Finite Group Databasebeta

← #33095613

Subgroups — #33095613

Order 18688.

1102 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989115C211yesmaximal, characteristic
2C2×#17988643C211yesmaximal, characteristic, complemented
3C2×#17988609C211yesmaximal, characteristic, complemented
4#22610869C212yesmaximal, complemented
5#22610727C212yesmaximal, complemented
6#22610227C212yesmaximal, complemented
7#22610225C212yesmaximal, complemented
8#22609915C211yesmaximal, characteristic, complemented
9#22609912C211yesmaximal, characteristic, complemented
10#22609912C211yesmaximal, characteristic, complemented
11C73×#1798C211yesmaximal, characteristic, complemented
12C22×#11924011C2212yes—
13#17989115—24no—
14#17989115—24no—
15C2×#14556586C411yescharacteristic
16C2×#14556584C411yescharacteristic
17C2×#14556581C411yescharacteristic
18C2×#14556577C411yescharacteristic
19C2×#14556576C411yescharacteristic
20C2×#14556573C411yescharacteristic
21C2×#14556569C411yescharacteristic
22C2×#14556564C411yescharacteristic
23C2×C4×Dic146C2211yescharacteristic
24C2×C4×D292C2211yescharacteristic
25C2×C4×C22⋊D73C2211yescharacteristic
26C2×C4×C22⋊D73C2211yescharacteristic
27C2×#14556548C2211yescharacteristic
28C2×C42×D73C2211yescharacteristic
29#17988643—24no—
30#17988609—24no—
31C2×C4⋊#10596831C2211yescharacteristic
32C2×C4⋊#10596831C2211yescharacteristic
33C2×#14556520C2212yes—
34C2×C22⋊#10596831C2212yes—
35C2×#14556503C2212yes—
36C2×#14556503C2212yes—
37C2×#14556503C2212yes—
38C2×#14556501C2212yes—
39#17988342C2212yes—
40#17988341C2212yes—
41#17988341C2212yes—
42C2×#117×C73C2211yescharacteristic
43C2×C4⋊C8×C73C2211yescharacteristic
44C2×C4⋊C8×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2212yes—
46#336×C73C2212yes—
47C22×Dic146C2×C411yescharacteristic
48C22×D292C2×C411yescharacteristic
49C22×C22⋊D73C2×C411yescharacteristic
50C22×C22⋊D73C2×C411yescharacteristic
51C22×C4×D73C2×C411yescharacteristic
52C22×C4×D73C2×C411yescharacteristic
53C22×C4×D73C2311yescharacteristic
54C22×C4×D73C2311yescharacteristic
55C2×#11924011—24no—
56C2×#11924011—42no—
57C2×#11924011—42no—
58C22×#10596831C2312yes—
59C22×#10596831C2312yes—
60#14556586—24no—
61#14556584—24no—
62#14556581—24no—
63#14556577—24no—
64#14556576—24no—
65#14556573—24no—
66#14556569—24no—
67#14556564—24no—
68C4×Dic146—22no—
69C4×Dic146—22no—
70C4×D292—22no—
71C4×D292—22no—
72C4×C22⋊D73—22no—
73C4×C22⋊D73—22no—
74C4×C22⋊D73—22no—
75C4×C22⋊D73—22no—
76#14556548—22no—
77#14556548—22no—
78C2×C4⋊Dic73C2×C411yescharacteristic
79C2×C4⋊Dic73C2×C411yescharacteristic
80C2×#11924007C2×C411yescharacteristic
81C2×#11924007C2×C411yescharacteristic
82C2×#11924007C2×C411yescharacteristic
83C2×#11924007C2×C411yescharacteristic
84C2×#11924007C2×C411yescharacteristic
85C2×#11924007C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×#11924005C2×C411yescharacteristic
89C2×#11924005C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×#11924005C2×C411yescharacteristic
93C2×#11924005C2×C411yescharacteristic
94C2×C4×Dic73C2×C411yescharacteristic
95C2×C4×Dic73C2×C411yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98C42×D73D414yes—
99C42×D73D414yes—
100C4⋊#10596831—22no—
101C4⋊#10596831—22no—
102#14556520—24no—
103C22⋊#10596831—42no—
104#14556503—24no—
105#14556503—42no—
106#14556503—42no—
107#14556501—24no—
108C23×C4×C73C2311yescharacteristic
109C22×C8×C73C2312yes—
110C22×C8×C73C2312yes—
111#117×C73—22no—
112#117×C73—22no—
113C2×C4⋊C4×C73C2×C411yescharacteristic
114C2×C4⋊C4×C73C2×C411yescharacteristic
115C2×C22⋊C4×C73C2×C411yescharacteristic
116C2×C22⋊C4×C73C2×C411yescharacteristic
117C2×C42×C73C2311yescharacteristic
118C2×C42×C73C2311yescharacteristic
119C4⋊C8×C73—22no—
120C4⋊C8×C73—22no—
121C22⋊C8×C73—42no—
122C23×D73C22×C411yescharacteristic
123C23×D73C22×C411yescharacteristic
124C2×Dic146—22no—
125C2×Dic146—42no—
126C2×D292—22no—
127C2×D292—42no—
128C2×C22⋊D73—22no—
129C2×C22⋊D73—22no—
130C2×C22⋊D73—42no—
131C2×C22⋊D73—42no—
132C22×Dic73C22×C411yescharacteristic
133C22×Dic73C22×C411yescharacteristic
134C22×Dic73C22×C411yescharacteristic
135C22×Dic73C22×C411yescharacteristic
136C22×Dic73C22×C411yescharacteristic
137C22×Dic73C22×C411yescharacteristic
138C2×C4×D73—21no—
139C2×C4×D73—21no—
140C2×C4×D73—21no—
141C2×C4×D73—21no—
142C2×C4×D73—21no—
143C2×C4×D73—21no—
144C2×C4×D73—21no—
145C2×C4×D73—21no—
146C2×C4×D73—21no—
147C2×C4×D73—21no—
148C2×C4×D73—42no—
149C2×C4×D73—42no—
150C2×C4×D73C22⋊C414yes—
151C2×C4×D73C22⋊C414yes—
152C2×C4×D73C2×D412yes—
153C2×C4×D73C2×D412yes—
154#11924011—48no—
155C2×#10596831—22no—
156C2×#10596831—22no—
157C2×#10596831—22no—
158C2×#10596831—22no—
159C2×#10596831—22no—
160C2×#10596831—22no—
161C4⋊Dic73—22no—
162C4⋊Dic73—22no—
163#11924007—22no—
164#11924007—22no—
165#11924007—22no—
166#11924007—22no—
167#11924007—22no—
168#11924007—22no—
169C22⋊Dic73—22no—
170C22⋊Dic73—22no—
171#11924005—22no—
172#11924005—22no—
173#11924005—22no—
174#11924005—22no—
175#11924005—22no—
176#11924005—22no—
177C4×Dic73—21no—
178C4×Dic73—21no—
179C4×Dic73C22⋊C414yes—
180C4×Dic73C22⋊C414yes—
181C4×Dic73C2×D412yes—
182C4×Dic73C2×D412yes—
183C24×C73C22×C411yescharacteristic
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73C22×C411yescharacteristic
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C22×C411yescharacteristic
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C22×C411yescharacteristic
195C22×C4×C73C2411yescharacteristic
196C2×C8×C73—22no—
197C2×C8×C73—22no—
198C2×C8×C73—22no—
199C2×C8×C73—22no—
200C2×C8×C73—22no—
201C2×C8×C73—22no—
202C4⋊C4×C73—22no—
203C4⋊C4×C73—22no—
204C22⋊C4×C73—22no—
205C22⋊C4×C73—22no—
206C42×C73—21no—
207C42×C73—21no—
208C42×C73C2×D412yes—
209C42×C73C2×D412yes—
210C23×C73—21no—
211C23×C73—21no—
212C23×C73—21no—
213C23×C73—22no—
214C23×C73—22no—
215C23×C73C23×C411yescharacteristic
216C22×D73—21no—
217C22×D73—21no—
218C22×D73—22no—
219C22×D73—22no—
220C22×D73—21no—
221C22×D73—21no—
222C22×D73—21no—
223C22×D73—22no—
224C22×D73—22no—
225C22×D73C2×C22⋊C412yes—
226C2×C4×C73—22no—
227C2×C4×C73—22no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—22no—
234C2×C4×C73—22no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73C2×C22⋊C412yes—
240C2×C4×C73C2×C22⋊C412yes—
241C2×C4×C73C22×D411yescharacteristic
242C2×C4×C73C22×D411yescharacteristic
243C2×C4×C73H(5,𝔽2)11yescharacteristic
244C2×C4×C73H(5,𝔽2)11yescharacteristic
245C2×C4×C732−1+411yescharacteristic
246C2×C4×C732−1+411yescharacteristic
247C22⋊D73—44no—
248C22⋊D73—44no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—22no—
252C2×Dic73—22no—
253C2×Dic73—21no—
254C2×Dic73—21no—
255C2×Dic73—21no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—22no—
259C2×Dic73—22no—
260C2×Dic73C2×C22⋊C412yes—
261C2×Dic73C2×C22⋊C412yes—
262C2×Dic73C2×C22⋊C412yes—
263D292—44no—
264C4×D73—22no—
265C4×D73—22no—
266C4×D73—22no—
267C4×D73—22no—
268C4×D73—44no—
269C4×D73—44no—
270C4×D73—41no—
271C4×D73—41no—
272C4×D73—41no—
273C4×D73—41no—
274Dic146—44no—
275C8×C73—42no—
276C8×C73—42no—
277#10596831—42no—
278#10596831—42no—
279C22×C73—41no—
280C22×C73—41no—
281C22×C73—41no—
282C22×C73—42no—
283C22×C73—42no—
284C22×C73C22×C22⋊C411yescharacteristic
285C22×C73#52011yescharacteristic
286C22×C73#52011yescharacteristic
287C22×C73#56812yes—
288C22×C73#56812yes—
289C2×D73—22no—
290C2×D73—22no—
291C2×D73—22no—
292C2×D73—42no—
293C2×D73—42no—
294C2×D73—41no—
295C2×D73—41no—
296C2×D73—41no—
297C2×D73—42no—
298C2×D73—42no—
299C4×C73—22no—
300C4×C73—22no—
301C4×C73—41no—
302C4×C73—41no—
303C4×C73—41no—
304C4×C73#53511yescharacteristic
305C4×C73#53611yescharacteristic
306C4×C73#53711yescharacteristic
307C4×C73#53711yescharacteristic
308Dic73—22no—
309Dic73—22no—
310Dic73—22no—
311Dic73—41no—
312Dic73—41no—
313Dic73—41no—
314#21854—731nomaximal, Sylow
315C2×C73—81no—
316C2×C73#231111yescharacteristic
317C2×C73#287911yescharacteristic
318C2×C73#287911yescharacteristic
319C2×C73#299512yes—
320C2×C73#299512yes—
321D73—42no—
322D73—81no—
323C2×#529—731no—
324C2×#432—731no—
325C2×#423—731no—
326#1985—732no—
327#1955—732no—
328#1870—732no—
329#1870—732no—
330#1798—731no—
331#1798—731no—
332#1798—731no—
333#1798D7311yescharacteristic, complemented
334C73#2185411yescharacteristic, complemented, Sylow
335C22×M16—732no—
336#529—1464no—
337#529—1464no—
338C2×#126—731no—
339C2×#126—731no—
340C2×#125—731no—
341C2×#124—731no—
342C2×#123—731no—
343C2×#123—731no—
344C2×C22⋊Q8—731no—
345C2×#121—731no—
346C2×C4×Q8—731no—
347C2×C4×D4—731no—
348C2×C4×D4—731no—
349C2×C4×D4—731no—
350C2×#117—731no—
351C2×#117C2×D7311yescharacteristic
352C22×C42—731no—
353#432—1464no—
354#423—1464no—
355C2×C4⋊C8—732no—
356C2×C4⋊C8—731no—
357C2×C4⋊C8—731no—
358C2×C4⋊C8C2×D7311yescharacteristic
359C2×C4⋊C8C2×D7311yescharacteristic
360C2×C22⋊C8—732no—
361C2×C22⋊C8—732no—
362C2×C22⋊C8—732no—
363C2×C22⋊C8—732no—
364C2×C22⋊C8C2×D7312yes—
365C2×#97—732no—
366#336—732no—
367#336—732no—
368#336—732no—
369#336C2×D7312yes—
370C22×Q8—731no—
371C22×D4—731no—
372C22×D4—731no—
373C22×D4—731no—
374C23×C4—731no—
375C23×C4—731no—
376C23×C4—731no—
377C23×C4—731no—
378C23×C4C22×D7311yescharacteristic
379C2×M16—2922no—
380C2×M16—2922no—
381C2×M16—1464no—
382C22×C8—732no—
383C22×C8—732no—
384C22×C8C22×D7312yes—
385C22×C8C22×D7312yes—
386#126—1464no—
387#126—1464no—
388#125—1464no—
389#124—1464no—
390#123—1464no—
391#123—1464no—
392C22⋊Q8—1464no—
393#121—1464no—
394C4×Q8—1462no—
395C4×Q8—1462no—
396C4×D4—1462no—
397C4×D4—1462no—
398C4×D4—1462no—
399C4×D4—1462no—
400C4×D4—1462no—
401C4×D4—1462no—
402#117—22no—
403#117—22no—
404#117—1462no—
405#117—1462no—
406C2×C4⋊C4—731no—
407C2×C4⋊C4—731no—
408C2×C4⋊C4—731no—
409C2×C4⋊C4—731no—
410C2×C4⋊C4—731no—
411C2×C4⋊C4—731no—
412C2×C4⋊C4—731no—
413C2×C4⋊C4—731no—
414C2×C4⋊C4C4×D7311yescharacteristic
415C2×C4⋊C4C4×D7311yescharacteristic
416C2×C22⋊C4—731no—
417C2×C22⋊C4—731no—
418C2×C22⋊C4—731no—
419C2×C22⋊C4—731no—
420C2×C22⋊C4—731no—
421C2×C22⋊C4—731no—
422C2×C22⋊C4—731no—
423C2×C22⋊C4—731no—
424C2×C22⋊C4C4×D7311yescharacteristic
425C2×C22⋊C4C4×D7311yescharacteristic
426C2×C42—731no—
427C2×C42—731no—
428C2×C42—731no—
429C2×C42—734no—
430C2×C42—734no—
431C2×C42—731no—
432C2×C42C22×D7311yescharacteristic
433C2×C42C22×D7311yescharacteristic
434C4⋊C8—22no—
435C4⋊C8—22no—
436C4⋊C8—1464no—
437C4⋊C8—1462no—
438C4⋊C8—1462no—
439C22⋊C8—42no—
440C22⋊C8—2922no—
441C22⋊C8—2922no—
442C22⋊C8—2922no—
443C22⋊C8—1464no—
444#97—1464no—
445C24—731no—
446C24—731no—
447C24C2×C4×D7311yescharacteristic
448C2×Q8—2922no—
449C2×Q8—1462no—
450C2×D4—2922no—
451C2×D4—2922no—
452C2×D4—2922no—
453C2×D4—1462no—
454C2×D4—1462no—
455C2×D4—1462no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—2922no—
463C22×C4—2922no—
464C22×C4—734no—
465C22×C4—734no—
466C22×C4—731no—
467C22×C4—731no—
468C22×C4—731no—
469C22×C4—732no—
470C22×C4—732no—
471C22×C4—731no—
472C22×C4—731no—
473C22×C4—731no—
474C22×C4—1461no—
475C22×C4—1461no—
476C22×C4—1461no—
477C22×C4—1461no—
478C22×C4—1461no—
479C22×C4—1461no—
480C22×C4—1461no—
481C22×C4—1461no—
482C22×C4—1461no—
483C22×C4—1461no—
484C22×C4C2×C4×D7311yescharacteristic
485C22×C4C2×C4×D7311yescharacteristic
486C22×C4C2×C4×D7311yescharacteristic
487C22×C4C2×C4×D7311yescharacteristic
488C22×C4C2×C4×D7311yescharacteristic
489C22×C4C23×D7311yescharacteristic
490M16—2928no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—1462no—
498C2×C8—1462no—
499C2×C8—1462no—
500C2×C8—1462no—
501C2×C8—1462no—
502C2×C8—1462no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—1462no—
506C4⋊C4—1462no—
507C4⋊C4—1462no—
508C4⋊C4—1462no—
509C4⋊C4—1462no—
510C4⋊C4—1462no—
511C4⋊C4—1462no—
512C4⋊C4—1462no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—1462no—
516C22⋊C4—1462no—
517C22⋊C4—1462no—
518C22⋊C4—1462no—
519C22⋊C4—1462no—
520C22⋊C4—1462no—
521C22⋊C4—1462no—
522C22⋊C4—1462no—
523C42—21no—
524C42—21no—
525C42—734no—
526C42—734no—
527C42—732no—
528C42—732no—
529C42—1461no—
530C42—1461no—
531C42D4×D7312yes—
532C42D4×D7312yes—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—22no—
537C23—22no—
538C23—732no—
539C23—1461no—
540C23—1461no—
541C23—1461no—
542C23—1462no—
543C23—1462no—
544C23—1461no—
545C23—1461no—
546C23—1462no—
547C23—1462no—
548C23C22×C4×D7311yescharacteristic
549Q8—2924no—
550D4—2924no—
551D4—2924no—
552D4—2924no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—2924no—
567C2×C4—2924no—
568C2×C4—2921no—
569C2×C4—2921no—
570C2×C4—2921no—
571C2×C4—2921no—
572C2×C4—732no—
573C2×C4—732no—
574C2×C4—732no—
575C2×C4—1461no—
576C2×C4—1461no—
577C2×C4—1461no—
578C2×C4—1461no—
579C2×C4—1461no—
580C2×C4—1462no—
581C2×C4—1462no—
582C2×C4—1461no—
583C2×C4—1461no—
584C2×C4—1462no—
585C2×C4—1462no—
586C2×C4—1462no—
587C2×C4—1462no—
588C2×C4—1462no—
589C2×C4—1462no—
590C2×C4C22⋊C4×D7312yes—
591C2×C4C22⋊C4×D7312yes—
592C2×C4C2×D4×D7311yescharacteristic
593C2×C4C2×D4×D7311yescharacteristic
594C2×C4#1455663611yescharacteristic
595C2×C4#1455663711yescharacteristic
596C2×C4#1455663811yescharacteristic
597C2×C4#1455663911yescharacteristic
598C8—42no—
599C8—42no—
600C8—2922no—
601C8—2922no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—42no—
606C22—42no—
607C22—2922no—
608C22—2922no—
609C22—2921no—
610C22—2921no—
611C22—2921no—
612C22—2922no—
613C22—2922no—
614C22—1462no—
615C22—1462no—
616C22—1462no—
617C22C2×C22⋊C4×D7311yescharacteristic
618C22#1798906711yescharacteristic
619C22#1798906811yescharacteristic
620C22#1798935212yes—
621C22#1798935212yes—
622C4—22no—
623C4—22no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—2921no—
628C4—2921no—
629C4—2921no—
630C4—1462no—
631C4—1462no—
632C4—1462no—
633C4#1798915311yescharacteristic
634C4#1798916011yescharacteristic
635C4#1798916611yescharacteristic
636C4#1798916711yescharacteristic
637C2—81no—
638C2—2922no—
639C2—5841no—
640C2#2261252011yescharacteristic
641C2#2261837311yescharacteristic
642C2#2261837311yescharacteristic
643C2#2261909612yes—
644C2#2261909912yes—
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1798C2
prime radicalC2×#14556564C4
cosocleC22×C4×C73C24
hypercenter#1798D73
hypocenterC73#21854
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. C2×#17988643C2semidirect
3. C2×#17988609C2semidirect
4. #22610869C2semidirect
5. #22610727C2semidirect
6. #22610227C2semidirect
7. #22610225C2semidirect
8. #22609915C2semidirect
9. #22609912C2semidirect
10. #22609912C2semidirect
11. C73×#1798C2semidirect
333. #1798D73semidirect
334. C73#21854semidirect

Maximal subgroups

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

subgroupindex
C2×#179891152
C2×#179886432
C2×#179886092
#226108692
#226107272
#226102272
#226102252
#226099152
#226099122
C73×#17982
#2185473