Finite Group Databasebeta

← #22616894

Subgroups — #22616894

Order 9344.

476 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556585C211yesmaximal, characteristic, complemented
2C2×#14556584C211yesmaximal, characteristic, complemented
3#17988524C211yesmaximal, characteristic, complemented
4#17988523C211yesmaximal, characteristic, complemented
5#17988511C211yesmaximal, characteristic, complemented
6#17988510C211yesmaximal, characteristic, complemented
7#17988503C211yesmaximal, characteristic
8#17988502C211yesmaximal, characteristic
9#17988487C211yesmaximal, characteristic
10#17988485C211yesmaximal, characteristic, complemented
11#17988484C211yesmaximal, characteristic, complemented
12#17988484C211yesmaximal, characteristic, complemented
13#17988483C211yesmaximal, characteristic, complemented
14#17988477C211yesmaximal, characteristic, complemented
15#388×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17#14556585—24no—
18#14556584—24no—
19C2×C4⋊Dic73C2211yescharacteristic
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×C4⋊Dic73C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×#11924007C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×C22⋊Dic73C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic
39C2×#11924005C2211yescharacteristic
40C2×C4×Dic73C2211yescharacteristic
41C2×C4×Dic73C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C2×C4⋊C4×C73C2211yescharacteristic
47C2×C22⋊C4×C73C2211yescharacteristic
48C2×C22⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C42×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C2×C22⋊D73—22no—
55C2×C22⋊D73—41no—
56C2×C22⋊D73—41no—
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C4⋊Dic73—22no—
65C4⋊Dic73—22no—
66C4⋊Dic73—22no—
67C4⋊Dic73—41no—
68#11924007—22no—
69#11924007—22no—
70#11924007—22no—
71#11924007—22no—
72#11924007—41no—
73#11924007—41no—
74#11924007—41no—
75#11924007D414yescomplemented
76C22⋊Dic73—22no—
77C22⋊Dic73—22no—
78C22⋊Dic73—41no—
79#11924005—22no—
80#11924005—22no—
81#11924005—22no—
82#11924005—22no—
83#11924005—41no—
84#11924005—41no—
85C4×Dic73—22no—
86C4×Dic73—41no—
87C24×C73C2311yescharacteristic
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C4⋊C4×C73—41no—
95C22⋊C4×C73—22no—
96C22⋊C4×C73—22no—
97C22⋊C4×C73—41no—
98C42×C73—22no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73C2411yescharacteristic
107C22×D73—21no—
108C22×D73—21no—
109C22×D73—21no—
110C22×D73—21no—
111C22×D73—21no—
112C22×D73—21no—
113C22×D73—21no—
114C2×C4×C73—21no—
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×C73—21no—
130C2×C4×C73C2×D412yes—
131C2×C4×C73#4112yes—
132C22⋊D73—44no—
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—21no—
151C2×Dic73C2×D412yes—
152C2×Dic73C2×D412yes—
153C2×Dic73#4112yes—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73C22×D411yescharacteristic
162C22×C73C2×#4111yescharacteristic
163C22×C73C2×#4111yescharacteristic
164C22×C73H(5,𝔽2)11yescharacteristic
165C22×C73H(5,𝔽2)11yescharacteristic
166C22×C732−1+411yescharacteristic
167C22×C732−1+411yescharacteristic
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C2×D73—41no—
172C2×D73—41no—
173C2×D73—41no—
174C2×D73—41no—
175C4×C73—22no—
176C4×C73—22no—
177C4×C73—41no—
178C4×C73—41no—
179C4×C73—41no—
180C4×C73—41no—
181Dic73—22no—
182Dic73—22no—
183Dic73—22no—
184Dic73—41no—
185Dic73—41no—
186Dic73—41no—
187Dic73—41no—
188C2×C73—81no—
189C2×C73#53711yescharacteristic
190C2×C73#53811yescharacteristic
191C2×C73#53911yescharacteristic
192C2×C73#54711yescharacteristic
193C2×C73#55011yescharacteristic
194C2×C73#55611yescharacteristic
195C2×C73#56311yescharacteristic
196D73—81no—
197#2727—731nomaximal, Sylow
198C73#272711yescharacteristic, complemented, Sylow
199C2×#126—731no—
200C2×#126—731no—
201#399—731no—
202#399—731no—
203#396—731no—
204#396—731no—
205#394—731no—
206#394—731no—
207#390—731no—
208#389—731no—
209#389—731no—
210#389—731no—
211#389—731no—
212#388—731no—
213#388D7311yescharacteristic, complemented
214C22×D4—731no—
215#126—1464no—
216#126—1464no—
217C2×C4⋊C4—731no—
218C2×C4⋊C4—731no—
219C2×C4⋊C4—731no—
220C2×C4⋊C4—731no—
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⋊C4—731no—
237C2×C22⋊C4—731no—
238C2×C22⋊C4—731no—
239C2×C22⋊C4C2×D7311yescharacteristic
240C2×C22⋊C4C2×D7311yescharacteristic
241C2×C22⋊C4C2×D7311yescharacteristic
242C2×C42—731no—
243C2×C42—731no—
244C2×C42C2×D7311yescharacteristic
245#95—731no—
246#95—731no—
247#95—731no—
248#95—731no—
249#95C2×D7311yescharacteristic
250#95C2×D7311yescharacteristic
251C24—731no—
252C24C22×D7311yescharacteristic
253C2×D4—2921no—
254C2×D4—2921no—
255C2×D4—1462no—
256C22×C4—731no—
257C22×C4—731no—
258C22×C4—731no—
259C22×C4—731no—
260C22×C4—731no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4C22×D7311yescharacteristic
264C22×C4C22×D7311yescharacteristic
265C22×C4C22×D7311yescharacteristic
266C22×C4C22×D7311yescharacteristic
267C22×C4C22×D7311yescharacteristic
268C22×C4C22×D7311yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—2921no—
271C4⋊C4—2921no—
272C4⋊C4—2921no—
273C4⋊C4—2921no—
274C4⋊C4—734no—
275C4⋊C4—1462no—
276C4⋊C4—1462no—
277C4⋊C4—1462no—
278C4⋊C4—1462no—
279C4⋊C4—1462no—
280C4⋊C4—1462no—
281C4⋊C4—1462no—
282C22⋊C4—22no—
283C22⋊C4—22no—
284C22⋊C4—41no—
285C22⋊C4—2921no—
286C22⋊C4—2921no—
287C22⋊C4—2921no—
288C22⋊C4—1462no—
289C22⋊C4—1462no—
290C22⋊C4—1462no—
291C22⋊C4—1462no—
292C22⋊C4—1462no—
293C22⋊C4—1462no—
294C42—22no—
295C42—2921no—
296C42—1462no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—1461no—
305C23—1461no—
306C23—1461no—
307C23—1461no—
308C23—1461no—
309C23—1461no—
310C23—1461no—
311C23C23×D7311yescharacteristic
312D4—2924no—
313C2×C4—21no—
314C2×C4—21no—
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—732no—
330C2×C4—732no—
331C2×C4—732no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4—1461no—
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×C4D4×D7312yes—
351C2×C4#1192402812yes—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—2921no—
360C22—2921no—
361C22—2921no—
362C22—2921no—
363C22—2921no—
364C22—2921no—
365C22—2921no—
366C22C2×D4×D7311yescharacteristic
367C22#41×D7311yescharacteristic
368C22C2×#1192402811yescharacteristic
369C22#1455663611yescharacteristic
370C22#1455663711yescharacteristic
371C22#1455663811yescharacteristic
372C22#1455663811yescharacteristic
373C4—22no—
374C4—22no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—2921no—
380C4—2921no—
381C4—2921no—
382C4—2921no—
383C4—1462no—
384C4—1462no—
385C4—1462no—
386C2—81no—
387C2—5841no—
388C2#1798916611yescharacteristic
389C2#1798917111yescharacteristic
390C2#1798917911yescharacteristic
391C2#1798923511yescharacteristic
392C2#1798925811yescharacteristic
393C2#1798930511yescharacteristic
394C2#1798933911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#388×C73C2
hypercenter#388D73
hypocenterC73#2727
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14556585C2semidirect
2. C2×#14556584C2semidirect
3. #17988524C2semidirect
4. #17988523C2semidirect
5. #17988511C2semidirect
6. #17988510C2semidirect
10. #17988485C2semidirect
11. #17988484C2semidirect
12. #17988484C2semidirect
13. #17988483C2semidirect
14. #17988477C2semidirect
15. #388×C73C2semidirect
75. #11924007D4semidirect
198. C73#2727semidirect
213. #388D73semidirect