Finite Group Databasebeta

← #33093985

Subgroups — #33093985

Order 18688.

818 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988940C211yesmaximal, characteristic
2#22612671C211yesmaximal, characteristic, complemented
3#22612641C211yesmaximal, characteristic
4#22610898C211yesmaximal, characteristic, complemented
5#22610746C211yesmaximal, characteristic
6#22610621C211yesmaximal, characteristic, complemented
7#22610617C211yesmaximal, characteristic
8#22610606C211yesmaximal, characteristic, complemented
9#22610057C211yesmaximal, characteristic, complemented
10#22609760C211yesmaximal, characteristic, complemented
11#22609758C211yesmaximal, characteristic
12#22609750C211yesmaximal, characteristic, complemented
13#102×Dic73C211yesmaximal, characteristic
14#22609619C211yesmaximal, characteristic, complemented
15C73×#1936C211yesmaximal, characteristic
16C2×#14556582C2211yescharacteristic
17C2×#14556578C2211yescharacteristic
18C2×#14556556C2211yescharacteristic
19C2×D4×Dic73C2211yescharacteristic
20#17988940C418yescomplemented
21C2×#14556516C2211yescharacteristic
22C2×#14556516C2211yescharacteristic
23C2×#14556514C2211yescharacteristic
24C2×#14556514C2211yescharacteristic
25C2×#14556512C2211yescharacteristic
26C2×#14556512C2211yescharacteristic
27C2×#14556501C2211yescharacteristic
28C2×#14556501C2211yescharacteristic
29C2×C4×#10596831C2211yescharacteristic
30C2×C8×Dic73C2211yescharacteristic
31C2×C8×Dic73C2211yescharacteristic
32#17988493C2211yescharacteristic
33#17988485C2211yescharacteristic
34#17988483—21no—
35#17988482—21no—
36#17988481—21no—
37#17988481—21no—
38#17988472—21no—
39#17988469—21no—
40#17988459—21no—
41#17988459—21no—
42#17988456C2211yescharacteristic
43#17988456C2211yescharacteristic
44C4⋊C4×Dic73C2211yescharacteristic
45C4⋊C4×Dic73C2211yescharacteristic
46#17988433C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53C2×#102×C73C2211yescharacteristic
54C2×#102×C73C2211yescharacteristic
55C2×#97×C73C2211yescharacteristic
56#390×C73C2211yescharacteristic
57#389×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60C22×Dic146C2311yescharacteristic
61C23×Dic73—21no—
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64#14556582—22no—
65#14556582C2×C414yescomplemented
66#14556578—22no—
67#14556578C2×C414yes—
68#14556556—22no—
69#14556556—22no—
70D4×Dic73—22no—
71D4×Dic73—22no—
72C2×C4⋊Dic73—21no—
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×#11924007—21no—
77C2×#11924007—21no—
78C2×#11924007—21no—
79C2×#11924007—21no—
80C2×#11924007—21no—
81C2×#11924007—21no—
82C2×#11924007—21no—
83C2×C22⋊Dic73—21no—
84C2×C22⋊Dic73—21no—
85C2×C22⋊Dic73—21no—
86C2×C4×Dic73—21no—
87C2×C4×Dic73—21no—
88C2×C4×Dic73—21no—
89C2×C4×Dic73C2311yescharacteristic
90C2×C4×Dic73C2311yescharacteristic
91#14556516—22no—
92#14556516C2×C414yescomplemented
93#14556514—22no—
94#14556514C2×C414yescomplemented
95#14556512—22no—
96#14556512C2×C414yes—
97#14556501—22no—
98#14556501—22no—
99C4×#10596831—22no—
100C8×Dic73—22no—
101C8×Dic73C2×C414yescomplemented
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498D411yescharacteristic
108#14556498D411yescharacteristic
109#14556498D411yescharacteristic
110#14556498D411yescharacteristic
111C22×D4×C73C2311yescharacteristic
112C22×C8×C73C2311yescharacteristic
113C22×C8×C73C2311yescharacteristic
114C2×C4⋊C4×C73—21no—
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73—21no—
120C2×C42×C73C2311yescharacteristic
121#102×C73—22no—
122#102×C73C2×C414yes—
123#97×C73—22no—
124#95×C73—21no—
125C2×Dic146—21no—
126C2×Dic146—21no—
127C2×Dic146—21no—
128C2×Dic146—21no—
129C2×Dic146—21no—
130C2×Dic146C22×C412yes—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—42no—
136C22×Dic73—81no—
137C22×Dic73—81no—
138C22×Dic73C2×D411yescharacteristic
139C22×Dic73C2×D411yescharacteristic
140C22×Dic73C2×D411yescharacteristic
141C22×Dic73C2×D411yescharacteristic
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831C22×C412yes—
147C2×#10596831#4112yes—
148C4⋊Dic73—21no—
149C4⋊Dic73—24no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73C22×C412yes—
155#11924007—24no—
156#11924007—42no—
157#11924007—81no—
158#11924007—81no—
159#11924007—81no—
160#11924007—81no—
161#11924007—81no—
162C22⋊Dic73—24no—
163C22⋊Dic73—24no—
164C22⋊Dic73—42no—
165C4×Dic73—42no—
166C4×Dic73—81no—
167C4×Dic73—81no—
168C4×Dic73C22×C412yes—
169C4×Dic73#4112yes—
170C4×Dic73#4112yes—
171C4×Dic73#4112yes—
172C24×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—21no—
175C2×D4×C73—21no—
176C2×D4×C73—21no—
177C2×D4×C73—21no—
178C2×D4×C73C22×C412yes—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2411yescharacteristic
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73C22×C412yes—
190C2×C8×C73#4112yes—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—81no—
197C4⋊C4×C73C22×C412yes—
198C22⋊C4×C73—81no—
199C22⋊C4×C73—81no—
200C42×C73—21no—
201C42×C73—21no—
202C23×C73—22no—
203C23×C73—41no—
204C23×C73—41no—
205C23×C73—41no—
206C23×C73—41no—
207C23×C73—41no—
208C23×C73—41no—
209C23×C73C22×D411yescharacteristic
210D4×C73—22no—
211D4×C73—22no—
212D4×C73—41no—
213D4×C73—41no—
214C2×C4×C73—22no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73C23×C411yescharacteristic
230C2×C4×C73C2×#4111yescharacteristic
231C2×C4×C73C2×#4111yescharacteristic
232C2×C4×C73C2×#4111yescharacteristic
233C2×C4×C73C2×#4111yescharacteristic
234C2×C4×C73C2×#4111yescharacteristic
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—22no—
244C2×Dic73—22no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253C2×Dic73—41no—
254C2×Dic73—41no—
255C2×Dic73—84no—
256C2×Dic73C4×D412yes—
257C2×Dic73C4×D412yes—
258C2×Dic73#12412yes—
259C2×Dic73#12412yes—
260Dic146—22no—
261Dic146—22no—
262Dic146—41no—
263Dic146—41no—
264C8×C73—22no—
265C8×C73—22no—
266#10596831—22no—
267#10596831—22no—
268C22×C73—42no—
269C22×C73—42no—
270C22×C73—42no—
271C22×C73—81no—
272C22×C73—81no—
273C22×C73—81no—
274C22×C73—81no—
275C22×C73C2×C4×D411yescharacteristic
276C22×C73C2×#12411yescharacteristic
277C22×C73#53211yescharacteristic
278C22×C73#57611yescharacteristic
279C22×C73#57711yescharacteristic
280C22×C73#57711yescharacteristic
281C22×C73#57811yescharacteristic
282C4×C73—41no—
283C4×C73—41no—
284C4×C73—42no—
285C4×C73—81no—
286C4×C73—81no—
287C4×C73C4×#4111yescharacteristic
288C4×C73C4×#4111yescharacteristic
289C4×C73#52911yescharacteristic
290C4×C73#52911yescharacteristic
291Dic73—22no—
292Dic73—22no—
293Dic73—22no—
294Dic73—22no—
295Dic73—42no—
296Dic73—42no—
297Dic73—81no—
298Dic73—81no—
299#21643—731nomaximal, Sylow
300C2×C73—82no—
301C2×C73C4×#12411yescharacteristic
302C2×C73#295111yescharacteristic
303C2×C73#295211yescharacteristic
304C2×C73#313611yescharacteristic
305C2×C73#313711yescharacteristic
306C2×C73#317811yescharacteristic
307C2×C73#317911yescharacteristic
308C2×#488—731no—
309#2330—731no—
310#2326—731no—
311#1992—731no—
312#1959—731no—
313#1936D7311yescharacteristic
314#1935—731no—
315#1934—731no—
316#1933—731no—
317#1834—731no—
318#1763—731no—
319#1762—731no—
320C4×#103—731no—
321C4×#102—731no—
322#1726—731no—
323C73#2164311yescharacteristic, complemented, Sylow
324C2×#125—731no—
325C2×#124—731no—
326C2×C4×Q8—731no—
327C2×C4×D4—731no—
328#488—738no—
329C2×#103—731no—
330C2×#103—731no—
331C2×#103—731no—
332C2×#103—731no—
333C2×#102—731no—
334C2×#102—731no—
335C2×#102C2×D7311yescharacteristic
336C2×#102C2×D7311yescharacteristic
337C2×#97—731no—
338C2×#97—731no—
339C2×#97C2×D7311yescharacteristic
340C2×C4×C8—731no—
341C2×C4×C8—731no—
342C2×C4×C8—731no—
343#391—731no—
344#390C2×D7311yescharacteristic
345#389—731no—
346#389—1461no—
347#389—1461no—
348#389C2×D7311yescharacteristic
349#388—1461no—
350#388—1461no—
351#387—1461no—
352#387—1461no—
353#385—1461no—
354#385—1461no—
355#384—731no—
356#384—731no—
357C4×C4⋊C4—731no—
358C4×C4⋊C4—731no—
359#376—731no—
360#340—731no—
361#340—731no—
362#340—731no—
363#340—731no—
364#340—731no—
365#340—731no—
366#340C2×D7311yescharacteristic
367#340C2×D7311yescharacteristic
368C22×Q8—731no—
369C22×D4C22×D7311yescharacteristic
370C23×C4—1461no—
371C22×C8—731no—
372C22×C8—731no—
373C22×C8C22×D7311yescharacteristic
374C22×C8C22×D7311yescharacteristic
375#125—734no—
376#125—1462no—
377#124—734no—
378#124—1462no—
379C4×Q8—1462no—
380C4×Q8—1462no—
381C4×D4—1462no—
382C4×D4—1462no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—731no—
385C2×C4⋊C4—731no—
386C2×C4⋊C4—731no—
387C2×C4⋊C4—1461no—
388C2×C4⋊C4—1461no—
389C2×C4⋊C4—1461no—
390C2×C4⋊C4—1461no—
391C2×C4⋊C4—1461no—
392C2×C4⋊C4—1461no—
393C2×C4⋊C4—1461no—
394C2×C4⋊C4—1461no—
395C2×C4⋊C4C22×D7311yescharacteristic
396C2×C4⋊C4C22×D7311yescharacteristic
397C2×C4⋊C4C22×D7311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—1461no—
401C2×C22⋊C4—1461no—
402C2×C22⋊C4—1461no—
403C2×C42—731no—
404C2×C42—731no—
405C2×C42—1461no—
406C2×C42—1461no—
407C2×C42—1461no—
408C2×C42C22×D7311yescharacteristic
409#103—734no—
410#103—734no—
411#103—1462no—
412#103—1462no—
413#102—22no—
414#102—734no—
415#102—1462no—
416#102C4×D7314yes—
417#97—22no—
418#97—1462no—
419#97—1462no—
420C4×C8—734no—
421C4×C8—1462no—
422C4×C8—1462no—
423#95—21no—
424#95—731no—
425#95—731no—
426#95—731no—
427#95—731no—
428#95—1461no—
429#95—1461no—
430#95—1461no—
431#95—1461no—
432#95—1461no—
433C24—21no—
434C2×Q8—732no—
435C2×Q8—1461no—
436C2×Q8—1461no—
437C2×Q8—1461no—
438C2×Q8—1461no—
439C2×Q8—1461no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4C2×C4×D7312yes—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—2922no—
450C22×C4—5841no—
451C22×C4—5841no—
452C22×C4—731no—
453C22×C4—731no—
454C22×C4—731no—
455C22×C4—731no—
456C22×C4—1461no—
457C22×C4—1461no—
458C22×C4—1461no—
459C22×C4—1461no—
460C22×C4D4×D7311yescharacteristic
461C22×C4D4×D7311yescharacteristic
462C22×C4C23×D7311yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—732no—
468C2×C8—732no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8C2×C4×D7312yes—
474C2×C8#1192402712yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—81no—
481C4⋊C4—2922no—
482C4⋊C4—5841no—
483C4⋊C4—5841no—
484C4⋊C4—5841no—
485C4⋊C4—5841no—
486C4⋊C4—5841no—
487C4⋊C4—732no—
488C4⋊C4—1464no—
489C4⋊C4—1464no—
490C4⋊C4—1461no—
491C4⋊C4—1461no—
492C4⋊C4—1461no—
493C4⋊C4—1461no—
494C4⋊C4—1461no—
495C4⋊C4C2×C4×D7312yes—
496C22⋊C4—81no—
497C22⋊C4—81no—
498C22⋊C4—2922no—
499C22⋊C4—1464no—
500C22⋊C4—1464no—
501C42—21no—
502C42—21no—
503C42—2922no—
504C42—5841no—
505C42—5841no—
506C42—732no—
507C42—732no—
508C42—732no—
509C42—732no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23C2×D4×D7311yescharacteristic
518Q8—2921no—
519Q8—2921no—
520Q8—1462no—
521Q8—1462no—
522D4—22no—
523D4—22no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—2921no—
551C2×C4—5844no—
552C2×C4—732no—
553C2×C4—732no—
554C2×C4—732no—
555C2×C4—732no—
556C2×C4—1462no—
557C2×C4—1462no—
558C2×C4—1461no—
559C2×C4—1461no—
560C2×C4—1461no—
561C2×C4—1461no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4C22×C4×D7311yescharacteristic
567C2×C4#41×D7311yescharacteristic
568C2×C4#41×D7311yescharacteristic
569C2×C4#41×D7311yescharacteristic
570C2×C4#41×D7311yescharacteristic
571C2×C4C2×#1192402711yescharacteristic
572C8—22no—
573C8—22no—
574C8—1462no—
575C8—1462no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22C4×D4×D7311yescharacteristic
584C22#124×D7311yescharacteristic
585C22#1798913211yescharacteristic
586C22#1798939111yescharacteristic
587C22#1798939711yescharacteristic
588C22#1798939711yescharacteristic
589C22#1798940311yescharacteristic
590C4—41no—
591C4—42no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—2922no—
596C4—2922no—
597C4—5841no—
598C4—5841no—
599C4—1462no—
600C4—1462no—
601C4—1462no—
602C4—1462no—
603C4C4×#1192402711yescharacteristic
604C4#1798905511yescharacteristic
605C4#1798911411yescharacteristic
606C4#1798912011yescharacteristic
607C2—82no—
608C2#2261247211yescharacteristic
609C2#2261880311yescharacteristic
610C2#2261881311yescharacteristic
611C2#2262028611yescharacteristic
612C2#2262029311yescharacteristic
613C2#2262059211yescharacteristic
614C2#2262061511yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1936C2
socleC23×C73C22×D4
prime radicalC22×D4×C73C23
cosocleC22×C4×C73C24
hypercenter#1936D73
hypocenterC73#21643
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
2. #22612671C2semidirect
4. #22610898C2semidirect
6. #22610621C2semidirect
8. #22610606C2semidirect
9. #22610057C2semidirect
10. #22609760C2semidirect
12. #22609750C2semidirect
14. #22609619C2semidirect
20. #17988940C4semidirect
65. #14556582C2×C4semidirect
92. #14556516C2×C4semidirect
94. #14556514C2×C4semidirect
101. C8×Dic73C2×C4semidirect
323. C73#21643semidirect

Maximal subgroups

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

subgroupindex
C2×#179889402
#226126712
#226126412
#226108982
#226107462
#226106212
#226106172
#226106062
#226100572
#226097602
#226097582
#226097502
#102×Dic732
#226096192
C73×#19362
#2164373