Finite Group Databasebeta

← #22616252

Subgroups — #22616252

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×#14556573C211yesmaximal, characteristic, complemented
2C2×#14556562C211yesmaximal, characteristic, complemented
3C2×#14556560C211yesmaximal, characteristic, complemented
4#17988512C211yesmaximal, characteristic, complemented
5#17988510C211yesmaximal, characteristic, complemented
6#17988501C211yesmaximal, characteristic, complemented
7#17988501C211yesmaximal, characteristic, complemented
8#17988495C211yesmaximal, characteristic, complemented
9#17988495C211yesmaximal, characteristic, complemented
10#17988490C211yesmaximal, characteristic, complemented
11#17988487C211yesmaximal, characteristic, complemented
12#17988480C211yesmaximal, characteristic, complemented
13#17988463C211yesmaximal, characteristic, complemented
14#17988443C211yesmaximal, characteristic, complemented
15C2×#120×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic, complemented
20C22×C4×D73C2211yescharacteristic, complemented
21#14556573—24no—
22#14556562—24no—
23#14556560—24no—
24C2×C4⋊Dic73C2211yescharacteristic, complemented
25C2×C4⋊Dic73C2211yescharacteristic, 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×C22⋊Dic73C2211yescharacteristic, 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—41no—
62C2×C22⋊D73—41no—
63C2×C22⋊D73—41no—
64C2×C22⋊D73—41no—
65C2×C22⋊D73—41no—
66C2×C22⋊D73—41no—
67C2×C22⋊D73D414yescomplemented
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C22×Dic73C2311yescharacteristic
71C22×Dic73C2311yescharacteristic
72C22×Dic73C2311yescharacteristic
73C22×Dic73C2311yescharacteristic
74C22×Dic73C2311yescharacteristic
75C2×C4×D73—22no—
76C2×C4×D73—22no—
77C2×C4×D73—41no—
78C4⋊Dic73—22no—
79C4⋊Dic73—22no—
80#11924007—22no—
81#11924007—41no—
82C22⋊Dic73—22no—
83C22⋊Dic73—22no—
84C22⋊Dic73—22no—
85C22⋊Dic73—22no—
86C22⋊Dic73—22no—
87C22⋊Dic73—22no—
88C22⋊Dic73—41no—
89C22⋊Dic73—41no—
90C22⋊Dic73—41no—
91C22⋊Dic73—41no—
92C22⋊Dic73—41no—
93C22⋊Dic73—41no—
94#11924005—22no—
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—22no—
113C2×D4×C73—41no—
114C2×D4×C73—41no—
115C2×D4×C73—41no—
116C2×D4×C73—41no—
117C22×C4×C73C2311yescharacteristic
118C22×C4×C73C2311yescharacteristic
119C22×C4×C73C2311yescharacteristic
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×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—21no—
148C23×C73—44no—
149C23×C73—44no—
150C23×C73—44no—
151C23×C73—44no—
152C23×C73—44no—
153C23×C73—44no—
154C23×C73—44no—
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×D73C2×D412yes—
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×C73C2×D412yes—
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—21no—
202C2×Dic73C2×D412yes—
203C4×D73—44no—
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—416no—
214C22×C73—41no—
215C22×C73—41no—
216C22×C73—41no—
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—22no—
241C2×D73—22no—
242C2×D73—22no—
243C2×D73—41no—
244C2×D73—41no—
245C2×D73—41no—
246C2×D73—41no—
247C4×C73—22no—
248C4×C73—22no—
249C4×C73—41no—
250Dic73—22no—
251Dic73—41no—
252Dic73—41no—
253Dic73—41no—
254Dic73—41no—
255Dic73—41no—
256Dic73—41no—
257C2×C73—42no—
258C2×C73—42no—
259C2×C73—42no—
260C2×C73—81no—
261C2×C73#53411yescharacteristic
262C2×C73#53511yescharacteristic
263C2×C73#53811yescharacteristic
264C2×C73D4211yescharacteristic
265C2×C73#54611yescharacteristic
266C2×C73#54611yescharacteristic
267C2×C73#56011yescharacteristic
268D73—42no—
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—22no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—2921no—
347C2×D4—2921no—
348C2×D4—2921no—
349C2×D4—2921no—
350C2×D4—2921no—
351C2×D4—2921no—
352C2×D4—734no—
353C2×D4—1462no—
354C2×D4—1462no—
355C2×D4—1462no—
356C2×D4—1462no—
357C2×D4—1462no—
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—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—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—44no—
419C23—44no—
420C23—44no—
421C23—44no—
422C23—44no—
423C23—44no—
424C23—44no—
425C23—732no—
426C23—1461no—
427C23—1461no—
428C23—1461no—
429C23—1461no—
430C23—1461no—
431C23—1461no—
432C23D4×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—2924no—
451C2×C4—732no—
452C2×C4—1461no—
453C2×C4—1461no—
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×C4C2×C22⋊D7312yes—
473C2×C4C2×C22⋊D7312yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—416no—
484C22—41no—
485C22—41no—
486C22—41no—
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—1462no—
508C22—1462no—
509C22—1462no—
510C22C2×D4×D7311yescharacteristic
511C22C22×C22⋊D7311yescharacteristic
512C22C2×#1192402711yescharacteristic
513C22#1455663611yescharacteristic
514C22#1455663611yescharacteristic
515C22#1455663611yescharacteristic
516C22#1455663611yescharacteristic
517C4—22no—
518C4—22no—
519C4—41no—
520C4—2921no—
521C4—2921no—
522C4—2921no—
523C4—2921no—
524C4—2921no—
525C4—2921no—
526C4—1462no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—81no—
531C2—2922no—
532C2#1798914711yescharacteristic
533C2#1798915411yescharacteristic
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×#14556573C2semidirect
2. C2×#14556562C2semidirect
3. C2×#14556560C2semidirect
4. #17988512C2semidirect
5. #17988510C2semidirect
6. #17988501C2semidirect
7. #17988501C2semidirect
8. #17988495C2semidirect
9. #17988495C2semidirect
10. #17988490C2semidirect
11. #17988487C2semidirect
12. #17988480C2semidirect
13. #17988463C2semidirect
14. #17988443C2semidirect
15. C2×#120×C73C2semidirect
19. C22×C22⋊D73C22semidirect
20. C22×C4×D73C22semidirect
24. C2×C4⋊Dic73C22semidirect
25. C2×C4⋊Dic73C22semidirect
26. C2×#11924007C22semidirect
27. C2×#11924007C22semidirect
37. C2×C22⋊Dic73C22semidirect
38. C2×C22⋊Dic73C22semidirect
39. C2×C22⋊Dic73C22semidirect
40. C2×#11924005C22semidirect
41. C2×#11924005C22semidirect
42. C2×C4×Dic73C22semidirect
43. #14556498C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
67. C2×C22⋊D73D4semidirect
122. C22⋊C4×C73D4semidirect
270. C73#2678semidirect
274. C2×#120D73semidirect
391. C22⋊C4C22⋊D73semidirect