Finite Group Databasebeta

← #22619174

Subgroups — #22619174

Order 9344.

758 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D73C211yesmaximal, characteristic, complemented
2C2×#14556623C211yesmaximal, characteristic, complemented
3C2×#14556618C211yesmaximal, characteristic, complemented
4#17989100C211yesmaximal, characteristic, complemented
5#17988748C211yesmaximal, characteristic, complemented
6#17988747C211yesmaximal, characteristic, complemented
7#17988746C211yesmaximal, characteristic, complemented
8#17988735C211yesmaximal, characteristic, complemented
9#17988734C211yesmaximal, characteristic, complemented
10#17988733C211yesmaximal, characteristic, complemented
11#17988732C211yesmaximal, characteristic, complemented
12#17988594C211yesmaximal, characteristic, complemented
13#17988590C211yesmaximal, characteristic, complemented
14#17988549C211yesmaximal, characteristic, complemented
15#452×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×#11924029C2211yescharacteristic
18C2×#11924028—21no—
19C2×#11924028C2211yescharacteristic
20C2×#11924027—21no—
21C2×#11924027C2211yescharacteristic
22#41×D73—24no—
23#41×D73—24no—
24C2×Q8×D73C2211yescharacteristic
25C2×D4×D73—21no—
26C2×D4×D73C2211yescharacteristic
27C22×C4×D73—21no—
28C22×C4×D73C2211yescharacteristic
29#14556623—24no—
30#14556618—24no—
31C2×#11924018C2211yescharacteristic, complemented
32C2×#11924017C2211yescharacteristic, complemented
33C2×#11924015C2211yescharacteristic, complemented
34C2×#11924015C2211yescharacteristic, complemented
35C2×D584C2211yescharacteristic, complemented
36C2×#11924013C2211yescharacteristic, complemented
37C2×#11924011C2211yescharacteristic
38C2×#11924011C2211yescharacteristic
39#14556576—21no—
40#14556567C2211yescharacteristic, complemented
41#14556566C2211yescharacteristic, complemented
42#14556565C2211yescharacteristic, complemented
43#14556561—21no—
44#14556553—21no—
45#14556551—21no—
46#14556549C2211yescharacteristic
47#14556516C2211yescharacteristic, complemented
48#14556515C2211yescharacteristic, complemented
49#14556514C2211yescharacteristic, complemented
50#14556513C2211yescharacteristic, complemented
51#14556512C2211yescharacteristic, complemented
52#14556511C2211yescharacteristic, complemented
53C22⋊#10596831C2211yescharacteristic, complemented
54#14556503C2211yescharacteristic, complemented
55#14556503C2211yescharacteristic, complemented
56C2×#41×C73C2211yescharacteristic
57C2×Q16×C73C2211yescharacteristic, complemented
58C2×SD16×C73C2211yescharacteristic, complemented
59C22⋊Q8×C73C2211yescharacteristic, complemented
60#103×C73C2211yescharacteristic, complemented
61#102×C73C2211yescharacteristic, complemented
62C22⋊C8×C73C2211yescharacteristic, complemented
63C23×D73—21no—
64C23×D73D411yescharacteristic
65#11924029—22no—
66#11924029—22no—
67#11924029—22no—
68#11924029—22no—
69#11924028—28no—
70#11924028—22no—
71#11924028—22no—
72#11924027—28no—
73#11924027—22no—
74#11924027—22no—
75C2×Dic146—21no—
76C2×Dic146C2311yescharacteristic
77Q8×D73—22no—
78Q8×D73D414yescomplemented
79C2×D292—21no—
80C2×D292—21no—
81C2×D292—21no—
82C2×D292C2311yescharacteristic
83C2×D292C2311yescharacteristic
84C2×C22⋊D73—21no—
85C2×C22⋊D73—21no—
86C2×C22⋊D73—21no—
87C2×C22⋊D73—21no—
88D4×D73—28no—
89D4×D73—22no—
90D4×D73D414yescomplemented
91C22×Dic73—21no—
92C22×Dic73D411yescharacteristic
93C2×C4×D73—28no—
94C2×C4×D73—21no—
95C2×C4×D73—21no—
96C2×C4×D73—21no—
97C2×C4×D73—22no—
98C2×C4×D73—22no—
99C2×C4×D73—21no—
100C2×C4×D73D411yescharacteristic
101C2×C4×D73D411yescharacteristic
102C2×C4×D73C2311yescharacteristic
103C2×C4×D73C2311yescharacteristic
104#11924018—22no—
105#11924017—22no—
106#11924015—22no—
107#11924015—22no—
108D584—22no—
109#11924013—22no—
110#11924011—22no—
111#11924011—22no—
112C2×#10596831C2311yescharacteristic
113C2×#10596831C2311yescharacteristic
114C4⋊Dic73C2311yescharacteristic
115#11924007—21no—
116#11924005—21no—
117#11924005—21no—
118#11924005—21no—
119#11924005—21no—
120C4×Dic73—21no—
121#41×C73—22no—
122#41×C73—22no—
123C2×Q8×C73C2311yescharacteristic
124C2×Q8×C73C2311yescharacteristic
125C2×D4×C73—21no—
126C2×D4×C73C2311yescharacteristic
127C22×C4×C73—21no—
128C22×C4×C73C2311yescharacteristic
129Q16×C73—22no—
130SD16×C73—22no—
131C2×C8×C73C2311yescharacteristic
132C2×C8×C73C2311yescharacteristic
133C4⋊C4×C73—21no—
134C4⋊C4×C73C2311yescharacteristic
135C22⋊C4×C73—21no—
136C23×C73—21no—
137C23×C73C2×D411yescharacteristic
138C22×D73—21no—
139C22×D73—22no—
140C22×D73—24no—
141C22×D73—21no—
142C22×D73—41no—
143C22×D73—41no—
144C22×D73—42no—
145C22×D73—42no—
146C22×D73C2×D411yescharacteristic
147C22×D73C2×D411yescharacteristic
148Q8×C73—21no—
149Q8×C73—21no—
150Q8×C73—21no—
151Q8×C73C2×D412yes—
152D4×C73—24no—
153D4×C73—21no—
154D4×C73C2×D412yes—
155C2×C4×C73—24no—
156C2×C4×C73—21no—
157C2×C4×C73—21no—
158C2×C4×C73—21no—
159C2×C4×C73—21no—
160C2×C4×C73—21no—
161C2×C4×C73C2×D411yescharacteristic
162C2×C4×C73C2411yescharacteristic
163C22⋊D73—24no—
164C22⋊D73—24no—
165C22⋊D73—24no—
166C22⋊D73—42no—
167C2×Dic73—24no—
168C2×Dic73—21no—
169C2×Dic73—22no—
170C2×Dic73—21no—
171C2×Dic73C2×D411yescharacteristic
172C2×Dic73C2×D411yescharacteristic
173D292—24no—
174D292—21no—
175D292—21no—
176D292—21no—
177D292—42no—
178D292—42no—
179D292C2×D412yes—
180C4×D73—24no—
181C4×D73—24no—
182C4×D73—22no—
183C4×D73—24no—
184C4×D73—21no—
185C4×D73—21no—
186C4×D73—22no—
187C4×D73—42no—
188C4×D73C2×D412yes—
189C4×D73C2×D412yes—
190Dic146—21no—
191Dic146—24no—
192Dic146C2×D412yes—
193C8×C73—21no—
194C8×C73—21no—
195#10596831—21no—
196#10596831—21no—
197C22×C73—21no—
198C22×C73—22no—
199C22×C73—21no—
200C22×C73—21no—
201C22×C73—41no—
202C22×C73—41no—
203C22×C73C22×D411yescharacteristic
204C2×D73—21no—
205C2×D73—21no—
206C2×D73—21no—
207C2×D73—22no—
208C2×D73—21no—
209C2×D73—21no—
210C2×D73—44no—
211C2×D73—48no—
212C2×D73—41no—
213C2×D73—41no—
214C2×D73—41no—
215C2×D73—41no—
216C2×D73—41no—
217C2×D73#12012yes—
218C4×C73—22no—
219C4×C73—21no—
220C4×C73—41no—
221C4×C73—41no—
222C4×C73C22×D411yescharacteristic
223C4×C73C22×D411yescharacteristic
224Dic73—22no—
225Dic73—21no—
226Dic73—41no—
227Dic73#12012yes—
228C2×C73—41no—
229C2×C73—42no—
230C2×C73C2×#12011yescharacteristic
231C2×C73#57511yescharacteristic
232C2×C73#57511yescharacteristic
233D73—22no—
234D73—41no—
235D73—42no—
236D73—81no—
237#3005—731nomaximal, Sylow
238C73#300511yescharacteristic, complemented, Sylow
239C22×#41—731no—
240C2×#137—731no—
241C2×AGL(1,ℤ/8)—731no—
242#525—731no—
243#452—731no—
244#452—731no—
245#452—731no—
246#452D7311yescharacteristic, complemented
247#449—731no—
248#449—731no—
249#449—731no—
250#449—731no—
251#419—731no—
252#418—731no—
253#407—731no—
254C2×#41—731no—
255C2×#41—731no—
256C2×#41—731no—
257C2×#41—731no—
258C2×#41—1461no—
259C2×#41—1461no—
260C2×#41—1464no—
261C2×#41—1464no—
262C2×#41C2×D7311yescharacteristic
263C22×Q8—731no—
264C22×D4—731no—
265C22×D4—1461no—
266C23×C4—731no—
267C23×C4—1461no—
268#137—1464no—
269AGL(1,ℤ/8)—1464no—
270C2×Q16—731no—
271C2×Q16C2×D7311yescharacteristic, complemented
272C2×SD16—731no—
273C2×SD16—731no—
274C2×SD16—731no—
275C2×SD16C2×D7311yescharacteristic, complemented
276C2×D8—731no—
277C2×D8—731no—
278C2×M16—731no—
279C2×M16—731no—
280#123—1461no—
281C22⋊Q8—731no—
282C22⋊Q8C2×D7311yescharacteristic, complemented
283#121—731no—
284#121—731no—
285#120—1461no—
286C4×D4—1461no—
287C4×D4—1461no—
288#117—731no—
289#103—731no—
290#103—731no—
291#103—731no—
292#103C2×D7311yescharacteristic, complemented
293#102—731no—
294#102—731no—
295#102—731no—
296#102C2×D7311yescharacteristic, complemented
297C22⋊C8—731no—
298C22⋊C8—731no—
299C22⋊C8—731no—
300C22⋊C8C2×D7311yescharacteristic, complemented
301C24—731no—
302C24—1461no—
303#41—22no—
304#41—22no—
305#41—1462no—
306#41—1462no—
307#41—1468no—
308#41—1462no—
309#41—1462no—
310#41—1462no—
311#41—1468no—
312#41—1462no—
313#41—1462no—
314#41—1462no—
315C2×Q8—734no—
316C2×Q8—731no—
317C2×Q8—1461no—
318C2×Q8—1462no—
319C2×Q8C22×D7311yescharacteristic
320C2×Q8C22×D7311yescharacteristic
321C2×D4—21no—
322C2×D4—734no—
323C2×D4—731no—
324C2×D4—731no—
325C2×D4—1461no—
326C2×D4—1461no—
327C2×D4—1461no—
328C2×D4—1462no—
329C2×D4—1461no—
330C2×D4—1468no—
331C2×D4—1461no—
332C2×D4—1461no—
333C2×D4—1461no—
334C2×D4C22×D7311yescharacteristic
335C22×C4—21no—
336C22×C4—731no—
337C22×C4—731no—
338C22×C4—731no—
339C22×C4—731no—
340C22×C4—731no—
341C22×C4—1461no—
342C22×C4—1462no—
343C22×C4—1462no—
344C22×C4—1461no—
345C22×C4—1461no—
346C22×C4—1468no—
347C22×C4—1461no—
348C22×C4—1461no—
349C22×C4C22×D7311yescharacteristic
350Q16—22no—
351Q16—1462no—
352SD16—22no—
353SD16—1462no—
354SD16—1462no—
355SD16—1462no—
356D8—1462no—
357D8—1462no—
358M16—1462no—
359M16—1462no—
360C2×C8—731no—
361C2×C8—731no—
362C2×C8C22×D7311yescharacteristic
363C2×C8C22×D7311yescharacteristic
364C4⋊C4—21no—
365C4⋊C4—731no—
366C4⋊C4—1461no—
367C4⋊C4C22×D7311yescharacteristic
368C22⋊C4—21no—
369C22⋊C4—1461no—
370C22⋊C4—1461no—
371C22⋊C4—1461no—
372C22⋊C4—1461no—
373C42—1461no—
374C23—21no—
375C23—2921no—
376C23—2921no—
377C23—2922no—
378C23—2922no—
379C23—731no—
380C23—731no—
381C23—1464no—
382C23—1462no—
383C23—1461no—
384C23—1461no—
385C23D4×D7311yescharacteristic
386Q8—21no—
387Q8—21no—
388Q8—21no—
389Q8—732no—
390Q8—1464no—
391Q8—1461no—
392Q8D4×D7312yes—
393D4—24no—
394D4—21no—
395D4—2922no—
396D4—2922no—
397D4—2922no—
398D4—732no—
399D4—1464no—
400D4—1464no—
401D4—1464no—
402D4—1464no—
403D4—1461no—
404D4—1461no—
405D4—1461no—
406D4D4×D7312yes—
407C2×C4—24no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—2922no—
414C2×C4—731no—
415C2×C4—732no—
416C2×C4—732no—
417C2×C4—731no—
418C2×C4—1462no—
419C2×C4—1462no—
420C2×C4—1464no—
421C2×C4—1464no—
422C2×C4—1464no—
423C2×C4—1461no—
424C2×C4—1462no—
425C2×C4—1464no—
426C2×C4—1461no—
427C2×C4—1461no—
428C2×C4—1461no—
429C2×C4D4×D7311yescharacteristic
430C2×C4C23×D7311yescharacteristic
431C8—21no—
432C8—21no—
433C8—1461no—
434C8—1461no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—2924no—
442C22—2928no—
443C22—2921no—
444C22—2921no—
445C22—2921no—
446C22—2921no—
447C22—2921no—
448C22—732no—
449C22—1461no—
450C22—1461no—
451C22—1462no—
452C22—1461no—
453C22—1461no—
454C22—1461no—
455C22C2×D4×D7311yescharacteristic
456C4—21no—
457C4—22no—
458C4—41no—
459C4—41no—
460C4—2921no—
461C4—732no—
462C4—1461no—
463C4—1462no—
464C4C2×D4×D7311yescharacteristic
465C4C2×D4×D7311yescharacteristic
466C2—41no—
467C2—42no—
468C2—2922no—
469C2—2921no—
470C2—5841no—
471C2—1462no—
472C2#120×D7311yescharacteristic
473C2#1798938411yescharacteristic
474C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#452×C73C2
socleC22×C73C22×D4
hypercenter#452D73
hypocenterC73#3005
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#41×D73C2semidirect
2. C2×#14556623C2semidirect
3. C2×#14556618C2semidirect
4. #17989100C2semidirect
5. #17988748C2semidirect
6. #17988747C2semidirect
7. #17988746C2semidirect
8. #17988735C2semidirect
9. #17988734C2semidirect
10. #17988733C2semidirect
11. #17988732C2semidirect
12. #17988594C2semidirect
13. #17988590C2semidirect
14. #17988549C2semidirect
15. #452×C73C2semidirect
31. C2×#11924018C22semidirect
32. C2×#11924017C22semidirect
33. C2×#11924015C22semidirect
34. C2×#11924015C22semidirect
35. C2×D584C22semidirect
36. C2×#11924013C22semidirect
40. #14556567C22semidirect
41. #14556566C22semidirect
42. #14556565C22semidirect
47. #14556516C22semidirect
48. #14556515C22semidirect
49. #14556514C22semidirect
50. #14556513C22semidirect
51. #14556512C22semidirect
52. #14556511C22semidirect
53. C22⋊#10596831C22semidirect
54. #14556503C22semidirect
55. #14556503C22semidirect
57. C2×Q16×C73C22semidirect
58. C2×SD16×C73C22semidirect
59. C22⋊Q8×C73C22semidirect
60. #103×C73C22semidirect
61. #102×C73C22semidirect
62. C22⋊C8×C73C22semidirect
78. Q8×D73D4semidirect
90. D4×D73D4semidirect
238. C73#3005semidirect
246. #452D73semidirect
271. C2×Q16C2×D73semidirect
275. C2×SD16C2×D73semidirect
282. C22⋊Q8C2×D73semidirect
292. #103C2×D73semidirect
296. #102C2×D73semidirect
300. C22⋊C8C2×D73semidirect