Finite Group Databasebeta

← #22613876

Subgroups — #22613876

Order 9344.

532 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556581C211yesmaximal, characteristic, complemented
2C2×D4×Dic73C211yesmaximal, characteristic
3#17988515C211yesmaximal, characteristic, complemented
4#17988510C211yesmaximal, characteristic, complemented
5#17988501C211yesmaximal, characteristic
6#17988480C211yesmaximal, characteristic, complemented
7#17988475C211yesmaximal, characteristic, complemented
8#17988472C211yesmaximal, characteristic, complemented
9#17988470C211yesmaximal, characteristic, complemented
10#17988468C211yesmaximal, characteristic, complemented
11#17988459C211yesmaximal, characteristic, complemented
12#17988459C211yesmaximal, characteristic, complemented
13#17988445C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
15#394×C73C211yesmaximal, characteristic
16C23×Dic73C2211yescharacteristic
17C23×Dic73C2211yescharacteristic
18#14556581—24no—
19D4×Dic73—24no—
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×C22⋊Dic73C2211yescharacteristic
34C2×C4×Dic73C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
36C2×C4×Dic73C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C22×D4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C22⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C22×Dic73—22no—
54C22×Dic73—22no—
55C22×Dic73—22no—
56C22×Dic73—22no—
57C22×Dic73—41no—
58C22×Dic73—41no—
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C4⋊Dic73—22no—
68C4⋊Dic73D414yes—
69#11924007—22no—
70#11924007—22no—
71#11924007—22no—
72#11924007—22no—
73#11924007—22no—
74#11924007—41no—
75C22⋊Dic73—22no—
76C22⋊Dic73—22no—
77C22⋊Dic73—22no—
78C22⋊Dic73—22no—
79C22⋊Dic73—22no—
80C22⋊Dic73—22no—
81C4×Dic73—22no—
82C4×Dic73—22no—
83C4×Dic73—41no—
84C24×C73C2311yescharacteristic
85C24×C73C2311yescharacteristic
86C2×D4×C73—22no—
87C2×D4×C73—22no—
88C2×D4×C73—22no—
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C4⋊C4×C73—22no—
95C22⋊C4×C73—22no—
96C22⋊C4×C73—22no—
97C22⋊C4×C73—41no—
98C22⋊C4×C73—41no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73#4112yes—
112C23×C73#4112yes—
113C23×C73C2411yescharacteristic
114D4×C73—28no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
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—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73C2×D412yes—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—44no—
151C2×Dic73—44no—
152C2×Dic73C2×D412yes—
153C2×Dic73C2×D412yes—
154C2×Dic73#4112yes—
155C2×Dic73#4112yes—
156C22×C73—22no—
157C22×C73—22no—
158C22×C73—22no—
159C22×C73—22no—
160C22×C73—22no—
161C22×C73—22no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73C22×D411yescharacteristic
171C22×C73C2×#4111yescharacteristic
172C22×C73C2×#4111yescharacteristic
173C22×C73C2×#4111yescharacteristic
174C22×C73C2×#4111yescharacteristic
175C22×C73H(5,𝔽2)11yescharacteristic
176C22×C732−1+411yescharacteristic
177C4×C73—22no—
178C4×C73—41no—
179C4×C73—41no—
180C4×C73—41no—
181C4×C73—41no—
182Dic73—22no—
183Dic73—22no—
184Dic73—22no—
185Dic73—22no—
186Dic73—41no—
187Dic73—41no—
188Dic73—41no—
189Dic73—41no—
190C2×C73—42no—
191C2×C73—42no—
192C2×C73#52511yescharacteristic
193C2×C73#52911yescharacteristic
194C2×C73#53911yescharacteristic
195C2×C73#54611yescharacteristic
196C2×C73#54811yescharacteristic
197C2×C73#55211yescharacteristic
198C2×C73#55311yescharacteristic
199#2460—731nomaximal, Sylow
200C73#246011yescharacteristic, complemented, Sylow
201C2×#125—731no—
202C2×C4×D4—731no—
203#397—731no—
204#396—731no—
205#394—731no—
206#394D7311yescharacteristic
207#388—731no—
208#388—731no—
209#387—731no—
210#387—731no—
211#387—731no—
212#385—731no—
213#385—731no—
214#380—731no—
215C4×C22⋊C4—731no—
216C22×D4C2×D7311yescharacteristic
217C23×C4—731no—
218C23×C4—731no—
219#125—1464no—
220C4×D4—1464no—
221C2×C4⋊C4—731no—
222C2×C4⋊C4—731no—
223C2×C4⋊C4—731no—
224C2×C4⋊C4—731no—
225C2×C4⋊C4—731no—
226C2×C4⋊C4—731no—
227C2×C4⋊C4—731no—
228C2×C4⋊C4—731no—
229C2×C4⋊C4C2×D7311yescharacteristic
230C2×C22⋊C4—731no—
231C2×C22⋊C4—731no—
232C2×C22⋊C4—731no—
233C2×C22⋊C4—731no—
234C2×C22⋊C4—731no—
235C2×C22⋊C4—731no—
236C2×C22⋊C4C2×D7311yescharacteristic
237C2×C22⋊C4C2×D7311yescharacteristic
238C2×C22⋊C4C2×D7311yescharacteristic
239C2×C22⋊C4C2×D7311yescharacteristic
240C2×C42—731no—
241C2×C42—731no—
242C2×C42—731no—
243#95—731no—
244#95—731no—
245#95—731no—
246#95—731no—
247#95—731no—
248#95—731no—
249#95—731no—
250#95—731no—
251#95—731no—
252#95C2×D7311yescharacteristic
253C24C22×D7311yescharacteristic
254C24C22×D7311yescharacteristic
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—22no—
258C22×C4—2921no—
259C22×C4—2921no—
260C22×C4—731no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4—731no—
264C22×C4—731no—
265C22×C4—731no—
266C22×C4—731no—
267C22×C4—731no—
268C22×C4—1462no—
269C22×C4—1462no—
270C22×C4—1462no—
271C22×C4—1462no—
272C22×C4C22×D7311yescharacteristic
273C22×C4C22×D7311yescharacteristic
274C22×C4C22×D7311yescharacteristic
275C22×C4C22×D7311yescharacteristic
276C22×C4C22×D7311yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—2921no—
279C4⋊C4—734no—
280C4⋊C4—1462no—
281C4⋊C4—1462no—
282C4⋊C4—1462no—
283C4⋊C4—1462no—
284C4⋊C4—1462no—
285C4⋊C4—1462no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—1462no—
291C22⋊C4—1462no—
292C22⋊C4—1462no—
293C22⋊C4—1462no—
294C22⋊C4—1462no—
295C22⋊C4—1462no—
296C42—2921no—
297C42—1462no—
298C42—1462no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23#1192402712yes—
312C23#1192402712yes—
313C23C23×D7311yescharacteristic
314D4—28no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—2924no—
330C2×C4—2924no—
331C2×C4—732no—
332C2×C4—732no—
333C2×C4—732no—
334C2×C4—732no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4D4×D7312yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22C2×D4×D7311yescharacteristic
371C22#41×D7311yescharacteristic
372C22#41×D7311yescharacteristic
373C22C2×#1192402711yescharacteristic
374C22C2×#1192402711yescharacteristic
375C22#1455663611yescharacteristic
376C22#1455663811yescharacteristic
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—2921no—
383C4—2921no—
384C4—2921no—
385C4—2921no—
386C4—1462no—
387C4—1462no—
388C4—1462no—
389C4—1462no—
390C2—42no—
391C2—42no—
392C2#1798909311yescharacteristic
393C2#1798911411yescharacteristic
394C2#1798918211yescharacteristic
395C2#1798923411yescharacteristic
396C2#1798924511yescharacteristic
397C2#1798927411yescharacteristic
398C2#1798928011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2460
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14556581C2semidirect
3. #17988515C2semidirect
4. #17988510C2semidirect
6. #17988480C2semidirect
7. #17988475C2semidirect
8. #17988472C2semidirect
9. #17988470C2semidirect
10. #17988468C2semidirect
11. #17988459C2semidirect
12. #17988459C2semidirect
13. #17988445C2semidirect
14. C22⋊C4×Dic73C2semidirect
200. C73#2460semidirect