Finite Group Databasebeta

← #22624340

Subgroups — #22624340

Order 9344.

1002 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989340C212yesmaximal, complemented
2#17989336C212yesmaximal, complemented
3#17989321C212yesmaximal, complemented
4#17989317C212yesmaximal, complemented
5#17989308C212yesmaximal, complemented
6#17989305C212yesmaximal, complemented
7Q8×C22⋊D73C212yesmaximal, complemented
8#17989250C212yesmaximal, complemented
9#17989205C214yesmaximal, complemented
10#17989201C214yesmaximal, complemented
11#17989160C212yesmaximal, complemented
12#17989158C211yesmaximal, characteristic, complemented
13#17989139C212yesmaximal, complemented
14#17989133C211yesmaximal, characteristic
15#536×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18C2×Q8×D73C2212yes—
19#14556590C2212yes—
20#14556590C2214yes—
21#14556590C2214yes—
22#14556589C2211yescharacteristic
23#14556589C2212yes—
24#14556589C2212yes—
25#14556589C2214yes—
26#14556587C2211yescharacteristic
27#14556586C2214yes—
28#14556585C2214yes—
29#14556584C2214yes—
30#14556584C2214yes—
31#14556581C2214yes—
32#14556580C2211yescharacteristic
33#14556578C2211yescharacteristic
34#14556578C2212yes—
35#14556577C2214yes—
36#14556577C2214yes—
37#14556577C2214yes—
38#14556576C2214yes—
39#14556573C2214yes—
40#14556572C2212yes—
41#14556572C2212yes—
42#14556571C2212yes—
43#14556570C2212yes—
44#14556570C2212yes—
45#14556570C2214yes—
46#14556569C2214yes—
47#14556568C2214yes—
48#14556568C2214yes—
49#14556567C2212yes—
50#14556567C2214yes—
51#14556563C2212yes—
52#14556563C2212yes—
53Q8×Dic73C2212yes—
54C4×Dic146C2214yes—
55#14556556C2212yes—
56#14556556C2214yes—
57#14556556C2214yes—
58C4×C22⋊D73C2212yes—
59C4×C22⋊D73C2212yes—
60C4×C22⋊D73C2214yes—
61#14556551C2214yes—
62#14556550C2211yescharacteristic
63#14556549C2212yes—
64#14556547C2214yes—
65C2×C4×Dic73C2211yescharacteristic
66C2×#41×C73C2211yescharacteristic
67C22×Q8×C73C2211yescharacteristic
68C4⋊Q8×C73C2212yes—
69#124×C73C2212yes—
70#123×C73C2212yes—
71#123×C73C2212yes—
72C22⋊Q8×C73C2212yes—
73C22⋊Q8×C73C2212yes—
74#117×C73C2211yescharacteristic
75#11924028—42no—
76C2×Dic146—42no—
77C2×Dic146C2314yes—
78C2×Dic146C2312yes—
79C2×Dic146C2314yes—
80C2×Dic146C2312yes—
81C2×Dic146C2311yescharacteristic
82Q8×D73—44no—
83C2×D292C2311yescharacteristic
84C2×C22⋊D73C2312yes—
85C2×C22⋊D73C2312yes—
86C2×C22⋊D73C2312yes—
87C22×Dic73C2312yes—
88C22×Dic73C2312yes—
89C2×C4×D73C2312yes—
90C2×C4×D73C2314yes—
91C4⋊Dic73C2312yes—
92C4⋊Dic73C2314yes—
93C4⋊Dic73C2314yes—
94#11924007C2314yes—
95#11924007C2314yes—
96#11924007C2314yes—
97#11924007C2312yes—
98#11924007C2312yes—
99#11924007C2314yes—
100#11924007C2314yes—
101#11924007C2314yes—
102#11924007C2314yes—
103C22⋊Dic73C2314yes—
104C22⋊Dic73C2312yes—
105C22⋊Dic73C2312yes—
106C22⋊Dic73C2312yes—
107C22⋊Dic73C2314yes—
108#11924005C2314yes—
109#11924005C2314yes—
110#11924005C2312yes—
111#11924005C2312yes—
112#11924005C2314yes—
113C4×Dic73C2312yes—
114C4×Dic73C2311yescharacteristic
115C4×Dic73C2311yescharacteristic
116C4×Dic73C2314yes—
117C4×Dic73C2314yes—
118C4×Dic73C2314yes—
119C4×Dic73C2312yes—
120#41×C73—42no—
121C2×Q8×C73—42no—
122C2×Q8×C73C2312yes—
123C2×Q8×C73C2312yes—
124C2×Q8×C73C2311yescharacteristic
125C2×D4×C73C2311yescharacteristic
126C2×D4×C73C2311yescharacteristic
127C2×D4×C73C2311yescharacteristic
128C22×C4×C73C2311yescharacteristic
129C22×C4×C73C2311yescharacteristic
130C22×C4×C73C2311yescharacteristic
131C22×C4×C73C2312yes—
132C4⋊C4×C73C2312yes—
133C4⋊C4×C73C2314yes—
134C4⋊C4×C73C2314yes—
135C22⋊C4×C73C2312yes—
136C22⋊C4×C73C2314yes—
137C22⋊C4×C73C2314yes—
138C42×C73C2312yes—
139C23×C73C2411yescharacteristic
140C23×C73C2411yescharacteristic
141C23×C73C2411yescharacteristic
142C22×D73C2412yes—
143Q8×C73—24no—
144Q8×C73—42no—
145Q8×C73—41no—
146D4×C73—41no—
147D4×C73—41no—
148D4×C73—41no—
149C2×C4×C73—22no—
150C2×C4×C73—22no—
151C2×C4×C73—22no—
152C2×C4×C73—42no—
153C2×C4×C73C2411yescharacteristic
154C2×C4×C73C2414yes—
155C2×C4×C73C2414yes—
156C2×C4×C73C2411yescharacteristic
157C2×C4×C73C2411yescharacteristic
158C2×C4×C73C2411yescharacteristic
159C22⋊D73—24no—
160C22⋊D73—24no—
161C22⋊D73—42no—
162C2×Dic73—24no—
163C2×Dic73—42no—
164C2×Dic73C2414yes—
165C2×Dic73C2412yes—
166C2×Dic73C2412yes—
167C2×Dic73C2414yes—
168C2×Dic73C2412yes—
169D292—41no—
170C4×D73—24no—
171C4×D73—44no—
172Dic146—24no—
173Dic146—28no—
174Dic146—44no—
175Dic146—42no—
176Dic146—41no—
177C22×C73—21no—
178C22×C73—21no—
179C22×C73—21no—
180C22×C73—22no—
181C22×C73—22no—
182C22×C73—22no—
183C22×C73C2511yescharacteristic
184C2×D73—22no—
185C2×D73—22no—
186C2×D73—22no—
187C4×C73—21no—
188C4×C73—24no—
189C4×C73—21no—
190C4×C73—21no—
191C4×C73—24no—
192C4×C73H(5,𝔽2)12yes—
193Dic73—24no—
194Dic73—22no—
195Dic73—24no—
196Dic73—22no—
197Dic732−1+414yes—
198C2×C73—41no—
199C2×C73—41no—
200C2×C73—41no—
201C2×C73C2×H(5,𝔽2)11yescharacteristic
202C2×C73C2×2−1+412yes—
203D73—42no—
204#3550—731nomaximal, Sylow
205C73#355011yescharacteristic, complemented, Sylow
206#563—732no—
207#563—732no—
208#559—732no—
209Q82—732no—
210#556—732no—
211#556—732no—
212D4×Q8—732no—
213D4×Q8—732no—
214#542—734no—
215#542—734no—
216#536—731no—
217#536—732no—
218#536D7311yescharacteristic, complemented
219#533—732no—
220#532—731no—
221C2×#41—731no—
222C2×#41C2×D7311yescharacteristic
223C22×Q8—732no—
224C22×Q8—731no—
225C22×Q8C2×D7311yescharacteristic
226C4⋊Q8—731no—
227C4⋊Q8—732no—
228C4⋊Q8—732no—
229C4⋊Q8—734no—
230C4⋊Q8—732no—
231C4⋊Q8—734no—
232C4⋊Q8—734no—
233C4⋊Q8C2×D7312yes—
234#127—731no—
235#126—734no—
236#126—734no—
237#126—734no—
238#126—734no—
239#125—734no—
240#124—731no—
241#124—731no—
242#124—732no—
243#124—734no—
244#124—734no—
245#124—734no—
246#124C2×D7312yes—
247#123—732no—
248#123—732no—
249#123—734no—
250#123—734no—
251#123C2×D7312yes—
252#123C2×D7312yes—
253C22⋊Q8—732no—
254C22⋊Q8—734no—
255C22⋊Q8—732no—
256C22⋊Q8—732no—
257C22⋊Q8—734no—
258C22⋊Q8—732no—
259C22⋊Q8—734no—
260C22⋊Q8—734no—
261C22⋊Q8—734no—
262C22⋊Q8C2×D7312yes—
263C22⋊Q8C2×D7312yes—
264#121—732no—
265#121—732no—
266C4×Q8—732no—
267C4×Q8—732no—
268C4×Q8—734no—
269C4×Q8—734no—
270C4×Q8—734no—
271C4×D4—732no—
272C4×D4—732no—
273C4×D4—734no—
274C4×D4—734no—
275#117—731no—
276#117—732no—
277#117—734no—
278#117C2×D7311yescharacteristic
279C2×C42—731no—
280#41—42no—
281#41—2922no—
282C2×Q8—42no—
283C2×Q8—2922no—
284C2×Q8—2924no—
285C2×Q8—734no—
286C2×Q8—732no—
287C2×Q8—731no—
288C2×Q8—734no—
289C2×Q8—732no—
290C2×Q8C22×D7312yes—
291C2×Q8C22×D7312yes—
292C2×Q8C22×D7311yescharacteristic
293C2×D4—732no—
294C2×D4—732no—
295C2×D4—732no—
296C2×D4—731no—
297C2×D4C22×D7311yescharacteristic
298C2×D4C22×D7311yescharacteristic
299C2×D4C22×D7311yescharacteristic
300C22×C4—732no—
301C22×C4—734no—
302C22×C4—732no—
303C22×C4—732no—
304C22×C4C22×D7311yescharacteristic
305C22×C4C22×D7311yescharacteristic
306C22×C4C22×D7311yescharacteristic
307C22×C4C22×D7312yes—
308C4⋊C4—734no—
309C4⋊C4—734no—
310C4⋊C4—734no—
311C4⋊C4—732no—
312C4⋊C4—732no—
313C4⋊C4—734no—
314C4⋊C4—734no—
315C4⋊C4—734no—
316C4⋊C4—734no—
317C4⋊C4—732no—
318C4⋊C4—734no—
319C4⋊C4—734no—
320C4⋊C4C22×D7312yes—
321C4⋊C4C22×D7314yes—
322C4⋊C4C22×D7314yes—
323C22⋊C4—734no—
324C22⋊C4—732no—
325C22⋊C4—732no—
326C22⋊C4—732no—
327C22⋊C4—734no—
328C22⋊C4—734no—
329C22⋊C4—732no—
330C22⋊C4—732no—
331C22⋊C4—734no—
332C22⋊C4—734no—
333C22⋊C4C22×D7314yes—
334C22⋊C4C22×D7312yes—
335C22⋊C4C22×D7314yes—
336C42—732no—
337C42—731no—
338C42—731no—
339C42—734no—
340C42—734no—
341C42—732no—
342C42—734no—
343C42C22×D7312yes—
344C23—732no—
345C23C23×D7311yescharacteristic
346C23C23×D7311yescharacteristic
347C23C23×D7311yescharacteristic
348Q8—24no—
349Q8—42no—
350Q8—41no—
351Q8—2922no—
352Q8—2924no—
353Q8—2921no—
354Q8—1468no—
355Q8—1464no—
356D4—41no—
357D4—41no—
358D4—41no—
359D4—2921no—
360D4—2922no—
361D4—1464no—
362D4—1464no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—42no—
367C2×C4—2924no—
368C2×C4—2922no—
369C2×C4—732no—
370C2×C4—734no—
371C2×C4—732no—
372C2×C4—732no—
373C2×C4—734no—
374C2×C4—1464no—
375C2×C4—1464no—
376C2×C4C23×D7314yes—
377C2×C4C23×D7311yescharacteristic
378C2×C4C23×D7311yescharacteristic
379C2×C4C23×D7314yes—
380C2×C4C23×D7311yescharacteristic
381C2×C4C23×D7311yescharacteristic
382C22—21no—
383C22—21no—
384C22—21no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—1462no—
389C22—1462no—
390C22—1462no—
391C22C24×D7311yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—24no—
396C4—24no—
397C4—734no—
398C4—1464no—
399C4—1462no—
400C4—1462no—
401C4—1464no—
402C4#1455663612yes—
403C2—41no—
404C2—41no—
405C2—41no—
406C2—2922no—
407C2C2×#1455663611yescharacteristic
408C22−1+4×D7312yes—
subgroupG/H
center, FrattiniC22C24×D73
commutator, socleC22×C73C25
Fitting#536×C73C2
hypercenter#536D73
hypocenterC73#3550
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #17989340C2semidirect
2. #17989336C2semidirect
3. #17989321C2semidirect
4. #17989317C2semidirect
5. #17989308C2semidirect
6. #17989305C2semidirect
7. Q8×C22⋊D73C2semidirect
8. #17989250C2semidirect
9. #17989205C2semidirect
10. #17989201C2semidirect
11. #17989160C2semidirect
12. #17989158C2semidirect
13. #17989139C2semidirect
15. #536×C73C2semidirect
205. C73#3550semidirect
218. #536D73semidirect