Finite Group Databasebeta

← #33098090

Subgroups — #33098090

Order 18688.

836 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
1C2×#17988865C211yesmaximal, characteristic
2#22612502C211yesmaximal, characteristic, complemented
3#22612393C211yesmaximal, characteristic
4#22610881C211yesmaximal, characteristic, complemented
5#22610693C211yesmaximal, characteristic, complemented
6#22610669C211yesmaximal, characteristic, complemented
7#22610666C211yesmaximal, characteristic, complemented
8#22610631C211yesmaximal, characteristic
9#22610561C211yesmaximal, characteristic
10#22610560C211yesmaximal, characteristic
11#22610522C211yesmaximal, characteristic, complemented
12#22610521C211yesmaximal, characteristic, complemented
13#22609929C211yesmaximal, characteristic
14#22609785C211yesmaximal, characteristic, complemented
15C73×#1936C211yesmaximal, characteristic
16C2×#14556590C2211yescharacteristic
17C2×#14556556—21no—
18C2×D4×Dic73C2211yescharacteristic
19C2×#14556547—21no—
20#17988865C418yescomplemented
21C2×#14556525C2211yescharacteristic
22C2×#14556524C2211yescharacteristic
23C2×#14556523C2211yescharacteristic
24C2×#14556522C2211yescharacteristic
25C2×#14556520C2211yescharacteristic
26C2×#14556520C2211yescharacteristic
27C2×#14556512C2211yescharacteristic
28C2×#14556512C2211yescharacteristic
29C2×#14556502C2211yescharacteristic
30#17988491—21no—
31#17988490C2211yescharacteristic
32#17988485C2211yescharacteristic
33#17988485C2211yescharacteristic
34#17988483C2211yescharacteristic
35#17988482—21no—
36#17988481—21no—
37#17988475—21no—
38#17988456C2211yescharacteristic
39C4⋊C4×Dic73C2211yescharacteristic
40C4⋊C4×Dic73C2211yescharacteristic
41C4⋊C4×Dic73C2211yescharacteristic
42#17988438—21no—
43C22⋊C4×Dic73—21no—
44C42×Dic73C2211yescharacteristic
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53C2×#102×C73C2211yescharacteristic
54C2×#102×C73C2211yescharacteristic
55C2×#97×C73C2211yescharacteristic
56#390×C73C2211yescharacteristic
57#389×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60C22×Dic146—21no—
61C23×Dic73—21no—
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64#14556590—22no—
65#14556590C2×C414yes—
66#14556556—44no—
67D4×Dic73—22no—
68D4×Dic73C2×C414yes—
69#14556547—44no—
70C2×C4⋊Dic73C2311yescharacteristic
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×#11924007—21no—
75C2×#11924007—21no—
76C2×#11924007—21no—
77C2×#11924007—21no—
78C2×#11924007—21no—
79C2×#11924007—21no—
80C2×C22⋊Dic73—21no—
81C2×C22⋊Dic73—21no—
82C2×C22⋊Dic73—21no—
83C2×C4×Dic73—21no—
84C2×C4×Dic73—21no—
85C2×C4×Dic73—21no—
86C2×C4×Dic73D411yescharacteristic
87C2×C4×Dic73D411yescharacteristic
88C2×C4×Dic73D411yescharacteristic
89C2×C4×Dic73D411yescharacteristic
90C2×C4×Dic73C2311yescharacteristic
91C2×C4×Dic73C2311yescharacteristic
92#14556525C2×C414yes—
93#14556524C2×C414yes—
94#14556523—41no—
95#14556522—41no—
96#14556520—22no—
97#14556520C2×C414yes—
98#14556512—41no—
99#14556512C2×C414yes—
100#14556502—41no—
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107C22×D4×C73C2311yescharacteristic
108C22×C8×C73C2311yescharacteristic
109C22×C8×C73C2311yescharacteristic
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73C2311yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C22⋊C4×C73—21no—
115C2×C22⋊C4×C73—21no—
116C2×C42×C73C2311yescharacteristic
117#102×C73—41no—
118#102×C73C2×C414yes—
119#97×C73—41no—
120#95×C73—21no—
121C2×Dic146—24no—
122C2×Dic146—42no—
123C2×Dic146—42no—
124C22×Dic73—21no—
125C22×Dic73—21no—
126C22×Dic73—24no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—42no—
130C22×Dic73—42no—
131C22×Dic73C2×D411yescharacteristic
132C22×Dic73C2×D411yescharacteristic
133C22×Dic73C2×D411yescharacteristic
134C22×Dic73C2×D411yescharacteristic
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831C22×C412yes—
141C4⋊Dic73—21no—
142C4⋊Dic73—21no—
143C4⋊Dic73—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73C22×C412yes—
148C4⋊Dic73C22×C412yes—
149#11924007—24no—
150#11924007—42no—
151#11924007—42no—
152#11924007—42no—
153#11924007—42no—
154#11924007—42no—
155C22⋊Dic73—24no—
156C22⋊Dic73—42no—
157C22⋊Dic73—42no—
158C4×Dic73—21no—
159C4×Dic73—21no—
160C4×Dic73—22no—
161C4×Dic73—22no—
162C4×Dic73—22no—
163C4×Dic73—41no—
164C4×Dic73—42no—
165C4×Dic73—42no—
166C4×Dic73—42no—
167C4×Dic73C22×C412yes—
168C4×Dic73#4112yes—
169C24×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—21no—
175C2×D4×C73C22×C412yes—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2411yescharacteristic
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73C22×C412yes—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—42no—
194C4⋊C4×C73C22×C412yes—
195C22⋊C4×C73—42no—
196C22⋊C4×C73—42no—
197C42×C73—21no—
198C42×C73—21no—
199C23×C73—22no—
200C23×C73—41no—
201C23×C73—41no—
202C23×C73—41no—
203C23×C73—41no—
204C23×C73—41no—
205C23×C73—41no—
206C23×C73C22×D411yescharacteristic
207D4×C73—22no—
208D4×C73—22no—
209D4×C73—41no—
210D4×C73—41no—
211C2×C4×C73—22no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73C23×C411yescharacteristic
227C2×C4×C73C2×#4111yescharacteristic
228C2×C4×C73H(5,𝔽2)11yescharacteristic
229C2×C4×C732−1+411yescharacteristic
230C2×C4×C732−1+411yescharacteristic
231C2×C4×C732−1+411yescharacteristic
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—22no—
237C2×Dic73—22no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—48no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73C4×D412yes—
253C2×Dic73C4×D412yes—
254C2×Dic73AGL(1,ℤ/8)12yes—
255C2×Dic73AGL(1,ℤ/8)12yes—
256C2×Dic73#13712yes—
257Dic146—48no—
258C8×C73—22no—
259C8×C73—41no—
260#10596831—22no—
261#10596831—41no—
262C22×C73—42no—
263C22×C73—42no—
264C22×C73—42no—
265C22×C73—81no—
266C22×C73—81no—
267C22×C73—81no—
268C22×C73—81no—
269C22×C73C2×C4×D411yescharacteristic
270C22×C73#53611yescharacteristic
271C22×C73#53711yescharacteristic
272C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C73C2×#13711yescharacteristic
275C22×C73#57511yescharacteristic
276C4×C73—42no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—81no—
280C4×C73—81no—
281C4×C73#51911yescharacteristic
282C4×C73#52011yescharacteristic
283C4×C73#54111yescharacteristic
284C4×C73#54211yescharacteristic
285Dic73—22no—
286Dic73—22no—
287Dic73—42no—
288Dic73—42no—
289Dic73—41no—
290Dic73—81no—
291Dic73—81no—
292Dic73#44214yes—
293#22116—731nomaximal, Sylow
294C2×C73—82no—
295C2×C73#232311yescharacteristic
296C2×C73C2×#44211yescharacteristic
297C2×C73C4×#13711yescharacteristic
298C2×C73#323511yescharacteristic
299C2×C73#323911yescharacteristic
300C2×C73#325111yescharacteristic
301C2×C73#325411yescharacteristic
302C2×#474—731no—
303C4×C4⋊Q8—731no—
304#2293—731no—
305#1988—731no—
306#1948—731no—
307#1943—731no—
308#1943—731no—
309#1936—731no—
310#1936D7311yescharacteristic
311#1926—731no—
312#1926—731no—
313#1921—731no—
314#1921—731no—
315#1802—731no—
316#1767—731no—
317C73#2211611yescharacteristic, complemented, Sylow
318C2×C4⋊Q8—731no—
319C2×C4×Q8—1461no—
320C2×C4×D4—731no—
321C2×#117—1461no—
322#474—738no—
323C2×#107—731no—
324C2×#107—731no—
325C2×#106—731no—
326C2×#106—731no—
327C2×C4⋊C8—731no—
328C2×C4⋊C8—731no—
329C2×#102—731no—
330C2×#102—731no—
331C2×#102C2×D7311yescharacteristic
332C2×#102C2×D7311yescharacteristic
333C2×#97—731no—
334C2×#97C2×D7311yescharacteristic
335#391—1461no—
336#390—731no—
337#390C2×D7311yescharacteristic
338#389—731no—
339#389—731no—
340#389—731no—
341#389—1461no—
342#389C2×D7311yescharacteristic
343#388—1461no—
344#388—1461no—
345#384—731no—
346C4×C4⋊C4—731no—
347C4×C4⋊C4—731no—
348C4×C4⋊C4—731no—
349C4×C4⋊C4—1461no—
350C4×C22⋊C4—1461no—
351C43—731no—
352#340—731no—
353#340—731no—
354#340—731no—
355#340—731no—
356#340—731no—
357#340—731no—
358#340C2×D7311yescharacteristic
359#340C2×D7311yescharacteristic
360#336—731no—
361#336—731no—
362C22×Q8—1461no—
363C22×D4C22×D7311yescharacteristic
364C23×C4—1461no—
365C22×C8—731no—
366C22×C8—731no—
367C22×C8C22×D7311yescharacteristic
368C22×C8C22×D7311yescharacteristic
369C4⋊Q8—734no—
370C4⋊Q8—1462no—
371C4×Q8—2924no—
372C4×D4—734no—
373C4×D4—1462no—
374#117—2924no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—731no—
377C2×C4⋊C4—731no—
378C2×C4⋊C4—731no—
379C2×C4⋊C4—731no—
380C2×C4⋊C4—1461no—
381C2×C4⋊C4—1461no—
382C2×C4⋊C4—1461no—
383C2×C4⋊C4—1461no—
384C2×C4⋊C4—1461no—
385C2×C4⋊C4—1461no—
386C2×C4⋊C4C22×D7311yescharacteristic
387C2×C4⋊C4C22×D7311yescharacteristic
388C2×C4⋊C4C22×D7311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—1461no—
392C2×C22⋊C4—1461no—
393C2×C22⋊C4—1461no—
394C2×C42—731no—
395C2×C42—731no—
396C2×C42—731no—
397C2×C42—731no—
398C2×C42—731no—
399C2×C42—731no—
400C2×C42—1461no—
401C2×C42—1461no—
402C2×C42—1461no—
403C2×C42C22×D7311yescharacteristic
404#107—734no—
405#107—734no—
406#106—2921no—
407#106—2921no—
408C4⋊C8—734no—
409C4⋊C8—1462no—
410#102—41no—
411#102—2921no—
412#102—734no—
413#102C4×D7314yes—
414#97—41no—
415#97—2921no—
416#95—21no—
417#95—1461no—
418#95—1461no—
419#95—1461no—
420#95—1461no—
421#95—1461no—
422#95—1461no—
423C24—21no—
424C2×Q8—2922no—
425C2×Q8—2922no—
426C2×Q8—1464no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4C2×C4×D7312yes—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—2922no—
437C22×C4—2922no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4—731no—
441C22×C4—731no—
442C22×C4—1461no—
443C22×C4—1461no—
444C22×C4—1464no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4D4×D7311yescharacteristic
448C22×C4D4×D7311yescharacteristic
449C22×C4C23×D7311yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—732no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8—1461no—
460C2×C8—1461no—
461C2×C8C2×C4×D7312yes—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—42no—
468C4⋊C4—2922no—
469C4⋊C4—2922no—
470C4⋊C4—2922no—
471C4⋊C4—2922no—
472C4⋊C4—2922no—
473C4⋊C4—732no—
474C4⋊C4—732no—
475C4⋊C4—1464no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4C2×C4×D7312yes—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—2922no—
486C22⋊C4—2922no—
487C22⋊C4—1464no—
488C42—21no—
489C42—21no—
490C42—2921no—
491C42—2922no—
492C42—2922no—
493C42—2922no—
494C42—732no—
495C42—732no—
496C42—1462no—
497C42—1462no—
498C42—1462no—
499C42—1461no—
500C42—1461no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23C2×D4×D7311yescharacteristic
509Q8—2928no—
510D4—22no—
511D4—22no—
512D4—41no—
513D4—41no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—2921no—
530C2×C4—2921no—
531C2×C4—2921no—
532C2×C4—2921no—
533C2×C4—2928no—
534C2×C4—2921no—
535C2×C4—2921no—
536C2×C4—2921no—
537C2×C4—2921no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—732no—
541C2×C4—732no—
542C2×C4—732no—
543C2×C4—732no—
544C2×C4—732no—
545C2×C4—1461no—
546C2×C4—1461no—
547C2×C4—1462no—
548C2×C4—1462no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4C22×C4×D7311yescharacteristic
555C2×C4#41×D7311yescharacteristic
556C2×C4#1455663611yescharacteristic
557C2×C4#1455663811yescharacteristic
558C2×C4#1455663811yescharacteristic
559C2×C4#1455663811yescharacteristic
560C8—22no—
561C8—41no—
562C8—2921no—
563C8—1462no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22C4×D4×D7311yescharacteristic
572C22#1798915711yescharacteristic
573C22#1798916411yescharacteristic
574C22AGL(1,ℤ/8)×D7311yescharacteristic
575C22AGL(1,ℤ/8)×D7311yescharacteristic
576C22#137×D7311yescharacteristic
577C22#1798938311yescharacteristic
578C4—42no—
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—2922no—
584C4—2922no—
585C4—2921no—
586C4—5841no—
587C4—5841no—
588C4—734no—
589C4—1462no—
590C4—1462no—
591C4#1798906411yescharacteristic
592C4#1798906611yescharacteristic
593C4#1798919411yescharacteristic
594C4#1798920511yescharacteristic
595C2—82no—
596C2#2261260611yescharacteristic
597C2#442×D7311yescharacteristic
598C2#2261875311yescharacteristic
599C2#2262112411yescharacteristic
600C2#2262115711yescharacteristic
601C2#2262128611yescharacteristic
602C2#2262131311yescharacteristic
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#22116
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. #22612502C2semidirect
4. #22610881C2semidirect
5. #22610693C2semidirect
6. #22610669C2semidirect
7. #22610666C2semidirect
11. #22610522C2semidirect
12. #22610521C2semidirect
14. #22609785C2semidirect
20. #17988865C4semidirect
317. C73#22116semidirect

Maximal subgroups

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

subgroupindex
C2×#179888652
#226125022
#226123932
#226108812
#226106932
#226106692
#226106662
#226106312
#226105612
#226105602
#226105222
#226105212
#226099292
#226097852
C73×#19362
#2211673