Finite Group Databasebeta

← #22616250

Subgroups — #22616250

Order 9344.

802 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556565C211yesmaximal, characteristic, complemented
2C2×#14556561C211yesmaximal, characteristic, complemented
3C2×#14556559C211yesmaximal, characteristic, complemented
4#17988513C211yesmaximal, characteristic, complemented
5#17988509C211yesmaximal, characteristic, complemented
6#17988504C211yesmaximal, characteristic, complemented
7#17988502C211yesmaximal, characteristic, complemented
8#17988496C211yesmaximal, characteristic, complemented
9#17988495C211yesmaximal, characteristic, complemented
10#17988488C211yesmaximal, characteristic, complemented
11#17988487C211yesmaximal, characteristic, complemented
12#17988480C211yesmaximal, characteristic, complemented
13#17988466C211yesmaximal, characteristic, complemented
14#17988442C211yesmaximal, characteristic, complemented
15C2×#123×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C22×D292C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic
20C22×C22⋊D73C2211yescharacteristic
21C22×C22⋊D73C2211yescharacteristic
22C22×C22⋊D73C2211yescharacteristic, complemented
23#14556565—24no—
24#14556561—24no—
25#14556559—24no—
26C2×C4⋊Dic73C2211yescharacteristic, complemented
27C2×#11924007C2211yescharacteristic, complemented
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic, complemented
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
42C2×C4×Dic73C2211yescharacteristic, complemented
43#14556498C2211yescharacteristic, complemented
44#14556498C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46#14556498C2211yescharacteristic, complemented
47C22×D4×C73C2211yescharacteristic
48C23×C4×C73C2211yescharacteristic, complemented
49#123×C73—24no—
50C2×C4⋊C4×C73C2211yescharacteristic, complemented
51C2×C4⋊C4×C73C2211yescharacteristic, complemented
52C2×C22⋊C4×C73C2211yescharacteristic
53C2×C22⋊C4×C73C2211yescharacteristic
54C2×C22⋊C4×C73C2211yescharacteristic, complemented
55C23×D73—22no—
56C23×D73—22no—
57C23×D73—22no—
58C23×D73—41no—
59C23×D73—41no—
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×D292—41no—
71C2×C22⋊D73—22no—
72C2×C22⋊D73—22no—
73C2×C22⋊D73—22no—
74C2×C22⋊D73—22no—
75C2×C22⋊D73—41no—
76C2×C22⋊D73—41no—
77C2×C22⋊D73—41no—
78C2×C22⋊D73—41no—
79C2×C22⋊D73—41no—
80C2×C22⋊D73—41no—
81C2×C22⋊D73—41no—
82C2×C22⋊D73D414yescomplemented
83C22×Dic73C2311yescharacteristic
84C22×Dic73C2311yescharacteristic
85C22×Dic73C2311yescharacteristic
86C22×Dic73C2311yescharacteristic
87C22×Dic73C2311yescharacteristic
88C4⋊Dic73—22no—
89#11924007—41no—
90C22⋊Dic73—22no—
91C22⋊Dic73—41no—
92C22⋊Dic73—41no—
93#11924005—22no—
94#11924005—22no—
95#11924005—22no—
96#11924005—22no—
97#11924005—22no—
98#11924005—22no—
99#11924005—41no—
100#11924005—41no—
101#11924005—41no—
102#11924005—41no—
103#11924005—41no—
104C4×Dic73—41no—
105C24×C73C2311yescharacteristic
106C24×C73C2311yescharacteristic
107C2×D4×C73—22no—
108C2×D4×C73—22no—
109C2×D4×C73—41no—
110C22×C4×C73—22no—
111C22×C4×C73—22no—
112C22×C4×C73—41no—
113C22×C4×C73C2311yescharacteristic
114C22×C4×C73C2311yescharacteristic
115C22×C4×C73C2311yescharacteristic
116C22×C4×C73C2311yescharacteristic
117C22×C4×C73C2311yescharacteristic
118C4⋊C4×C73—22no—
119C4⋊C4×C73—22no—
120C22⋊C4×C73—22no—
121C22⋊C4×C73—22no—
122C22⋊C4×C73D414yescomplemented
123C23×C73—21no—
124C23×C73—21no—
125C23×C73—21no—
126C23×C73—21no—
127C23×C73—21no—
128C23×C73—21no—
129C23×C73—21no—
130C23×C73—21no—
131C23×C73—21no—
132C23×C73—21no—
133C23×C73—21no—
134C23×C73—21no—
135C23×C73C2×D412yes—
136C23×C73C2×D412yes—
137C23×C73C2411yescharacteristic
138C22×D73—21no—
139C22×D73—21no—
140C22×D73—21no—
141C22×D73—21no—
142C22×D73—21no—
143C22×D73—21no—
144C22×D73—21no—
145C22×D73—21no—
146C22×D73—21no—
147C22×D73—21no—
148C22×D73—21no—
149C22×D73—21no—
150C22×D73—21no—
151C22×D73—21no—
152C22×D73—21no—
153C22×D73—21no—
154C22×D73—21no—
155C22×D73—21no—
156C22×D73—21no—
157C22×D73—44no—
158C22×D73—44no—
159C22×D73—44no—
160C22×D73—44no—
161C22×D73—44no—
162C22×D73—44no—
163C22×D73—44no—
164C22×D73C2×D412yes—
165C22×D73#4112yes—
166D4×C73—44no—
167C2×C4×C73—21no—
168C2×C4×C73—21no—
169C2×C4×C73—21no—
170C2×C4×C73—21no—
171C2×C4×C73—21no—
172C2×C4×C73—21no—
173C2×C4×C73—21no—
174C2×C4×C73—21no—
175C2×C4×C73—21no—
176C2×C4×C73—21no—
177C2×C4×C73—21no—
178C2×C4×C73—21no—
179C2×C4×C73—21no—
180C2×C4×C73—44no—
181C2×C4×C73C2×D412yes—
182C2×C4×C73C2×D412yes—
183C22⋊D73—44no—
184C22⋊D73—44no—
185C22⋊D73—44no—
186C22⋊D73—44no—
187C2×Dic73—21no—
188C2×Dic73—21no—
189C2×Dic73—21no—
190C2×Dic73—21no—
191C2×Dic73—21no—
192C2×Dic73—21no—
193C2×Dic73—21no—
194C2×Dic73—21no—
195C2×Dic73—21no—
196C2×Dic73—21no—
197C2×Dic73—21no—
198C2×Dic73—21no—
199C2×Dic73—21no—
200C2×Dic73—21no—
201C2×Dic73C2×D412yes—
202D292—44no—
203D292—44no—
204C22×C73—22no—
205C22×C73—22no—
206C22×C73—22no—
207C22×C73—22no—
208C22×C73—22no—
209C22×C73—22no—
210C22×C73—41no—
211C22×C73—41no—
212C22×C73—41no—
213C22×C73—41no—
214C22×C73—41no—
215C22×C73—41no—
216C22×C73—41no—
217C22×C73—41no—
218C22×C73C22×D411yescharacteristic
219C22×C73C22×D411yescharacteristic
220C22×C73C2×#4111yescharacteristic
221C22×C73H(5,𝔽2)11yescharacteristic
222C22×C73H(5,𝔽2)11yescharacteristic
223C22×C73H(5,𝔽2)11yescharacteristic
224C22×C73H(5,𝔽2)11yescharacteristic
225C2×D73—22no—
226C2×D73—22no—
227C2×D73—22no—
228C2×D73—22no—
229C2×D73—22no—
230C2×D73—22no—
231C2×D73—416no—
232C2×D73—41no—
233C2×D73—41no—
234C2×D73—41no—
235C2×D73—41no—
236C2×D73—41no—
237C2×D73—41no—
238C2×D73—41no—
239C2×D73—41no—
240C2×D73—41no—
241C2×D73—41no—
242C2×D73—41no—
243C2×D73—41no—
244C2×D73—41no—
245C2×D73—41no—
246C2×D73—41no—
247C4×C73—22no—
248C4×C73—22no—
249C4×C73—41no—
250C4×C73—41no—
251C4×C73—41no—
252Dic73—22no—
253Dic73—41no—
254Dic73—41no—
255Dic73—41no—
256Dic73—41no—
257C2×C73—42no—
258C2×C73—42no—
259C2×C73#53411yescharacteristic
260C2×C73#53511yescharacteristic
261C2×C73#53811yescharacteristic
262C2×C73D4211yescharacteristic
263C2×C73#54611yescharacteristic
264C2×C73#54611yescharacteristic
265C2×C73#56011yescharacteristic
266D73—42no—
267D73—42no—
268D73—81no—
269#2678—731nomaximal, Sylow
270C73#267811yescharacteristic, complemented, Sylow
271C2×#123D7311yescharacteristic, complemented
272C2×#121—731no—
273C2×#120—731no—
274C2×#120—731no—
275#397—731no—
276#396—731no—
277#394—731no—
278#394—731no—
279#392—731no—
280#392—731no—
281#390—731no—
282#390—731no—
283#388—731no—
284#386—731no—
285#379—731no—
286C25—731no—
287C22×D4—731no—
288C22×D4—731no—
289C22×D4—731no—
290C22×D4—731no—
291C22×D4—731no—
292C22×D4—731no—
293C22×D4C2×D7311yescharacteristic
294C23×C4C2×D7311yescharacteristic, complemented
295#123—24no—
296#121—1464no—
297#120—1464no—
298#120—1464no—
299C2×C4⋊C4—731no—
300C2×C4⋊C4—731no—
301C2×C4⋊C4C2×D7311yescharacteristic, complemented
302C2×C4⋊C4C2×D7311yescharacteristic, complemented
303C2×C22⋊C4—731no—
304C2×C22⋊C4—731no—
305C2×C22⋊C4—731no—
306C2×C22⋊C4—731no—
307C2×C22⋊C4—731no—
308C2×C22⋊C4—731no—
309C2×C22⋊C4—731no—
310C2×C22⋊C4—731no—
311C2×C22⋊C4—731no—
312C2×C22⋊C4—731no—
313C2×C22⋊C4—731no—
314C2×C22⋊C4—731no—
315C2×C22⋊C4—731no—
316C2×C22⋊C4—731no—
317C2×C22⋊C4C2×D7311yescharacteristic
318C2×C22⋊C4C2×D7311yescharacteristic
319C2×C22⋊C4C2×D7311yescharacteristic, complemented
320C2×C42—731no—
321#95—731no—
322#95—731no—
323#95—731no—
324#95—731no—
325C24—2921no—
326C24—2921no—
327C24—2921no—
328C24—2921no—
329C24—731no—
330C24—731no—
331C24—731no—
332C24—1462no—
333C24—1462no—
334C24—1462no—
335C24C22×D7311yescharacteristic
336C24C22×D7311yescharacteristic
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—41no—
340C2×D4—2921no—
341C2×D4—2921no—
342C2×D4—2921no—
343C2×D4—2921no—
344C2×D4—2921no—
345C2×D4—2921no—
346C2×D4—2921no—
347C2×D4—2921no—
348C2×D4—2921no—
349C2×D4—734no—
350C2×D4—1462no—
351C2×D4—1462no—
352C2×D4—1462no—
353C2×D4—1462no—
354C2×D4—1462no—
355C2×D4—1462no—
356C2×D4—1462no—
357C2×D4—1462no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—41no—
361C22×C4—731no—
362C22×C4—731no—
363C22×C4—731no—
364C22×C4—731no—
365C22×C4—731no—
366C22×C4C22×D7311yescharacteristic
367C22×C4C22×D7311yescharacteristic
368C22×C4C22×D7311yescharacteristic
369C22×C4C22×D7311yescharacteristic
370C22×C4C22×D7311yescharacteristic
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—2921no—
374C4⋊C4—1462no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—2921no—
378C22⋊C4—2921no—
379C22⋊C4—2921no—
380C22⋊C4—2921no—
381C22⋊C4—2921no—
382C22⋊C4—2921no—
383C22⋊C4—2921no—
384C22⋊C4—1462no—
385C22⋊C4—1462no—
386C22⋊C4—1462no—
387C22⋊C4—1462no—
388C22⋊C4—1462no—
389C22⋊C4—1462no—
390C22⋊C4—1462no—
391C22⋊C4C22⋊D7314yescomplemented
392C42—2921no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—2924no—
406C23—2924no—
407C23—2924no—
408C23—2924no—
409C23—2924no—
410C23—2924no—
411C23—2924no—
412C23—732no—
413C23—732no—
414C23—1461no—
415C23—1461no—
416C23—1461no—
417C23—1461no—
418C23—1461no—
419C23—1461no—
420C23—1461no—
421C23—1461no—
422C23—1461no—
423C23—1461no—
424C23—1461no—
425C23—1461no—
426C23—1461no—
427C23—1461no—
428C23—1461no—
429C23—1461no—
430C23—1461no—
431C23—1461no—
432C23—1461no—
433C23D4×D7312yes—
434C23C2×C22⋊D7312yes—
435C23C23×D7311yescharacteristic
436D4—44no—
437D4—2924no—
438D4—2924no—
439D4—2924no—
440D4—2924no—
441D4—2924no—
442D4—2924no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—44no—
457C2×C4—732no—
458C2×C4—1461no—
459C2×C4—1461no—
460C2×C4—1461no—
461C2×C4—1461no—
462C2×C4—1461no—
463C2×C4—1461no—
464C2×C4—1461no—
465C2×C4—1461no—
466C2×C4—1461no—
467C2×C4—1461no—
468C2×C4—1461no—
469C2×C4—1461no—
470C2×C4—1461no—
471C2×C4—1461no—
472C2×C4C2×C22⋊D7312yes—
473C2×C4C2×C22⋊D7312yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—29216no—
489C22—2921no—
490C22—2921no—
491C22—2921no—
492C22—2921no—
493C22—2921no—
494C22—2921no—
495C22—2921no—
496C22—2921no—
497C22—2921no—
498C22—2921no—
499C22—2921no—
500C22—2921no—
501C22—2921no—
502C22—2921no—
503C22—2921no—
504C22—1462no—
505C22—1462no—
506C22—1462no—
507C22—1462no—
508C22—1462no—
509C22—1462no—
510C22C2×D4×D7311yescharacteristic
511C22C22×C22⋊D7311yescharacteristic
512C22#41×D7311yescharacteristic
513C22#1455663611yescharacteristic
514C22#1455663711yescharacteristic
515C22#1455663711yescharacteristic
516C22#1455663711yescharacteristic
517C4—22no—
518C4—22no—
519C4—41no—
520C4—41no—
521C4—41no—
522C4—2921no—
523C4—2921no—
524C4—2921no—
525C4—2921no—
526C4—1462no—
527C2—42no—
528C2—42no—
529C2—2922no—
530C2—2922no—
531C2—5841no—
532C2#1798914811yescharacteristic
533C2#1798915111yescharacteristic
534C2#1798917311yescharacteristic
535C2D4×C22⋊D7311yescharacteristic
536C2#1798922511yescharacteristic
537C2#1798922911yescharacteristic
538C2#1798932711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#123×C73C2
hypercenterC2×#123D73
hypocenterC73#2678
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#14556565C2semidirect
2. C2×#14556561C2semidirect
3. C2×#14556559C2semidirect
4. #17988513C2semidirect
5. #17988509C2semidirect
6. #17988504C2semidirect
7. #17988502C2semidirect
8. #17988496C2semidirect
9. #17988495C2semidirect
10. #17988488C2semidirect
11. #17988487C2semidirect
12. #17988480C2semidirect
13. #17988466C2semidirect
14. #17988442C2semidirect
15. C2×#123×C73C2semidirect
22. C22×C22⋊D73C22semidirect
26. C2×C4⋊Dic73C22semidirect
27. C2×#11924007C22semidirect
30. C2×C22⋊Dic73C22semidirect
39. C2×#11924005C22semidirect
40. C2×#11924005C22semidirect
41. C2×#11924005C22semidirect
42. C2×C4×Dic73C22semidirect
43. #14556498C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
48. C23×C4×C73C22semidirect
50. C2×C4⋊C4×C73C22semidirect
51. C2×C4⋊C4×C73C22semidirect
54. C2×C22⋊C4×C73C22semidirect
82. C2×C22⋊D73D4semidirect
122. C22⋊C4×C73D4semidirect
270. C73#2678semidirect
271. C2×#123D73semidirect
294. C23×C4C2×D73semidirect
301. C2×C4⋊C4C2×D73semidirect
302. C2×C4⋊C4C2×D73semidirect
319. C2×C22⋊C4C2×D73semidirect
391. C22⋊C4C22⋊D73semidirect