Finite Group Databasebeta

← #33145035

Subgroups — #33145035

Order 18688.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22615166C211yesmaximal, characteristic, complemented
2#22612904C211yesmaximal, characteristic
3#22611457C211yesmaximal, characteristic
4#22611454C211yesmaximal, characteristic
5#22611301C211yesmaximal, characteristic
6#22611301C211yesmaximal, characteristic
7#22610702C211yesmaximal, characteristic, complemented
8#22610701C211yesmaximal, characteristic, complemented
9#22610693C211yesmaximal, characteristic, complemented
10#22610647C211yesmaximal, characteristic, complemented
11#22610526C211yesmaximal, characteristic, complemented
12#22610505C211yesmaximal, characteristic, complemented
13#22610093C211yesmaximal, characteristic, complemented
14C4×#14556512C211yesmaximal, characteristic
15C73×#1804C211yesmaximal, characteristic
16C2×#14556525C2211yescharacteristic
17C2×#14556524C2211yescharacteristic
18C2×#14556524C2211yescharacteristic
19C2×#14556523C2211yescharacteristic
20C2×#14556522C2211yescharacteristic
21C2×#14556522C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×#14556512C2211yescharacteristic
25C2×#14556512C2211yescharacteristic
26C2×C4×#10596831C2211yescharacteristic
27#17988529—21no—
28#17988519—21no—
29#17988490C2211yescharacteristic
30#17988490C2211yescharacteristic
31#17988486C2211yescharacteristic
32#17988486C2211yescharacteristic
33#17988480—21no—
34#17988480—21no—
35#17988474—21no—
36#17988470—21no—
37#17988456C2211yescharacteristic
38#17988453C2211yescharacteristic
39#17988452C2211yescharacteristic
40#17988450—21no—
41C4⋊C4×Dic73C2211yescharacteristic
42C4⋊C4×Dic73C2211yescharacteristic
43C4×C4⋊Dic73C2211yescharacteristic
44C4×C4⋊Dic73C2211yescharacteristic
45C4×C22⋊Dic73—21no—
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C2×C4×D4×C73C2211yescharacteristic
53C2×C4⋊C8×C73C2211yescharacteristic
54C2×#102×C73C2211yescharacteristic
55C2×#102×C73C2211yescharacteristic
56#382×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59C22×#10596831C2311yescharacteristic
60C22×#10596831C2311yescharacteristic
61C2×C4⋊Dic73—21no—
62C2×C4⋊Dic73—21no—
63C2×C4⋊Dic73D411yescharacteristic
64C2×C4⋊Dic73D411yescharacteristic
65C2×C4⋊Dic73C2311yescharacteristic
66C2×C4⋊Dic73C2311yescharacteristic
67C2×C4⋊Dic73C2311yescharacteristic
68C2×C4⋊Dic73C2311yescharacteristic
69C2×#11924007—21no—
70C2×#11924007—21no—
71C2×C22⋊Dic73—21no—
72C2×C22⋊Dic73—21no—
73C2×C22⋊Dic73—21no—
74C2×C22⋊Dic73—21no—
75C2×C4×Dic73—21no—
76C2×C4×Dic73—21no—
77C2×C4×Dic73—21no—
78C2×C4×Dic73C2311yescharacteristic
79C2×C4×Dic73C2311yescharacteristic
80#14556525—41no—
81#14556524—22no—
82#14556524—22no—
83#14556523—41no—
84#14556522—41no—
85#14556522—41no—
86#14556520—22no—
87#14556520—22no—
88#14556512—22no—
89#14556512—22no—
90C4×#10596831—22no—
91#14556498—21no—
92#14556498—21no—
93#14556498—21no—
94#14556498—21no—
95#14556498—21no—
96#14556498—21no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100#14556498D411yescharacteristic
101#14556498D411yescharacteristic
102C22×D4×C73C2311yescharacteristic
103C23×C4×C73—21no—
104C22×C8×C73C2311yescharacteristic
105C22×C8×C73C2311yescharacteristic
106C4×D4×C73—22no—
107C4×D4×C73Q814yes—
108C2×C4⋊C4×C73C2311yescharacteristic
109C2×C4⋊C4×C73C2311yescharacteristic
110C2×C4⋊C4×C73C2311yescharacteristic
111C2×C22⋊C4×C73—21no—
112C2×C42×C73C2311yescharacteristic
113C4⋊C8×C73—22no—
114#102×C73—41no—
115#102×C73—41no—
116#95×C73—21no—
117#95×C73—21no—
118C22×Dic73—21no—
119C22×Dic73—21no—
120C22×Dic73—21no—
121C22×Dic73—21no—
122C22×Dic73C2×D411yescharacteristic
123C22×Dic73C2×D411yescharacteristic
124C22×Dic73C2×D411yescharacteristic
125C22×Dic73C2×D411yescharacteristic
126C2×#10596831—21no—
127C2×#10596831—21no—
128C2×#10596831—21no—
129C2×#10596831—21no—
130C2×#10596831#4112yes—
131C2×#10596831#4112yes—
132C4⋊Dic73—22no—
133C4⋊Dic73—21no—
134C4⋊Dic73—21no—
135C4⋊Dic73—21no—
136C4⋊Dic73—21no—
137C4⋊Dic73—21no—
138C4⋊Dic73—21no—
139C4⋊Dic73—21no—
140C4⋊Dic73—21no—
141C4⋊Dic73—41no—
142C4⋊Dic73—42no—
143C4⋊Dic73—81no—
144#11924007—42no—
145#11924007—81no—
146C22⋊Dic73—42no—
147C22⋊Dic73—42no—
148C22⋊Dic73—81no—
149C22⋊Dic73—81no—
150C4×Dic73—21no—
151C4×Dic73—21no—
152C4×Dic73—21no—
153C4×Dic73—21no—
154C4×Dic73—81no—
155C4×Dic73—81no—
156C4×Dic73—81no—
157C24×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
160C2×D4×C73—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×C73C2×Q812yes—
164C22×C4×C73—21no—
165C22×C4×C73—24no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—81no—
169C22×C4×C73—81no—
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2411yescharacteristic
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73C2×Q812yes—
185C22⋊C4×C73—24no—
186C42×C73C2×Q812yes—
187C42×C73#4112yes—
188C23×C73—22no—
189C23×C73—41no—
190C23×C73—41no—
191C23×C73—41no—
192C23×C73—41no—
193C23×C73—41no—
194C23×C73—41no—
195C23×C73C22×D411yescharacteristic
196D4×C73—22no—
197D4×C73—22no—
198D4×C73—41no—
199D4×C73—41no—
200C2×C4×C73—21no—
201C2×C4×C73—21no—
202C2×C4×C73—21no—
203C2×C4×C73—21no—
204C2×C4×C73—22no—
205C2×C4×C73—41no—
206C2×C4×C73—41no—
207C2×C4×C73—41no—
208C2×C4×C73—41no—
209C2×C4×C73—41no—
210C2×C4×C73—41no—
211C2×C4×C73—41no—
212C2×C4×C73—41no—
213C2×C4×C73—84no—
214C2×C4×C73C22⋊Q812yes—
215C2×C4×C73C22⋊Q812yes—
216C2×C4×C73C22×Q811yescharacteristic
217C2×C4×C73C2×#4111yescharacteristic
218C2×C4×C73C2×#4111yescharacteristic
219C2×C4×C73C2×#4111yescharacteristic
220C2×C4×C73H(5,𝔽2)11yescharacteristic
221C2×C4×C732−1+411yescharacteristic
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—41no—
234C2×Dic73—41no—
235C2×Dic73—41no—
236C2×Dic73—41no—
237C2×Dic73—41no—
238C2×Dic73—41no—
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73#13512yes—
246C8×C73—41no—
247C8×C73—41no—
248#10596831—22no—
249#10596831—22no—
250C22×C73—42no—
251C22×C73—42no—
252C22×C73—42no—
253C22×C73—81no—
254C22×C73—81no—
255C22×C73—81no—
256C22×C73—81no—
257C22×C73C2×C22⋊Q811yescharacteristic
258C22×C73#54711yescharacteristic
259C22×C73#55011yescharacteristic
260C22×C73C2×#13511yescharacteristic
261C22×C73#57511yescharacteristic
262C22×C73#57611yescharacteristic
263C22×C73#57711yescharacteristic
264C4×C73—22no—
265C4×C73—22no—
266C4×C73—42no—
267C4×C73—81no—
268C4×C73—81no—
269C4×C73#53311yescharacteristic
270C4×C73#54411yescharacteristic
271C4×C73#55211yescharacteristic
272C4×C73#55311yescharacteristic
273Dic73—22no—
274Dic73—41no—
275Dic73—41no—
276Dic73—41no—
277Dic73—81no—
278Dic73—81no—
279Dic73—81no—
280Dic73—81no—
281#26094—731nomaximal, Sylow
282C2×C73—82no—
283C2×C73#244111yescharacteristic
284C2×C73#307611yescharacteristic
285C2×C73#308111yescharacteristic
286C2×C73#333711yescharacteristic
287C2×C73#335511yescharacteristic
288C2×C73#339611yescharacteristic
289C2×C73#340111yescharacteristic
290#2570—731no—
291#2357—731no—
292#2093—731no—
293#2092—731no—
294#2065—731no—
295#2065—731no—
296#1949—731no—
297#1949—731no—
298#1948—731no—
299#1939—731no—
300#1921—731no—
301#1918—731no—
302#1846—731no—
303#1804D7311yescharacteristic
304C4×#102—731no—
305C73#2609411yescharacteristic, complemented, Sylow
306C2×C4×D4C2×D7311yescharacteristic
307C2×#107—731no—
308C2×#107—731no—
309C2×#107—731no—
310C2×#106—731no—
311C2×#106—731no—
312C2×#106—731no—
313C2×C4⋊C8—731no—
314C2×C4⋊C8—731no—
315C2×C4⋊C8C2×D7311yescharacteristic
316C2×#102—731no—
317C2×#102—731no—
318C2×#102C2×D7311yescharacteristic
319C2×#102C2×D7311yescharacteristic
320C2×C4×C8—731no—
321#400—1461no—
322#398—1461no—
323#390—731no—
324#390—731no—
325#389—731no—
326#389—731no—
327#388—1461no—
328#388—1461no—
329#387—1461no—
330#387—1461no—
331#384—731no—
332#382—731no—
333#382—731no—
334#382C2×D7311yescharacteristic
335#381—1461no—
336C4×C4⋊C4—731no—
337C4×C4⋊C4—731no—
338C4×C4⋊C4—731no—
339C4×C4⋊C4—731no—
340C4×C22⋊C4—1461no—
341#340—731no—
342#340—731no—
343#340—731no—
344#340—731no—
345#340C2×D7311yescharacteristic
346#340C2×D7311yescharacteristic
347#336—731no—
348#336—731no—
349C22×D4C22×D7311yescharacteristic
350C23×C4—21no—
351C22×C8—731no—
352C22×C8—731no—
353C22×C8C22×D7311yescharacteristic
354C22×C8C22×D7311yescharacteristic
355C4×D4—22no—
356C4×D4Dic14614yes—
357C2×C4⋊C4—731no—
358C2×C4⋊C4—731no—
359C2×C4⋊C4—731no—
360C2×C4⋊C4—731no—
361C2×C4⋊C4—731no—
362C2×C4⋊C4—731no—
363C2×C4⋊C4—1461no—
364C2×C4⋊C4—1461no—
365C2×C4⋊C4—1461no—
366C2×C4⋊C4—1461no—
367C2×C4⋊C4C22×D7311yescharacteristic
368C2×C4⋊C4C22×D7311yescharacteristic
369C2×C4⋊C4C22×D7311yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—1461no—
372C2×C22⋊C4—1461no—
373C2×C22⋊C4—1461no—
374C2×C22⋊C4—1461no—
375C2×C42—731no—
376C2×C42—731no—
377C2×C42—1461no—
378C2×C42—1461no—
379C2×C42—1461no—
380C2×C42C22×D7311yescharacteristic
381#107—2921no—
382#107—1462no—
383#107—1462no—
384#106—2921no—
385#106—2921no—
386#106—2921no—
387C4⋊C8—22no—
388C4⋊C8—1462no—
389C4⋊C8—1462no—
390#102—41no—
391#102—41no—
392#102—1462no—
393#102—1462no—
394C4×C8—1462no—
395#95—21no—
396#95—21no—
397#95—731no—
398#95—731no—
399#95—1461no—
400#95—1461no—
401#95—1461no—
402#95—1461no—
403#95—1461no—
404#95—1461no—
405#95—1461no—
406#95—1461no—
407#95—1461no—
408C24—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4C2×Dic14612yes—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—81no—
420C22×C4—81no—
421C22×C4—731no—
422C22×C4—731no—
423C22×C4—731no—
424C22×C4—731no—
425C22×C4—1461no—
426C22×C4—1461no—
427C22×C4—1461no—
428C22×C4—1461no—
429C22×C4D4×D7311yescharacteristic
430C22×C4D4×D7311yescharacteristic
431C22×C4C23×D7311yescharacteristic
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—732no—
439C2×C8—732no—
440C2×C8—1461no—
441C2×C8—1461no—
442C2×C8—1461no—
443C2×C8—1461no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—2921no—
450C4⋊C4—2922no—
451C4⋊C4—2922no—
452C4⋊C4—5841no—
453C4⋊C4—5841no—
454C4⋊C4—1462no—
455C4⋊C4—1461no—
456C4⋊C4—1461no—
457C4⋊C4—1461no—
458C4⋊C4—1461no—
459C4⋊C4—1461no—
460C4⋊C4—1461no—
461C4⋊C4—1461no—
462C4⋊C4—1461no—
463C4⋊C4C2×Dic14612yes—
464C22⋊C4—24no—
465C22⋊C4—2922no—
466C22⋊C4—2922no—
467C22⋊C4—5841no—
468C22⋊C4—5841no—
469C42—5841no—
470C42—5841no—
471C42—5841no—
472C42—1461no—
473C42—1461no—
474C42—1461no—
475C42—1461no—
476C42C2×Dic14612yes—
477C42#1192402712yes—
478C23—22no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23C2×D4×D7311yescharacteristic
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—84no—
504C2×C4—2921no—
505C2×C4—2921no—
506C2×C4—2921no—
507C2×C4—2921no—
508C2×C4—2921no—
509C2×C4—2921no—
510C2×C4—2921no—
511C2×C4—2921no—
512C2×C4—2921no—
513C2×C4—2921no—
514C2×C4—2921no—
515C2×C4—2921no—
516C2×C4—732no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4—1461no—
520C2×C4—1461no—
521C2×C4—1461no—
522C2×C4—1461no—
523C2×C4—1461no—
524C2×C4—1461no—
525C2×C4—1461no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4#1455656812yes—
529C2×C4#1455656812yes—
530C2×C4C22×Dic14611yescharacteristic
531C2×C4#41×D7311yescharacteristic
532C2×C4#41×D7311yescharacteristic
533C2×C4C2×#1192402711yescharacteristic
534C2×C4#1455663611yescharacteristic
535C2×C4#1455663911yescharacteristic
536C8—41no—
537C8—41no—
538C8—1462no—
539C8—1462no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C2×#1455656811yescharacteristic
548C22#1798923911yescharacteristic
549C22#1798925511yescharacteristic
550C22#135×D7311yescharacteristic
551C22#1798938411yescharacteristic
552C22#1798939111yescharacteristic
553C22#1798939711yescharacteristic
554C4—22no—
555C4—22no—
556C4—42no—
557C4—81no—
558C4—81no—
559C4—2921no—
560C4—2921no—
561C4—2921no—
562C4—5841no—
563C4—5841no—
564C4—5841no—
565C4—5841no—
566C4—1462no—
567C4#1798914011yescharacteristic
568C4#1798921811yescharacteristic
569C4#1798927111yescharacteristic
570C4#1798928411yescharacteristic
571C2—82no—
572C2#2261364511yescharacteristic
573C2#2261971511yescharacteristic
574C2#2261976411yescharacteristic
575C2#2262231711yescharacteristic
576C2#2262253411yescharacteristic
577C2#2262293811yescharacteristic
578C2#2262299511yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#1804C2
socleC23×C73C22×D4
prime radicalC22×D4×C73C23
hypercenter#1804D73
hypocenterC73#26094
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
1. #22615166C2semidirect
7. #22610702C2semidirect
8. #22610701C2semidirect
9. #22610693C2semidirect
10. #22610647C2semidirect
11. #22610526C2semidirect
12. #22610505C2semidirect
13. #22610093C2semidirect
305. C73#26094semidirect

Maximal subgroups

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

subgroupindex
#226151662
#226129042
#226114572
#226114542
#226113012
#226107022
#226107012
#226106932
#226106472
#226105262
#226105052
#226100932
C4×#145565122
C73×#18042
#2609473