Finite Group Databasebeta

← #22621046

Subgroups — #22621046

Order 9344.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989210C211yesmaximal, characteristic, complemented
2#17989161C211yesmaximal, characteristic, complemented
3#17988980C211yesmaximal, characteristic, complemented
4#17988972C211yesmaximal, characteristic, complemented
5#17988948C211yesmaximal, characteristic, complemented
6#17988936C211yesmaximal, characteristic, complemented
7#17988811C211yesmaximal, characteristic, complemented
8#17988805C211yesmaximal, characteristic, complemented
9#17988795C211yesmaximal, characteristic, complemented
10#17988791C211yesmaximal, characteristic, complemented
11#17988747C211yesmaximal, characteristic, complemented
12#17988734C211yesmaximal, characteristic
13#17988726C211yesmaximal, characteristic, complemented
14#17988645C211yesmaximal, characteristic, complemented
15#451×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924017C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20C2×#11924015C2211yescharacteristic
21C2×#11924015C2211yescharacteristic
22C2×D584C2211yescharacteristic
23#14556590C2211yescharacteristic
24#14556589C2211yescharacteristic
25#14556589C2211yescharacteristic
26#14556586—21no—
27#14556580C2211yescharacteristic
28#14556580C2211yescharacteristic
29#14556580C2211yescharacteristic
30#14556577—21no—
31#14556574—21no—
32#14556574—21no—
33#14556573—21no—
34#14556571—21no—
35#14556567—21no—
36#14556567—21no—
37#14556565C2211yescharacteristic
38Q8×Dic73C2211yescharacteristic
39#14556553C2211yescharacteristic
40#14556550C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C22×Q8×C73C2211yescharacteristic
53C2×Q16×C73C2211yescharacteristic
54C2×Q16×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—41no—
60#11924028—41no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63C2×D292C2311yescharacteristic
64C2×D292C2311yescharacteristic
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69#11924018—41no—
70#11924017—41no—
71#11924015—41no—
72#11924015—41no—
73#11924015—41no—
74D584—41no—
75C2×#10596831C2311yescharacteristic
76C2×#10596831C2311yescharacteristic
77C4⋊Dic73—21no—
78C4⋊Dic73D411yescharacteristic
79C4⋊Dic73D411yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86C22⋊Dic73D411yescharacteristic
87C22⋊Dic73D411yescharacteristic
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96C4×Dic73—21no—
97C4×Dic73C2311yescharacteristic
98C4×Dic73C2311yescharacteristic
99C2×Q8×C73—21no—
100C2×Q8×C73—41no—
101C2×Q8×C73—41no—
102C2×Q8×C73C2311yescharacteristic
103C2×Q8×C73C2311yescharacteristic
104C2×Q8×C73C2311yescharacteristic
105C22×C4×C73—21no—
106C22×C4×C73C2311yescharacteristic
107Q16×C73—41no—
108Q16×C73—41no—
109C2×C8×C73C2311yescharacteristic
110C2×C8×C73C2311yescharacteristic
111C4⋊C4×C73—21no—
112C4⋊C4×C73C2311yescharacteristic
113C22⋊C4×C73—21no—
114C23×C73C2×D411yescharacteristic
115C22×D73—21no—
116C22×D73—21no—
117Q8×C73—21no—
118Q8×C73—21no—
119Q8×C73—21no—
120Q8×C73—21no—
121Q8×C73—21no—
122Q8×C73—21no—
123Q8×C73—42no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—42no—
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2411yescharacteristic
133C22⋊D73—42no—
134C22⋊D73—81no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139C2×Dic73C2×D411yescharacteristic
140C2×Dic73C2×D411yescharacteristic
141D292—21no—
142D292—21no—
143D292—21no—
144D292—21no—
145C4×D73—42no—
146C4×D73—81no—
147Dic146—21no—
148Dic146—21no—
149Dic146—81no—
150C8×C73—21no—
151C8×C73—21no—
152#10596831—21no—
153#10596831—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73C22×D411yescharacteristic
158C2×D73—41no—
159C2×D73—41no—
160C2×D73—41no—
161C2×D73—41no—
162C2×D73—41no—
163C2×D73—41no—
164C4×C73—21no—
165C4×C73—41no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73H(5,𝔽2)11yescharacteristic
170C4×C73H(5,𝔽2)11yescharacteristic
171Dic73—21no—
172Dic73—21no—
173Dic73—21no—
174Dic73—21no—
175Dic73—41no—
176Dic73—41no—
177C2×C73—41no—
178C2×C73#53511yescharacteristic
179C2×C73#57711yescharacteristic
180C2×C73#57811yescharacteristic
181D73—81no—
182D73—81no—
183#3225—731nomaximal, Sylow
184C73#322511yescharacteristic, complemented, Sylow
185#542—731no—
186#536—731no—
187#497—731no—
188#495—731no—
189#489—731no—
190#487—731no—
191#464—731no—
192#463—731no—
193#462—731no—
194#461—731no—
195#452—731no—
196#451D7311yescharacteristic, complemented
197#449—731no—
198#448—731no—
199#433—731no—
200C2×#41—731no—
201C22×Q8C2×D7311yescharacteristic
202C2×Q16—731no—
203C2×Q16C2×D7311yescharacteristic
204C2×Q16C2×D7311yescharacteristic
205C2×SD16—731no—
206C2×SD16—731no—
207C2×SD16—731no—
208C2×SD16—731no—
209C2×D8—731no—
210C4⋊Q8—731no—
211C4⋊Q8—731no—
212C4⋊Q8—731no—
213#126—1461no—
214#124—731no—
215#124—731no—
216#124—731no—
217#124—1461no—
218#123—1461no—
219#123—1461no—
220#123—1461no—
221C22⋊Q8—1461no—
222C22⋊Q8—1461no—
223C22⋊Q8—1461no—
224C22⋊Q8C2×D7311yescharacteristic
225#121—731no—
226C4×Q8—731no—
227C4×D4—731no—
228#117—731no—
229C4⋊C8—731no—
230C4⋊C8—731no—
231#103—731no—
232#103—731no—
233#103—731no—
234#103—731no—
235#103C2×D7311yescharacteristic
236#103C2×D7311yescharacteristic
237#102—731no—
238#102—731no—
239C22⋊C8—731no—
240C22⋊C8C2×D7311yescharacteristic
241#97—731no—
242C4×C8—731no—
243#41—2921no—
244#41—2921no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—731no—
249C2×Q8—1461no—
250C2×Q8C22×D7311yescharacteristic
251C2×Q8C22×D7311yescharacteristic
252C2×Q8C22×D7311yescharacteristic
253C2×D4—731no—
254C2×D4—731no—
255C2×D4—1461no—
256C2×D4—1461no—
257C22×C4—21no—
258C22×C4—1461no—
259C22×C4—1461no—
260C22×C4C22×D7311yescharacteristic
261Q16—41no—
262Q16—41no—
263Q16—2921no—
264SD16—2921no—
265SD16—2921no—
266SD16—2921no—
267SD16—2921no—
268D8—2921no—
269C2×C8—731no—
270C2×C8—731no—
271C2×C8C22×D7311yescharacteristic
272C2×C8C22×D7311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—731no—
275C4⋊C4—731no—
276C4⋊C4—731no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4—1461no—
282C4⋊C4—1461no—
283C4⋊C4C22×D7311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—731no—
286C22⋊C4—731no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C42—731no—
296C42—731no—
297C42—1461no—
298C23—1461no—
299C23—1461no—
300C23D4×D7311yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—5841no—
309Q8—1461no—
310Q8—1461no—
311D4—2922no—
312D4—5841no—
313D4—1461no—
314D4—1461no—
315D4—1461no—
316D4—1461no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—2922no—
325C2×C4—5841no—
326C2×C4—731no—
327C2×C4—731no—
328C2×C4—731no—
329C2×C4—731no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4D4×D7311yescharacteristic
333C2×C4C23×D7311yescharacteristic
334C8—21no—
335C8—21no—
336C8—1461no—
337C8—1461no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—2921no—
342C22—2921no—
343C22—2921no—
344C22—2921no—
345C22—2921no—
346C22—2921no—
347C22C2×D4×D7311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—2921no—
354C4—2921no—
355C4—1461no—
356C4—1461no—
357C4—1461no—
358C4—1461no—
359C4#1455663611yescharacteristic
360C4#1455663611yescharacteristic
361C2—41no—
362C2—5841no—
363C2—5841no—
364C2#1798915211yescharacteristic
365C2#1798939611yescharacteristic
366C2#1798940011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#451×C73C2
socleC22×C73C22×D4
hypercenter#451D73
hypocenterC73#3225
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #17989210C2semidirect
2. #17989161C2semidirect
3. #17988980C2semidirect
4. #17988972C2semidirect
5. #17988948C2semidirect
6. #17988936C2semidirect
7. #17988811C2semidirect
8. #17988805C2semidirect
9. #17988795C2semidirect
10. #17988791C2semidirect
11. #17988747C2semidirect
13. #17988726C2semidirect
14. #17988645C2semidirect
15. #451×C73C2semidirect
184. C73#3225semidirect
196. #451D73semidirect