Finite Group Databasebeta

← #22616152

Subgroups — #22616152

Order 9344.

796 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×#14556580C211yesmaximal, characteristic, complemented
2C2×#14556561C211yesmaximal, characteristic, complemented
3C2×#14556559C211yesmaximal, characteristic, complemented
4#17988503C211yesmaximal, characteristic, complemented
5#17988502C211yesmaximal, characteristic, complemented
6#17988498C211yesmaximal, characteristic, complemented
7#17988496C211yesmaximal, characteristic, complemented
8#17988496C211yesmaximal, characteristic, complemented
9#17988495C211yesmaximal, characteristic, complemented
10#17988489C211yesmaximal, characteristic, complemented
11#17988487C211yesmaximal, characteristic, complemented
12#17988480C211yesmaximal, characteristic, complemented
13#17988478C211yesmaximal, characteristic, complemented
14#17988442C211yesmaximal, characteristic, complemented
15C2×#124×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C22×D292C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic
20C22×C22⋊D73C2211yescharacteristic
21C22×C22⋊D73C2211yescharacteristic
22C22×C22⋊D73C2211yescharacteristic, complemented
23#14556580—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×Q8×C73C2211yescharacteristic, complemented
48C22×D4×C73C2211yescharacteristic
49#124×C73—24no—
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73C2211yescharacteristic, complemented
53C2×C22⋊C4×C73C2211yescharacteristic, complemented
54C2×C42×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⋊D73—41no—
83C22×Dic73C2311yescharacteristic
84C22×Dic73C2311yescharacteristic
85C22×Dic73C2311yescharacteristic
86C22×Dic73C2311yescharacteristic
87C22×Dic73C2311yescharacteristic
88C4⋊Dic73—41no—
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#11924005D414yescomplemented
104C4×Dic73—22no—
105C24×C73C2311yescharacteristic
106C24×C73C2311yescharacteristic
107C2×Q8×C73—22no—
108C2×Q8×C73—22no—
109C2×Q8×C73—41no—
110C2×D4×C73—22no—
111C2×D4×C73—22no—
112C2×D4×C73—41no—
113C22×C4×C73C2311yescharacteristic
114C22×C4×C73C2311yescharacteristic
115C22×C4×C73C2311yescharacteristic
116C22×C4×C73C2311yescharacteristic
117C22×C4×C73C2311yescharacteristic
118C22⋊C4×C73—22no—
119C22⋊C4×C73—22no—
120C22⋊C4×C73—22no—
121C22⋊C4×C73D414yescomplemented
122C42×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×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—
166Q8×C73—44no—
167D4×C73—44no—
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×C73C2×D412yes—
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—41no—
208C22×C73—41no—
209C22×C73—41no—
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—22no—
250C4×C73—41no—
251C4×C73—41no—
252Dic73—22no—
253Dic73—41no—
254Dic73—41no—
255Dic73—41no—
256Dic73—41no—
257C2×C73—42no—
258C2×C73—81no—
259C2×C73#53511yescharacteristic
260C2×C73#53511yescharacteristic
261C2×C73#53811yescharacteristic
262C2×C73D4211yescharacteristic
263C2×C73#54611yescharacteristic
264C2×C73#54611yescharacteristic
265C2×C73H(3,𝔽4)11yescharacteristic
266D73—42no—
267D73—42no—
268D73—81no—
269#2670—731nomaximal, Sylow
270C73#267011yescharacteristic, complemented, Sylow
271C2×#124—731no—
272C2×#124D7311yescharacteristic, complemented
273C2×#120—731no—
274C2×#120—731no—
275#394—731no—
276#394—731no—
277#393—731no—
278#392—731no—
279#392—731no—
280#392—731no—
281#390—731no—
282#390—731no—
283#388—731no—
284#388—731no—
285#379—731no—
286C25—731no—
287C22×Q8C2×D7311yescharacteristic, complemented
288C22×D4—731no—
289C22×D4—731no—
290C22×D4—731no—
291C22×D4—731no—
292C22×D4—731no—
293C22×D4—731no—
294C22×D4C2×D7311yescharacteristic
295#124—24no—
296#124—1464no—
297#120—1464no—
298#120—1464no—
299C2×C4⋊C4—731no—
300C2×C4⋊C4—731no—
301C2×C22⋊C4—731no—
302C2×C22⋊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⋊C4C2×D7311yescharacteristic
316C2×C22⋊C4C2×D7311yescharacteristic
317C2×C22⋊C4C2×D7311yescharacteristic, complemented
318C2×C22⋊C4C2×D7311yescharacteristic, complemented
319C2×C42—731no—
320C2×C42C2×D7311yescharacteristic, complemented
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×Q8—22no—
338C2×Q8—22no—
339C2×Q8—41no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—41no—
343C2×D4—2921no—
344C2×D4—2921no—
345C2×D4—2921no—
346C2×D4—2921no—
347C2×D4—2921no—
348C2×D4—2921no—
349C2×D4—2921no—
350C2×D4—2921no—
351C2×D4—2921no—
352C2×D4—2921no—
353C2×D4—1462no—
354C2×D4—1462no—
355C2×D4—1462no—
356C2×D4—1462no—
357C2×D4—1462no—
358C2×D4—1462no—
359C2×D4—1462no—
360C2×D4—1462no—
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—2921no—
372C4⋊C4—2921no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—2921no—
377C22⋊C4—2921no—
378C22⋊C4—2921no—
379C22⋊C4—2921no—
380C22⋊C4—2921no—
381C22⋊C4—2921no—
382C22⋊C4—734no—
383C22⋊C4—1462no—
384C22⋊C4—1462no—
385C22⋊C4—1462no—
386C22⋊C4—1462no—
387C22⋊C4—1462no—
388C22⋊C4—1462no—
389C22⋊C4—1462no—
390C22⋊C4C22⋊D7314yescomplemented
391C42—22no—
392C42—1462no—
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—2924no—
407C23—2924no—
408C23—2924no—
409C23—2924no—
410C23—2924no—
411C23—2924no—
412C23—2924no—
413C23—732no—
414C23—732no—
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—
433C23—1461no—
434C23C2×C22⋊D7312yes—
435C23C23×D7311yescharacteristic
436Q8—44no—
437D4—44no—
438D4—2924no—
439D4—2924no—
440D4—2924no—
441D4—2924no—
442D4—2924no—
443D4—2924no—
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—732no—
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×C4D4×D7312yes—
472C2×C4C2×C22⋊D7312yes—
473C2×C4C2×C22⋊D7312yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—41no—
478C22—41no—
479C22—41no—
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—22no—
520C4—41no—
521C4—41no—
522C4—2921no—
523C4—2921no—
524C4—2921no—
525C4—2921no—
526C4—1462no—
527C2—42no—
528C2—81no—
529C2—2922no—
530C2—2922no—
531C2—5841no—
532C2#1798915111yescharacteristic
533C2#1798915511yescharacteristic
534C2#1798917111yescharacteristic
535C2D4×C22⋊D7311yescharacteristic
536C2#1798922511yescharacteristic
537C2#1798923011yescharacteristic
538C2#1798932911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#124×C73C2
hypercenterC2×#124D73
hypocenterC73#2670
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14556580C2semidirect
2. C2×#14556561C2semidirect
3. C2×#14556559C2semidirect
4. #17988503C2semidirect
5. #17988502C2semidirect
6. #17988498C2semidirect
7. #17988496C2semidirect
8. #17988496C2semidirect
9. #17988495C2semidirect
10. #17988489C2semidirect
11. #17988487C2semidirect
12. #17988480C2semidirect
13. #17988478C2semidirect
14. #17988442C2semidirect
15. C2×#124×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
47. C22×Q8×C73C22semidirect
52. C2×C22⋊C4×C73C22semidirect
53. C2×C22⋊C4×C73C22semidirect
54. C2×C42×C73C22semidirect
103. #11924005D4semidirect
121. C22⋊C4×C73D4semidirect
270. C73#2670semidirect
272. C2×#124D73semidirect
287. C22×Q8C2×D73semidirect
317. C2×C22⋊C4C2×D73semidirect
318. C2×C22⋊C4C2×D73semidirect
320. C2×C42C2×D73semidirect
390. C22⋊C4C22⋊D73semidirect