Finite Group Databasebeta

← #22615276

Subgroups — #22615276

Order 9344.

584 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D73C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic, complemented
3#17988521C211yesmaximal, characteristic, complemented
4#17988518C211yesmaximal, characteristic, complemented
5#17988510C211yesmaximal, characteristic, complemented
6#17988510C211yesmaximal, characteristic, complemented
7#17988472C211yesmaximal, characteristic, complemented
8#17988468C211yesmaximal, characteristic, complemented
9#17988463C211yesmaximal, characteristic
10#17988463C211yesmaximal, characteristic
11#17988461C211yesmaximal, characteristic, complemented
12#17988460C211yesmaximal, characteristic, complemented
13#17988458C211yesmaximal, characteristic, complemented
14#17988446C211yesmaximal, characteristic, complemented
15#385×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20C4×C22⋊D73—24no—
21C2×C4⋊Dic73C2211yescharacteristic
22C2×C4⋊Dic73C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C4⋊C4×D73—24no—
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×C22⋊Dic73C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×C4×Dic73C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C23×C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C2×C22⋊D73—22no—
55C2×C22⋊D73—22no—
56C2×C22⋊D73Q814yes—
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C2×C4×D73—22no—
65C2×C4×D73—22no—
66C2×C4×D73—22no—
67C2×C4×D73—22no—
68C2×C4×D73—41no—
69C2×C4×D73—41no—
70C2×C4×D73—41no—
71C2×C4×D73—41no—
72C2×C4×D73D414yes—
73C4⋊Dic73—22no—
74C4⋊Dic73—22no—
75#11924007—22no—
76#11924007—22no—
77#11924007—22no—
78#11924007—22no—
79#11924007—41no—
80#11924007—41no—
81#11924007—41no—
82C22⋊Dic73—22no—
83C22⋊Dic73—22no—
84C22⋊Dic73—41no—
85#11924005—22no—
86#11924005—22no—
87#11924005—22no—
88C4×Dic73—22no—
89C24×C73C2311yescharacteristic
90C22×C4×C73—22no—
91C22×C4×C73—41no—
92C22×C4×C73—41no—
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96C22×C4×C73C2311yescharacteristic
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C4⋊C4×C73—22no—
100C4⋊C4×C73—41no—
101C22⋊C4×C73—22no—
102C22⋊C4×C73—41no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73C2×Q812yes—
110C23×C73C2411yescharacteristic
111C22×D73—21no—
112C22×D73—21no—
113C22×D73—21no—
114C22×D73—21no—
115C22×D73C2×D412yes—
116C22×D73C2×Q812yes—
117C22×D73#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—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—44no—
135C2×C4×C73C2×D412yes—
136C2×C4×C73#4112yes—
137C22⋊D73—28no—
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×Dic73—21no—
152C2×Dic73—21no—
153C2×Dic73—21no—
154C2×Dic73—21no—
155C2×Dic73—21no—
156C2×Dic73C2×D412yes—
157C2×Dic73C2×Q812yes—
158C2×Dic73#4112yes—
159C4×D73—28no—
160C4×D73—44no—
161C4×D73—44no—
162C22×C73—22no—
163C22×C73—22no—
164C22×C73—22no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73C22×D411yescharacteristic
170C22×C73C22×Q811yescharacteristic
171C22×C73C2×#4111yescharacteristic
172C22×C73C2×#4111yescharacteristic
173C22×C73C2×#4111yescharacteristic
174C22×C73H(5,𝔽2)11yescharacteristic
175C22×C73H(5,𝔽2)11yescharacteristic
176C2×D73—22no—
177C2×D73—22no—
178C2×D73—22no—
179C2×D73—22no—
180C2×D73—22no—
181C2×D73—22no—
182C2×D73C22⋊Q814yes—
183C4×C73—22no—
184C4×C73—22no—
185C4×C73—41no—
186C4×C73—41no—
187C4×C73—41no—
188C4×C73—41no—
189Dic73—22no—
190Dic73—22no—
191Dic73—22no—
192Dic73—41no—
193Dic73—41no—
194Dic73—41no—
195Dic73—41no—
196C2×C73—42no—
197C2×C73C2×C22⋊Q811yescharacteristic
198C2×C73#52511yescharacteristic
199C2×C73#53411yescharacteristic
200C2×C73#55311yescharacteristic
201C2×C73#55311yescharacteristic
202C2×C73#55411yescharacteristic
203C2×C73#55411yescharacteristic
204D73—24no—
205#2579—731nomaximal, Sylow
206C73#257911yescharacteristic, complemented, Sylow
207C2×C4×D4—731no—
208C22×C4⋊C4—731no—
209#398—731no—
210#398—731no—
211#396—731no—
212#396—731no—
213#387—731no—
214#387—731no—
215#386—731no—
216#386—731no—
217#385—731no—
218#385—731no—
219#385—731no—
220#385D7311yescharacteristic, complemented
221#380—731no—
222C22×D4—731no—
223C23×C4—731no—
224C23×C4—731no—
225C23×C4—731no—
226C23×C4C2×D7311yescharacteristic
227C4×D4—1464no—
228C2×C4⋊C4—731no—
229C2×C4⋊C4—731no—
230C2×C4⋊C4—731no—
231C2×C4⋊C4—731no—
232C2×C4⋊C4—731no—
233C2×C4⋊C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—731no—
236C2×C4⋊C4—731no—
237C2×C4⋊C4—1464no—
238C2×C4⋊C4C2×D7311yescharacteristic
239C2×C4⋊C4C2×D7311yescharacteristic
240C2×C22⋊C4—731no—
241C2×C22⋊C4—731no—
242C2×C22⋊C4—731no—
243C2×C22⋊C4—731no—
244C2×C22⋊C4—731no—
245C2×C22⋊C4—731no—
246C2×C22⋊C4C2×D7311yescharacteristic
247C2×C22⋊C4C2×D7311yescharacteristic
248C2×C42—731no—
249#95—731no—
250#95—731no—
251#95—731no—
252#95—731no—
253#95—731no—
254#95—731no—
255#95—731no—
256#95—731no—
257#95C2×D7311yescharacteristic
258#95C2×D7311yescharacteristic
259C24—731no—
260C24C22×D7311yescharacteristic
261C2×D4—734no—
262C2×D4—1462no—
263C2×D4—1462no—
264C22×C4—22no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—2921no—
268C22×C4—2921no—
269C22×C4—2921no—
270C22×C4—2921no—
271C22×C4—734no—
272C22×C4—731no—
273C22×C4—731no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—1462no—
280C22×C4—1462no—
281C22×C4—1462no—
282C22×C4—1462no—
283C22×C4C22×D7311yescharacteristic
284C22×C4C22×D7311yescharacteristic
285C22×C4C22×D7311yescharacteristic
286C22×C4C22×D7311yescharacteristic
287C22×C4C22×D7311yescharacteristic
288C22×C4C22×D7311yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—2921no—
292C4⋊C4—2921no—
293C4⋊C4—2921no—
294C4⋊C4—1462no—
295C4⋊C4—1462no—
296C4⋊C4—1462no—
297C4⋊C4—1462no—
298C4⋊C4—1462no—
299C4⋊C4—1462no—
300C22⋊C4—22no—
301C22⋊C4—41no—
302C22⋊C4—2921no—
303C22⋊C4—1462no—
304C22⋊C4—1462no—
305C22⋊C4—1462no—
306C22⋊C4—1462no—
307C22⋊C4—1462no—
308C42—1462no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—732no—
316C23—732no—
317C23—732no—
318C23—1461no—
319C23—1461no—
320C23—1461no—
321C23—1461no—
322C23Q8×D7312yes—
323C23C23×D7311yescharacteristic
324D4—1468no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—44no—
342C2×C4—2924no—
343C2×C4—2924no—
344C2×C4—732no—
345C2×C4—732no—
346C2×C4—732no—
347C2×C4—1468no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4—1461no—
363C2×C4—1461no—
364C2×C4—1461no—
365C2×C4—1461no—
366C2×C4D4×D7312yes—
367C2×C4#1192402812yes—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—734no—
376C22—1462no—
377C22—1462no—
378C22—1462no—
379C22—1462no—
380C22—1462no—
381C22—1462no—
382C22C2×D4×D7311yescharacteristic
383C22C2×Q8×D7311yescharacteristic
384C22#41×D7311yescharacteristic
385C22#41×D7311yescharacteristic
386C22C2×#1192402811yescharacteristic
387C22#1455663611yescharacteristic
388C22#1455663611yescharacteristic
389C4—22no—
390C4—22no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—2921no—
396C4—2921no—
397C4—2921no—
398C4—2921no—
399C4—1462no—
400C4—1462no—
401C4—1462no—
402C2—42no—
403C2—1464no—
404C2C22⋊Q8×D7311yescharacteristic
405C2#1798909611yescharacteristic
406C2#1798914711yescharacteristic
407C2#1798928211yescharacteristic
408C2#1798928711yescharacteristic
409C2#1798929111yescharacteristic
410C2#1798929211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2579
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D73C2semidirect
3. #17988521C2semidirect
4. #17988518C2semidirect
5. #17988510C2semidirect
6. #17988510C2semidirect
7. #17988472C2semidirect
8. #17988468C2semidirect
11. #17988461C2semidirect
12. #17988460C2semidirect
13. #17988458C2semidirect
14. #17988446C2semidirect
15. #385×C73C2semidirect
206. C73#2579semidirect
220. #385D73semidirect