Finite Group Databasebeta

← #32975654

Subgroups — #32975654

Order 18688.

1058 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988549C211yesmaximal, characteristic
2C2×#17988549C211yesmaximal, characteristic
3C4×C22⋊C4×D73C211yesmaximal, characteristic
4#22607779C211yesmaximal, characteristic, complemented
5#22607778C211yesmaximal, characteristic, complemented
6#22607777C211yesmaximal, characteristic, complemented
7C73×#1282C211yesmaximal, characteristic, complemented
8C23×C4×D73C2211yescharacteristic
9C22×#11924011—21no—
10C22×#11924011C412yescomplemented
11C2×C22⋊C4×D73C412yes—
12C2×C42×D73—21no—
13#17988549—21no—
14#17988549—21no—
15#17988549—21no—
16#17988549—21no—
17#17988549—21no—
18#17988549—21no—
19#17988549C412yescomplemented
20#17988549C412yescomplemented
21C2×C22⋊#10596831C2211yescharacteristic
22C2×C22⋊#10596831C2211yescharacteristic
23C2×#14556503—21no—
24C2×#14556503C412yescomplemented
25C22⋊C4×Dic73C412yes—
26C4×#11924005—21no—
27C4×C22⋊Dic73C2211yescharacteristic
28#17988434—21no—
29#95×D73—21no—
30C2×C22⋊C8×C73C2211yescharacteristic
31C2×C22⋊C8×C73C2211yescharacteristic
32C4×C22⋊C4×C73C2211yescharacteristic
33C24×D73C2×C411yescharacteristic
34C23×Dic73C2×C411yescharacteristic
35C22×C4×D73—22no—
36C22×C4×D73—44no—
37C22×C4×D73C2×C411yescharacteristic
38C22×C4×D73C2×C411yescharacteristic
39C22×C4×D73C2×C411yescharacteristic
40C22×C4×D73C2×C411yescharacteristic
41C22×C4×D73D411yescharacteristic
42C22×C4×D73D411yescharacteristic
43C22×C4×D73D411yescharacteristic
44C22×C4×D73D411yescharacteristic
45C22×C4×D73D411yescharacteristic
46C22×C4×D73D411yescharacteristic
47C22×C4×D73Q811yescharacteristic
48C22×C4×D73Q811yescharacteristic
49C2×#11924011—22no—
50C2×#11924011—22no—
51C2×#11924011—22no—
52C2×#11924011—22no—
53C2×#11924011—44no—
54C2×#11924011—44no—
55C22×#10596831—21no—
56C22×#10596831C2×C412yescomplemented
57C2×C22⋊Dic73C2×C412yes—
58C2×#11924005—22no—
59C22⋊C4×D73—24no—
60C22⋊C4×D73—24no—
61C2×C4×Dic73—22no—
62C2×C4×Dic73—21no—
63C42×D73—44no—
64C22⋊#10596831—21no—
65C22⋊#10596831—21no—
66C22⋊#10596831—21no—
67C22⋊#10596831C2×C412yescomplemented
68#14556503—22no—
69#14556503—22no—
70#14556503—22no—
71#14556503—22no—
72#14556498—22no—
73#14556498—21no—
74C23×C4×C73C2311yescharacteristic
75C22×C8×C73—21no—
76C22×C8×C73C2×C412yescomplemented
77C2×C22⋊C4×C73C2×C412yes—
78C2×C42×C73—21no—
79C22⋊C8×C73—21no—
80C22⋊C8×C73—21no—
81C22⋊C8×C73—21no—
82C22⋊C8×C73C2×C412yescomplemented
83#95×C73—21no—
84C23×D73—22no—
85C23×D73—22no—
86C23×D73—42no—
87C23×D73—42no—
88C23×D73C4211yescharacteristic
89C23×D73C4211yescharacteristic
90C23×D73C22⋊C411yescharacteristic
91C23×D73C22⋊C411yescharacteristic
92C23×D73C4⋊C411yescharacteristic
93C23×D73C4⋊C411yescharacteristic
94C22×Dic73—22no—
95C22×Dic73—42no—
96C22×Dic73C4211yescharacteristic
97C22×Dic73C4211yescharacteristic
98C22×Dic73C22⋊C411yescharacteristic
99C22×Dic73C22⋊C411yescharacteristic
100C22×Dic73C4⋊C411yescharacteristic
101C22×Dic73C4⋊C411yescharacteristic
102C2×C4×D73—24no—
103C2×C4×D73—24no—
104C2×C4×D73—24no—
105C2×C4×D73—28no—
106C2×C4×D73—42no—
107C2×C4×D73—42no—
108C2×C4×D73—42no—
109C2×C4×D73—42no—
110C2×C4×D73—42no—
111C2×C4×D73—42no—
112C2×C4×D73—42no—
113C2×C4×D73—42no—
114C2×C4×D73—42no—
115C2×C4×D73—44no—
116C2×C4×D73—44no—
117C2×C4×D73C22⋊C411yescharacteristic
118C2×C4×D73C22⋊C411yescharacteristic
119C2×C4×D73C22⋊C411yescharacteristic
120C2×C4×D73C22⋊C411yescharacteristic
121C2×C4×D73C22⋊C411yescharacteristic
122C2×C4×D73C22⋊C411yescharacteristic
123C2×C4×D73C22⋊C411yescharacteristic
124C2×C4×D73C22⋊C411yescharacteristic
125C2×C4×D73C4⋊C411yescharacteristic
126C2×C4×D73C4⋊C411yescharacteristic
127C2×C4×D73C4⋊C411yescharacteristic
128C2×C4×D73C4⋊C411yescharacteristic
129C2×C4×D73C4⋊C411yescharacteristic
130C2×C4×D73C4⋊C411yescharacteristic
131C2×C4×D73C4⋊C411yescharacteristic
132C2×C4×D73C4⋊C411yescharacteristic
133#11924011—44no—
134#11924011—44no—
135#11924011—44no—
136#11924011—44no—
137C2×#10596831—22no—
138C2×#10596831—22no—
139C2×#10596831—42no—
140C2×#10596831—42no—
141C22⋊Dic73—22no—
142C22⋊Dic73M1614yescomplemented
143#11924005—28no—
144C4×Dic73—44no—
145C4×Dic73—42no—
146C24×C73C22×C411yescharacteristic
147C22×C4×C73—22no—
148C22×C4×C73—42no—
149C22×C4×C73C22×C411yescharacteristic
150C22×C4×C73C22×C411yescharacteristic
151C22×C4×C73C2×D411yescharacteristic
152C22×C4×C73C2×D411yescharacteristic
153C22×C4×C73C2×D411yescharacteristic
154C22×C4×C73C2×Q811yescharacteristic
155C2×C8×C73—22no—
156C2×C8×C73—22no—
157C2×C8×C73—42no—
158C2×C8×C73—42no—
159C22⋊C4×C73—22no—
160C22⋊C4×C73M1614yescomplemented
161C42×C73—42no—
162C23×C73—41no—
163C23×C73—41no—
164C23×C73C2×C4211yescharacteristic
165C23×C73C2×C22⋊C411yescharacteristic
166C23×C73C2×C4⋊C411yescharacteristic
167C23×C73C2×M1612yes—
168C23×C73C2×M1612yes—
169C22×D73—22no—
170C22×D73—22no—
171C22×D73—22no—
172C22×D73—21no—
173C22×D73—21no—
174C22×D73—21no—
175C22×D73—21no—
176C22×D73—22no—
177C22×D73—22no—
178C22×D73—22no—
179C22×D73—22no—
180C22×D73—22no—
181C22×D73—22no—
182C22×D73—22no—
183C22×D73—41no—
184C22×D73—41no—
185C22×D73—41no—
186C22×D73—41no—
187C22×D73—41no—
188C22×D73—41no—
189C22×D73—48no—
190C22×D73—48no—
191C22×D73#9511yescharacteristic
192C22×D73#9511yescharacteristic
193C22×D73#9511yescharacteristic
194C22×D73#9511yescharacteristic
195C2×C4×C73—22no—
196C2×C4×C73—22no—
197C2×C4×C73—22no—
198C2×C4×C73—24no—
199C2×C4×C73—41no—
200C2×C4×C73—41no—
201C2×C4×C73—41no—
202C2×C4×C73—42no—
203C2×C4×C73—42no—
204C2×C4×C73C2×C22⋊C411yescharacteristic
205C2×C4×C73C2×C22⋊C411yescharacteristic
206C2×C4×C73C2×C4⋊C411yescharacteristic
207C2×C4×C73C2×C4⋊C411yescharacteristic
208C2×Dic73—22no—
209C2×Dic73—22no—
210C2×Dic73—22no—
211C2×Dic73—24no—
212C2×Dic73—41no—
213C2×Dic73—41no—
214C2×Dic73—41no—
215C2×Dic73—42no—
216C2×Dic73—42no—
217C2×Dic73#9511yescharacteristic
218C2×Dic73#9511yescharacteristic
219C2×Dic73#9511yescharacteristic
220C2×Dic73#9511yescharacteristic
221C4×D73—22no—
222C4×D73—22no—
223C4×D73—22no—
224C4×D73—22no—
225C4×D73—22no—
226C4×D73—22no—
227C4×D73—22no—
228C4×D73—22no—
229C4×D73—22no—
230C4×D73—41no—
231C4×D73—41no—
232C4×D73—41no—
233C4×D73—41no—
234C4×D73—41no—
235C4×D73—41no—
236C4×D73—416no—
237C4×D73#9914yes—
238C8×C73—42no—
239C8×C73—42no—
240#10596831—42no—
241#10596831—42no—
242C22×C73—21no—
243C22×C73—21no—
244C22×C73—21no—
245C22×C73—21no—
246C22×C73—21no—
247C22×C73—21no—
248C22×C73—42no—
249C22×C73—42no—
250C22×C73C2×#9511yescharacteristic
251C22×C73C4×M1611yescharacteristic
252C22×C73C4×M1611yescharacteristic
253C22×C73#40712yes—
254C22×C73#42312yes—
255C2×D73—28no—
256C2×D73—21no—
257C2×D73—21no—
258C2×D73—21no—
259C2×D73—21no—
260C2×D73—21no—
261C2×D73—21no—
262C2×D73—21no—
263C2×D73—21no—
264C2×D73—21no—
265C2×D73—21no—
266C2×D73—42no—
267C2×D73—42no—
268C2×D73—44no—
269C2×D73—42no—
270C2×D73—42no—
271C2×D73—44no—
272C2×D73—44no—
273C2×D73#34212yes—
274C2×D73#34412yes—
275C4×C73—21no—
276C4×C73—21no—
277C4×C73—21no—
278C4×C73—44no—
279C4×C73C2×#9912yes—
280Dic73—21no—
281Dic73—21no—
282Dic73—21no—
283Dic73—44no—
284Dic73#34212yes—
285#7929—731nomaximal, Sylow
286C2×C73—22no—
287C2×C73—21no—
288C2×C73—21no—
289C2×C73—22no—
290C2×C73#172811yescharacteristic
291C2×C73C2×#34211yescharacteristic
292C2×C73C2×#34411yescharacteristic
293D73—22no—
294D73—22no—
295D73—41no—
296D73—41no—
297C2×#407—731no—
298C2×#407—731no—
299C2×C4×C22⋊C4—731no—
300#1282—731no—
301#1282—731no—
302#1282—731no—
303#1282D7311yescharacteristic, complemented
304C73#792911yescharacteristic, complemented, Sylow
305C24×C4—731no—
306C22×M16—732no—
307C22×M16—1461no—
308C22×C22⋊C4—732no—
309C22×C42—1461no—
310#407—732no—
311#407—732no—
312#407—1461no—
313#407—1461no—
314#407—1461no—
315#407—1461no—
316#407—1461no—
317#407—1461no—
318C2×C22⋊C8—731no—
319C2×C22⋊C8—731no—
320C2×C22⋊C8—732no—
321C2×C22⋊C8—1461no—
322C2×C22⋊C8C2×D7311yescharacteristic
323C2×C22⋊C8C2×D7311yescharacteristic
324C4×C22⋊C4—731no—
325C4×C22⋊C4—732no—
326C4×C22⋊C4—1461no—
327C4×C22⋊C4—1461no—
328C4×C22⋊C4C2×D7311yescharacteristic
329C2×#95—1461no—
330C25—731no—
331C23×C4—2924no—
332C23×C4—731no—
333C23×C4—731no—
334C23×C4—731no—
335C23×C4—731no—
336C23×C4—731no—
337C23×C4—731no—
338C23×C4—731no—
339C23×C4—731no—
340C23×C4—731no—
341C23×C4—731no—
342C23×C4—731no—
343C23×C4—731no—
344C23×C4—731no—
345C23×C4—1462no—
346C23×C4C22×D7311yescharacteristic
347C2×M16—2924no—
348C2×M16—2924no—
349C2×M16—1462no—
350C2×M16—1462no—
351C2×M16—1462no—
352C2×M16—1462no—
353C22×C8—21no—
354C22×C8—732no—
355C22×C8—1461no—
356C22×C8C4×D7312yescomplemented
357C2×C22⋊C4—732no—
358C2×C22⋊C4—1464no—
359C2×C22⋊C4—1462no—
360C2×C22⋊C4—1464no—
361C2×C22⋊C4C4×D7312yes—
362C2×C42—21no—
363C2×C42—2924no—
364C2×C42—1462no—
365C2×C42—1461no—
366C22⋊C8—21no—
367C22⋊C8—21no—
368C22⋊C8—21no—
369C22⋊C8—732no—
370C22⋊C8—1462no—
371C22⋊C8—1462no—
372C22⋊C8—1462no—
373C22⋊C8—1462no—
374C22⋊C8—1461no—
375C22⋊C8—1461no—
376C22⋊C8—1461no—
377C22⋊C8C4×D7312yescomplemented
378#95—21no—
379#95—1462no—
380#95—1461no—
381C24—2922no—
382C24—2922no—
383C24—731no—
384C24—731no—
385C24—731no—
386C24—731no—
387C24—731no—
388C24—731no—
389C24—1462no—
390C24—1462no—
391C24C2×C4×D7311yescharacteristic
392C22×C4—22no—
393C22×C4—42no—
394C22×C4—2922no—
395C22×C4—2922no—
396C22×C4—2922no—
397C22×C4—2924no—
398C22×C4—2924no—
399C22×C4—2922no—
400C22×C4—2922no—
401C22×C4—2922no—
402C22×C4—2922no—
403C22×C4—2922no—
404C22×C4—2922no—
405C22×C4—2922no—
406C22×C4—731no—
407C22×C4—731no—
408C22×C4—731no—
409C22×C4—731no—
410C22×C4—731no—
411C22×C4—731no—
412C22×C4—731no—
413C22×C4—731no—
414C22×C4—731no—
415C22×C4—731no—
416C22×C4—731no—
417C22×C4—731no—
418C22×C4—731no—
419C22×C4—731no—
420C22×C4—731no—
421C22×C4—731no—
422C22×C4—731no—
423C22×C4—731no—
424C22×C4—731no—
425C22×C4—731no—
426C22×C4—731no—
427C22×C4—731no—
428C22×C4—1468no—
429C22×C4—1464no—
430C22×C4—1464no—
431C22×C4—1464no—
432C22×C4—1462no—
433C22×C4C2×C4×D7311yescharacteristic
434C22×C4C2×C4×D7311yescharacteristic
435C22×C4D4×D7311yescharacteristic
436C22×C4D4×D7311yescharacteristic
437C22×C4D4×D7311yescharacteristic
438C22×C4Q8×D7311yescharacteristic
439M16—2924no—
440M16—2924no—
441M16—2924no—
442M16—2924no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—42no—
446C2×C8—42no—
447C2×C8—2922no—
448C2×C8—2922no—
449C2×C8—1462no—
450C2×C8—1462no—
451C22⋊C4—22no—
452C22⋊C4—734no—
453C22⋊C4—1468no—
454C22⋊C4—1462no—
455C22⋊C4#1192401114yescomplemented
456C42—42no—
457C42—2922no—
458C42—2924no—
459C23—41no—
460C23—41no—
461C23—2921no—
462C23—2921no—
463C23—2921no—
464C23—2921no—
465C23—2921no—
466C23—2921no—
467C23—2928no—
468C23—2928no—
469C23—731no—
470C23—731no—
471C23—731no—
472C23—731no—
473C23—1462no—
474C23—1462no—
475C23—1462no—
476C23—1462no—
477C23—1462no—
478C23—1462no—
479C23—1462no—
480C23—1462no—
481C23—1461no—
482C23—1461no—
483C23—1461no—
484C23—1461no—
485C23—1462no—
486C23—1462no—
487C23C42×D7311yescharacteristic
488C23C22⋊C4×D7311yescharacteristic
489C23C4⋊C4×D7311yescharacteristic
490C23M16×D7312yes—
491C23C2×#1192401112yes—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—2921no—
502C2×C4—2921no—
503C2×C4—2921no—
504C2×C4—2921no—
505C2×C4—2921no—
506C2×C4—2921no—
507C2×C4—29216no—
508C2×C4—2922no—
509C2×C4—2922no—
510C2×C4—2921no—
511C2×C4—2921no—
512C2×C4—2921no—
513C2×C4—731no—
514C2×C4—734no—
515C2×C4—731no—
516C2×C4—731no—
517C2×C4—731no—
518C2×C4—1462no—
519C2×C4—1462no—
520C2×C4—1462no—
521C2×C4—1462no—
522C2×C4—1462no—
523C2×C4—1462no—
524C2×C4—1464no—
525C2×C4—1462no—
526C2×C4—1462no—
527C2×C4—1462no—
528C2×C4—1462no—
529C2×C4—1462no—
530C2×C4—1462no—
531C2×C4C22⋊C4×D7311yescharacteristic
532C2×C4C22⋊C4×D7311yescharacteristic
533C2×C4C4⋊C4×D7311yescharacteristic
534C2×C4C4⋊C4×D7311yescharacteristic
535C8—42no—
536C8—42no—
537C8—2922no—
538C8—2922no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—42no—
546C22—42no—
547C22—2924no—
548C22—2924no—
549C22—2924no—
550C22—2922no—
551C22—2922no—
552C22—2922no—
553C22—2922no—
554C22—732no—
555C22—732no—
556C22—1468no—
557C22—1461no—
558C22—1461no—
559C22—1461no—
560C22—1461no—
561C22—1461no—
562C22—1461no—
563C22—1461no—
564C22—1461no—
565C22—1461no—
566C22—1461no—
567C22#95×D7311yescharacteristic
568C22C4×#1192401111yescharacteristic
569C22#1798853911yescharacteristic
570C22#1798854912yes—
571C22#1798860912yes—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—44no—
576C4—2924no—
577C4—732no—
578C4—1461no—
579C4—1461no—
580C4—1461no—
581C4#99×D7312yes—
582C2—22no—
583C2—22no—
584C2—21no—
585C2—21no—
586C2—2921no—
587C2—2921no—
588C2—1462no—
589C2—1462no—
590C2#2260962311yescharacteristic
591C2#342×D7311yescharacteristic
592C2#344×D7311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D73
commutatorC23×C73C2×C42
FrattiniC23×C4C22×D73
FittingC73×#1282C2
socleC22×C73C2×#95
prime radicalC24×D73C2×C4
cosocleC23×C4×C73C23
hypercenter#1282D73
hypocenterC73#7929
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
4. #22607779C2semidirect
5. #22607778C2semidirect
6. #22607777C2semidirect
7. C73×#1282C2semidirect
10. C22×#11924011C4semidirect
19. #17988549C4semidirect
20. #17988549C4semidirect
24. C2×#14556503C4semidirect
56. C22×#10596831C2×C4semidirect
67. C22⋊#10596831C2×C4semidirect
76. C22×C8×C73C2×C4semidirect
82. C22⋊C8×C73C2×C4semidirect
142. C22⋊Dic73M16semidirect
160. C22⋊C4×C73M16semidirect
303. #1282D73semidirect
304. C73#7929semidirect
356. C22×C8C4×D73semidirect
377. C22⋊C8C4×D73semidirect
455. C22⋊C4#11924011semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179885492
C4×C22⋊C4×D732
#226077792
#226077782
#226077772
C73×#12822
#792973