Finite Group Databasebeta

← #22619429

Subgroups — #22619429

Order 9344.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556615C211yesmaximal, characteristic, complemented
2C2×D8×D73C211yesmaximal, characteristic, complemented
3#17989150C211yesmaximal, characteristic, complemented
4#17989059C211yesmaximal, characteristic, complemented
5#17988803C211yesmaximal, characteristic, complemented
6#17988802C211yesmaximal, characteristic, complemented
7#17988801C211yesmaximal, characteristic, complemented
8#17988800C211yesmaximal, characteristic, complemented
9#17988781C211yesmaximal, characteristic, complemented
10#17988780C211yesmaximal, characteristic, complemented
11#17988779C211yesmaximal, characteristic, complemented
12#17988612C211yesmaximal, characteristic, complemented
13#17988590C211yesmaximal, characteristic, complemented
14#17988580C211yesmaximal, characteristic, complemented
15#459×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×D4×D73C2211yescharacteristic
18C2×D4×D73C2211yescharacteristic
19#14556615—24no—
20C2×#11924017C2211yescharacteristic, complemented
21C2×#11924016C2211yescharacteristic, complemented
22C2×D584C2211yescharacteristic
23C2×#11924013C2211yescharacteristic
24C2×#11924013C2211yescharacteristic
25C2×#11924013C2211yescharacteristic, complemented
26D8×D73—24no—
27C2×#11924011C2211yescharacteristic
28C2×C8×D73C2211yescharacteristic
29#14556587C2211yescharacteristic, complemented
30#14556579C2211yescharacteristic, complemented
31#14556578C2211yescharacteristic, complemented
32#14556563—21no—
33#14556563—21no—
34#14556559—21no—
35#14556559—21no—
36C4×D292C2211yescharacteristic, complemented
37D4×Dic73C2211yescharacteristic, complemented
38#14556553C2211yescharacteristic, complemented
39C4×C22⋊D73—21no—
40#14556551—21no—
41#14556549C2211yescharacteristic
42#14556548C2211yescharacteristic
43C2×#11924005—21no—
44C22⋊C4×D73—21no—
45C4⋊#10596831C2211yescharacteristic, complemented
46#14556520C2211yescharacteristic, complemented
47#14556520C2211yescharacteristic, complemented
48#14556516C2211yescharacteristic, complemented
49#14556514C2211yescharacteristic, complemented
50#14556513C2211yescharacteristic, complemented
51#14556512C2211yescharacteristic, complemented
52#14556512C2211yescharacteristic, complemented
53#14556511C2211yescharacteristic, complemented
54C2×D8×C73C2211yescharacteristic
55C2×D8×C73C2211yescharacteristic, complemented
56#127×C73C2211yescharacteristic, complemented
57C4×D4×C73C2211yescharacteristic, complemented
58C4⋊C8×C73C2211yescharacteristic, complemented
59#102×C73C2211yescharacteristic, complemented
60#102×C73C2211yescharacteristic, complemented
61C23×D73—21no—
62C23×D73—21no—
63#11924027—22no—
64#11924027—22no—
65C2×Dic146C2311yescharacteristic
66C2×D292C2311yescharacteristic
67C2×D292C2311yescharacteristic
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C22⋊D73—21no—
73D4×D73—22no—
74D4×D73—22no—
75D4×D73—22no—
76D4×D73D414yescomplemented
77C22×Dic73—21no—
78C22×Dic73—21no—
79C2×C4×D73—21no—
80C2×C4×D73—21no—
81C2×C4×D73C2311yescharacteristic
82#11924017—22no—
83#11924016—22no—
84D584—22no—
85#11924013—22no—
86#11924013—22no—
87#11924013—22no—
88#11924011—22no—
89C2×#10596831C2311yescharacteristic
90C2×#10596831C2311yescharacteristic
91C8×D73—22no—
92C4⋊Dic73C2311yescharacteristic
93#11924007D411yescharacteristic
94#11924007D411yescharacteristic
95C22⋊Dic73—21no—
96C22⋊Dic73—21no—
97C22⋊Dic73—21no—
98#11924005—21no—
99#11924005—21no—
100#11924005—21no—
101#11924005—21no—
102#11924005—21no—
103#11924005D411yescharacteristic
104#11924005D411yescharacteristic
105C4×Dic73—21no—
106C4×Dic73C2311yescharacteristic
107C2×D4×C73—21no—
108C2×D4×C73—21no—
109C2×D4×C73C2311yescharacteristic
110C2×D4×C73C2311yescharacteristic
111C2×D4×C73C2311yescharacteristic
112C22×C4×C73—21no—
113D8×C73—22no—
114D8×C73—22no—
115C2×C8×C73C2311yescharacteristic
116C2×C8×C73C2311yescharacteristic
117C4⋊C4×C73C2311yescharacteristic
118C22⋊C4×C73—21no—
119C42×C73C2311yescharacteristic
120C23×C73—21no—
121C23×C73—21no—
122C23×C73—21no—
123C22×D73—21no—
124C22×D73—24no—
125C22×D73—21no—
126C22×D73—42no—
127C22×D73—81no—
128C22×D73—81no—
129C22×D73—81no—
130C22×D73—81no—
131C22×D73C2×D411yescharacteristic
132D4×C73—21no—
133D4×C73—21no—
134D4×C73—21no—
135D4×C73—21no—
136D4×C73—21no—
137D4×C73—81no—
138D4×C73—81no—
139D4×C73C2×D412yes—
140C2×C4×C73—21no—
141C2×C4×C73—81no—
142C2×C4×C73C2×D411yescharacteristic
143C2×C4×C73C2×D411yescharacteristic
144C2×C4×C73C2411yescharacteristic
145C22⋊D73—24no—
146C22⋊D73—42no—
147C22⋊D73—42no—
148C22⋊D73—81no—
149C22⋊D73—81no—
150C2×Dic73—21no—
151C2×Dic73—21no—
152C2×Dic73—42no—
153C2×Dic73—81no—
154C2×Dic73C2×D411yescharacteristic
155C2×Dic73C2×D411yescharacteristic
156C2×Dic73C2×D411yescharacteristic
157D292—21no—
158D292—21no—
159D292—21no—
160D292C2×D412yes—
161C4×D73—81no—
162C4×D73—81no—
163C4×D73C2×D412yes—
164C4×D73#4112yes—
165Dic146—21no—
166Dic146—21no—
167C8×C73—21no—
168C8×C73—21no—
169#10596831—21no—
170#10596831—21no—
171C22×C73—22no—
172C22×C73—41no—
173C22×C73—41no—
174C22×C73—41no—
175C22×C73—41no—
176C22×C73—41no—
177C22×C73—41no—
178C22×C73—41no—
179C22×C73—41no—
180C22×C73C22×D411yescharacteristic
181C2×D73—21no—
182C2×D73—21no—
183C2×D73—22no—
184C2×D73—41no—
185C2×D73—41no—
186C2×D73—41no—
187C2×D73—41no—
188C2×D73—41no—
189C2×D73—84no—
190C2×D73—84no—
191C2×D73#12112yes—
192C4×C73—21no—
193C4×C73—21no—
194C4×C73—41no—
195C4×C73C22×D411yescharacteristic
196C4×C73C2×#4111yescharacteristic
197Dic73—21no—
198Dic73—21no—
199Dic73—41no—
200Dic73—41no—
201Dic73#12112yes—
202C2×C73—42no—
203C2×C73—81no—
204C2×C73—81no—
205C2×C73C2×#12111yescharacteristic
206C2×C73#57611yescharacteristic
207C2×C73#57611yescharacteristic
208D73—22no—
209D73—42no—
210D73—81no—
211#3041—731nomaximal, Sylow
212C73#304111yescharacteristic, complemented, Sylow
213C2×AGL(1,ℤ/8)—731no—
214C22×D8—731no—
215#535—731no—
216#518—731no—
217#463—731no—
218#463—731no—
219#463—731no—
220#463—731no—
221#459—731no—
222#459—731no—
223#459—731no—
224#459D7311yescharacteristic, complemented
225#424—731no—
226#418—731no—
227#416—731no—
228C2×#41—731no—
229C22×D4—731no—
230C22×D4—731no—
231AGL(1,ℤ/8)—1464no—
232C2×SD16—731no—
233C2×SD16—731no—
234C2×D8—731no—
235C2×D8—731no—
236C2×D8—731no—
237C2×D8—731no—
238C2×D8—1464no—
239C2×D8C2×D7311yescharacteristic
240C2×D8C2×D7311yescharacteristic, complemented
241C2×M16—731no—
242C22×C8—731no—
243#127—731no—
244#127C2×D7311yescharacteristic, complemented
245#124—731no—
246#124—731no—
247#121—1461no—
248#121—1461no—
249#120—1461no—
250#120—1461no—
251C4×D4—731no—
252C4×D4—731no—
253C4×D4—731no—
254C4×D4—1461no—
255C4×D4—1461no—
256C4×D4C2×D7311yescharacteristic, complemented
257#117—731no—
258#117—731no—
259C2×C22⋊C4—1461no—
260C2×C22⋊C4—1461no—
261C4⋊C8—731no—
262C4⋊C8—731no—
263C4⋊C8—731no—
264C4⋊C8C2×D7311yescharacteristic, complemented
265#103—731no—
266#103—731no—
267#102—731no—
268#102—731no—
269#102—731no—
270#102—731no—
271#102C2×D7311yescharacteristic, complemented
272#102C2×D7311yescharacteristic, complemented
273C24—1461no—
274C24—1461no—
275#41—1462no—
276#41—1462no—
277C2×Q8—731no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—734no—
281C2×D4—731no—
282C2×D4—731no—
283C2×D4—1462no—
284C2×D4—1462no—
285C2×D4—1462no—
286C2×D4—1461no—
287C2×D4—1461no—
288C2×D4—1461no—
289C2×D4—1461no—
290C2×D4—1461no—
291C2×D4C22×D7311yescharacteristic
292C2×D4C22×D7311yescharacteristic
293C2×D4C22×D7311yescharacteristic
294C22×C4—21no—
295C22×C4—731no—
296C22×C4—1461no—
297C22×C4—1461no—
298C22×C4—1461no—
299C22×C4—1461no—
300SD16—1462no—
301SD16—1462no—
302D8—22no—
303D8—22no—
304D8—1462no—
305D8—1462no—
306D8—1462no—
307D8—1462no—
308M16—1462no—
309C2×C8—731no—
310C2×C8—731no—
311C2×C8—1462no—
312C2×C8C22×D7311yescharacteristic
313C2×C8C22×D7311yescharacteristic
314C4⋊C4—731no—
315C4⋊C4—731no—
316C4⋊C4—731no—
317C4⋊C4C22×D7311yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—731no—
320C22⋊C4—731no—
321C22⋊C4—1461no—
322C22⋊C4—1461no—
323C22⋊C4—1461no—
324C22⋊C4—1461no—
325C22⋊C4—1461no—
326C22⋊C4—1461no—
327C22⋊C4—1461no—
328C22⋊C4—1461no—
329C42—731no—
330C42—1461no—
331C42C22×D7311yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—2922no—
336C23—5841no—
337C23—5841no—
338C23—5841no—
339C23—5841no—
340C23—731no—
341C23—1464no—
342C23—1461no—
343C23—1461no—
344Q8—1461no—
345Q8—1461no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—81no—
352D4—81no—
353D4—2922no—
354D4—2922no—
355D4—5841no—
356D4—5841no—
357D4—732no—
358D4—1464no—
359D4—1461no—
360D4—1461no—
361D4—1461no—
362D4D4×D7312yes—
363C2×C4—21no—
364C2×C4—81no—
365C2×C4—2922no—
366C2×C4—5841no—
367C2×C4—5841no—
368C2×C4—5841no—
369C2×C4—731no—
370C2×C4—732no—
371C2×C4—732no—
372C2×C4—731no—
373C2×C4—731no—
374C2×C4—1461no—
375C2×C4—1461no—
376C2×C4D4×D7311yescharacteristic
377C2×C4D4×D7311yescharacteristic
378C2×C4C23×D7311yescharacteristic
379C8—21no—
380C8—21no—
381C8—1461no—
382C8—1461no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—2921no—
393C22—2921no—
394C22—2921no—
395C22—2921no—
396C22—2921no—
397C22—5844no—
398C22—5844no—
399C22—732no—
400C22—1462no—
401C22—1461no—
402C22—1461no—
403C22C2×D4×D7311yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—2921no—
408C4—2921no—
409C4—732no—
410C4—1461no—
411C4—1461no—
412C4C2×D4×D7311yescharacteristic
413C4#41×D7311yescharacteristic
414C2—42no—
415C2—81no—
416C2—81no—
417C2—2922no—
418C2—5841no—
419C2—1462no—
420C2#121×D7311yescharacteristic
421C2#1798938811yescharacteristic
422C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#459×C73C2
socleC22×C73C22×D4
hypercenter#459D73
hypocenterC73#3041
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#14556615C2semidirect
2. C2×D8×D73C2semidirect
3. #17989150C2semidirect
4. #17989059C2semidirect
5. #17988803C2semidirect
6. #17988802C2semidirect
7. #17988801C2semidirect
8. #17988800C2semidirect
9. #17988781C2semidirect
10. #17988780C2semidirect
11. #17988779C2semidirect
12. #17988612C2semidirect
13. #17988590C2semidirect
14. #17988580C2semidirect
15. #459×C73C2semidirect
20. C2×#11924017C22semidirect
21. C2×#11924016C22semidirect
25. C2×#11924013C22semidirect
29. #14556587C22semidirect
30. #14556579C22semidirect
31. #14556578C22semidirect
36. C4×D292C22semidirect
37. D4×Dic73C22semidirect
38. #14556553C22semidirect
45. C4⋊#10596831C22semidirect
46. #14556520C22semidirect
47. #14556520C22semidirect
48. #14556516C22semidirect
49. #14556514C22semidirect
50. #14556513C22semidirect
51. #14556512C22semidirect
52. #14556512C22semidirect
53. #14556511C22semidirect
55. C2×D8×C73C22semidirect
56. #127×C73C22semidirect
57. C4×D4×C73C22semidirect
58. C4⋊C8×C73C22semidirect
59. #102×C73C22semidirect
60. #102×C73C22semidirect
76. D4×D73D4semidirect
212. C73#3041semidirect
224. #459D73semidirect
240. C2×D8C2×D73semidirect
244. #127C2×D73semidirect
256. C4×D4C2×D73semidirect
264. C4⋊C8C2×D73semidirect
271. #102C2×D73semidirect
272. #102C2×D73semidirect