Finite Group Databasebeta

← #22616491

Subgroups — #22616491

Order 9344.

680 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556576C211yesmaximal, characteristic, complemented
2C2×#14556561C211yesmaximal, characteristic
3#17988516C211yesmaximal, characteristic, complemented
4#17988516C211yesmaximal, characteristic, complemented
5#17988510C211yesmaximal, characteristic, complemented
6#17988509C211yesmaximal, characteristic, complemented
7#17988505C211yesmaximal, characteristic, complemented
8#17988502C211yesmaximal, characteristic, complemented
9#17988489C211yesmaximal, characteristic, complemented
10#17988478C211yesmaximal, characteristic, complemented
11#17988465C211yesmaximal, characteristic, complemented
12#17988463C211yesmaximal, characteristic, complemented
13#17988442C211yesmaximal, characteristic, complemented
14#17988442C211yesmaximal, characteristic, complemented
15#388×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C22×D292C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic, complemented
21#14556576—24no—
22#14556561—24no—
23C2×C4⋊Dic73C2211yescharacteristic, complemented
24C2×#11924007C2211yescharacteristic, complemented
25C2×#11924007C2211yescharacteristic, complemented
26C2×#11924007C2211yescharacteristic, complemented
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic
39C2×#11924005C2211yescharacteristic, complemented
40C2×#11924005C2211yescharacteristic, complemented
41C2×#11924005C2211yescharacteristic, complemented
42#14556498C2211yescharacteristic, complemented
43#14556498C2211yescharacteristic, complemented
44#14556498C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46C2×C4⋊C4×C73C2211yescharacteristic, complemented
47C2×C22⋊C4×C73C2211yescharacteristic
48C2×C22⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C42×C73C2211yescharacteristic, complemented
51#95×C73C2211yescharacteristic, complemented
52#95×C73C2211yescharacteristic, complemented
53C23×D73—22no—
54C23×D73—22no—
55C23×D73—22no—
56C23×D73—41no—
57C23×D73—41no—
58C23×D73—41no—
59C23×D73—41no—
60C23×D73C2311yescharacteristic
61C23×D73C2311yescharacteristic
62C23×D73C2311yescharacteristic
63C2×D292—22no—
64C2×D292—22no—
65C2×D292—41no—
66C2×D292—41no—
67C2×D292—41no—
68C2×D292D414yes—
69C2×C22⋊D73—22no—
70C2×C22⋊D73—22no—
71C2×C22⋊D73—41no—
72C22×Dic73C2311yescharacteristic
73C22×Dic73C2311yescharacteristic
74C22×Dic73C2311yescharacteristic
75C22×Dic73C2311yescharacteristic
76C22×Dic73C2311yescharacteristic
77C2×C4×D73—22no—
78C2×C4×D73—41no—
79C2×C4×D73—41no—
80C4⋊Dic73—41no—
81#11924007—22no—
82#11924007—41no—
83#11924007—41no—
84C22⋊Dic73—41no—
85C22⋊Dic73—41no—
86#11924005—22no—
87#11924005—22no—
88#11924005—22no—
89#11924005—22no—
90#11924005—22no—
91#11924005—22no—
92#11924005—41no—
93#11924005—41no—
94#11924005—41no—
95#11924005—41no—
96#11924005—41no—
97#11924005—41no—
98#11924005—41no—
99C24×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102C22×C4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104C22×C4×C73C2311yescharacteristic
105C22×C4×C73C2311yescharacteristic
106C4⋊C4×C73—22no—
107C22⋊C4×C73—22no—
108C22⋊C4×C73—22no—
109C22⋊C4×C73—41no—
110C42×C73—41no—
111C23×C73—21no—
112C23×C73—21no—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73#4112yes—
118C23×C73C2411yescharacteristic
119C22×D73—21no—
120C22×D73—21no—
121C22×D73—21no—
122C22×D73—21no—
123C22×D73—21no—
124C22×D73—21no—
125C22×D73—21no—
126C22×D73—21no—
127C22×D73—21no—
128C22×D73—21no—
129C22×D73—21no—
130C22×D73—21no—
131C22×D73—21no—
132C22×D73—21no—
133C22×D73—21no—
134C22×D73—21no—
135C22×D73—21no—
136C22×D73—21no—
137C22×D73—44no—
138C22×D73—44no—
139C22×D73—44no—
140C22×D73—44no—
141C22×D73—44no—
142C22×D73—44no—
143C22×D73—44no—
144C22×D73C2×D412yes—
145C22×D73C2×D412yes—
146C22×D73#4112yes—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—21no—
152C2×C4×C73—21no—
153C2×C4×C73—21no—
154C2×C4×C73—21no—
155C2×C4×C73—21no—
156C2×C4×C73—21no—
157C2×C4×C73—21no—
158C2×C4×C73—21no—
159C2×C4×C73—21no—
160C2×C4×C73—21no—
161C2×C4×C73—21no—
162C2×C4×C73—21no—
163C2×C4×C73—21no—
164C2×C4×C73C2×D412yes—
165C22⋊D73—44no—
166C2×Dic73—21no—
167C2×Dic73—21no—
168C2×Dic73—21no—
169C2×Dic73—21no—
170C2×Dic73—21no—
171C2×Dic73—21no—
172C2×Dic73—21no—
173C2×Dic73—21no—
174C2×Dic73—21no—
175C2×Dic73—21no—
176C2×Dic73—21no—
177C2×Dic73—21no—
178C2×Dic73—21no—
179C2×Dic73—21no—
180C2×Dic73—21no—
181D292—44no—
182D292—44no—
183C4×D73—44no—
184C22×C73—22no—
185C22×C73—22no—
186C22×C73—22no—
187C22×C73—41no—
188C22×C73—41no—
189C22×C73—41no—
190C22×C73—41no—
191C22×C73C22×D411yescharacteristic
192C22×C73C2×#4111yescharacteristic
193C22×C73C2×#4111yescharacteristic
194C22×C73H(5,𝔽2)11yescharacteristic
195C22×C73H(5,𝔽2)11yescharacteristic
196C22×C73H(5,𝔽2)11yescharacteristic
197C22×C73H(5,𝔽2)11yescharacteristic
198C2×D73—22no—
199C2×D73—22no—
200C2×D73—22no—
201C2×D73—22no—
202C2×D73—22no—
203C2×D73—22no—
204C2×D73—22no—
205C2×D73—22no—
206C2×D73—22no—
207C2×D73—416no—
208C2×D73—41no—
209C2×D73—41no—
210C2×D73—41no—
211C2×D73—41no—
212C2×D73—41no—
213C2×D73—41no—
214C2×D73—41no—
215C2×D73—41no—
216C2×D73—41no—
217C2×D73—41no—
218C2×D73—41no—
219C2×D73—41no—
220C4×C73—22no—
221C4×C73—41no—
222C4×C73—41no—
223C4×C73—41no—
224C4×C73—41no—
225C4×C73—41no—
226Dic73—41no—
227Dic73—41no—
228Dic73—41no—
229Dic73—41no—
230Dic73—41no—
231C2×C73—42no—
232C2×C73#53411yescharacteristic
233C2×C73#53811yescharacteristic
234C2×C73#53811yescharacteristic
235C2×C73#54611yescharacteristic
236C2×C73#54611yescharacteristic
237C2×C73#55111yescharacteristic
238C2×C73#56011yescharacteristic
239D73—42no—
240D73—42no—
241D73—42no—
242#2697—731nomaximal, Sylow
243C73#269711yescharacteristic, complemented, Sylow
244C2×#123—731no—
245C2×#120—731no—
246#397—731no—
247#397—731no—
248#396—731no—
249#396—731no—
250#394—731no—
251#394—731no—
252#390—731no—
253#388—731no—
254#388D7311yescharacteristic, complemented
255#386—731no—
256#386—731no—
257#379—731no—
258#379—731no—
259C25—731no—
260C22×D4—731no—
261C22×D4—731no—
262C22×D4—731no—
263C23×C4—731no—
264#123—1464no—
265#120—1464no—
266C2×C4⋊C4—731no—
267C2×C4⋊C4—731no—
268C2×C4⋊C4—731no—
269C2×C4⋊C4—731no—
270C2×C4⋊C4C2×D7311yescharacteristic, complemented
271C2×C22⋊C4—731no—
272C2×C22⋊C4—731no—
273C2×C22⋊C4—731no—
274C2×C22⋊C4—731no—
275C2×C22⋊C4—731no—
276C2×C22⋊C4—731no—
277C2×C22⋊C4—731no—
278C2×C22⋊C4—731no—
279C2×C22⋊C4—731no—
280C2×C22⋊C4—731no—
281C2×C22⋊C4—731no—
282C2×C22⋊C4—731no—
283C2×C22⋊C4—731no—
284C2×C22⋊C4—731no—
285C2×C22⋊C4—731no—
286C2×C22⋊C4C2×D7311yescharacteristic
287C2×C22⋊C4C2×D7311yescharacteristic
288C2×C22⋊C4C2×D7311yescharacteristic
289C2×C42C2×D7311yescharacteristic, complemented
290#95—731no—
291#95—731no—
292#95—731no—
293#95—731no—
294#95C2×D7311yescharacteristic, complemented
295#95C2×D7311yescharacteristic, complemented
296C24—2921no—
297C24—2921no—
298C24—2921no—
299C24—2921no—
300C24—731no—
301C24—731no—
302C24—731no—
303C24—1462no—
304C24—1462no—
305C24—1462no—
306C24C22×D7311yescharacteristic
307C2×D4—2921no—
308C2×D4—2921no—
309C2×D4—2921no—
310C2×D4—2921no—
311C2×D4—734no—
312C2×D4—1462no—
313C2×D4—1462no—
314C2×D4—1462no—
315C2×D4—1462no—
316C22×C4—2921no—
317C22×C4—2921no—
318C22×C4—731no—
319C22×C4—731no—
320C22×C4—731no—
321C22×C4—731no—
322C22×C4—731no—
323C22×C4—1462no—
324C22×C4C22×D7311yescharacteristic
325C22×C4C22×D7311yescharacteristic
326C22×C4C22×D7311yescharacteristic
327C22×C4C22×D7311yescharacteristic
328C22×C4C22×D7311yescharacteristic
329C22×C4C22×D7311yescharacteristic
330C4⋊C4—22no—
331C4⋊C4—2921no—
332C4⋊C4—2921no—
333C4⋊C4—2921no—
334C4⋊C4—1462no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—41no—
338C22⋊C4—2921no—
339C22⋊C4—2921no—
340C22⋊C4—2921no—
341C22⋊C4—2921no—
342C22⋊C4—2921no—
343C22⋊C4—2921no—
344C22⋊C4—2921no—
345C22⋊C4—2921no—
346C22⋊C4—2921no—
347C22⋊C4—1462no—
348C22⋊C4—1462no—
349C22⋊C4—1462no—
350C22⋊C4—1462no—
351C22⋊C4—1462no—
352C22⋊C4—1462no—
353C42—41no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—2924no—
361C23—2924no—
362C23—2924no—
363C23—2924no—
364C23—2924no—
365C23—2924no—
366C23—2924no—
367C23—732no—
368C23—732no—
369C23—732no—
370C23—1461no—
371C23—1461no—
372C23—1461no—
373C23—1461no—
374C23—1461no—
375C23—1461no—
376C23—1461no—
377C23—1461no—
378C23—1461no—
379C23—1461no—
380C23—1461no—
381C23—1461no—
382C23—1461no—
383C23—1461no—
384C23—1461no—
385C23—1461no—
386C23—1461no—
387C23—1461no—
388C23#1192402812yes—
389C23C23×D7311yescharacteristic
390D4—2924no—
391D4—2924no—
392D4—2924no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—2924no—
411C2×C4—1461no—
412C2×C4—1461no—
413C2×C4—1461no—
414C2×C4—1461no—
415C2×C4—1461no—
416C2×C4—1461no—
417C2×C4—1461no—
418C2×C4—1461no—
419C2×C4—1461no—
420C2×C4—1461no—
421C2×C4—1461no—
422C2×C4—1461no—
423C2×C4—1461no—
424C2×C4—1461no—
425C2×C4—1461no—
426C2×C4D4×D7312yes—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—29216no—
435C22—2921no—
436C22—2921no—
437C22—2921no—
438C22—2921no—
439C22—2921no—
440C22—2921no—
441C22—2921no—
442C22—2921no—
443C22—2921no—
444C22—2921no—
445C22—2921no—
446C22—2921no—
447C22—1462no—
448C22—1462no—
449C22—1462no—
450C22—1462no—
451C22—1462no—
452C22—1462no—
453C22—1462no—
454C22—1462no—
455C22—1462no—
456C22C2×D4×D7311yescharacteristic
457C22#41×D7311yescharacteristic
458C22C2×#1192402811yescharacteristic
459C22#1455663611yescharacteristic
460C22#1455663711yescharacteristic
461C22#1455663711yescharacteristic
462C22#1455663711yescharacteristic
463C4—22no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—2921no—
470C4—2921no—
471C4—2921no—
472C4—2921no—
473C4—2921no—
474C2—42no—
475C2—2922no—
476C2—2922no—
477C2—2922no—
478C2#1798914511yescharacteristic
479C2#1798917011yescharacteristic
480C2#1798917311yescharacteristic
481C2#1798923011yescharacteristic
482C2#1798923311yescharacteristic
483C2#1798926111yescharacteristic
484C2#1798932811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#388×C73C2
hypercenter#388D73
hypocenterC73#2697
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14556576C2semidirect
3. #17988516C2semidirect
4. #17988516C2semidirect
5. #17988510C2semidirect
6. #17988509C2semidirect
7. #17988505C2semidirect
8. #17988502C2semidirect
9. #17988489C2semidirect
10. #17988478C2semidirect
11. #17988465C2semidirect
12. #17988463C2semidirect
13. #17988442C2semidirect
14. #17988442C2semidirect
15. #388×C73C2semidirect
20. C22×C4×D73C22semidirect
23. C2×C4⋊Dic73C22semidirect
24. C2×#11924007C22semidirect
25. C2×#11924007C22semidirect
26. C2×#11924007C22semidirect
39. C2×#11924005C22semidirect
40. C2×#11924005C22semidirect
41. C2×#11924005C22semidirect
42. #14556498C22semidirect
43. #14556498C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
46. C2×C4⋊C4×C73C22semidirect
50. C2×C42×C73C22semidirect
51. #95×C73C22semidirect
52. #95×C73C22semidirect
243. C73#2697semidirect
254. #388D73semidirect
270. C2×C4⋊C4C2×D73semidirect
289. C2×C42C2×D73semidirect
294. #95C2×D73semidirect
295. #95C2×D73semidirect