Finite Group Databasebeta

← #33096106

Subgroups — #33096106

Order 18688.

694 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
1#22612411C211yesmaximal, characteristic
2#22610498C211yesmaximal, characteristic, complemented
3#22610496C211yesmaximal, characteristic, complemented
4#22610495C211yesmaximal, characteristic, complemented
5#22610490C211yesmaximal, characteristic, complemented
6#22610487C211yesmaximal, characteristic, complemented
7#22610486C211yesmaximal, characteristic, complemented
8#22610485C211yesmaximal, characteristic, complemented
9#22610001C211yesmaximal, characteristic
10#22610001C211yesmaximal, characteristic
11#22609910C211yesmaximal, characteristic
12#22609908C211yesmaximal, characteristic
13#22609700C211yesmaximal, characteristic
14#22609696C211yesmaximal, characteristic
15C73×#1917C211yesmaximal, characteristic, complemented
16C2×#14556548C2211yescharacteristic
17C2×#14556548C2211yescharacteristic
18C2×C42×D73C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic
20C2×#14556520C2211yescharacteristic
21C2×#14556520C2211yescharacteristic
22C2×#14556503C2211yescharacteristic
23C2×#14556503C2211yescharacteristic
24C2×#14556503C2211yescharacteristic
25C2×#14556503C2211yescharacteristic
26C2×#14556501C2211yescharacteristic
27C2×C4×#10596831C2211yescharacteristic
28C2×C8×Dic73C2211yescharacteristic
29#17988484C411yescharacteristic
30#17988484C411yescharacteristic
31#17988482C411yescharacteristic
32#17988482C411yescharacteristic
33#17988461C411yescharacteristic
34#17988461C411yescharacteristic
35#17988458C411yescharacteristic
36#17988458C411yescharacteristic
37C4×#11924007C2211yescharacteristic
38C4×#11924007C2211yescharacteristic
39C4×C4⋊Dic73C2211yescharacteristic
40#17988342C2211yescharacteristic
41#17988342C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988341C2211yescharacteristic
45#17988341C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C2×C4⋊C8×C73C2211yescharacteristic
53C2×#97×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55#336×C73C2211yescharacteristic
56#336×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×C4×D73C2×C411yescharacteristic
60C22×C4×D73C2×C411yescharacteristic
61C22×C4×D73C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66#14556548—22no—
67#14556548—22no—
68#14556548—41no—
69#14556548—41no—
70C2×C4⋊Dic73C2×C411yescharacteristic
71C2×C4⋊Dic73C2×C411yescharacteristic
72C2×#11924007C2×C411yescharacteristic
73C2×#11924007C2×C411yescharacteristic
74C2×#11924007C2×C411yescharacteristic
75C2×#11924007C2×C411yescharacteristic
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×#11924007C2×C411yescharacteristic
80C2×#11924005C2×C411yescharacteristic
81C2×#11924005C2×C411yescharacteristic
82C2×#11924005C2×C411yescharacteristic
83C2×#11924005C2×C411yescharacteristic
84C2×C4×Dic73C2×C411yescharacteristic
85C2×C4×Dic73C2×C411yescharacteristic
86C2×C4×Dic73C2311yescharacteristic
87C2×C4×Dic73C2311yescharacteristic
88C2×C4×Dic73C2311yescharacteristic
89C42×D73—41no—
90C42×D73—41no—
91C4⋊#10596831—41no—
92#14556520—41no—
93#14556520—41no—
94#14556503—22no—
95#14556503—22no—
96#14556503—22no—
97#14556503—22no—
98#14556501—41no—
99C4×#10596831—41no—
100C8×Dic73—41no—
101#14556498C2×C411yescharacteristic
102#14556498C2×C411yescharacteristic
103#14556498C2×C411yescharacteristic
104#14556498C2×C411yescharacteristic
105#14556498C2×C411yescharacteristic
106#14556498C2×C411yescharacteristic
107C22×C8×C73C2311yescharacteristic
108C22×C8×C73C2311yescharacteristic
109C22×C8×C73C2311yescharacteristic
110C22×C8×C73C2311yescharacteristic
111C2×C4⋊C4×C73C2×C411yescharacteristic
112C2×C4⋊C4×C73C2×C411yescharacteristic
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115C2×C42×C73C2311yescharacteristic
116C4⋊C8×C73—41no—
117#97×C73—41no—
118#95×C73C2×C411yescharacteristic
119#95×C73C2×C411yescharacteristic
120C23×D73C22×C411yescharacteristic
121C22×Dic73C22×C411yescharacteristic
122C22×Dic73C22×C411yescharacteristic
123C22×Dic73C22×C411yescharacteristic
124C22×Dic73C22×C411yescharacteristic
125C22×Dic73C22×C411yescharacteristic
126C22×Dic73C22×C411yescharacteristic
127C22×Dic73C22×C411yescharacteristic
128C2×C4×D73—21no—
129C2×C4×D73—21no—
130C2×C4×D73—21no—
131C2×C4×D73—21no—
132C2×C4×D73—22no—
133C2×C4×D73—22no—
134C2×C4×D73—41no—
135C2×C4×D73—41no—
136C2×C4×D73—41no—
137C2×C4×D73—41no—
138C2×C4×D73#4112yes—
139C2×C4×D73#4112yes—
140C2×#10596831—21no—
141C2×#10596831—21no—
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—
152C4⋊Dic73—22no—
153C4⋊Dic73—41no—
154#11924007—22no—
155#11924007—22no—
156#11924007—22no—
157#11924007—22no—
158#11924007—41no—
159#11924007—41no—
160#11924007—41no—
161#11924007—41no—
162#11924005—22no—
163#11924005—22no—
164#11924005—41no—
165#11924005—41no—
166C4×Dic73—21no—
167C4×Dic73—21no—
168C4×Dic73—21no—
169C4×Dic73—21no—
170C4×Dic73—21no—
171C4×Dic73—21no—
172C4×Dic73—41no—
173C4×Dic73—41no—
174C22×C4×C73C22×C411yescharacteristic
175C22×C4×C73C22×C411yescharacteristic
176C22×C4×C73C22×C411yescharacteristic
177C22×C4×C73C22×C411yescharacteristic
178C22×C4×C73C22×C411yescharacteristic
179C22×C4×C73C22×C411yescharacteristic
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×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C4⋊C4×C73—22no—
194C4⋊C4×C73—41no—
195C42×C73—21no—
196C42×C73—21no—
197C42×C73—21no—
198C42×C73—21no—
199C42×C73—21no—
200C42×C73—21no—
201C23×C73C23×C411yescharacteristic
202C22×D73—21no—
203C22×D73—21no—
204C22×D73—21no—
205C22×D73—21no—
206C22×D73—21no—
207C22×D73—21no—
208C22×D73#11712yes—
209C2×C4×C73—21no—
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—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73#13112yes—
227C2×C4×C73C2×#4111yescharacteristic
228C2×C4×C73C2×#4111yescharacteristic
229C2×C4×C73H(5,𝔽2)11yescharacteristic
230C2×C4×C73H(5,𝔽2)11yescharacteristic
231C2×C4×C732−1+411yescharacteristic
232C2×C4×C732−1+411yescharacteristic
233C2×Dic73—21no—
234C2×Dic73—21no—
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—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—21no—
252C2×Dic73#11712yes—
253C2×Dic73#13112yes—
254C4×D73—22no—
255C4×D73—22no—
256C4×D73—22no—
257C4×D73—22no—
258C4×D73—44no—
259C4×D73—44no—
260C8×C73—41no—
261C8×C73—41no—
262C8×C73—41no—
263C8×C73—41no—
264#10596831—41no—
265#10596831—41no—
266#10596831—41no—
267#10596831—41no—
268C22×C73C2×#11711yescharacteristic
269C22×C73#51811yescharacteristic
270C22×C73#51911yescharacteristic
271C22×C73C2×#13111yescharacteristic
272C22×C73C2×#13111yescharacteristic
273C22×C73#56811yescharacteristic
274C22×C73#56811yescharacteristic
275C2×D73—22no—
276C2×D73—22no—
277C2×D73—22no—
278C2×D73—41no—
279C2×D73—41no—
280C2×D73—41no—
281C2×D73—41no—
282C4×C73—22no—
283C4×C73—41no—
284C4×C73—41no—
285C4×C73—41no—
286C4×C73—41no—
287C4×C73—41no—
288C4×C73#53911yescharacteristic
289C4×C73#53911yescharacteristic
290C4×C73#53911yescharacteristic
291C4×C73#53911yescharacteristic
292Dic73—22no—
293Dic73—22no—
294Dic73—41no—
295Dic73—41no—
296Dic73—41no—
297Dic73—41no—
298Dic73—41no—
299#21919—731nomaximal, Sylow
300C2×C73#231311yescharacteristic
301C2×C73#292511yescharacteristic
302C2×C73#292511yescharacteristic
303C2×C73#297711yescharacteristic
304C2×C73#297811yescharacteristic
305C2×C73#298511yescharacteristic
306C2×C73#298511yescharacteristic
307D73—42no—
308#2296—731no—
309#1917—731no—
310#1917—731no—
311#1917—731no—
312#1917D7311yescharacteristic, complemented
313#1916—731no—
314#1916—731no—
315#1916—731no—
316#1916—731no—
317#1818—731no—
318#1818—731no—
319#1797—731no—
320#1797—731no—
321#1750—731no—
322#1750—731no—
323C73#2191911yescharacteristic, complemented, Sylow
324C2×#117—731no—
325C2×#117—731no—
326C22×C42—731no—
327C2×C4⋊C8—731no—
328C2×C4⋊C8—731no—
329C2×C4⋊C8—731no—
330C2×C4⋊C8C2×D7311yescharacteristic
331C2×C22⋊C8—731no—
332C2×C22⋊C8—731no—
333C2×C22⋊C8—731no—
334C2×C22⋊C8—731no—
335C2×#97—731no—
336C2×#97C2×D7311yescharacteristic
337C2×C4×C8—731no—
338C2×C4×C8—731no—
339#389—731no—
340#389—731no—
341#389—731no—
342#389—731no—
343#385—731no—
344#385—731no—
345#385—731no—
346#385—731no—
347C4×C4⋊C4—731no—
348C4×C4⋊C4—731no—
349C4×C4⋊C4—731no—
350C4×C4⋊C4C2×D7311yescharacteristic
351#336—731no—
352#336—731no—
353#336—731no—
354#336—731no—
355#336—731no—
356#336—731no—
357#336—731no—
358#336—731no—
359#336—731no—
360#336—731no—
361#336—731no—
362#336—731no—
363#336C2×D7311yescharacteristic
364#336C2×D7311yescharacteristic
365#336C2×D7311yescharacteristic
366#336C2×D7311yescharacteristic
367C23×C4—731no—
368C23×C4—731no—
369C23×C4—731no—
370C22×C8—731no—
371C22×C8—731no—
372C22×C8—731no—
373C22×C8—731no—
374C22×C8C22×D7311yescharacteristic
375C22×C8C22×D7311yescharacteristic
376C22×C8C22×D7311yescharacteristic
377C22×C8C22×D7311yescharacteristic
378#117—2921no—
379#117—2921no—
380#117—1462no—
381#117—1462no—
382C2×C4⋊C4—731no—
383C2×C4⋊C4—731no—
384C2×C4⋊C4—731no—
385C2×C4⋊C4—731no—
386C2×C4⋊C4—731no—
387C2×C4⋊C4—731no—
388C2×C4⋊C4—731no—
389C2×C4⋊C4—731no—
390C2×C4⋊C4—731no—
391C2×C4⋊C4—731no—
392C2×C4⋊C4C4×D7311yescharacteristic
393C2×C4⋊C4C4×D7311yescharacteristic
394C2×C22⋊C4—731no—
395C2×C22⋊C4—731no—
396C2×C22⋊C4—731no—
397C2×C22⋊C4—731no—
398C2×C42—2921no—
399C2×C42—2921no—
400C2×C42—731no—
401C2×C42—731no—
402C2×C42—731no—
403C2×C42—731no—
404C2×C42—731no—
405C2×C42C22×D7311yescharacteristic
406C2×C42C22×D7311yescharacteristic
407C2×C42C22×D7311yescharacteristic
408C4⋊C8—41no—
409C4⋊C8—2921no—
410C4⋊C8—2921no—
411C4⋊C8—2921no—
412C22⋊C8—1462no—
413C22⋊C8—1462no—
414C22⋊C8—1462no—
415C22⋊C8—1462no—
416#97—41no—
417#97—2921no—
418C4×C8—2921no—
419C4×C8—2921no—
420#95—731no—
421#95—731no—
422#95—731no—
423#95—731no—
424#95—731no—
425#95—731no—
426#95C4×D7311yescharacteristic
427#95C4×D7311yescharacteristic
428C24—731no—
429C22×C4—2921no—
430C22×C4—2921no—
431C22×C4—2921no—
432C22×C4—2921no—
433C22×C4—731no—
434C22×C4—731no—
435C22×C4—732no—
436C22×C4—732no—
437C22×C4—731no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4—731no—
441C22×C4—731no—
442C22×C4—1462no—
443C22×C4—1462no—
444C22×C4—1461no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4—1461no—
448C22×C4C2×C4×D7311yescharacteristic
449C22×C4C2×C4×D7311yescharacteristic
450C22×C4C2×C4×D7311yescharacteristic
451C22×C4C2×C4×D7311yescharacteristic
452C22×C4C2×C4×D7311yescharacteristic
453C22×C4C2×C4×D7311yescharacteristic
454C22×C4C23×D7311yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8—1461no—
477C2×C8—1461no—
478C2×C8—1461no—
479C4⋊C4—22no—
480C4⋊C4—41no—
481C4⋊C4—2921no—
482C4⋊C4—2921no—
483C4⋊C4—2921no—
484C4⋊C4—2921no—
485C4⋊C4—2921no—
486C4⋊C4—1462no—
487C4⋊C4—1462no—
488C4⋊C4—1462no—
489C4⋊C4—1462no—
490C4⋊C4—1462no—
491C22⋊C4—2921no—
492C22⋊C4—2921no—
493C22⋊C4—1462no—
494C22⋊C4—1462no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—2921no—
502C42—2921no—
503C42—1461no—
504C42—1461no—
505C42—1461no—
506C42—1461no—
507C42—1461no—
508C42—1461no—
509C23—732no—
510C23—1461no—
511C23—1461no—
512C23—1461no—
513C23—1461no—
514C23—1461no—
515C23—1461no—
516C23C22×C4×D7311yescharacteristic
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—2924no—
535C2×C4—2924no—
536C2×C4—732no—
537C2×C4—732no—
538C2×C4—1461no—
539C2×C4—1461no—
540C2×C4—1461no—
541C2×C4—1461no—
542C2×C4—1461no—
543C2×C4—1461no—
544C2×C4—1461no—
545C2×C4—1461no—
546C2×C4—1461no—
547C2×C4—1461no—
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×C4—1461no—
557C2×C4—1462no—
558C2×C4—1462no—
559C2×C4—1462no—
560C2×C4—1462no—
561C2×C4#1455659912yes—
562C2×C4#41×D7311yescharacteristic
563C2×C4#41×D7311yescharacteristic
564C2×C4#1455663611yescharacteristic
565C2×C4#1455663711yescharacteristic
566C2×C4#1455663811yescharacteristic
567C2×C4#1455663911yescharacteristic
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—2921no—
573C8—2921no—
574C8—2921no—
575C8—2921no—
576C22—2921no—
577C22—2921no—
578C22—2921no—
579C22—2921no—
580C22—1462no—
581C22—1462no—
582C22—1462no—
583C22#117×D7311yescharacteristic
584C22#1798905911yescharacteristic
585C22#1798906311yescharacteristic
586C22#131×D7311yescharacteristic
587C22C2×#1455659911yescharacteristic
588C22#1798935211yescharacteristic
589C22#1798935311yescharacteristic
590C4—22no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—2921no—
597C4—2921no—
598C4—2921no—
599C4—2921no—
600C4—2921no—
601C4—1462no—
602C4—1462no—
603C4#1798917811yescharacteristic
604C4#1798918011yescharacteristic
605C4#1798918311yescharacteristic
606C4#1798918511yescharacteristic
607C2—2922no—
608C2#2261253011yescharacteristic
609C2#2261859411yescharacteristic
610C2#2261859811yescharacteristic
611C2#2261898211yescharacteristic
612C2#2261898811yescharacteristic
613C2#2261902411yescharacteristic
614C2#2261902711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1917C2
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenter#1917D73
hypocenterC73#21919
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
2. #22610498C2semidirect
3. #22610496C2semidirect
4. #22610495C2semidirect
5. #22610490C2semidirect
6. #22610487C2semidirect
7. #22610486C2semidirect
8. #22610485C2semidirect
15. C73×#1917C2semidirect
312. #1917D73semidirect
323. C73#21919semidirect

Maximal subgroups

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

subgroupindex
#226124112
#226104982
#226104962
#226104952
#226104902
#226104872
#226104862
#226104852
#226100012
#226099102
#226099082
#226097002
#226096962
C73×#19172
#2191973