Finite Group Databasebeta

← #22613675

Subgroups — #22613675

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×#14556563C211yesmaximal, characteristic
2#17988525C211yesmaximal, characteristic, complemented
3#17988515C211yesmaximal, characteristic, complemented
4#17988513C211yesmaximal, characteristic, complemented
5#17988502C211yesmaximal, characteristic, complemented
6#17988478C211yesmaximal, characteristic, complemented
7#17988471C211yesmaximal, characteristic, complemented
8#17988467C211yesmaximal, characteristic, complemented
9#17988466C211yesmaximal, characteristic, complemented
10#17988466C211yesmaximal, characteristic, complemented
11#17988464C211yesmaximal, characteristic, complemented
12#17988459C211yesmaximal, characteristic, complemented
13#17988450C211yesmaximal, characteristic, complemented
14C2×#14556498C211yesmaximal, characteristic, complemented
15C2×C4×D4×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C23×Dic73C2211yescharacteristic
19C23×Dic73C2211yescharacteristic
20#14556563—24no—
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×C22⋊Dic73C2211yescharacteristic
25C2×C22⋊Dic73C2211yescharacteristic
26C2×C22⋊Dic73C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33#14556498C2211yescharacteristic
34#14556498C2211yescharacteristic
35#14556498C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45C22×D4×C73C2211yescharacteristic
46C23×C4×C73C2211yescharacteristic
47C23×C4×C73C2211yescharacteristic
48C4×D4×C73—24no—
49C2×C4⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C42×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C2×C22⋊D73—22no—
55C2×C22⋊D73—22no—
56C2×C22⋊D73—22no—
57C2×C22⋊D73—22no—
58C2×C22⋊D73—22no—
59C2×C22⋊D73—41no—
60C22×Dic73—22no—
61C22×Dic73—22no—
62C22×Dic73—22no—
63C22×Dic73—41no—
64C22×Dic73—41no—
65C22×Dic73—41no—
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C22×Dic73C2311yescharacteristic
71C22×Dic73C2311yescharacteristic
72C22×Dic73C2311yescharacteristic
73#11924007—22no—
74#11924007—22no—
75#11924007—41no—
76C22⋊Dic73—22no—
77C22⋊Dic73—22no—
78C22⋊Dic73—41no—
79C22⋊Dic73—41no—
80#11924005—22no—
81#11924005—22no—
82#11924005—41no—
83#11924005—41no—
84#11924005—41no—
85C24×C73C2311yescharacteristic
86C24×C73C2311yescharacteristic
87C2×D4×C73—22no—
88C2×D4×C73—22no—
89C2×D4×C73D414yes—
90C22×C4×C73—22no—
91C22×C4×C73—22no—
92C22×C4×C73—22no—
93C22×C4×C73—22no—
94C22×C4×C73—41no—
95C22×C4×C73—41no—
96C22×C4×C73C2311yescharacteristic
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C4⋊C4×C73—22no—
102C22⋊C4×C73—22no—
103C22⋊C4×C73—22no—
104C42×C73—22no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—21no—
112C23×C73—21no—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73C2×D412yes—
116C23×C73C2×D412yes—
117C23×C73#4112yes—
118C23×C73#4112yes—
119C23×C73C2411yescharacteristic
120C22×D73—21no—
121C22×D73—21no—
122C22×D73—21no—
123C22×D73—21no—
124C22×D73—21no—
125C22×D73—21no—
126C22×D73—21no—
127D4×C73—28no—
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—44no—
142C2×C4×C73—44no—
143C2×C4×C73C2×D412yes—
144C2×C4×C73#4112yes—
145C22⋊D73—44no—
146C22⋊D73—44no—
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×Dic73—21no—
157C2×Dic73—21no—
158C2×Dic73—21no—
159C2×Dic73—21no—
160C2×Dic73—21no—
161C2×Dic73—21no—
162C2×Dic73—21no—
163C2×Dic73—21no—
164C2×Dic73—21no—
165C2×Dic73—21no—
166C2×Dic73—21no—
167C2×Dic73—44no—
168C2×Dic73—44no—
169C2×Dic73#4112yes—
170C22×C73—22no—
171C22×C73—22no—
172C22×C73—22no—
173C22×C73—22no—
174C22×C73—22no—
175C22×C73—22no—
176C22×C73—22no—
177C22×C73—22no—
178C22×C73—22no—
179C22×C73—41no—
180C22×C73—41no—
181C22×C73—41no—
182C22×C73—41no—
183C22×C73#12314yes—
184C22×C73C22×D411yescharacteristic
185C22×C73C2×#4111yescharacteristic
186C22×C73C2×#4111yescharacteristic
187C22×C73C2×#4111yescharacteristic
188C22×C73C2×#4111yescharacteristic
189C22×C73H(5,𝔽2)11yescharacteristic
190C22×C73H(5,𝔽2)11yescharacteristic
191C2×D73—41no—
192C2×D73—41no—
193C2×D73—41no—
194C2×D73—41no—
195C2×D73—41no—
196C2×D73—41no—
197C2×D73—41no—
198C4×C73—22no—
199C4×C73—22no—
200C4×C73—41no—
201C4×C73—41no—
202C4×C73—41no—
203Dic73—22no—
204Dic73—41no—
205Dic73—41no—
206Dic73—41no—
207Dic73—41no—
208Dic73—41no—
209Dic73—41no—
210C2×C73—24no—
211C2×C73—42no—
212C2×C73C2×#12311yescharacteristic
213C2×C73#52911yescharacteristic
214C2×C73#53811yescharacteristic
215C2×C73#54611yescharacteristic
216C2×C73#54611yescharacteristic
217C2×C73#55311yescharacteristic
218C2×C73#55311yescharacteristic
219D73—81no—
220#2444—731nomaximal, Sylow
221C73#244411yescharacteristic, complemented, Sylow
222C2×#121—731no—
223C2×C4×D4D7311yescharacteristic, complemented
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#381—731no—
236C2×#95—731no—
237C22×D4—731no—
238C22×D4—731no—
239C22×D4C2×D7311yescharacteristic
240C23×C4—731no—
241C23×C4—731no—
242C23×C4C2×D7311yescharacteristic
243C23×C4C2×D7311yescharacteristic
244#121—1464no—
245C4×D4—24no—
246C2×C4⋊C4—731no—
247C2×C4⋊C4—731no—
248C2×C4⋊C4—731no—
249C2×C4⋊C4C2×D7311yescharacteristic
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×C42C2×D7311yescharacteristic
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#95—731no—
271#95—731no—
272#95—731no—
273#95—731no—
274C24—731no—
275C24C22×D7311yescharacteristic
276C24C22×D7311yescharacteristic
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—2921no—
280C2×D4—1462no—
281C2×D4—1462no—
282C2×D4—1462no—
283C2×D4—1462no—
284C2×D4—1462no—
285C2×D4C22⋊D7314yes—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—2921no—
293C22×C4—2921no—
294C22×C4—2921no—
295C22×C4—731no—
296C22×C4—731no—
297C22×C4—731no—
298C22×C4—731no—
299C22×C4—731no—
300C22×C4—731no—
301C22×C4—731no—
302C22×C4—1462no—
303C22×C4—1462no—
304C22×C4—1462no—
305C22×C4C22×D7311yescharacteristic
306C22×C4C22×D7311yescharacteristic
307C22×C4C22×D7311yescharacteristic
308C22×C4C22×D7311yescharacteristic
309C22×C4C22×D7311yescharacteristic
310C4⋊C4—22no—
311C4⋊C4—2921no—
312C4⋊C4—1462no—
313C4⋊C4—1462no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—2921no—
317C22⋊C4—2921no—
318C22⋊C4—2921no—
319C22⋊C4—2921no—
320C22⋊C4—2921no—
321C22⋊C4—1462no—
322C22⋊C4—1462no—
323C22⋊C4—1462no—
324C22⋊C4—1462no—
325C42—22no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—1461no—
337C23—1461no—
338C23—1461no—
339C23—1461no—
340C23—1461no—
341C23—1461no—
342C23—1461no—
343C23C2×C22⋊D7312yes—
344C23C2×C22⋊D7312yes—
345C23#1192402812yes—
346C23#1192402812yes—
347C23C23×D7311yescharacteristic
348D4—28no—
349D4—2924no—
350D4—2924no—
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—44no—
365C2×C4—44no—
366C2×C4—2924no—
367C2×C4—2924no—
368C2×C4—732no—
369C2×C4—1461no—
370C2×C4—1461no—
371C2×C4—1461no—
372C2×C4—1461no—
373C2×C4—1461no—
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×C4C2×C22⋊D7312yes—
390C2×C4#1192402712yes—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—2921no—
405C22—2921no—
406C22—2921no—
407C22—2921no—
408C22—2921no—
409C22—2921no—
410C22—2921no—
411C22#1455657414yes—
412C22C22×C22⋊D7311yescharacteristic
413C22#41×D7311yescharacteristic
414C22C2×#1192402711yescharacteristic
415C22C2×#1192402811yescharacteristic
416C22C2×#1192402811yescharacteristic
417C22#1455663611yescharacteristic
418C22#1455663711yescharacteristic
419C4—22no—
420C4—22no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—2921no—
425C4—2921no—
426C4—2921no—
427C4—2921no—
428C4—2921no—
429C4—2921no—
430C4—1462no—
431C2—24no—
432C2—42no—
433C2—5841no—
434C2C2×#1455657411yescharacteristic
435C2#1798911711yescharacteristic
436C2#1798917011yescharacteristic
437C2#1798922511yescharacteristic
438C2#1798923111yescharacteristic
439C2#1798928311yescharacteristic
440C2#1798928611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×C4×D4×C73C2
hypercenterC2×C4×D4D73
hypocenterC73#2444
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #17988525C2semidirect
3. #17988515C2semidirect
4. #17988513C2semidirect
5. #17988502C2semidirect
6. #17988478C2semidirect
7. #17988471C2semidirect
8. #17988467C2semidirect
9. #17988466C2semidirect
10. #17988466C2semidirect
11. #17988464C2semidirect
12. #17988459C2semidirect
13. #17988450C2semidirect
14. C2×#14556498C2semidirect
15. C2×C4×D4×C73C2semidirect
221. C73#2444semidirect
223. C2×C4×D4D73semidirect