Finite Group Databasebeta

← #22613680

Subgroups — #22613680

Order 9344.

610 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556564C211yesmaximal, characteristic
2C2×C4×C22⋊D73C211yesmaximal, characteristic, complemented
3#17988528C211yesmaximal, characteristic, complemented
4#17988516C211yesmaximal, characteristic, complemented
5#17988515C211yesmaximal, characteristic, complemented
6#17988503C211yesmaximal, characteristic, complemented
7#17988476C211yesmaximal, characteristic, complemented
8#17988470C211yesmaximal, characteristic, complemented
9#17988466C211yesmaximal, characteristic, complemented
10#17988465C211yesmaximal, characteristic, complemented
11#17988465C211yesmaximal, characteristic, complemented
12#17988463C211yesmaximal, characteristic, complemented
13#17988461C211yesmaximal, characteristic, complemented
14#95×D73C211yesmaximal, characteristic, complemented
15#381×C73C211yesmaximal, characteristic, complemented
16C22×D292C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic
21C22×C4×D73C2211yescharacteristic
22#14556564—24no—
23C4×C22⋊D73—24no—
24C2×C4⋊Dic73C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
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×C22⋊C4×C73C2211yescharacteristic
48C2×C22⋊C4×C73C2211yescharacteristic
49#95×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C23×D73C2311yescharacteristic
55C2×D292—22no—
56C2×D292—22no—
57C2×D292—22no—
58C2×C22⋊D73—22no—
59C2×C22⋊D73—22no—
60C2×C22⋊D73—22no—
61C2×C22⋊D73—22no—
62C2×C22⋊D73—41no—
63C2×C22⋊D73D414yes—
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C2×C4×D73—22no—
71C2×C4×D73—22no—
72C2×C4×D73—22no—
73C2×C4×D73—22no—
74C2×C4×D73—22no—
75C2×C4×D73—41no—
76C2×C4×D73—41no—
77C2×C4×D73—41no—
78C2×C4×D73—41no—
79C4⋊Dic73—22no—
80#11924007—22no—
81#11924007—22no—
82#11924007—41no—
83C22⋊Dic73—22no—
84C22⋊Dic73—41no—
85#11924005—22no—
86#11924005—22no—
87#11924005—22no—
88#11924005—22no—
89#11924005—41no—
90#11924005—41no—
91#11924005—41no—
92C4×Dic73—22no—
93C24×C73C2311yescharacteristic
94C22×C4×C73—22no—
95C22×C4×C73—22no—
96C22×C4×C73—41no—
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102C22×C4×C73C2311yescharacteristic
103C22⋊C4×C73—22no—
104C22⋊C4×C73—41no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73C2×D412yes—
112C23×C73C2411yescharacteristic
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—21no—
118C22×D73—21no—
119C22×D73—21no—
120C22×D73—21no—
121C22×D73—21no—
122C22×D73—21no—
123C22×D73—21no—
124C22×D73C2×D412yes—
125C22×D73#4112yes—
126C22×D73#4112yes—
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—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—44no—
145C2×C4×C73#4112yes—
146C22⋊D73—28no—
147C22⋊D73—44no—
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×Dic73—21no—
157C2×Dic73—21no—
158C2×Dic73—21no—
159C2×Dic73—21no—
160C2×Dic73—21no—
161C2×Dic73—21no—
162C2×Dic73—21no—
163C2×Dic73—21no—
164C2×Dic73C2×D412yes—
165C2×Dic73#4112yes—
166D292—44no—
167C4×D73—44no—
168C4×D73—44no—
169C4×D73—44no—
170C22×C73—22no—
171C22×C73—22no—
172C22×C73—22no—
173C22×C73—41no—
174C22×C73—41no—
175C22×C73—41no—
176C22×C73—41no—
177C22×C73C22×D411yescharacteristic
178C22×C73C2×#4111yescharacteristic
179C22×C73C2×#4111yescharacteristic
180C22×C73C2×#4111yescharacteristic
181C22×C73C2×#4111yescharacteristic
182C22×C73H(5,𝔽2)11yescharacteristic
183C22×C73H(5,𝔽2)11yescharacteristic
184C2×D73—22no—
185C2×D73—22no—
186C2×D73—22no—
187C2×D73—22no—
188C2×D73—22no—
189C2×D73—22no—
190C2×D73—41no—
191C2×D73—41no—
192C2×D73—41no—
193C2×D73—41no—
194C2×D73—41no—
195C2×D73—41no—
196C2×D73—41no—
197C2×D73#12314yes—
198C4×C73—22no—
199C4×C73—41no—
200C4×C73—41no—
201C4×C73—41no—
202C4×C73—41no—
203C4×C73—41no—
204Dic73—22no—
205Dic73—22no—
206Dic73—41no—
207Dic73—41no—
208Dic73—41no—
209Dic73—41no—
210C2×C73—42no—
211C2×C73C2×#12311yescharacteristic
212C2×C73#52911yescharacteristic
213C2×C73#53811yescharacteristic
214C2×C73#54611yescharacteristic
215C2×C73#54611yescharacteristic
216C2×C73#55311yescharacteristic
217C2×C73#55311yescharacteristic
218D73—24no—
219D73—81no—
220#2444—731nomaximal, Sylow
221C73#244411yescharacteristic, complemented, Sylow
222C2×#121—731no—
223C2×C4×D4—731no—
224#400—731no—
225#397—731no—
226#397—731no—
227#394—731no—
228#388—731no—
229#387—731no—
230#386—731no—
231#386—731no—
232#386—731no—
233#386—731no—
234#385—731no—
235#381D7311yescharacteristic, complemented
236C2×#95—731no—
237C22×D4—731no—
238C22×D4—731no—
239C22×D4—731no—
240C23×C4—731no—
241C23×C4—731no—
242C23×C4—731no—
243C23×C4C2×D7311yescharacteristic
244#121—1464no—
245C4×D4—1464no—
246C2×C4⋊C4—731no—
247C2×C4⋊C4—731no—
248C2×C4⋊C4—731no—
249C2×C4⋊C4—731no—
250C2×C22⋊C4—731no—
251C2×C22⋊C4—731no—
252C2×C22⋊C4—731no—
253C2×C22⋊C4—731no—
254C2×C22⋊C4—731no—
255C2×C22⋊C4—731no—
256C2×C22⋊C4—731no—
257C2×C22⋊C4—731no—
258C2×C22⋊C4—731no—
259C2×C22⋊C4C2×D7311yescharacteristic
260C2×C22⋊C4C2×D7311yescharacteristic
261C2×C42—731no—
262#95—731no—
263#95—731no—
264#95—731no—
265#95—731no—
266#95—731no—
267#95—731no—
268#95—731no—
269#95—731no—
270#95C2×D7311yescharacteristic
271#95C2×D7311yescharacteristic
272#95C2×D7311yescharacteristic
273#95C2×D7311yescharacteristic
274C24—731no—
275C24—731no—
276C24C22×D7311yescharacteristic
277C2×D4—2921no—
278C2×D4—734no—
279C2×D4—1462no—
280C2×D4—1462no—
281C2×D4—1462no—
282C2×D4—1462no—
283C2×D4—1462no—
284C2×D4—1462no—
285C2×D4—1462no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—2921no—
290C22×C4—2921no—
291C22×C4—2921no—
292C22×C4—2921no—
293C22×C4—731no—
294C22×C4—731no—
295C22×C4—731no—
296C22×C4—731no—
297C22×C4—731no—
298C22×C4—731no—
299C22×C4—1462no—
300C22×C4—1462no—
301C22×C4—1462no—
302C22×C4—1462no—
303C22×C4—1462no—
304C22×C4C22×D7311yescharacteristic
305C22×C4C22×D7311yescharacteristic
306C22×C4C22×D7311yescharacteristic
307C22×C4C22×D7311yescharacteristic
308C22×C4C22×D7311yescharacteristic
309C22×C4C22×D7311yescharacteristic
310C4⋊C4—2921no—
311C4⋊C4—1462no—
312C4⋊C4—1462no—
313C4⋊C4—1462no—
314C22⋊C4—22no—
315C22⋊C4—41no—
316C22⋊C4—2921no—
317C22⋊C4—2921no—
318C22⋊C4—2921no—
319C22⋊C4—2921no—
320C22⋊C4—1462no—
321C22⋊C4—1462no—
322C22⋊C4—1462no—
323C22⋊C4—1462no—
324C22⋊C4—1462no—
325C42—1462no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—732no—
333C23—732no—
334C23—732no—
335C23—1461no—
336C23—1461no—
337C23—1461no—
338C23—1461no—
339C23—1461no—
340C23—1461no—
341C23—1461no—
342C23—1461no—
343C23—1461no—
344C23—1461no—
345C23—1461no—
346C23D4×D7312yes—
347C23C23×D7311yescharacteristic
348D4—2924no—
349D4—2924no—
350D4—1468no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—44no—
369C2×C4—2924no—
370C2×C4—2924no—
371C2×C4—2924no—
372C2×C4—732no—
373C2×C4—732no—
374C2×C4—1461no—
375C2×C4—1461no—
376C2×C4—1461no—
377C2×C4—1461no—
378C2×C4—1461no—
379C2×C4—1461no—
380C2×C4—1461no—
381C2×C4—1461no—
382C2×C4—1461no—
383C2×C4—1461no—
384C2×C4—1461no—
385C2×C4—1461no—
386C2×C4—1461no—
387C2×C4—1461no—
388C2×C4—1461no—
389C2×C4—1461no—
390C2×C4#1192402812yes—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—2921no—
399C22—2921no—
400C22—2921no—
401C22—2921no—
402C22—2921no—
403C22—2921no—
404C22—2921no—
405C22—734no—
406C22—1462no—
407C22—1462no—
408C22—1462no—
409C22—1462no—
410C22—1462no—
411C22—1462no—
412C22C2×D4×D7311yescharacteristic
413C22#41×D7311yescharacteristic
414C22#41×D7311yescharacteristic
415C22#41×D7311yescharacteristic
416C22C2×#1192402811yescharacteristic
417C22#1455663611yescharacteristic
418C22#1455663711yescharacteristic
419C4—22no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4—2921no—
426C4—2921no—
427C4—2921no—
428C4—2921no—
429C4—1462no—
430C4—1462no—
431C2—42no—
432C2—5841no—
433C2—1464no—
434C2#123×D7311yescharacteristic
435C2#1798911511yescharacteristic
436C2#1798917311yescharacteristic
437C2#1798922711yescharacteristic
438C2#1798922911yescharacteristic
439C2#1798928111yescharacteristic
440C2#1798928211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#381×C73C2
hypercenter#381D73
hypocenterC73#2444
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D73C2semidirect
3. #17988528C2semidirect
4. #17988516C2semidirect
5. #17988515C2semidirect
6. #17988503C2semidirect
7. #17988476C2semidirect
8. #17988470C2semidirect
9. #17988466C2semidirect
10. #17988465C2semidirect
11. #17988465C2semidirect
12. #17988463C2semidirect
13. #17988461C2semidirect
14. #95×D73C2semidirect
15. #381×C73C2semidirect
221. C73#2444semidirect
235. #381D73semidirect