Finite Group Databasebeta

← #22621803

Subgroups — #22621803

Order 9344.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989292C211yesmaximal, characteristic
2Q8×C22⋊D73C211yesmaximal, characteristic
3#17988936C211yesmaximal, characteristic, complemented
4#17988922C211yesmaximal, characteristic, complemented
5#17988921C211yesmaximal, characteristic, complemented
6#17988880C211yesmaximal, characteristic, complemented
7#17988828C211yesmaximal, characteristic, complemented
8#17988827C211yesmaximal, characteristic, complemented
9#17988796C211yesmaximal, characteristic, complemented
10#17988744C211yesmaximal, characteristic, complemented
11#17988743C211yesmaximal, characteristic, complemented
12#17988679C211yesmaximal, characteristic, complemented
13C8×C22⋊D73C211yesmaximal, characteristic
14#103×D73C211yesmaximal, characteristic, complemented
15C2×#103×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic
17C2×Dic292C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924018C2211yescharacteristic
20C2×C8×D73C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556589—21no—
23#14556589C2211yescharacteristic
24#14556581—21no—
25#14556571C2211yescharacteristic
26#14556570—21no—
27#14556570—21no—
28#14556570C2211yescharacteristic
29#14556570C2211yescharacteristic
30#14556569—21no—
31#14556567—21no—
32#14556567C2211yescharacteristic
33Q8×Dic73C2211yescharacteristic
34#14556556C2211yescharacteristic
35C4×C22⋊D73—21no—
36C4×C22⋊D73—21no—
37C4×C22⋊D73C2211yescharacteristic
38C4⋊C4×D73C2211yescharacteristic
39#14556525C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556524C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556514C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C22×Q8×C73C2211yescharacteristic
53C22×C8×C73C2211yescharacteristic
54C2×C4⋊C4×C73C2211yescharacteristic
55#103×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146—21no—
61C2×Dic146C2311yescharacteristic
62C2×Dic146C2311yescharacteristic
63Q8×D73—22no—
64Q8×D73—41no—
65C2×C22⋊D73D411yescharacteristic
66C2×C4×D73—21no—
67C2×C4×D73—21no—
68C2×C4×D73C2311yescharacteristic
69Dic292—41no—
70#11924018—22no—
71#11924018—41no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C8×D73—41no—
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007D411yescharacteristic
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73D411yescharacteristic
91#11924005—21no—
92#11924005—21no—
93#11924005D411yescharacteristic
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97C2×Q8×C73—21no—
98C2×Q8×C73—22no—
99C2×Q8×C73—41no—
100C2×Q8×C73C2311yescharacteristic
101C2×Q8×C73C2311yescharacteristic
102C22×C4×C73—21no—
103C22×C4×C73—21no—
104C22×C4×C73C2311yescharacteristic
105C2×C8×C73—41no—
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C23×C73C2×D411yescharacteristic
112C22×D73C2×D411yescharacteristic
113Q8×C73—21no—
114Q8×C73—21no—
115Q8×C73—21no—
116Q8×C73—42no—
117Q8×C73#4112yes—
118C2×C4×C73—21no—
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—81no—
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2411yescharacteristic
128C22⋊D73Q1614yescomplemented
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73C2×D411yescharacteristic
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136C4×D73—21no—
137C4×D73—21no—
138C4×D73—42no—
139C4×D73—81no—
140Dic146—21no—
141Dic146—21no—
142Dic146—21no—
143Dic146—21no—
144Dic146—42no—
145Dic146—81no—
146C8×C73—21no—
147C8×C73—21no—
148#10596831—21no—
149#10596831—21no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73C2×Q1612yes—
153C22×C73C22×D411yescharacteristic
154C2×D73—21no—
155C2×D73—21no—
156C2×D73C2×Q1612yes—
157C4×C73—22no—
158C4×C73—21no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73C2×#4111yescharacteristic
163C4×C73H(5,𝔽2)11yescharacteristic
164Dic73—21no—
165Dic73—21no—
166Dic73—41no—
167Dic73—41no—
168Dic73—41no—
169Dic73—41no—
170Dic73C2×Q1612yes—
171C2×C73—22no—
172C2×C73#54611yescharacteristic
173C2×C73C22×Q1611yescharacteristic
174C2×C73#57711yescharacteristic
175D73—22no—
176#3299—731nomaximal, Sylow
177C73#329911yescharacteristic, complemented, Sylow
178#554—731no—
179D4×Q8—731no—
180#487—731no—
181#484—731no—
182#484—731no—
183#477—731no—
184#467—731no—
185#467—731no—
186#462—731no—
187#451—731no—
188#451—731no—
189C4×Q16—731no—
190C8×D4—731no—
191C2×#103—731no—
192C2×#103D7311yescharacteristic, complemented
193C22×Q8—731no—
194C22×Q8C2×D7311yescharacteristic
195C2×Q16—731no—
196C2×Q16—731no—
197C2×Q16—731no—
198C22×C8—731no—
199C22×C8C2×D7311yescharacteristic
200C4⋊Q8—731no—
201C4⋊Q8—731no—
202C4⋊Q8—1461no—
203#125—1461no—
204C22⋊Q8—731no—
205C22⋊Q8—731no—
206C22⋊Q8—731no—
207C22⋊Q8—731no—
208C22⋊Q8—1461no—
209C22⋊Q8—1461no—
210C22⋊Q8—1461no—
211C22⋊Q8—1461no—
212C4×Q8—731no—
213C4×Q8—731no—
214C4×D4—731no—
215C4×D4—1461no—
216C4×D4—1461no—
217C2×C4⋊C4—731no—
218C2×C4⋊C4C2×D7311yescharacteristic
219#107—731no—
220#107—731no—
221#107—731no—
222C4⋊C8—731no—
223#103—731no—
224#103—731no—
225#103—731no—
226#103—731no—
227#103—731no—
228#103—731no—
229#103C2×D7311yescharacteristic
230#103C2×D7311yescharacteristic
231#103C2×D7311yescharacteristic
232#103C2×D7311yescharacteristic
233C22⋊C8—731no—
234C22⋊C8—731no—
235C4×C8—731no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—2921no—
240C2×Q8—731no—
241C2×Q8—731no—
242C2×Q8—1461no—
243C2×Q8—1461no—
244C2×Q8—1462no—
245C2×Q8C22×D7311yescharacteristic
246C2×Q8C22×D7311yescharacteristic
247C2×D4—731no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—731no—
251C22×C4—1461no—
252C22×C4—1461no—
253C22×C4C22×D7311yescharacteristic
254Q16—2921no—
255Q16—2921no—
256Q16—1462no—
257C2×C8—41no—
258C2×C8—2921no—
259C2×C8—731no—
260C2×C8—731no—
261C2×C8C22×D7311yescharacteristic
262C2×C8C22×D7311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—731no—
265C4⋊C4—731no—
266C4⋊C4—731no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4C22×D7311yescharacteristic
278C4⋊C4C22×D7311yescharacteristic
279C22⋊C4—731no—
280C22⋊C4—731no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C42—731no—
286C42—1461no—
287C42—1461no—
288C23—731no—
289C23D4×D7311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—42no—
294Q8—2922no—
295Q8—5841no—
296Q8—1461no—
297Q8—1461no—
298Q8—1461no—
299Q8—1461no—
300Q8#1192402812yes—
301D4—734no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—2922no—
311C2×C4—5841no—
312C2×C4—731no—
313C2×C4—731no—
314C2×C4—731no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4D4×D7311yescharacteristic
322C2×C4C23×D7311yescharacteristic
323C8—21no—
324C8—21no—
325C8—1461no—
326C8—1461no—
327C22—21no—
328C22—21no—
329C22—732no—
330C22—1461no—
331C22—1461no—
332C22Q16×D7312yes—
333C22C2×D4×D7311yescharacteristic
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—2921no—
340C4—2921no—
341C4—2921no—
342C4—2921no—
343C4—732no—
344C4—1461no—
345C4—1461no—
346C4C2×#1192402811yescharacteristic
347C4#1455663611yescharacteristic
348C2—22no—
349C2—1462no—
350C2#1798922711yescharacteristic
351C2C2×Q16×D7311yescharacteristic
352C2#1798939311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#103×C73C2
socleC22×C73C22×D4
hypercenterC2×#103D73
hypocenterC73#3299
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #17988936C2semidirect
4. #17988922C2semidirect
5. #17988921C2semidirect
6. #17988880C2semidirect
7. #17988828C2semidirect
8. #17988827C2semidirect
9. #17988796C2semidirect
10. #17988744C2semidirect
11. #17988743C2semidirect
12. #17988679C2semidirect
14. #103×D73C2semidirect
15. C2×#103×C73C2semidirect
128. C22⋊D73Q16semidirect
177. C73#3299semidirect
192. C2×#103D73semidirect