Finite Group Databasebeta

← #22613398

Subgroups — #22613398

Order 9344.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556573C211yesmaximal, characteristic, complemented
2C2×#14556561C211yesmaximal, characteristic
3C2×C4×D292C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D73C211yesmaximal, characteristic, complemented
5#17988524C211yesmaximal, characteristic, complemented
6#17988512C211yesmaximal, characteristic, complemented
7#17988504C211yesmaximal, characteristic, complemented
8#17988503C211yesmaximal, characteristic, complemented
9#17988478C211yesmaximal, characteristic, complemented
10#17988465C211yesmaximal, characteristic, complemented
11#17988465C211yesmaximal, characteristic, complemented
12#17988461C211yesmaximal, characteristic, complemented
13#17988444C211yesmaximal, characteristic, complemented
14#17988442C211yesmaximal, characteristic, complemented
15#388×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C22×D292C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic
21C22×C4×D73C2211yescharacteristic
22C22×C4×D73C2211yescharacteristic, complemented
23#14556573—24no—
24#14556561—24no—
25C4×D292—24no—
26C2×C4⋊Dic73C2211yescharacteristic, complemented
27C2×C4⋊Dic73C2211yescharacteristic, complemented
28C2×C4⋊Dic73C2211yescharacteristic, complemented
29C2×#11924007C2211yescharacteristic, complemented
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic
39C2×#11924005C2211yescharacteristic
40C2×#11924005C2211yescharacteristic, complemented
41C2×#11924005C2211yescharacteristic, complemented
42C2×#11924005C2211yescharacteristic, complemented
43C22⋊C4×D73—24no—
44#14556498C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46#14556498C2211yescharacteristic, complemented
47#14556498C2211yescharacteristic, complemented
48C2×C4⋊C4×C73C2211yescharacteristic, complemented
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C42×C73C2211yescharacteristic, complemented
53#95×C73C2211yescharacteristic, complemented
54#95×C73C2211yescharacteristic, complemented
55C23×D73—22no—
56C23×D73—22no—
57C23×D73—22no—
58C23×D73—22no—
59C23×D73—22no—
60C23×D73—41no—
61C23×D73—41no—
62C23×D73C2311yescharacteristic
63C23×D73C2311yescharacteristic
64C23×D73C2311yescharacteristic
65C2×D292—22no—
66C2×D292—22no—
67C2×D292—22no—
68C2×D292—22no—
69C2×D292—41no—
70C2×D292D414yes—
71C2×C22⋊D73—22no—
72C2×C22⋊D73—22no—
73C2×C22⋊D73—41no—
74C22×Dic73C2311yescharacteristic
75C22×Dic73C2311yescharacteristic
76C22×Dic73C2311yescharacteristic
77C22×Dic73C2311yescharacteristic
78C22×Dic73C2311yescharacteristic
79C2×C4×D73—22no—
80C2×C4×D73—22no—
81C2×C4×D73—22no—
82C2×C4×D73—22no—
83C2×C4×D73—22no—
84C2×C4×D73—22no—
85C2×C4×D73—41no—
86C2×C4×D73—41no—
87C2×C4×D73—41no—
88C4⋊Dic73—22no—
89C4⋊Dic73—22no—
90C4⋊Dic73—41no—
91#11924007—22no—
92C22⋊Dic73—22no—
93C22⋊Dic73—22no—
94#11924005—22no—
95#11924005—22no—
96#11924005—22no—
97#11924005—22no—
98#11924005—22no—
99#11924005—22no—
100#11924005—22no—
101#11924005—22no—
102#11924005—22no—
103#11924005—41no—
104#11924005—41no—
105C24×C73C2311yescharacteristic
106C22×C4×C73C2311yescharacteristic
107C22×C4×C73C2311yescharacteristic
108C22×C4×C73C2311yescharacteristic
109C22×C4×C73C2311yescharacteristic
110C22×C4×C73C2311yescharacteristic
111C22×C4×C73C2311yescharacteristic
112C4⋊C4×C73—41no—
113C22⋊C4×C73—22no—
114C22⋊C4×C73—41no—
115C22⋊C4×C73D414yescomplemented
116C42×C73—22no—
117C23×C73—21no—
118C23×C73—21no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73—21no—
122C23×C73—21no—
123C23×C73C2×D412yes—
124C23×C73C2411yescharacteristic
125C22×D73—21no—
126C22×D73—21no—
127C22×D73—21no—
128C22×D73—21no—
129C22×D73—28no—
130C22×D73—21no—
131C22×D73—21no—
132C22×D73—21no—
133C22×D73—21no—
134C22×D73—21no—
135C22×D73—21no—
136C22×D73—21no—
137C22×D73—21no—
138C22×D73—21no—
139C22×D73—21no—
140C22×D73—21no—
141C22×D73—21no—
142C22×D73—44no—
143C22×D73—44no—
144C22×D73—44no—
145C22×D73—44no—
146C22×D73—44no—
147C22×D73—44no—
148C22×D73C2×D412yes—
149C22×D73C2×D412yes—
150C22×D73#4112yes—
151C22×D73#4112yes—
152C22×D73#4112yes—
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×C73—21no—
165C2×C4×C73—21no—
166C2×C4×C73—21no—
167C2×C4×C73—21no—
168C2×C4×C73C2×D412yes—
169C2×C4×C73C2×D412yes—
170C2×C4×C73C2×D412yes—
171C22⋊D73—44no—
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—
181C2×Dic73—21no—
182C2×Dic73—21no—
183C2×Dic73—21no—
184C2×Dic73—21no—
185C2×Dic73—21no—
186C2×Dic73—21no—
187D292—28no—
188D292—44no—
189C4×D73—44no—
190C4×D73—44no—
191C4×D73—44no—
192C22×C73—22no—
193C22×C73—22no—
194C22×C73—22no—
195C22×C73—41no—
196C22×C73—41no—
197C22×C73—41no—
198C22×C73—41no—
199C22×C73C22×D411yescharacteristic
200C22×C73C22×D411yescharacteristic
201C22×C73C2×#4111yescharacteristic
202C22×C73C2×#4111yescharacteristic
203C22×C73C2×#4111yescharacteristic
204C22×C73H(5,𝔽2)11yescharacteristic
205C22×C73H(5,𝔽2)11yescharacteristic
206C2×D73—22no—
207C2×D73—22no—
208C2×D73—22no—
209C2×D73—22no—
210C2×D73—22no—
211C2×D73—22no—
212C2×D73—22no—
213C2×D73—22no—
214C2×D73—22no—
215C2×D73—22no—
216C2×D73—22no—
217C2×D73—22no—
218C2×D73—416no—
219C2×D73—41no—
220C2×D73—41no—
221C2×D73—41no—
222C2×D73—41no—
223C2×D73—41no—
224C2×D73—41no—
225C2×D73—41no—
226C2×D73—41no—
227C2×D73#12314yescomplemented
228C4×C73—22no—
229C4×C73—22no—
230C4×C73—22no—
231C4×C73—41no—
232C4×C73—41no—
233C4×C73—41no—
234Dic73—41no—
235Dic73—41no—
236Dic73—41no—
237Dic73—41no—
238Dic73—41no—
239C2×C73—42no—
240C2×C73C2×#12311yescharacteristic
241C2×C73#52511yescharacteristic
242C2×C73#53811yescharacteristic
243C2×C73D4211yescharacteristic
244C2×C73#54611yescharacteristic
245C2×C73#54611yescharacteristic
246C2×C73#55111yescharacteristic
247D73—24no—
248D73—42no—
249D73—42no—
250#2418—731nomaximal, Sylow
251C73#241811yescharacteristic, complemented, Sylow
252C2×#123—731no—
253C2×#120—731no—
254C2×C4×D4—731no—
255C22×C22⋊C4—731no—
256#399—731no—
257#397—731no—
258#394—731no—
259#394—731no—
260#388—731no—
261#388D7311yescharacteristic, complemented
262#386—731no—
263#386—731no—
264#385—731no—
265#380—731no—
266#379—731no—
267C25—731no—
268C22×D4—731no—
269C22×D4—731no—
270C22×D4—731no—
271C23×C4—731no—
272C23×C4—731no—
273C23×C4—731no—
274#123—1464no—
275#120—1464no—
276C4×D4—1464no—
277C2×C4⋊C4—731no—
278C2×C4⋊C4—731no—
279C2×C4⋊C4—731no—
280C2×C4⋊C4—731no—
281C2×C4⋊C4C2×D7311yescharacteristic, complemented
282C2×C22⋊C4—731no—
283C2×C22⋊C4—731no—
284C2×C22⋊C4—731no—
285C2×C22⋊C4—731no—
286C2×C22⋊C4—731no—
287C2×C22⋊C4—731no—
288C2×C22⋊C4—731no—
289C2×C22⋊C4—731no—
290C2×C22⋊C4—731no—
291C2×C22⋊C4—731no—
292C2×C22⋊C4—731no—
293C2×C22⋊C4—731no—
294C2×C22⋊C4—731no—
295C2×C22⋊C4—1464no—
296C2×C22⋊C4C2×D7311yescharacteristic
297C2×C22⋊C4C2×D7311yescharacteristic
298C2×C22⋊C4C2×D7311yescharacteristic
299C2×C42C2×D7311yescharacteristic, complemented
300#95—731no—
301#95—731no—
302#95—731no—
303#95—731no—
304#95C2×D7311yescharacteristic, complemented
305#95C2×D7311yescharacteristic, complemented
306C24—2921no—
307C24—2921no—
308C24—731no—
309C24—731no—
310C24—731no—
311C24—1462no—
312C24—1462no—
313C24—1462no—
314C24—1462no—
315C24—1462no—
316C24C22×D7311yescharacteristic
317C2×D4—2921no—
318C2×D4—2921no—
319C2×D4—734no—
320C2×D4—1462no—
321C2×D4—1462no—
322C2×D4—1462no—
323C2×D4—1462no—
324C2×D4—1462no—
325C2×D4—1462no—
326C22×C4—2921no—
327C22×C4—2921no—
328C22×C4—2921no—
329C22×C4—731no—
330C22×C4—731no—
331C22×C4—731no—
332C22×C4—731no—
333C22×C4—731no—
334C22×C4—1462no—
335C22×C4—1462no—
336C22×C4—1462no—
337C22×C4—1462no—
338C22×C4—1462no—
339C22×C4—1462no—
340C22×C4C22×D7311yescharacteristic
341C22×C4C22×D7311yescharacteristic
342C22×C4C22×D7311yescharacteristic
343C22×C4C22×D7311yescharacteristic
344C22×C4C22×D7311yescharacteristic
345C22×C4C22×D7311yescharacteristic
346C4⋊C4—41no—
347C4⋊C4—2921no—
348C4⋊C4—1462no—
349C4⋊C4—1462no—
350C4⋊C4—1462no—
351C22⋊C4—22no—
352C22⋊C4—41no—
353C22⋊C4—2921no—
354C22⋊C4—2921no—
355C22⋊C4—1462no—
356C22⋊C4—1462no—
357C22⋊C4—1462no—
358C22⋊C4—1462no—
359C22⋊C4—1462no—
360C22⋊C4—1462no—
361C22⋊C4—1462no—
362C22⋊C4—1462no—
363C22⋊C4—1462no—
364C22⋊C4—1462no—
365C22⋊C4—1462no—
366C22⋊C4D29214yescomplemented
367C42—22no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—2924no—
375C23—2924no—
376C23—2924no—
377C23—2924no—
378C23—2924no—
379C23—2924no—
380C23—732no—
381C23—732no—
382C23—732no—
383C23—732no—
384C23—732no—
385C23—1468no—
386C23—1461no—
387C23—1461no—
388C23—1461no—
389C23—1461no—
390C23—1461no—
391C23—1461no—
392C23—1461no—
393C23—1461no—
394C23—1461no—
395C23—1461no—
396C23—1461no—
397C23—1461no—
398C23—1461no—
399C23—1461no—
400C23—1461no—
401C23—1461no—
402C23C2×D29212yes—
403C23C23×D7311yescharacteristic
404D4—2924no—
405D4—2924no—
406D4—1468no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—2924no—
423C2×C4—2924no—
424C2×C4—2924no—
425C2×C4—1461no—
426C2×C4—1461no—
427C2×C4—1461no—
428C2×C4—1461no—
429C2×C4—1461no—
430C2×C4—1461no—
431C2×C4—1461no—
432C2×C4—1461no—
433C2×C4—1461no—
434C2×C4—1461no—
435C2×C4—1461no—
436C2×C4—1461no—
437C2×C4—1461no—
438C2×C4—1461no—
439C2×C4—1461no—
440C2×C4D4×D7312yes—
441C2×C4C2×D29212yes—
442C2×C4C2×D29212yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—29216no—
451C22—2921no—
452C22—2921no—
453C22—2921no—
454C22—2921no—
455C22—2921no—
456C22—2921no—
457C22—2921no—
458C22—2921no—
459C22—734no—
460C22—1462no—
461C22—1462no—
462C22—1462no—
463C22—1462no—
464C22—1462no—
465C22—1462no—
466C22—1462no—
467C22—1462no—
468C22—1462no—
469C22—1462no—
470C22—1462no—
471C22—1462no—
472C22C2×D4×D7311yescharacteristic
473C22C22×D29211yescharacteristic
474C22#41×D7311yescharacteristic
475C22#41×D7311yescharacteristic
476C22#41×D7311yescharacteristic
477C22#1455663611yescharacteristic
478C22#1455663711yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—2921no—
486C4—2921no—
487C4—2921no—
488C4—2921no—
489C4—2921no—
490C2—42no—
491C2—2922no—
492C2—2922no—
493C2—1464no—
494C2#123×D7311yescharacteristic
495C2#1798909911yescharacteristic
496C2#1798917111yescharacteristic
497C2D4×D29211yescharacteristic
498C2#1798923211yescharacteristic
499C2#1798923411yescharacteristic
500C2#1798926211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#388×C73C2
hypercenter#388D73
hypocenterC73#2418
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14556573C2semidirect
3. C2×C4×D292C2semidirect
4. C2×C22⋊C4×D73C2semidirect
5. #17988524C2semidirect
6. #17988512C2semidirect
7. #17988504C2semidirect
8. #17988503C2semidirect
9. #17988478C2semidirect
10. #17988465C2semidirect
11. #17988465C2semidirect
12. #17988461C2semidirect
13. #17988444C2semidirect
14. #17988442C2semidirect
15. #388×C73C2semidirect
22. C22×C4×D73C22semidirect
26. C2×C4⋊Dic73C22semidirect
27. C2×C4⋊Dic73C22semidirect
28. C2×C4⋊Dic73C22semidirect
29. C2×#11924007C22semidirect
40. C2×#11924005C22semidirect
41. C2×#11924005C22semidirect
42. C2×#11924005C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
47. #14556498C22semidirect
48. C2×C4⋊C4×C73C22semidirect
52. C2×C42×C73C22semidirect
53. #95×C73C22semidirect
54. #95×C73C22semidirect
115. C22⋊C4×C73D4semidirect
227. C2×D73#123semidirect
251. C73#2418semidirect
261. #388D73semidirect
281. C2×C4⋊C4C2×D73semidirect
299. C2×C42C2×D73semidirect
304. #95C2×D73semidirect
305. #95C2×D73semidirect
366. C22⋊C4D292semidirect