Finite Group Databasebeta

← #33056068

Subgroups — #33056068

Order 18688.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619991C211yesmaximal, characteristic
2#22619042C211yesmaximal, characteristic, complemented
3#22619009C211yesmaximal, characteristic, complemented
4#22608806C211yesmaximal, characteristic, complemented
5#22608792C211yesmaximal, characteristic, complemented
6#22608771C211yesmaximal, characteristic, complemented
7#22608757C211yesmaximal, characteristic, complemented
8#22608752C211yesmaximal, characteristic, complemented
9#22608746C211yesmaximal, characteristic, complemented
10#22608728C211yesmaximal, characteristic, complemented
11#22608723C211yesmaximal, characteristic, complemented
12#22608717C211yesmaximal, characteristic, complemented
13#22608331C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#1488C211yesmaximal, characteristic, complemented
16#17989137C2211yescharacteristic
17#17988911C411yescharacteristic
18#17988911C411yescharacteristic
19#17988882C411yescharacteristic
20#17988877C411yescharacteristic
21#17988787C411yescharacteristic
22#17988782C411yescharacteristic
23#17988732C411yescharacteristic
24#17988732C411yescharacteristic
25Q8×#10596831C2211yescharacteristic
26Q8×#10596831C2211yescharacteristic
27C4×#11924015C2211yescharacteristic
28C4×#11924015C2211yescharacteristic
29C4×#11924013C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988664C2211yescharacteristic
32#17988664C2211yescharacteristic
33#17988660—21no—
34#17988660—21no—
35D4×#10596831—21no—
36D4×#10596831—21no—
37D4×#10596831C2211yescharacteristic
38D4×#10596831C2211yescharacteristic
39#17988652C2211yescharacteristic
40#17988652C2211yescharacteristic
41#17988640—21no—
42#17988640C2211yescharacteristic
43#17988640C2211yescharacteristic
44C2×C4⋊#10596831—21no—
45C2×C4⋊#10596831C2211yescharacteristic
46#17988552—21no—
47#17988552—21no—
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988337C2211yescharacteristic
52#17988316C2211yescharacteristic
53#17988316C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60C4×#41×C73C2211yescharacteristic
61#432×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×#11924015C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72C2×#11924011—21no—
73C2×#11924011—21no—
74C22×#10596831—21no—
75C22×#10596831—21no—
76C22×#10596831—21no—
77C2×C8×D73—21no—
78C2×C8×D73—21no—
79#14556591C2×C411yescharacteristic
80#14556588C2×C411yescharacteristic
81#14556579—21no—
82#14556565—21no—
83#14556565C2×C411yescharacteristic
84#14556565C2×C411yescharacteristic
85C4×D292—21no—
86C4×D292C2311yescharacteristic
87C4×D292C2311yescharacteristic
88#14556524C2×C411yescharacteristic
89#14556524C2×C411yescharacteristic
90#14556522C2×C411yescharacteristic
91#14556522C2×C411yescharacteristic
92C4⋊#10596831—21no—
93C4⋊#10596831—21no—
94C4⋊#10596831—21no—
95C4⋊#10596831C2×C411yescharacteristic
96C4⋊#10596831C2×C411yescharacteristic
97C4⋊#10596831D411yescharacteristic
98C4⋊#10596831D411yescharacteristic
99C4⋊#10596831C2311yescharacteristic
100C4⋊#10596831C2311yescharacteristic
101#14556515C2×C411yescharacteristic
102#14556515C2×C411yescharacteristic
103#14556512C2×C411yescharacteristic
104#14556512C2×C411yescharacteristic
105#14556511C2×C411yescharacteristic
106#14556511C2×C411yescharacteristic
107#14556511C2×C411yescharacteristic
108#14556511C2×C411yescharacteristic
109C22⋊#10596831—21no—
110C22⋊#10596831—21no—
111C22⋊#10596831C2×C411yescharacteristic
112C22⋊#10596831C2×C411yescharacteristic
113C22⋊#10596831D411yescharacteristic
114C22⋊#10596831D411yescharacteristic
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119C4×#10596831—21no—
120C4×#10596831—21no—
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C2×#41×C73C2×C411yescharacteristic
126C4×Q8×C73C2×C411yescharacteristic
127C4×Q8×C73C2311yescharacteristic
128C4×D4×C73—21no—
129C4×D4×C73—21no—
130C4×D4×C73C2×C411yescharacteristic
131C4×D4×C73C2311yescharacteristic
132#117×C73—21no—
133#117×C73C2×C411yescharacteristic
134C2×C42×C73—21no—
135C2×C42×C73C2311yescharacteristic
136C4⋊C8×C73—21no—
137C4⋊C8×C73C2311yescharacteristic
138C4⋊C8×C73C2311yescharacteristic
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141#97×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—81no—
145#11924028—81no—
146C2×Dic146—21no—
147C2×D292—21no—
148C2×D292—21no—
149C2×D292C22×C411yescharacteristic
150C2×D292C22×C411yescharacteristic
151C2×C22⋊D73—21no—
152C2×C22⋊D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155#11924015—22no—
156#11924015—22no—
157#11924013—22no—
158#11924013—22no—
159#11924011—81no—
160#11924011—81no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—81no—
164C2×#10596831—81no—
165C2×#10596831—81no—
166C2×#10596831C22×C411yescharacteristic
167C2×#10596831C22×C411yescharacteristic
168C2×#10596831C22×C411yescharacteristic
169C2×#10596831C22×C411yescharacteristic
170C2×#10596831C2×D411yescharacteristic
171C2×#10596831C2×D411yescharacteristic
172C2×#10596831C2×D411yescharacteristic
173C2×#10596831C2×D411yescharacteristic
174C8×D73—81no—
175C8×D73—81no—
176C4⋊Dic73—21no—
177C4⋊Dic73C22×C411yescharacteristic
178C4⋊Dic73C22×C411yescharacteristic
179#11924005—21no—
180#11924005—21no—
181#11924005—21no—
182#11924005—21no—
183#41×C73—22no—
184#41×C73—22no—
185C2×Q8×C73C22×C411yescharacteristic
186C2×D4×C73—21no—
187C2×D4×C73C22×C411yescharacteristic
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73#4111yescharacteristic
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73C22×C411yescharacteristic
201C4⋊C4×C73C22×C411yescharacteristic
202C22⋊C4×C73—21no—
203C22⋊C4×C73—21no—
204C22⋊C4×C73—21no—
205C42×C73—21no—
206C42×C73—21no—
207C42×C73—21no—
208C42×C73C22×C411yescharacteristic
209C42×C73C2×D411yescharacteristic
210C42×C73#4111yescharacteristic
211C42×C73C2411yescharacteristic
212C23×C73—21no—
213C23×C73C4×D411yescharacteristic
214C22×D73—21no—
215C22×D73—21no—
216Q8×C73—21no—
217Q8×C73#13112yes—
218D4×C73—24no—
219D4×C73—21no—
220D4×C73#13112yes—
221C2×C4×C73—24no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—81no—
233C2×C4×C73C4×D411yescharacteristic
234C2×C4×C73C4×D411yescharacteristic
235C2×C4×C73C4×D411yescharacteristic
236C2×C4×C73C23×C411yescharacteristic
237C2×C4×C73C22×D411yescharacteristic
238C2×C4×C73C2×#4111yescharacteristic
239C22⋊D73—81no—
240C22⋊D73—81no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243D292—21no—
244D292—21no—
245D292—21no—
246D292—21no—
247D292—81no—
248D292—81no—
249C4×D73—41no—
250C4×D73—41no—
251C4×D73—41no—
252C4×D73—41no—
253Dic146—81no—
254C8×C73—41no—
255C8×C73—41no—
256C8×C73—41no—
257C8×C73—41no—
258#10596831—21no—
259#10596831—21no—
260#10596831—21no—
261#10596831—21no—
262#10596831—21no—
263#10596831—21no—
264#10596831—21no—
265#10596831—21no—
266#10596831—41no—
267#10596831—41no—
268C22×C73—21no—
269C22×C73—22no—
270C22×C73—21no—
271C22×C73—21no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73C2×C4×D411yescharacteristic
275C2×D73—41no—
276C2×D73—41no—
277C2×D73—41no—
278C2×D73—41no—
279C2×D73—41no—
280C2×D73—41no—
281C4×C73—21no—
282C4×C73—22no—
283C4×C73—21no—
284C4×C73—21no—
285C4×C73—21no—
286C4×C73—41no—
287C4×C73—41no—
288C4×C73C2×#13111yescharacteristic
289C4×C73C2×#13111yescharacteristic
290C4×C73#57611yescharacteristic
291C4×C73#57711yescharacteristic
292Dic73—41no—
293Dic73—41no—
294#17920—731nomaximal, Sylow
295C2×C73—41no—
296C2×C73—42no—
297C2×C73#292911yescharacteristic
298C2×C73#294611yescharacteristic
299C2×C73#295711yescharacteristic
300D73—81no—
301D73—81no—
302#3106—731no—
303#2988—731no—
304#2981—731no—
305#1588—731no—
306#1586—731no—
307#1583—731no—
308#1581—731no—
309#1580—731no—
310SD16⋊C8—731no—
311C8×SD16—731no—
312C8×D8—731no—
313#1573—731no—
314#1488D7311yescharacteristic, complemented
315#1480—731no—
316#1454—731no—
317C73#1792011yescharacteristic, complemented, Sylow
318#532—731no—
319C4×#41C2×D7311yescharacteristic
320#482—731no—
321#482—731no—
322#477—731no—
323#476—731no—
324#460—731no—
325#459—731no—
326#449—731no—
327#449—731no—
328C8×Q8—731no—
329C8×Q8—731no—
330C4×SD16—731no—
331C4×SD16—731no—
332C4×D8—731no—
333C4×D8—731no—
334#436—731no—
335#436—731no—
336#435—1461no—
337#435—1461no—
338C8×D4—731no—
339C8×D4—731no—
340C8×D4—731no—
341C8×D4—731no—
342C8×D4—1461no—
343C8×D4—1461no—
344#432C2×D7311yescharacteristic
345#431—731no—
346#431—731no—
347#431—1461no—
348#431C2×D7311yescharacteristic
349C2×C4⋊C8—731no—
350C2×C4⋊C8—1461no—
351#408—1461no—
352#408—1461no—
353#335—731no—
354#335—731no—
355#334—731no—
356#334—731no—
357Q8⋊C8C2×D7311yescharacteristic
358Q8⋊C8C2×D7311yescharacteristic
359D4⋊C8—731no—
360D4⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8C2×D7311yescharacteristic
364D4⋊C8C2×D7311yescharacteristic
365#322—731no—
366#322—731no—
367#322—731no—
368C82—731no—
369C2×#41—1461no—
370C2×#41C4×D7311yescharacteristic
371C2×SD16—731no—
372C2×SD16—731no—
373C2×D8—731no—
374C2×D8—731no—
375C2×M16—1461no—
376C2×M16—1461no—
377C22×C8—1461no—
378C22×C8—1461no—
379C22×C8—1461no—
380C22×C8—1461no—
381C22×C8—1461no—
382C4⋊Q8—731no—
383#127—731no—
384#124—1461no—
385#121—731no—
386#121—731no—
387#121—1461no—
388C4×Q8C4×D7311yescharacteristic
389C4×Q8C22×D7311yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—731no—
393C4×D4—731no—
394C4×D4—1461no—
395C4×D4C4×D7311yescharacteristic
396C4×D4C22×D7311yescharacteristic
397#117—21no—
398#117C4×D7311yescharacteristic
399C2×C42—21no—
400C2×C42C22×D7311yescharacteristic
401#107—731no—
402#107—731no—
403#106—731no—
404#106—731no—
405C4⋊C8—21no—
406C4⋊C8—731no—
407C4⋊C8—731no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8—1461no—
413C4⋊C8—1461no—
414C4⋊C8—1461no—
415C4⋊C8C22×D7311yescharacteristic
416C4⋊C8C22×D7311yescharacteristic
417#103—731no—
418#103—731no—
419#102—731no—
420#102—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424#102—731no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—731no—
428C22⋊C8—731no—
429C22⋊C8—731no—
430C22⋊C8—731no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8—1461no—
436C22⋊C8—1461no—
437#97—21no—
438C4×C8—731no—
439C4×C8—731no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—1461no—
443C4×C8—1461no—
444C4×C8C22×D7311yescharacteristic
445C4×C8C22×D7311yescharacteristic
446#41—22no—
447#41—22no—
448#41—5841no—
449#41—5841no—
450C2×Q8—1461no—
451C2×Q8C2×C4×D7311yescharacteristic
452C2×D4—21no—
453C2×D4—731no—
454C2×D4—731no—
455C2×D4—1461no—
456C2×D4—1461no—
457C2×D4—1461no—
458C2×D4—1461no—
459C2×D4C2×C4×D7311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—1461no—
464C22×C4—1461no—
465C22×C4C2×C4×D7311yescharacteristic
466C22×C4D4×D7311yescharacteristic
467C22×C4#1192402711yescharacteristic
468SD16—1462no—
469SD16—1462no—
470D8—1462no—
471D8—1462no—
472M16—5841no—
473M16—5841no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—5841no—
479C2×C8—5841no—
480C2×C8—5841no—
481C2×C8—5841no—
482C2×C8—5841no—
483C2×C8—731no—
484C2×C8—731no—
485C2×C8—731no—
486C2×C8—731no—
487C2×C8—731no—
488C2×C8—731no—
489C2×C8—731no—
490C2×C8—731no—
491C2×C8—1461no—
492C2×C8—1461no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—731no—
496C4⋊C4—731no—
497C4⋊C4—1461no—
498C4⋊C4C2×C4×D7311yescharacteristic
499C4⋊C4C2×C4×D7311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—1461no—
504C22⋊C4—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42C2×C4×D7311yescharacteristic
511C42D4×D7311yescharacteristic
512C42#1192402711yescharacteristic
513C42C23×D7311yescharacteristic
514C23—21no—
515C23—1461no—
516C23—1461no—
517C23#1455655111yescharacteristic
518Q8—21no—
519Q8—5841no—
520Q8#1455659912yes—
521D4—24no—
522D4—21no—
523D4—5841no—
524D4—5841no—
525D4—5841no—
526D4—5841no—
527D4—1461no—
528D4—1461no—
529D4—1461no—
530D4—1461no—
531D4#1455659912yes—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4#1455655111yescharacteristic
551C2×C4#1455655111yescharacteristic
552C2×C4#1455655111yescharacteristic
553C2×C4C22×C4×D7311yescharacteristic
554C2×C4C2×D4×D7311yescharacteristic
555C2×C4C2×#1192402711yescharacteristic
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—2921no—
561C8—2921no—
562C8—1461no—
563C8—1461no—
564C8—1461no—
565C8—1461no—
566C8—1461no—
567C8—1461no—
568C8—1461no—
569C8—1461no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—2921no—
577C22—2921no—
578C22—2921no—
579C22—2921no—
580C22—2921no—
581C22—2921no—
582C22C2×#1455655111yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—2921no—
591C4—2921no—
592C4C2×#1455659911yescharacteristic
593C4C2×#1455659911yescharacteristic
594C4#1798938911yescharacteristic
595C4#1798939411yescharacteristic
596C2—41no—
597C2—42no—
598C2—5841no—
599C2—5841no—
600C2#2261862111yescharacteristic
601C2#2261876611yescharacteristic
602C2#2261884411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1488C2
socleC22×C73C2×C4×D4
prime radical#22619991C2
cosocleC42×C73C24
hypercenter#1488D73
hypocenterC73#17920
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #22619042C2semidirect
3. #22619009C2semidirect
4. #22608806C2semidirect
5. #22608792C2semidirect
6. #22608771C2semidirect
7. #22608757C2semidirect
8. #22608752C2semidirect
9. #22608746C2semidirect
10. #22608728C2semidirect
11. #22608723C2semidirect
12. #22608717C2semidirect
13. #22608331C2semidirect
14. #22608231C2semidirect
15. C73×#1488C2semidirect
314. #1488D73semidirect
317. C73#17920semidirect

Maximal subgroups

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

subgroupindex
#226199912
#226190422
#226190092
#226088062
#226087922
#226087712
#226087572
#226087522
#226087462
#226087282
#226087232
#226087172
#226083312
#226082312
C73×#14882
#1792073