Finite Group Databasebeta

← #33090354

Subgroups — #33090354

Order 18688.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988685C211yesmaximal, characteristic
2#22612575C211yesmaximal, characteristic
3#22610815C211yesmaximal, characteristic
4#22610788C211yesmaximal, characteristic
5#22610666C211yesmaximal, characteristic, complemented
6#22610661C211yesmaximal, characteristic, complemented
7#22610627C211yesmaximal, characteristic
8#22610624C211yesmaximal, characteristic, complemented
9#22610613C211yesmaximal, characteristic
10#22610610C211yesmaximal, characteristic, complemented
11#22609829C211yesmaximal, characteristic, complemented
12C4×#14556515C211yesmaximal, characteristic, complemented
13C4×#14556511C211yesmaximal, characteristic
14#22609618C211yesmaximal, characteristic, complemented
15C73×#2320C211yesmaximal, characteristic, complemented
16C22×#11924015C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18#17988685C418yescomplemented
19C2×#14556524C2211yescharacteristic
20C2×#14556524C2211yescharacteristic
21C2×#14556522C2211yescharacteristic
22C2×#14556515C2211yescharacteristic
23C2×#14556515C2211yescharacteristic
24C2×#14556515C2211yescharacteristic
25C2×#14556511C2211yescharacteristic
26C2×#14556511C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×#14556502C2211yescharacteristic
29C2×#14556502C2211yescharacteristic
30C2×#14556502C2211yescharacteristic
31C2×C4×#10596831C2211yescharacteristic
32C2×C4×#10596831C2211yescharacteristic
33C2×C4×#10596831C2211yescharacteristic
34#17988489C2211yescharacteristic
35#17988489C2211yescharacteristic
36#17988485C2211yescharacteristic
37#17988485C2211yescharacteristic
38#17988476—21no—
39#17988476—21no—
40#17988449—21no—
41#17988446—21no—
42C4×C4⋊Dic73C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49C2×C4×Q8×C73C2211yescharacteristic
50#391×C73C2211yescharacteristic
51#391×C73C2211yescharacteristic
52#389×C73C2211yescharacteristic
53#389×C73C2211yescharacteristic
54#387×C73—21no—
55#387×C73—21no—
56#383×C73—21no—
57#382×C73—21no—
58C4×C4⋊C4×C73C2211yescharacteristic
59#376×C73C2211yescharacteristic
60C22×D292C2311yescharacteristic
61C22×C4×D73—21no—
62C2×#11924015—22no—
63C2×#11924015—22no—
64C2×#11924015C2×C414yes—
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C4×D292—22no—
70C4×D292C2×C414yes—
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×#11924007—21no—
75C2×#11924007—21no—
76C2×#11924005—21no—
77C2×#11924005—21no—
78C2×#11924005—21no—
79C2×#11924005—21no—
80C2×#11924005—21no—
81C2×C4×Dic73—21no—
82#14556524—22no—
83#14556524C2×C414yes—
84#14556522—22no—
85#14556515—22no—
86#14556515—22no—
87#14556515C2×C414yes—
88#14556511—22no—
89#14556511—22no—
90#14556511C2×C414yes—
91#14556502—22no—
92#14556502—22no—
93#14556502C2×C414yes—
94C4×#10596831—22no—
95C4×#10596831—22no—
96C4×#10596831—22no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100C22×Q8×C73C2311yescharacteristic
101C4×Q8×C73—22no—
102C4×Q8×C73C2×C414yes—
103C2×C4⋊C4×C73—21no—
104C2×C4⋊C4×C73—21no—
105C2×C4⋊C4×C73—21no—
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73C2311yescharacteristic
109C2×C42×C73—21no—
110C2×C42×C73—21no—
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114#95×C73—21no—
115#95×C73—21no—
116#95×C73—21no—
117#95×C73—21no—
118#95×C73—21no—
119#95×C73—21no—
120#95×C73—21no—
121#95×C73D411yescharacteristic
122#95×C73D411yescharacteristic
123#95×C73D411yescharacteristic
124#95×C73D411yescharacteristic
125C23×D73—21no—
126C2×D292—21no—
127C2×D292—21no—
128C2×D292—21no—
129C2×D292—21no—
130C2×D292—21no—
131C2×D292C22×C412yes—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C2×C4×D73—24no—
136C2×C4×D73—81no—
137C2×C4×D73—81no—
138#11924015—28no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831C22×C412yes—
146C2×#10596831C22×C412yes—
147C2×#10596831#4112yes—
148C2×#10596831#4112yes—
149C2×#10596831#4112yes—
150C2×#10596831#4112yes—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73—21no—
155C4⋊Dic73—21no—
156C4⋊Dic73C22×C412yes—
157#11924007—81no—
158#11924007—81no—
159#11924005—24no—
160#11924005—81no—
161#11924005—81no—
162#11924005—81no—
163#11924005—81no—
164C4×Dic73—81no—
165C2×Q8×C73—21no—
166C2×Q8×C73—21no—
167C2×Q8×C73—21no—
168C2×Q8×C73—21no—
169C2×Q8×C73—21no—
170C2×Q8×C73C22×C412yes—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2411yescharacteristic
182C4⋊C4×C73—24no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—81no—
189C4⋊C4×C73—81no—
190C4⋊C4×C73C22×C412yes—
191C42×C73—24no—
192C42×C73—21no—
193C42×C73—21no—
194C42×C73—21no—
195C42×C73—21no—
196C42×C73—81no—
197C42×C73C22×C412yes—
198C42×C73#4112yes—
199C23×C73C22×D411yescharacteristic
200C22×D73—22no—
201C22×D73—41no—
202C22×D73—41no—
203C22×D73—41no—
204C22×D73—41no—
205C22×D73—41no—
206C22×D73—41no—
207Q8×C73—22no—
208Q8×C73—22no—
209Q8×C73—41no—
210Q8×C73—41no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—22no—
216C2×C4×C73—22no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
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—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73C4×D412yes—
240C2×C4×C73C4×D412yes—
241C2×C4×C73C23×C411yescharacteristic
242C2×C4×C73C2×#4111yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C2×C4×C73C2×#4111yescharacteristic
246C2×C4×C73C2×#4111yescharacteristic
247C2×Dic73—22no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253C2×Dic73—41no—
254C2×Dic73—41no—
255C2×Dic73—41no—
256D292—22no—
257D292—22no—
258D292—41no—
259D292—41no—
260C4×D73—84no—
261#10596831—22no—
262#10596831—22no—
263#10596831—22no—
264#10596831#11714yes—
265C22×C73C2×C4×D411yescharacteristic
266C22×C73#53211yescharacteristic
267C22×C73#53211yescharacteristic
268C22×C73#57611yescharacteristic
269C22×C73#57711yescharacteristic
270C22×C73#57711yescharacteristic
271C22×C73#57811yescharacteristic
272C2×D73—42no—
273C2×D73—42no—
274C2×D73—42no—
275C2×D73—81no—
276C2×D73—81no—
277C2×D73—81no—
278C2×D73—81no—
279C4×C73—22no—
280C4×C73—22no—
281C4×C73—41no—
282C4×C73—41no—
283C4×C73—41no—
284C4×C73—41no—
285C4×C73—42no—
286C4×C73—42no—
287C4×C73—81no—
288C4×C73—81no—
289C4×C73C2×#11711yescharacteristic
290C4×C73C4×#4111yescharacteristic
291C4×C73#52911yescharacteristic
292C4×C73#52911yescharacteristic
293Dic73—42no—
294Dic73—81no—
295Dic73—81no—
296#21291—731nomaximal, Sylow
297C2×C73#229311yescharacteristic
298C2×C73#294611yescharacteristic
299C2×C73#294711yescharacteristic
300C2×C73#317411yescharacteristic
301C2×C73#317511yescharacteristic
302C2×C73#317811yescharacteristic
303C2×C73#317911yescharacteristic
304D73—82no—
305C2×#440—731no—
306#2320D7311yescharacteristic, complemented
307#2319—731no—
308#1973—731no—
309#1968—731no—
310#1943—731no—
311#1942—731no—
312#1936—731no—
313#1935—731no—
314#1934—731no—
315#1933—731no—
316#1776—731no—
317C4×#103—731no—
318C4×#102—731no—
319#1726—731no—
320C73#2129111yescharacteristic, complemented, Sylow
321C22×SD16—731no—
322C2×C4×Q8C2×D7311yescharacteristic
323C2×C4×D4—731no—
324#440—738no—
325C2×#107—731no—
326C2×#107—731no—
327C2×#106—731no—
328C2×#103—731no—
329C2×#103—731no—
330C2×#103—731no—
331C2×#102—731no—
332C2×#102—731no—
333C2×#102—731no—
334C2×#97—731no—
335C2×#97—731no—
336C2×#97—731no—
337C2×C4×C8—731no—
338C2×C4×C8—731no—
339C2×C4×C8—731no—
340#391C2×D7311yescharacteristic
341#391C2×D7311yescharacteristic
342#390—731no—
343#390—731no—
344#389—731no—
345#389—731no—
346#389C2×D7311yescharacteristic
347#389C2×D7311yescharacteristic
348#388—1461no—
349#388—1461no—
350#387—21no—
351#387—21no—
352#383—21no—
353#382—21no—
354#381—1461no—
355#380—1461no—
356C4×C4⋊C4—731no—
357C4×C4⋊C4C2×D7311yescharacteristic
358#376C2×D7311yescharacteristic
359#340—731no—
360#340—731no—
361#340—731no—
362#340—731no—
363#340—731no—
364#340—731no—
365C22×Q8C22×D7311yescharacteristic
366C22×D4—731no—
367C23×C4—1461no—
368C2×SD16—734no—
369C2×SD16—1462no—
370C2×SD16—1462no—
371C22×C8—731no—
372C22×C8—731no—
373C22×C8—731no—
374C22×C8—731no—
375C4×Q8—22no—
376C4×Q8C4×D7314yes—
377C4×D4—734no—
378C4×D4—1462no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—731no—
383C2×C4⋊C4—731no—
384C2×C4⋊C4—731no—
385C2×C4⋊C4—1461no—
386C2×C4⋊C4—1461no—
387C2×C4⋊C4C22×D7311yescharacteristic
388C2×C4⋊C4C22×D7311yescharacteristic
389C2×C4⋊C4C22×D7311yescharacteristic
390C2×C22⋊C4—1461no—
391C2×C22⋊C4—1461no—
392C2×C22⋊C4—1461no—
393C2×C22⋊C4—1461no—
394C2×C22⋊C4—1461no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—1461no—
398C2×C42C22×D7311yescharacteristic
399C2×C42C22×D7311yescharacteristic
400C2×C42C22×D7311yescharacteristic
401#107—734no—
402#107—1462no—
403#106—1462no—
404#103—734no—
405#103—1462no—
406#103—1462no—
407#102—734no—
408#102—1462no—
409#102—1462no—
410#97—734no—
411#97—1462no—
412#97—1462no—
413C4×C8—1462no—
414C4×C8—1462no—
415C4×C8—1462no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—1461no—
424#95—1461no—
425#95—1461no—
426#95C22⋊D7311yescharacteristic
427#95C22⋊D7311yescharacteristic
428#95C22⋊D7311yescharacteristic
429#95C22⋊D7311yescharacteristic
430C24—1461no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C2×C4×D7312yes—
437C2×D4—732no—
438C2×D4—1461no—
439C2×D4—1461no—
440C2×D4—1461no—
441C2×D4—1461no—
442C2×D4—1461no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—5841no—
448C22×C4—5841no—
449C22×C4—1461no—
450C22×C4—1461no—
451C22×C4—1461no—
452C22×C4—1464no—
453C22×C4C2×C22⋊D7311yescharacteristic
454C22×C4C2×C22⋊D7311yescharacteristic
455C22×C4C2×C22⋊D7311yescharacteristic
456C22×C4C2×C22⋊D7311yescharacteristic
457C22×C4C2×C22⋊D7311yescharacteristic
458C22×C4C2×C22⋊D7311yescharacteristic
459C22×C4C23×D7311yescharacteristic
460SD16—1468no—
461C2×C8—732no—
462C2×C8—732no—
463C2×C8—732no—
464C2×C8—732no—
465C2×C8—732no—
466C2×C8—732no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C4⋊C4—24no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—5841no—
482C4⋊C4—5841no—
483C4⋊C4—732no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4—1461no—
487C4⋊C4—1461no—
488C4⋊C4—1461no—
489C4⋊C4C2×C4×D7312yes—
490C22⋊C4—5841no—
491C22⋊C4—5841no—
492C22⋊C4—5841no—
493C22⋊C4—5841no—
494C22⋊C4—1464no—
495C42—24no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—81no—
501C42—5841no—
502C42C2×C4×D7312yes—
503C42#1192402812yes—
504C23—2921no—
505C23—2921no—
506C23—2921no—
507C23—2921no—
508C23—2921no—
509C23—2921no—
510C23—1462no—
511C23C22×C22⋊D7311yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—2921no—
517D4—2921no—
518D4—1462no—
519D4—1462no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—2921no—
551C2×C4—2921no—
552C2×C4—2921no—
553C2×C4—2921no—
554C2×C4—2921no—
555C2×C4—2921no—
556C2×C4—5844no—
557C2×C4—1462no—
558C2×C4C4×C22⋊D7312yes—
559C2×C4C4×C22⋊D7312yes—
560C2×C4C22×C4×D7311yescharacteristic
561C2×C4#41×D7311yescharacteristic
562C2×C4#41×D7311yescharacteristic
563C2×C4#41×D7311yescharacteristic
564C2×C4#41×D7311yescharacteristic
565C2×C4C2×#1192402811yescharacteristic
566C8—734no—
567C8—1462no—
568C8—1462no—
569C8—1462no—
570C22—2922no—
571C22—2922no—
572C22—2922no—
573C22—5841no—
574C22—5841no—
575C22—5841no—
576C22—5841no—
577C22C2×C4×C22⋊D7311yescharacteristic
578C22#1798913311yescharacteristic
579C22#1798913311yescharacteristic
580C22#1798939011yescharacteristic
581C22#1798939511yescharacteristic
582C22#1798939511yescharacteristic
583C22#1798940211yescharacteristic
584C4—22no—
585C4—22no—
586C4—42no—
587C4—41no—
588C4—41no—
589C4—42no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—81no—
594C4—2922no—
595C4—5841no—
596C4—5841no—
597C4#117×D7311yescharacteristic
598C4#1798905511yescharacteristic
599C4#1798911511yescharacteristic
600C4#1798911511yescharacteristic
601C2—5842no—
602C2#2261239011yescharacteristic
603C2#2261875911yescharacteristic
604C2#2261877411yescharacteristic
605C2#2262056011yescharacteristic
606C2#2262056411yescharacteristic
607C2#2262060111yescharacteristic
608C2#2262060811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2320C2
socleC23×C73C22×D4
prime radicalC22×D292C23
cosocleC22×C4×C73C24
hypercenter#2320D73
hypocenterC73#21291
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ #376 ◁ #2320

Complements

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

NH ≅ G/Ntype
5. #22610666C2semidirect
6. #22610661C2semidirect
8. #22610624C2semidirect
10. #22610610C2semidirect
11. #22609829C2semidirect
12. C4×#14556515C2semidirect
14. #22609618C2semidirect
15. C73×#2320C2semidirect
18. #17988685C4semidirect
306. #2320D73semidirect
320. C73#21291semidirect

Maximal subgroups

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

subgroupindex
C2×#179886852
#226125752
#226108152
#226107882
#226106662
#226106612
#226106272
#226106242
#226106132
#226106102
#226098292
C4×#145565152
C4×#145565112
#226096182
C73×#23202
#2129173