Finite Group Databasebeta

← #33093708

Subgroups — #33093708

Order 18688.

868 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988890C211yesmaximal, characteristic
2#22612671C211yesmaximal, characteristic, complemented
3#22612291C211yesmaximal, characteristic
4#22610887C211yesmaximal, characteristic, complemented
5#22610688C211yesmaximal, characteristic, complemented
6#22610516C211yesmaximal, characteristic, complemented
7#22610181C211yesmaximal, characteristic
8#22610177C211yesmaximal, characteristic
9#22609930C211yesmaximal, characteristic
10#22609827C211yesmaximal, characteristic, complemented
11#107×Dic73C211yesmaximal, characteristic, complemented
12#22609787C211yesmaximal, characteristic, complemented
13#22609755C211yesmaximal, characteristic
14#22609745C211yesmaximal, characteristic
15C73×#1921C211yesmaximal, characteristic, complemented
16C2×#14556582C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18C2×#14556553C2211yescharacteristic
19C2×#14556553C2211yescharacteristic
20#17988890C418yescomplemented
21C2×#14556525C2211yescharacteristic
22C2×#14556524C2211yescharacteristic
23C2×#14556522C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×#14556520C2211yescharacteristic
26C2×#14556513C2211yescharacteristic
27C2×#14556513C2211yescharacteristic
28C2×#14556511C2211yescharacteristic
29C2×#14556511C2211yescharacteristic
30C2×#14556501C2211yescharacteristic
31C2×C8×Dic73C2211yescharacteristic
32#17988485C2211yescharacteristic
33#17988483—21no—
34#17988482—21no—
35#17988472—21no—
36#17988469—21no—
37#17988456C2211yescharacteristic
38C4⋊C4×Dic73C2211yescharacteristic
39C4⋊C4×Dic73C2211yescharacteristic
40C4⋊C4×Dic73C2211yescharacteristic
41C4⋊C4×Dic73C2211yescharacteristic
42C4×#11924005—21no—
43C4×#11924005—21no—
44#17988434—21no—
45#17988433C2211yescharacteristic
46#95×D73—21no—
47#17988350C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988342C2211yescharacteristic
53C2×#107×C73C2211yescharacteristic
54#389×C73C2211yescharacteristic
55C4×C4⋊C4×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60C22×D292C2311yescharacteristic
61C22×C4×D73—21no—
62C22×C4×D73—21no—
63C22×C4×D73—21no—
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66#14556582—22no—
67#14556582C2×C414yescomplemented
68C4×D292—22no—
69C4×D292—22no—
70#14556553—22no—
71#14556553—22no—
72#14556553C2×C414yes—
73#14556553Q814yes—
74C2×C4⋊Dic73—21no—
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C4⋊Dic73C2311yescharacteristic
77C2×C4⋊Dic73C2311yescharacteristic
78C2×#11924007—21no—
79C2×#11924007—21no—
80C2×#11924007—21no—
81C2×#11924007—21no—
82C2×#11924005—21no—
83C2×#11924005—21no—
84C2×#11924005—21no—
85C2×C4×Dic73—21no—
86C2×C4×Dic73—21no—
87C2×C4×Dic73—21no—
88C2×C4×Dic73—21no—
89C2×C4×Dic73C2311yescharacteristic
90C2×C4×Dic73C2311yescharacteristic
91#14556525—22no—
92#14556524—22no—
93#14556522C2×C414yescomplemented
94#14556520—22no—
95#14556520C2×C414yescomplemented
96#14556513—22no—
97#14556513C2×C414yes—
98#14556511—22no—
99#14556511C2×C414yes—
100#14556501—22no—
101C8×Dic73—22no—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498D411yescharacteristic
108#14556498D411yescharacteristic
109#14556498D411yescharacteristic
110#14556498D411yescharacteristic
111C22×C8×C73C2311yescharacteristic
112C22×C8×C73C2311yescharacteristic
113C2×C4⋊C4×C73—21no—
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C42×C73—21no—
119C2×C42×C73C2311yescharacteristic
120#107×C73C2×C414yescomplemented
121#95×C73—21no—
122#95×C73—21no—
123C23×D73—21no—
124C2×D292—21no—
125C2×D292—21no—
126C2×D292—21no—
127C2×D292C22×C412yes—
128C2×D292C2×Q812yes—
129C2×D292#4112yes—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73C2×D411yescharacteristic
134C22×Dic73C2×D411yescharacteristic
135C22×Dic73C2×D411yescharacteristic
136C22×Dic73C2×D411yescharacteristic
137C2×C4×D73—24no—
138C2×C4×D73—24no—
139C2×C4×D73—24no—
140C2×C4×D73—81no—
141C2×C4×D73—81no—
142C2×C4×D73—81no—
143C2×C4×D73—81no—
144C2×C4×D73—81no—
145C2×C4×D73—81no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831C22×C412yes—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73—24no—
155C4⋊Dic73—21no—
156C4⋊Dic73—21no—
157C4⋊Dic73C22×C412yes—
158C4⋊Dic73#4112yes—
159#11924007—24no—
160#11924007—81no—
161#11924007—81no—
162#11924007—81no—
163#11924005—24no—
164#11924005—24no—
165#11924005—24no—
166C4×Dic73—81no—
167C4×Dic73—81no—
168C4×Dic73—81no—
169C4×Dic73—81no—
170C4×Dic73C22×C412yes—
171C4×Dic73C2×Q812yes—
172C4×Dic73#4112yes—
173C4×Dic73#4112yes—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2411yescharacteristic
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73C22×C412yes—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—81no—
193C4⋊C4×C73C22×C412yes—
194C4⋊C4×C73C22×C412yes—
195C4⋊C4×C73C2×Q812yes—
196C42×C73—21no—
197C42×C73—21no—
198C42×C73—81no—
199C23×C73C22×D411yescharacteristic
200C22×D73—22no—
201C22×D73—22no—
202C22×D73—22no—
203C22×D73—41no—
204C22×D73—41no—
205C22×D73—41no—
206C22×D73—41no—
207C2×C4×C73—22no—
208C2×C4×C73—22no—
209C2×C4×C73—22no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
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×C73C23×C411yescharacteristic
226C2×C4×C73C22×Q811yescharacteristic
227C2×C4×C73C2×#4111yescharacteristic
228C2×C4×C73C2×#4111yescharacteristic
229C2×C4×C73C2×#4111yescharacteristic
230C2×C4×C73C2×#4111yescharacteristic
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—22no—
240C2×Dic73—22no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73C4×D412yes—
249C2×Dic73C4×D412yes—
250C2×Dic73C22⋊Q812yes—
251C2×Dic73C22⋊Q812yes—
252D292—22no—
253D292—22no—
254D292—22no—
255D292C4×Q814yes—
256C4×D73—84no—
257C4×D73—84no—
258C4×D73—84no—
259C8×C73—22no—
260C8×C73—41no—
261#10596831—22no—
262#10596831—41no—
263C22×C73C2×C4×D411yescharacteristic
264C22×C73C2×C22⋊Q811yescharacteristic
265C22×C73#52511yescharacteristic
266C22×C73#57611yescharacteristic
267C22×C73#57611yescharacteristic
268C22×C73#57711yescharacteristic
269C22×C73#57811yescharacteristic
270C2×D73—24no—
271C2×D73—42no—
272C2×D73—42no—
273C2×D73—42no—
274C2×D73—42no—
275C2×D73—42no—
276C2×D73—42no—
277C4×C73—42no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—42no—
281C4×C73—42no—
282C4×C73—81no—
283C4×C73C2×C4×Q811yescharacteristic
284C4×C73C4×#4111yescharacteristic
285C4×C73#52911yescharacteristic
286C4×C73#53311yescharacteristic
287Dic73—22no—
288Dic73—22no—
289Dic73—22no—
290Dic73—22no—
291Dic73—42no—
292Dic73—42no—
293Dic73—81no—
294#21620—731nomaximal, Sylow
295C2×C73C4×C22⋊Q811yescharacteristic
296C2×C73#294611yescharacteristic
297C2×C73#295111yescharacteristic
298C2×C73#308111yescharacteristic
299C2×C73#308311yescharacteristic
300C2×C73#312011yescharacteristic
301C2×C73#312211yescharacteristic
302D73—44no—
303C2×#478—731no—
304#2330—731no—
305#2275—731no—
306#1989—731no—
307#1947—731no—
308#1921D7311yescharacteristic, complemented
309#1920—731no—
310#1862—731no—
311#1862—731no—
312#1802—731no—
313#1776—731no—
314C4×#107—731no—
315#1768—731no—
316#1762—731no—
317C4×#102—731no—
318C73#2162011yescharacteristic, complemented, Sylow
319C2×#125—731no—
320C2×C4×D4—731no—
321C2×C4×D4—731no—
322C2×C4×D4—731no—
323#478—738no—
324C2×#107—731no—
325C2×#107—731no—
326C2×#107C2×D7311yescharacteristic
327C2×#106—731no—
328C2×C4⋊C8—731no—
329C2×C4⋊C8—731no—
330C2×#102—731no—
331C2×#102—731no—
332C2×#102—731no—
333C2×#102—731no—
334C2×#97—731no—
335C2×C4×C8—731no—
336#389—731no—
337#389—1461no—
338#389—1461no—
339#389C2×D7311yescharacteristic
340#387—1461no—
341#387—1461no—
342#384—731no—
343C4×C4⋊C4—731no—
344C4×C4⋊C4—731no—
345C4×C4⋊C4—731no—
346C4×C4⋊C4—731no—
347C4×C4⋊C4C2×D7311yescharacteristic
348C4×C22⋊C4—1461no—
349C4×C22⋊C4—1461no—
350C4×C22⋊C4—1461no—
351#376—731no—
352C2×#95—1461no—
353#340—731no—
354#340—731no—
355#340—731no—
356#340—731no—
357#340—731no—
358#340C2×D7311yescharacteristic
359#340C2×D7311yescharacteristic
360#340C2×D7311yescharacteristic
361#336—731no—
362#336C2×D7311yescharacteristic
363C22×D4—731no—
364C23×C4—1461no—
365C23×C4—1461no—
366C23×C4—1461no—
367C22×C8—731no—
368C22×C8—731no—
369C22×C8C22×D7311yescharacteristic
370C22×C8C22×D7311yescharacteristic
371#125—734no—
372#125—1462no—
373C4×D4—734no—
374C4×D4—734no—
375C4×D4—1462no—
376C4×D4—1462no—
377C4×D4—1462no—
378C4×D4—1462no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—731no—
381C2×C4⋊C4—731no—
382C2×C4⋊C4—731no—
383C2×C4⋊C4—1461no—
384C2×C4⋊C4—1461no—
385C2×C4⋊C4—1461no—
386C2×C4⋊C4—1461no—
387C2×C4⋊C4—1461no—
388C2×C4⋊C4C22×D7311yescharacteristic
389C2×C4⋊C4C22×D7311yescharacteristic
390C2×C4⋊C4C22×D7311yescharacteristic
391C2×C4⋊C4C22×D7311yescharacteristic
392C2×C22⋊C4—1461no—
393C2×C22⋊C4—1461no—
394C2×C22⋊C4—1461no—
395C2×C42—21no—
396C2×C42—731no—
397C2×C42—731no—
398C2×C42—1461no—
399C2×C42—1461no—
400C2×C42—1461no—
401C2×C42—1461no—
402C2×C42C22×D7311yescharacteristic
403#107—1462no—
404#107—1462no—
405#107C4×D7314yescomplemented
406#106—734no—
407C4⋊C8—734no—
408C4⋊C8—1462no—
409#102—734no—
410#102—734no—
411#102—1462no—
412#102—1462no—
413#97—1462no—
414C4×C8—1462no—
415#95—21no—
416#95—21no—
417#95—731no—
418#95—731no—
419#95—731no—
420#95—731no—
421#95—1461no—
422#95—1461no—
423#95—1461no—
424#95—1461no—
425#95—1461no—
426C24—1461no—
427C2×D4—732no—
428C2×D4—732no—
429C2×D4—732no—
430C2×D4—1461no—
431C2×D4—1461no—
432C2×D4—1461no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—5841no—
438C22×C4—5841no—
439C22×C4—5841no—
440C22×C4—5841no—
441C22×C4—5841no—
442C22×C4—5841no—
443C22×C4—731no—
444C22×C4—731no—
445C22×C4—731no—
446C22×C4—731no—
447C22×C4—1464no—
448C22×C4—1464no—
449C22×C4—1464no—
450C22×C4—1461no—
451C22×C4—1461no—
452C22×C4—1461no—
453C22×C4D4×D7311yescharacteristic
454C22×C4D4×D7311yescharacteristic
455C22×C4C23×D7311yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—732no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8C2×C4×D7312yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—81no—
474C4⋊C4—5841no—
475C4⋊C4—5841no—
476C4⋊C4—5841no—
477C4⋊C4—732no—
478C4⋊C4—732no—
479C4⋊C4—1464no—
480C4⋊C4—1464no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C4⋊C4C2×C4×D7312yes—
486C4⋊C4C2×C4×D7312yes—
487C4⋊C4Q8×D7312yes—
488C22⋊C4—1464no—
489C22⋊C4—1464no—
490C22⋊C4—1464no—
491C42—21no—
492C42—21no—
493C42—81no—
494C42—5841no—
495C42—5841no—
496C42—5841no—
497C42—5841no—
498C42—732no—
499C42—732no—
500C42—732no—
501C42—732no—
502C23—2921no—
503C23—2921no—
504C23—2921no—
505C23—2921no—
506C23—1462no—
507C23—1462no—
508C23—1462no—
509C23C2×D4×D7311yescharacteristic
510D4—734no—
511D4—1462no—
512D4—1462no—
513D4—1462no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—2921no—
533C2×C4—2921no—
534C2×C4—2921no—
535C2×C4—2921no—
536C2×C4—2921no—
537C2×C4—2921no—
538C2×C4—2921no—
539C2×C4—5844no—
540C2×C4—5844no—
541C2×C4—5844no—
542C2×C4—732no—
543C2×C4—732no—
544C2×C4—732no—
545C2×C4—732no—
546C2×C4—1462no—
547C2×C4—1462no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4—1461no—
556C2×C4C22×C4×D7311yescharacteristic
557C2×C4C2×Q8×D7311yescharacteristic
558C2×C4#41×D7311yescharacteristic
559C2×C4#41×D7311yescharacteristic
560C2×C4#41×D7311yescharacteristic
561C2×C4#41×D7311yescharacteristic
562C8—22no—
563C8—41no—
564C8—2921no—
565C8—1462no—
566C22—2922no—
567C22—2922no—
568C22—2922no—
569C22—2922no—
570C22—2922no—
571C22—2922no—
572C22—1464no—
573C22C4×D4×D7311yescharacteristic
574C22C22⋊Q8×D7311yescharacteristic
575C22#1798909511yescharacteristic
576C22#1798938911yescharacteristic
577C22#1798939111yescharacteristic
578C22#1798939711yescharacteristic
579C22#1798940011yescharacteristic
580C4—41no—
581C4—42no—
582C4—42no—
583C4—42no—
584C4—41no—
585C4—81no—
586C4—2922no—
587C4—2922no—
588C4—5841no—
589C4—1462no—
590C4—1462no—
591C4—1462no—
592C4—1462no—
593C4C4×Q8×D7311yescharacteristic
594C4#1798905511yescharacteristic
595C4#1798912011yescharacteristic
596C4#1798914311yescharacteristic
597C2—2924no—
598C2#2261246511yescharacteristic
599C2#2261876011yescharacteristic
600C2#2261880611yescharacteristic
601C2#2261975911yescharacteristic
602C2#2261977911yescharacteristic
603C2#2262014011yescharacteristic
604C2#2262017011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1921C2
socleC23×C73C22×D4
prime radicalC22×D292C23
cosocleC22×C4×C73C24
hypercenter#1921D73
hypocenterC73#21620
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
2. #22612671C2semidirect
4. #22610887C2semidirect
5. #22610688C2semidirect
6. #22610516C2semidirect
10. #22609827C2semidirect
11. #107×Dic73C2semidirect
12. #22609787C2semidirect
15. C73×#1921C2semidirect
20. #17988890C4semidirect
67. #14556582C2×C4semidirect
93. #14556522C2×C4semidirect
95. #14556520C2×C4semidirect
120. #107×C73C2×C4semidirect
308. #1921D73semidirect
318. C73#21620semidirect
405. #107C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179888902
#226126712
#226122912
#226108872
#226106882
#226105162
#226101812
#226101772
#226099302
#226098272
#107×Dic732
#226097872
#226097552
#226097452
C73×#19212
#2162073