Finite Group Databasebeta

← #33127398

Subgroups — #33127398

Order 18688.

794 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988884C211yesmaximal, characteristic, complemented
2C2×#17988648C211yesmaximal, characteristic, complemented
3#22612624C211yesmaximal, characteristic
4#22611367C211yesmaximal, characteristic, complemented
5#22611357C211yesmaximal, characteristic, complemented
6#22611120C211yesmaximal, characteristic
7#22611120C211yesmaximal, characteristic
8#22610889C211yesmaximal, characteristic, complemented
9#22610692C211yesmaximal, characteristic, complemented
10#22610671C211yesmaximal, characteristic, complemented
11#22610656C211yesmaximal, characteristic, complemented
12#22610627C211yesmaximal, characteristic, complemented
13#22610613C211yesmaximal, characteristic, complemented
14#22609928C211yesmaximal, characteristic, complemented
15C73×#2629C211yesmaximal, characteristic, complemented
16C2×#14556565C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18#17988884—24no—
19#17988648—24no—
20C2×#14556524C2211yescharacteristic
21C2×#14556522C2211yescharacteristic
22C2×#14556522C2211yescharacteristic
23C2×#14556522C2211yescharacteristic
24C2×C4⋊#10596831C2211yescharacteristic
25C2×C4⋊#10596831C2211yescharacteristic
26C2×#14556511C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×#14556511C2211yescharacteristic
29C2×#14556511C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×C22⋊#10596831C2211yescharacteristic
32C2×#14556502C2211yescharacteristic
33C2×C4×#10596831C2211yescharacteristic
34#17988489C2211yescharacteristic
35#17988487—21no—
36#17988485C2211yescharacteristic
37#17988477—21no—
38#17988463—21no—
39#17988458—21no—
40#17988447C2211yescharacteristic
41C4×C4⋊Dic73C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50C2×#125×C73C2211yescharacteristic
51C2×#117×C73C2211yescharacteristic
52#398×C73—21no—
53#398×C73—21no—
54#396×C73—21no—
55#396×C73—21no—
56#389×C73C2211yescharacteristic
57#389×C73C2211yescharacteristic
58#384×C73C2211yescharacteristic
59#380×C73C2211yescharacteristic
60#380×C73C2211yescharacteristic
61C22×D292C2311yescharacteristic
62C22×C22⋊D73—21no—
63C22×C4×D73—21no—
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68#14556565—22no—
69#14556565—22no—
70C4×D292—22no—
71C4×D292—22no—
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×#11924007—21no—
76C2×C22⋊Dic73—21no—
77C2×#11924005—21no—
78C2×#11924005—21no—
79C2×#11924005—21no—
80C2×#11924005—21no—
81C2×C4×Dic73—21no—
82#14556524—22no—
83#14556522—22no—
84#14556522—22no—
85#14556522—22no—
86C4⋊#10596831—22no—
87C4⋊#10596831D414yescomplemented
88#14556511—22no—
89#14556511—22no—
90#14556511—22no—
91#14556511—22no—
92C22⋊#10596831—22no—
93C22⋊#10596831—22no—
94#14556502—22no—
95C4×#10596831—22no—
96#14556498—21no—
97#14556498—21no—
98#14556498—21no—
99C23×C4×C73C2311yescharacteristic
100#125×C73—22no—
101#125×C73—22no—
102#117×C73—22no—
103#117×C73—22no—
104C2×C4⋊C4×C73—21no—
105C2×C4⋊C4×C73—21no—
106C2×C4⋊C4×C73—21no—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73D411yescharacteristic
111C2×C4⋊C4×C73D411yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C22⋊C4×C73—21no—
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73D411yescharacteristic
119C2×C22⋊C4×C73D411yescharacteristic
120C2×C42×C73C2311yescharacteristic
121C2×C42×C73C2311yescharacteristic
122#95×C73—21no—
123#95×C73—21no—
124#95×C73—21no—
125#95×C73—21no—
126C23×D73—21no—
127C2×D292—21no—
128C2×D292—21no—
129C2×D292—21no—
130C2×D292—21no—
131C2×D292—21no—
132C2×D292#4112yes—
133C2×C22⋊D73—24no—
134C2×C22⋊D73—81no—
135C2×C22⋊D73—81no—
136C22×Dic73—21no—
137C22×Dic73—21no—
138C22×Dic73—21no—
139C2×C4×D73—42no—
140C2×C4×D73—81no—
141C2×C4×D73—81no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831C2×D412yes—
153C2×#10596831C2×D412yes—
154C4⋊Dic73—21no—
155C4⋊Dic73—21no—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—21no—
159C4⋊Dic73#4112yes—
160#11924007—81no—
161C22⋊Dic73—81no—
162#11924005—24no—
163#11924005—42no—
164#11924005—81no—
165#11924005—81no—
166C4×Dic73—81no—
167C24×C73C2×D411yescharacteristic
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
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×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2411yescharacteristic
184C4⋊C4×C73—22no—
185C4⋊C4×C73—22no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—42no—
195C4⋊C4×C73—42no—
196C4⋊C4×C73—81no—
197C4⋊C4×C73—81no—
198C4⋊C4×C73—81no—
199C4⋊C4×C73—81no—
200C22⋊C4×C73—22no—
201C22⋊C4×C73—22no—
202C22⋊C4×C73—81no—
203C22⋊C4×C73—81no—
204C42×C73—21no—
205C42×C73—21no—
206C42×C73C2×D412yes—
207C42×C73#4112yes—
208C23×C73—21no—
209C23×C73—21no—
210C23×C73—21no—
211C23×C73—21no—
212C23×C73—21no—
213C23×C73—21no—
214C23×C73—21no—
215C23×C73C22×D411yescharacteristic
216C22×D73—22no—
217C22×D73—41no—
218C22×D73—41no—
219C22×D73—41no—
220C22×D73—41no—
221C22×D73—41no—
222C22×D73—41no—
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—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73#12112yes—
253C2×C4×C73#12112yes—
254C2×C4×C73C22×D411yescharacteristic
255C2×C4×C73C2×#4111yescharacteristic
256C2×C4×C73C2×#4111yescharacteristic
257C2×C4×C73C2×#4111yescharacteristic
258C2×C4×C732−1+411yescharacteristic
259C2×C4×C732−1+411yescharacteristic
260C22⋊D73—84no—
261C2×Dic73—22no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73—41no—
267C2×Dic73—41no—
268C2×Dic73—41no—
269C2×Dic73—41no—
270D292—22no—
271D292—22no—
272D292—41no—
273D292—41no—
274C4×D73—84no—
275#10596831—22no—
276#10596831—22no—
277#10596831—41no—
278#10596831—41no—
279C22×C73—41no—
280C22×C73—41no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73—41no—
284C22×C73—41no—
285C22×C73—41no—
286C22×C73C2×#12111yescharacteristic
287C22×C73#52511yescharacteristic
288C22×C73#53611yescharacteristic
289C22×C73#57611yescharacteristic
290C22×C73#57711yescharacteristic
291C22×C73#57711yescharacteristic
292C22×C73#57711yescharacteristic
293C2×D73—42no—
294C2×D73—42no—
295C2×D73—42no—
296C2×D73—81no—
297C2×D73—81no—
298C2×D73—81no—
299C2×D73—81no—
300C4×C73—22no—
301C4×C73—22no—
302C4×C73—41no—
303C4×C73—41no—
304C4×C73—41no—
305C4×C73—81no—
306C4×C73—81no—
307C4×C73—81no—
308C4×C73—81no—
309C4×C73#54711yescharacteristic
310C4×C73#54811yescharacteristic
311C4×C73#55211yescharacteristic
312C4×C73#55611yescharacteristic
313Dic73—42no—
314Dic73—81no—
315Dic73—81no—
316#24717—731nomaximal, Sylow
317C2×C73—81no—
318C2×C73#241511yescharacteristic
319C2×C73#306011yescharacteristic
320C2×C73#306211yescharacteristic
321C2×C73#311911yescharacteristic
322C2×C73#312311yescharacteristic
323C2×C73#324111yescharacteristic
324C2×C73#324411yescharacteristic
325D73—82no—
326C2×#478—731no—
327C2×#433—731no—
328#2629D7311yescharacteristic, complemented
329#2324—731no—
330#2077—731no—
331#2075—731no—
332#2034—731no—
333#2034—731no—
334#1989—731no—
335#1948—731no—
336#1944—731no—
337#1941—731no—
338#1936—731no—
339#1934—731no—
340#1802—731no—
341C73#2471711yescharacteristic, complemented, Sylow
342C2×#125C2×D7311yescharacteristic
343C2×#121—731no—
344C2×C4×D4—731no—
345C2×#117C2×D7311yescharacteristic
346#478—1464no—
347#433—1464no—
348C2×#107—731no—
349C2×#106—731no—
350C2×#106—731no—
351C2×#106—731no—
352C2×C4⋊C8—731no—
353C2×C4⋊C8—731no—
354C2×#102—731no—
355C2×#102—731no—
356C2×#102—731no—
357C2×#102—731no—
358C2×C22⋊C8—731no—
359C2×C22⋊C8—731no—
360C2×#97—731no—
361C2×C4×C8—731no—
362#398—21no—
363#398—21no—
364#396—21no—
365#396—21no—
366#390—731no—
367#390—1461no—
368#389—731no—
369#389C2×D7311yescharacteristic
370#389C2×D7311yescharacteristic
371#388—1461no—
372#386—1461no—
373#385—1461no—
374#384C2×D7311yescharacteristic
375#380—731no—
376#380C2×D7311yescharacteristic
377#380C2×D7311yescharacteristic
378C4×C4⋊C4—731no—
379#340—731no—
380#340—731no—
381#340—731no—
382#340—731no—
383#340—731no—
384#340—731no—
385#340—731no—
386#340—731no—
387C22×D4—731no—
388C22×D4—1461no—
389C23×C4—1461no—
390C23×C4C22×D7311yescharacteristic
391C22×C8—731no—
392C22×C8—731no—
393C22×C8—731no—
394C22×C8—731no—
395#125—22no—
396#125—22no—
397#121—1462no—
398#121—1462no—
399C4×D4—1462no—
400C4×D4—1462no—
401#117—22no—
402#117—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—731no—
410C2×C4⋊C4—731no—
411C2×C4⋊C4—731no—
412C2×C4⋊C4—1461no—
413C2×C4⋊C4C22⋊D7311yescharacteristic
414C2×C4⋊C4C22⋊D7311yescharacteristic
415C2×C4⋊C4C22×D7311yescharacteristic
416C2×C4⋊C4C22×D7311yescharacteristic
417C2×C4⋊C4C22×D7311yescharacteristic
418C2×C4⋊C4C22×D7311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—1461no—
422C2×C22⋊C4—1461no—
423C2×C22⋊C4—1461no—
424C2×C22⋊C4—1461no—
425C2×C22⋊C4—1461no—
426C2×C22⋊C4C22⋊D7311yescharacteristic
427C2×C22⋊C4C22⋊D7311yescharacteristic
428C2×C42—1461no—
429C2×C42C22×D7311yescharacteristic
430C2×C42C22×D7311yescharacteristic
431#107—1462no—
432#106—1462no—
433#106—1462no—
434#106—1462no—
435C4⋊C8—734no—
436C4⋊C8—1462no—
437#102—1462no—
438#102—1462no—
439#102—1462no—
440#102—1462no—
441C22⋊C8—1462no—
442C22⋊C8—1462no—
443#97—1462no—
444C4×C8—1462no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—1461no—
450#95—1461no—
451#95—1461no—
452C24—1461no—
453C24C2×C22⋊D7311yescharacteristic
454C2×D4—5841no—
455C2×D4—5841no—
456C2×D4—732no—
457C2×D4—1464no—
458C2×D4—1461no—
459C2×D4—1461no—
460C2×D4—1461no—
461C2×D4—1461no—
462C2×D4—1461no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—2922no—
474C22×C4—5841no—
475C22×C4—5841no—
476C22×C4—1461no—
477C22×C4—1461no—
478C22×C4—1461no—
479C22×C4C2×C22⋊D7311yescharacteristic
480C22×C4C2×C22⋊D7311yescharacteristic
481C22×C4C2×C22⋊D7311yescharacteristic
482C22×C4C2×C22⋊D7311yescharacteristic
483C22×C4C2×C22⋊D7311yescharacteristic
484C22×C4C23×D7311yescharacteristic
485C2×C8—732no—
486C2×C8—732no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8—1461no—
492C2×C8—1461no—
493C2×C8—1461no—
494C2×C8—1461no—
495C2×C8—1461no—
496C2×C8—1461no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—81no—
510C4⋊C4—81no—
511C4⋊C4—81no—
512C4⋊C4—81no—
513C4⋊C4—5841no—
514C4⋊C4—732no—
515C4⋊C4—1461no—
516C4⋊C4—1461no—
517C4⋊C4—1461no—
518C4⋊C4—1461no—
519C4⋊C4—1461no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—81no—
523C22⋊C4—81no—
524C22⋊C4—2922no—
525C22⋊C4—5841no—
526C22⋊C4—5841no—
527C22⋊C4—5841no—
528C22⋊C4—1464no—
529C42—21no—
530C42—21no—
531C42—5841no—
532C42D4×D7312yes—
533C42#1192402712yes—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—2921no—
542C23—2921no—
543C23—2921no—
544C23—2921no—
545C23—2921no—
546C23—2921no—
547C23—1462no—
548C23C22×C22⋊D7311yescharacteristic
549D4—2921no—
550D4—2921no—
551D4—5844no—
552D4—1462no—
553D4—1462no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—2921no—
584C2×C4—2921no—
585C2×C4—2921no—
586C2×C4—2921no—
587C2×C4—2921no—
588C2×C4—2921no—
589C2×C4—2921no—
590C2×C4—2921no—
591C2×C4—5844no—
592C2×C4—1462no—
593C2×C4#1455656312yes—
594C2×C4#1455656312yes—
595C2×C4C2×D4×D7311yescharacteristic
596C2×C4#41×D7311yescharacteristic
597C2×C4#41×D7311yescharacteristic
598C2×C4C2×#1192402711yescharacteristic
599C2×C4#1455663911yescharacteristic
600C2×C4#1455663911yescharacteristic
601C8—2921no—
602C8—2921no—
603C8—1462no—
604C8—1462no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—2922no—
613C22—2922no—
614C22—2922no—
615C22—5841no—
616C22—5841no—
617C22—5841no—
618C22—5841no—
619C22C2×#1455656311yescharacteristic
620C22#1798909411yescharacteristic
621C22#1798916111yescharacteristic
622C22#1798939011yescharacteristic
623C22#1798939511yescharacteristic
624C22#1798939511yescharacteristic
625C22#1798939811yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—2922no—
636C4—5841no—
637C4—5841no—
638C4#1798923911yescharacteristic
639C4#1798924711yescharacteristic
640C4#1798927111yescharacteristic
641C4#1798930811yescharacteristic
642C2—81no—
643C2—5842no—
644C2#2261336111yescharacteristic
645C2#2261959011yescharacteristic
646C2#2261961311yescharacteristic
647C2#2262012411yescharacteristic
648C2#2262017811yescharacteristic
649C2#2262118411yescharacteristic
650C2#2262122911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2629C2
socleC23×C73C22×D4
prime radicalC2×#14556565C22
hypercenter#2629D73
hypocenterC73#24717
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2629

Complements

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

NH ≅ G/Ntype
1. C2×#17988884C2semidirect
2. C2×#17988648C2semidirect
4. #22611367C2semidirect
5. #22611357C2semidirect
8. #22610889C2semidirect
9. #22610692C2semidirect
10. #22610671C2semidirect
11. #22610656C2semidirect
12. #22610627C2semidirect
13. #22610613C2semidirect
14. #22609928C2semidirect
15. C73×#2629C2semidirect
87. C4⋊#10596831D4semidirect
328. #2629D73semidirect
341. C73#24717semidirect

Maximal subgroups

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

subgroupindex
C2×#179888842
C2×#179886482
#226126242
#226113672
#226113572
#226111202
#226108892
#226106922
#226106712
#226106562
#226106272
#226106132
#226099282
C73×#26292
#2471773