal, characteristic, complemented
7#17988902C211yesmaximal, characteristic, complemented
8#17988893C211yesmaximal, characteristic, complemented
9#17988866C211yesmaximal, characteristic, complemented
10#17988834C211yesmaximal, characteristic, complemented
11#17988816C211yesmaximal, characteristic, complemented
12#17988686C211yesmaximal, characteristic, complemented
13#17988658C211yesmaximal, characteristic, complemented
14#17988628C211yesmaximal, characteristic, complemented
15C2×#107×C73C211yesmaximal, characteristic, complemented
16C2×#11924017C2211yescharacteristic
17C2×#11924011C2211yescharacteristic
18#14556590C2211yescharacteristic
19#14556586—21no—
20#14556582C2211yescharacteristic
21#14556581—21no—
22#14556576—21no—
23#14556571C2211yescharacteristic
24#14556570—21no—
25#14556570C2211yescharacteristic
26#14556569—21no—
27#14556566C2211yescharacteristic
28#14556565—21no—
29#14556565C2211yescharacteristic
30#14556556C2211yescharacteristic
31#14556553C2211yescharacteristic
32C4×C22⋊D73—21no—
33C4×C22⋊D73—21no—
34C4×C22⋊D73C2211yescharacteristic
35#14556549C2211yescharacteristic
36C4⋊C4×D73C2211yescharacteristic
37#14556524C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556501C2211yescharacteristic
52C22×C8×C73C2211yescharacteristic
53C2×C4⋊C4×C73C2211yescharacteristic
54C2×C4⋊C4×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic
57#107×C73C2211yescharacteristic
58#107×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C2×D292—21no—
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73D411yescharacteristic
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73C2311yescharacteristic
68#11924017—22no—
69#11924011—22no—
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007D411yescharacteristic
82C22⋊Dic73—21no—
83C22⋊Dic73D411yescharacteristic
84#11924005—21no—
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005D411yescharacteristic
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73C2311yescharacteristic
93C22×C4×C73—21no—
94C22×C4×C73—21no—
95C22×C4×C73C2311yescharacteristic
96C2×C8×C73—22no—
97C2×C8×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C23×C73C2×D411yescharacteristic
106C22×D73—21no—
107C22×D73C2×D411yescharacteristic
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—81no—
115C2×C4×C73—81no—
116C2×C4×C73C2×D411yescharacteristic
117C2×C4×C73C2411yescharacteristic
118C22⋊D73—22no—
119C22⋊D73—42no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73C2×D411yescharacteristic
124C2×Dic73C2×D411yescharacteristic
125C2×Dic73C2×D411yescharacteristic
126D292—21no—
127D292—21no—
128D292—81no—
129C4×D73—21no—
130C4×D73—21no—
131C4×D73—81no—
132C4×D73—81no—
133Dic146—21no—
134Dic146—21no—
135Dic146—81no—
136C8×C73—21no—
137C8×C73#4112yes—
138#10596831—21no—
139#10596831—21no—
140C22×C73—21no—
141C22×C73—21no—
142C22×C73#13712yes—
143C22×C73C22×D411yescharacteristic
144C2×D73—21no—
145C2×D73—21no—
146C2×D73—21no—
147C2×D73—41no—
148C2×D73—41no—
149C2×D73—41no—
150C4×C73—21no—
151C4×C73—41no—
152C4×C73—41no—
153C4×C73—41no—
154C4×C73—41no—
155C4×C73C2×#4111yescharacteristic
156C4×C732−1+411yescharacteristic
157Dic73—21no—
158Dic73—21no—
159Dic73—21no—
160Dic73—41no—
161Dic73—41no—
162Dic73—41no—
163C2×C73—22no—
164C2×C73#54711yescharacteristic
165C2×C73C2×#13711yescharacteristic
166C2×C73#57611yescharacteristic
167D73—41no—
168D73—81no—
169#3346—731nomaximal, Sylow
170C73#334611yescharacteristic, complemented, Sylow
171#554—731no—
172#553—731no—
173#501—731no—
174#485—731no—
175#484—731no—
176#481—731no—
177#480—731no—
178#479—731no—
179#474—731no—
180#468—731no—
181#465—731no—
182#440—731no—
183#435—731no—
184#428—731no—
185C2×#107D7311yescharacteristic, complemented
186C2×SD16—731no—
187C2×M16—731no—
188C22×C8C2×D7311yescharacteristic
189C4⋊Q8—731no—
190#126—1461no—
191#125—731no—
192#125—1461no—
193#123—1461no—
194C22⋊Q8—731no—
195C22⋊Q8—731no—
196C22⋊Q8—1461no—
197C22⋊Q8—1461no—
198#121—731no—
199#121—731no—
200#121—1461no—
201C4×Q8—731no—
202C4×D4—731no—
203C4×D4—731no—
204C4×D4—1461no—
205C4×D4—1461no—
206#117—731no—
207C2×C4⋊C4—731no—
208C2×C4⋊C4C2×D7311yescharacteristic
209C2×C4⋊C4C2×D7311yescharacteristic
210#107—731no—
211#107—731no—
212#107C2×D7311yescharacteristic
213#107C2×D7311yescharacteristic
214#107C2×D7311yescharacteristic
215#107C2×D7311yescharacteristic
216#106—731no—
217#106—731no—
218#106—731no—
219C4⋊C8—731no—
220#103—731no—
221#103—731no—
222#103—731no—
223#102—731no—
224#102—731no—
225#102—731no—
226C22⋊C8—731no—
227C22⋊C8—731no—
228#97—731no—
229C2×Q8—731no—
230C2×Q8—1461no—
231C2×D4—731no—
232C2×D4—731no—
233C2×D4—1461no—
234C2×D4—1461no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—731no—
238C22×C4—1461no—
239C22×C4—1461no—
240C22×C4C22×D7311yescharacteristic
241SD16—1462no—
242M16—1462no—
243C2×C8—22no—
244C2×C8—731no—
245C2×C8—731no—
246C2×C8C22×D7311yescharacteristic
247C2×C8C22×D7311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—731no—
251C4⋊C4—731no—
252C4⋊C4—731no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C4⋊C4C22×D7311yescharacteristic
261C4⋊C4C22×D7311yescharacteristic
262C4⋊C4C22×D7311yescharacteristic
263C4⋊C4C22×D7311yescharacteristic
264C22⋊C4—731no—
265C22⋊C4—731no—
266C22⋊C4—1461no—
267C22⋊C4—1461no—
268C22⋊C4—1461no—
269C22⋊C4—1461no—
270C22⋊C4—1461no—
271C22⋊C4—1461no—
272C42—731no—
273C42—1461no—
274C42—1461no—
275C23—731no—
276C23—1461no—
277C23D4×D7311yescharacteristic
278Q8—5841no—
279Q8—1461no—
280Q8—1461no—
281D4—2922no—
282D4—5841no—
283D4—1462no—
284D4—1461no—
285D4—1461no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—5841no—
295C2×C4—5841no—
296C2×C4—731no—
297C2×C4—731no—
298C2×C4—731no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4—1461no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4D4×D7311yescharacteristic
305C2×C4C23×D7311yescharacteristic
306C8—21no—
307C8—1461no—
308C8—1461no—
309C8#1192402812yes—
310C22—21no—
311C22—21no—
312C22—2921no—
313C22—2921no—
314C22—2921no—
315C22—1461no—
316C22—1461no—
317C22—1461no—
318C22#1455662312yes—
319C22C2×D4×D7311yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—2921no—
326C4—2921no—
327C4—2921no—
328C4—1461no—
329C4—1461no—
330C4—1461no—
331C4C2×#1192402811yescharacteristic
332C4#1455663911yescharacteristic
333C2—22no—
334C2—2921no—
335C2—5841no—
336C2#1798923811yescharacteristic
337C2C2×#1455662311yescharacteristic
338C2#1798938811yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#107×C73C2
socleC22×C73C22×D4
hypercenterC2×#107D73
hypocenterC73#3346
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. #17989292C2semidirect
3. #17988995C2semidirect
4. #17988930C2semidirect
5. #17988922C2semidirect
6. #17988905C2semidirect
7. #17988902C2semidirect
8. #17988893C2semidirect
9. #17988866C2semidirect
10. #17988834C2semidirect
11. #17988816C2semidirect
12. #17988686C2semidirect
13. #17988658C2semidirect
14. #17988628C2semidirect
15. C2×#107×C73C2semidirect
170. C73#3346semidirect
185. C2×#107D73semidirect