Finite Group Databasebeta

← #22616256

Subgroups — #22616256

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×#14556572C211yesmaximal, characteristic, complemented
2C2×#14556563C211yesmaximal, characteristic, complemented
3C2×#14556560C211yesmaximal, characteristic, complemented
4#17988515C211yesmaximal, characteristic, complemented
5#17988510C211yesmaximal, characteristic, complemented
6#17988503C211yesmaximal, characteristic, complemented
7#17988502C211yesmaximal, characteristic, complemented
8#17988495C211yesmaximal, characteristic, complemented
9#17988495C211yesmaximal, characteristic, complemented
10#17988490C211yesmaximal, characteristic, complemented
11#17988487C211yesmaximal, characteristic, complemented
12#17988481C211yesmaximal, characteristic, complemented
13#17988467C211yesmaximal, characteristic, complemented
14#17988443C211yesmaximal, characteristic, complemented
15C2×#120×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic, complemented
20C23×Dic73C2211yescharacteristic, complemented
21#14556572—24no—
22#14556563—24no—
23#14556560—24no—
24C2×C4⋊Dic73C2211yescharacteristic, complemented
25C2×#11924007C2211yescharacteristic, complemented
26C2×#11924007C2211yescharacteristic, complemented
27C2×#11924007C2211yescharacteristic, complemented
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×C22⋊Dic73C2211yescharacteristic
34C2×C22⋊Dic73C2211yescharacteristic
35C2×C22⋊Dic73C2211yescharacteristic
36C2×C22⋊Dic73C2211yescharacteristic
37C2×C22⋊Dic73C2211yescharacteristic, complemented
38C2×C22⋊Dic73C2211yescharacteristic, complemented
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
47C25×C73C2211yescharacteristic
48C22×D4×C73C2211yescharacteristic
49C22×D4×C73C2211yescharacteristic
50C22×D4×C73C2211yescharacteristic
51#120×C73—24no—
52C2×C22⋊C4×C73C2211yescharacteristic
53C2×C22⋊C4×C73C2211yescharacteristic
54C2×C22⋊C4×C73C2211yescharacteristic
55C23×D73C2311yescharacteristic
56C2×C22⋊D73—22no—
57C2×C22⋊D73—22no—
58C2×C22⋊D73—22no—
59C2×C22⋊D73—22no—
60C2×C22⋊D73—22no—
61C2×C22⋊D73—22no—
62C2×C22⋊D73—41no—
63C2×C22⋊D73—41no—
64C2×C22⋊D73—41no—
65C2×C22⋊D73—41no—
66C2×C22⋊D73—41no—
67C2×C22⋊D73—41no—
68C22×Dic73—22no—
69C22×Dic73—22no—
70C22×Dic73—41no—
71C22×Dic73C2311yescharacteristic
72C22×Dic73C2311yescharacteristic
73C22×Dic73C2311yescharacteristic
74C22×Dic73C2311yescharacteristic
75C22×Dic73C2311yescharacteristic
76C22×Dic73C2311yescharacteristic
77C22×Dic73C2311yescharacteristic
78C4⋊Dic73—41no—
79#11924007—22no—
80#11924007—22no—
81#11924007—22no—
82C22⋊Dic73—22no—
83C22⋊Dic73—22no—
84C22⋊Dic73—22no—
85C22⋊Dic73—22no—
86C22⋊Dic73—22no—
87C22⋊Dic73—41no—
88C22⋊Dic73—41no—
89C22⋊Dic73—41no—
90C22⋊Dic73—41no—
91C22⋊Dic73—41no—
92C22⋊Dic73D414yescomplemented
93#11924005—22no—
94#11924005—41no—
95#11924005—41no—
96C4×Dic73—41no—
97C24×C73—22no—
98C24×C73—22no—
99C24×C73—22no—
100C24×C73—41no—
101C24×C73—41no—
102C24×C73—41no—
103C24×C73—41no—
104C24×C73C2311yescharacteristic
105C24×C73C2311yescharacteristic
106C24×C73C2311yescharacteristic
107C24×C73C2311yescharacteristic
108C2×D4×C73—22no—
109C2×D4×C73—22no—
110C2×D4×C73—22no—
111C2×D4×C73—22no—
112C2×D4×C73—41no—
113C2×D4×C73—41no—
114C2×D4×C73—41no—
115C2×D4×C73—41no—
116C2×D4×C73D414yescomplemented
117C22×C4×C73C2311yescharacteristic
118C22×C4×C73C2311yescharacteristic
119C22×C4×C73C2311yescharacteristic
120C22⋊C4×C73—22no—
121C22⋊C4×C73—22no—
122C22⋊C4×C73—22no—
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×C73—21no—
136C23×C73—21no—
137C23×C73—21no—
138C23×C73—21no—
139C23×C73—21no—
140C23×C73—21no—
141C23×C73—21no—
142C23×C73—21no—
143C23×C73—21no—
144C23×C73—21no—
145C23×C73—21no—
146C23×C73—21no—
147C23×C73—44no—
148C23×C73—44no—
149C23×C73—44no—
150C23×C73—44no—
151C23×C73—44no—
152C23×C73—44no—
153C23×C73—44no—
154C23×C73C2×D412yes—
155C23×C73C2×D412yes—
156C23×C73C2×D412yes—
157C23×C73#4112yes—
158C23×C73C2411yescharacteristic
159C22×D73—21no—
160C22×D73—21no—
161C22×D73—21no—
162C22×D73—21no—
163C22×D73—21no—
164C22×D73—21no—
165C22×D73—21no—
166D4×C73—44no—
167D4×C73—44no—
168D4×C73—44no—
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×C73C2×D412yes—
178C22⋊D73—44no—
179C22⋊D73—44no—
180C22⋊D73—44no—
181C22⋊D73—44no—
182C2×Dic73—21no—
183C2×Dic73—21no—
184C2×Dic73—21no—
185C2×Dic73—21no—
186C2×Dic73—21no—
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×Dic73—44no—
202C2×Dic73C2×D412yes—
203C2×Dic73C2×D412yes—
204C22×C73—22no—
205C22×C73—22no—
206C22×C73—22no—
207C22×C73—22no—
208C22×C73—22no—
209C22×C73—22no—
210C22×C73—22no—
211C22×C73—22no—
212C22×C73—22no—
213C22×C73—22no—
214C22×C73—22no—
215C22×C73—22no—
216C22×C73—416no—
217C22×C73—41no—
218C22×C73—41no—
219C22×C73—41no—
220C22×C73—41no—
221C22×C73—41no—
222C22×C73—41no—
223C22×C73—41no—
224C22×C73—41no—
225C22×C73—41no—
226C22×C73—41no—
227C22×C73—41no—
228C22×C73—41no—
229C22×C73—41no—
230C22×C73—41no—
231C22×C73—41no—
232C22×C73—41no—
233C22×C73C22×D411yescharacteristic
234C22×C73C22×D411yescharacteristic
235C22×C73C2×#4111yescharacteristic
236C22×C73H(5,𝔽2)11yescharacteristic
237C22×C73H(5,𝔽2)11yescharacteristic
238C22×C73H(5,𝔽2)11yescharacteristic
239C22×C73H(5,𝔽2)11yescharacteristic
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—41no—
249C4×C73—41no—
250Dic73—22no—
251Dic73—22no—
252Dic73—41no—
253Dic73—41no—
254Dic73—41no—
255Dic73—41no—
256Dic73—41no—
257C2×C73—42no—
258C2×C73—42no—
259C2×C73—42no—
260C2×C73—42no—
261C2×C73#53411yescharacteristic
262C2×C73#53511yescharacteristic
263C2×C73#53811yescharacteristic
264C2×C73D4211yescharacteristic
265C2×C73#54611yescharacteristic
266C2×C73#54611yescharacteristic
267C2×C73#56011yescharacteristic
268D73—81no—
269#2678—731nomaximal, Sylow
270C73#267811yescharacteristic, complemented, Sylow
271C2×#123—731no—
272C2×#121—731no—
273C2×#120—731no—
274C2×#120D7311yescharacteristic, complemented
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—
286C25C2×D7311yescharacteristic
287C22×D4—731no—
288C22×D4—731no—
289C22×D4—731no—
290C22×D4—731no—
291C22×D4C2×D7311yescharacteristic
292C22×D4C2×D7311yescharacteristic
293C22×D4C2×D7311yescharacteristic
294C23×C4—731no—
295#123—1464no—
296#121—1464no—
297#120—24no—
298#120—1464no—
299C2×C4⋊C4—731no—
300C2×C4⋊C4—731no—
301C2×C4⋊C4—731no—
302C2×C4⋊C4—731no—
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
320C2×C42—731no—
321#95—731no—
322#95—731no—
323#95—731no—
324#95—731no—
325C24—22no—
326C24—22no—
327C24—22no—
328C24—41no—
329C24—41no—
330C24—41no—
331C24—41no—
332C24—731no—
333C24C22×D7311yescharacteristic
334C24C22×D7311yescharacteristic
335C24C22×D7311yescharacteristic
336C24C22×D7311yescharacteristic
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—2921no—
346C2×D4—2921no—
347C2×D4—2921no—
348C2×D4—2921no—
349C2×D4—2921no—
350C2×D4—2921no—
351C2×D4—1462no—
352C2×D4—1462no—
353C2×D4—1462no—
354C2×D4—1462no—
355C2×D4—1462no—
356C2×D4—1462no—
357C2×D4C22⋊D7314yescomplemented
358C22×C4—2921no—
359C22×C4—731no—
360C22×C4—731no—
361C22×C4—731no—
362C22×C4—731no—
363C22×C4—731no—
364C22×C4—731no—
365C22×C4—731no—
366C22×C4—1462no—
367C22×C4—1462no—
368C22×C4C22×D7311yescharacteristic
369C22×C4C22×D7311yescharacteristic
370C22×C4C22×D7311yescharacteristic
371C4⋊C4—2921no—
372C4⋊C4—1462no—
373C4⋊C4—1462no—
374C4⋊C4—1462no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—2921no—
379C22⋊C4—2921no—
380C22⋊C4—2921no—
381C22⋊C4—2921no—
382C22⋊C4—2921no—
383C22⋊C4—2921no—
384C22⋊C4—2921no—
385C22⋊C4—734no—
386C22⋊C4—1462no—
387C22⋊C4—1462no—
388C22⋊C4—1462no—
389C22⋊C4—1462no—
390C22⋊C4—1462no—
391C22⋊C4—1462no—
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—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—44no—
418C23—44no—
419C23—44no—
420C23—44no—
421C23—44no—
422C23—44no—
423C23—44no—
424C23—1461no—
425C23—1461no—
426C23—1461no—
427C23—1461no—
428C23—1461no—
429C23—1461no—
430C23—1461no—
431C23D4×D7312yes—
432C23C2×C22⋊D7312yes—
433C23C2×C22⋊D7312yes—
434C23#1192402712yes—
435C23C23×D7311yescharacteristic
436D4—44no—
437D4—44no—
438D4—44no—
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—2924no—
452C2×C4—732no—
453C2×C4—732no—
454C2×C4—1461no—
455C2×C4—1461no—
456C2×C4—1461no—
457C2×C4—1461no—
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×C4—1461no—
473C2×C4C2×C22⋊D7312yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—416no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—2921no—
504C22—2921no—
505C22—2921no—
506C22—2921no—
507C22—2921no—
508C22—2921no—
509C22—2921no—
510C22C2×D4×D7311yescharacteristic
511C22C22×C22⋊D7311yescharacteristic
512C22C2×#1192402711yescharacteristic
513C22#1455663611yescharacteristic
514C22#1455663611yescharacteristic
515C22#1455663611yescharacteristic
516C22#1455663611yescharacteristic
517C4—22no—
518C4—41no—
519C4—41no—
520C4—2921no—
521C4—2921no—
522C4—2921no—
523C4—2921no—
524C4—2921no—
525C4—1462no—
526C4—1462no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—42no—
531C2—5841no—
532C2#1798914611yescharacteristic
533C2#1798915211yescharacteristic
534C2#1798917211yescharacteristic
535C2D4×C22⋊D7311yescharacteristic
536C2#1798922411yescharacteristic
537C2#1798923111yescharacteristic
538C2#1798932611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#120×C73C2
hypercenterC2×#120D73
hypocenterC73#2678
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#14556572C2semidirect
2. C2×#14556563C2semidirect
3. C2×#14556560C2semidirect
4. #17988515C2semidirect
5. #17988510C2semidirect
6. #17988503C2semidirect
7. #17988502C2semidirect
8. #17988495C2semidirect
9. #17988495C2semidirect
10. #17988490C2semidirect
11. #17988487C2semidirect
12. #17988481C2semidirect
13. #17988467C2semidirect
14. #17988443C2semidirect
15. C2×#120×C73C2semidirect
19. C22×C22⋊D73C22semidirect
20. C23×Dic73C22semidirect
24. C2×C4⋊Dic73C22semidirect
25. C2×#11924007C22semidirect
26. C2×#11924007C22semidirect
27. C2×#11924007C22semidirect
37. C2×C22⋊Dic73C22semidirect
38. C2×C22⋊Dic73C22semidirect
39. C2×#11924005C22semidirect
40. C2×#11924005C22semidirect
41. C2×#11924005C22semidirect
42. C2×C4×Dic73C22semidirect
43. #14556498C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
92. C22⋊Dic73D4semidirect
116. C2×D4×C73D4semidirect
270. C73#2678semidirect
274. C2×#120D73semidirect
357. C2×D4C22⋊D73semidirect