Finite Group Databasebeta

← #33112132

Subgroups — #33112132

Order 18688.

706 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613194C211yesmaximal, characteristic
2#22610725C211yesmaximal, characteristic
3#22610653C211yesmaximal, characteristic, complemented
4#22610650C211yesmaximal, characteristic, complemented
5#22610545C211yesmaximal, characteristic, complemented
6#22610543C211yesmaximal, characteristic, complemented
7#22610535C211yesmaximal, characteristic, complemented
8#22610535C211yesmaximal, characteristic, complemented
9#22610488C211yesmaximal, characteristic, complemented
10#22610222C211yesmaximal, characteristic
11#22610110C211yesmaximal, characteristic, complemented
12#22610110C211yesmaximal, characteristic, complemented
13#22609914C211yesmaximal, characteristic, complemented
14#22609912C211yesmaximal, characteristic, complemented
15C73×#1916C211yesmaximal, characteristic, complemented
16C22×C8×D73C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18C2×#14556548C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic
20C2×C4⋊#10596831C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×#14556503C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556501C2211yescharacteristic
33C2×C4×#10596831C2211yescharacteristic
34#17988529C411yescharacteristic
35#17988522C411yescharacteristic
36#17988520C411yescharacteristic
37#17988516C411yescharacteristic
38#17988516C411yescharacteristic
39#17988513C411yescharacteristic
40#17988505C411yescharacteristic
41#17988504C411yescharacteristic
42C4×#11924007C2211yescharacteristic
43C4×#11924005C2211yescharacteristic
44C4×#11924005C2211yescharacteristic
45C4×#11924005C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C2×C4⋊C8×C73C2211yescharacteristic
53C2×C4×C8×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55#336×C73C2211yescharacteristic
56#336×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×D292C2×C411yescharacteristic
60C22×C4×D73C2311yescharacteristic
61C22×C4×D73C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C2×C8×D73—41no—
67C2×C8×D73—41no—
68C2×C8×D73—41no—
69C4×D292—41no—
70C4×D292—41no—
71#14556548—41no—
72#14556548—41no—
73C2×C4⋊Dic73C2×C411yescharacteristic
74C2×#11924007C2×C411yescharacteristic
75C2×#11924007C2×C411yescharacteristic
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924005C2×C411yescharacteristic
79C2×#11924005C2×C411yescharacteristic
80C2×#11924005C2×C411yescharacteristic
81C2×#11924005C2×C411yescharacteristic
82C2×#11924005C2×C411yescharacteristic
83C2×#11924005C2×C411yescharacteristic
84C2×#11924005C2×C411yescharacteristic
85C2×#11924005C2×C411yescharacteristic
86C2×#11924005C2×C411yescharacteristic
87C2×#11924005C2×C411yescharacteristic
88C2×C4×Dic73C2311yescharacteristic
89C2×C4×Dic73C2311yescharacteristic
90C4⋊#10596831—41no—
91C4⋊#10596831—41no—
92C4⋊#10596831—41no—
93#14556520—41no—
94#14556520—41no—
95#14556520—41no—
96#14556503—41no—
97#14556503—41no—
98#14556503—41no—
99#14556503—41no—
100#14556503—41no—
101#14556503—41no—
102#14556503—41no—
103#14556501—41no—
104C4×#10596831—41no—
105#14556498C2×C411yescharacteristic
106#14556498C2×C411yescharacteristic
107#14556498C2×C411yescharacteristic
108#14556498C2×C411yescharacteristic
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113C22×C8×C73C2311yescharacteristic
114C22×C8×C73C2311yescharacteristic
115C22×C8×C73C2311yescharacteristic
116C22×C8×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2×C411yescharacteristic
118C2×C4⋊C4×C73C2×C411yescharacteristic
119C2×C42×C73C2311yescharacteristic
120C2×C42×C73C2311yescharacteristic
121C2×C42×C73C2311yescharacteristic
122C4⋊C8×C73—41no—
123C4×C8×C73—41no—
124#95×C73C2×C411yescharacteristic
125#95×C73C2×C411yescharacteristic
126C23×D73C22×C411yescharacteristic
127C23×D73C22×C411yescharacteristic
128C2×D292—22no—
129C2×D292—22no—
130C2×D292—41no—
131C22×Dic73C22×C411yescharacteristic
132C22×Dic73C22×C411yescharacteristic
133C22×Dic73C22×C411yescharacteristic
134C22×Dic73C22×C411yescharacteristic
135C22×Dic73C22×C411yescharacteristic
136C22×Dic73C22×C411yescharacteristic
137C2×C4×D73—21no—
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—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C8×D73—44no—
162C4⋊Dic73—41no—
163#11924007—22no—
164#11924007—41no—
165#11924007—41no—
166#11924007—41no—
167#11924005—22no—
168#11924005—22no—
169#11924005—22no—
170#11924005—22no—
171#11924005—41no—
172#11924005—41no—
173#11924005—41no—
174#11924005—41no—
175#11924005—41no—
176#11924005—41no—
177C4×Dic73—21no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C22×C4×C73C22×C411yescharacteristic
182C22×C4×C73C22×C411yescharacteristic
183C22×C4×C73C22×C411yescharacteristic
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C2411yescharacteristic
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C4⋊C4×C73—22no—
201C4⋊C4×C73—22no—
202C42×C73—21no—
203C42×C73—21no—
204C42×C73—21no—
205C42×C73—21no—
206C42×C73—21no—
207C42×C73—21no—
208C23×C73C23×C411yescharacteristic
209C22×D73—21no—
210C22×D73—21no—
211C22×D73—21no—
212C22×D73—21no—
213C22×D73—21no—
214C22×D73—21no—
215C22×D73—21no—
216C22×D73—21no—
217C22×D73—21no—
218C22×D73—21no—
219C22×D73—21no—
220C22×D73—21no—
221C22×D73—21no—
222C22×D73#13112yes—
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—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73#13112yes—
240C2×C4×C73#13112yes—
241C2×C4×C73H(5,𝔽2)11yescharacteristic
242C2×C4×C73H(5,𝔽2)11yescharacteristic
243C2×C4×C73H(5,𝔽2)11yescharacteristic
244C2×C4×C73H(5,𝔽2)11yescharacteristic
245C2×C4×C732−1+411yescharacteristic
246C2×C4×C732−1+411yescharacteristic
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—21no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254C2×Dic73—21no—
255C2×Dic73—21no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—21no—
263C2×Dic73—21no—
264C2×Dic73—21no—
265D292—44no—
266C4×D73—41no—
267C4×D73—41no—
268C4×D73—41no—
269C4×D73—41no—
270C4×D73—41no—
271C4×D73—41no—
272C4×D73—41no—
273C4×D73—41no—
274C8×C73—41no—
275C8×C73—41no—
276C8×C73—41no—
277C8×C73—41no—
278#10596831—41no—
279#10596831—41no—
280#10596831—41no—
281#10596831—41no—
282C22×C73#51811yescharacteristic
283C22×C73#52011yescharacteristic
284C22×C73#52011yescharacteristic
285C22×C73C2×#13111yescharacteristic
286C22×C73C2×#13111yescharacteristic
287C22×C73C2×#13111yescharacteristic
288C22×C73#56811yescharacteristic
289C2×D73—22no—
290C2×D73—22no—
291C2×D73—22no—
292C2×D73—41no—
293C2×D73—41no—
294C2×D73—41no—
295C2×D73—41no—
296C2×D73—41no—
297C2×D73—41no—
298C2×D73—41no—
299C2×D73—41no—
300C2×D73—41no—
301C2×D73—41no—
302C2×D73—41no—
303C4×C73—22no—
304C4×C73—22no—
305C4×C73—41no—
306C4×C73—41no—
307C4×C73—41no—
308C4×C73—41no—
309C4×C73#56011yescharacteristic
310C4×C73#56211yescharacteristic
311C4×C73#56211yescharacteristic
312C4×C73#56311yescharacteristic
313Dic73—41no—
314Dic73—41no—
315Dic73—41no—
316Dic73—41no—
317Dic73—41no—
318Dic73—41no—
319#23319—731nomaximal, Sylow
320C2×C73#237611yescharacteristic
321C2×C73#297711yescharacteristic
322C2×C73#298111yescharacteristic
323C2×C73#299211yescharacteristic
324C2×C73#299311yescharacteristic
325C2×C73#299411yescharacteristic
326C2×C73#299411yescharacteristic
327D73—42no—
328D73—81no—
329#2395—731no—
330#1954—731no—
331#1940—731no—
332#1939—731no—
333#1924—731no—
334#1924—731no—
335#1923—731no—
336#1923—731no—
337#1916—731no—
338#1916D7311yescharacteristic, complemented
339#1869—731no—
340#1850—731no—
341#1850—731no—
342#1798—731no—
343#1798—731no—
344C73#2331911yescharacteristic, complemented, Sylow
345C23×C8—731no—
346C2×C4×D4—731no—
347C2×#117—731no—
348C2×C4⋊C8—731no—
349C2×C4⋊C8—731no—
350C2×C4⋊C8—731no—
351C2×C4⋊C8—731no—
352C2×C4⋊C8—731no—
353C2×C4⋊C8—731no—
354C2×C4⋊C8C2×D7311yescharacteristic
355C2×C22⋊C8—731no—
356C2×C22⋊C8—731no—
357C2×C22⋊C8—731no—
358C2×C22⋊C8—731no—
359C2×C22⋊C8—731no—
360C2×C22⋊C8—731no—
361C2×C22⋊C8—731no—
362C2×#97—731no—
363C2×C4×C8—731no—
364C2×C4×C8C2×D7311yescharacteristic
365#400—731no—
366#399—731no—
367#398—731no—
368#397—731no—
369#397—731no—
370#397—731no—
371#394—731no—
372#394—731no—
373C4×C4⋊C4—731no—
374C4×C4⋊C4C2×D7311yescharacteristic
375C4×C22⋊C4—731no—
376C4×C22⋊C4—731no—
377C4×C22⋊C4—731no—
378#336—731no—
379#336—731no—
380#336—731no—
381#336—731no—
382#336—731no—
383#336—731no—
384#336C2×D7311yescharacteristic
385#336C2×D7311yescharacteristic
386#336C2×D7311yescharacteristic
387#336C2×D7311yescharacteristic
388C22×D4—731no—
389C23×C4—731no—
390C23×C4—731no—
391C22×C8—2921no—
392C22×C8—2921no—
393C22×C8—2921no—
394C22×C8—731no—
395C22×C8—731no—
396C22×C8—731no—
397C22×C8—731no—
398C22×C8C22×D7311yescharacteristic
399C22×C8C22×D7311yescharacteristic
400C22×C8C22×D7311yescharacteristic
401C22×C8C22×D7311yescharacteristic
402C4×D4—2921no—
403C4×D4—2921no—
404#117—2921no—
405#117—2921no—
406C2×C4⋊C4—731no—
407C2×C4⋊C4—731no—
408C2×C4⋊C4—731no—
409C2×C4⋊C4—731no—
410C2×C4⋊C4—731no—
411C2×C4⋊C4C4×D7311yescharacteristic
412C2×C4⋊C4C4×D7311yescharacteristic
413C2×C22⋊C4—731no—
414C2×C22⋊C4—731no—
415C2×C22⋊C4—731no—
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×C42—731no—
424C2×C42—731no—
425C2×C42C22×D7311yescharacteristic
426C2×C42C22×D7311yescharacteristic
427C2×C42C22×D7311yescharacteristic
428C4⋊C8—41no—
429C4⋊C8—2921no—
430C4⋊C8—2921no—
431C4⋊C8—2921no—
432C4⋊C8—2921no—
433C4⋊C8—2921no—
434C4⋊C8—2921no—
435C22⋊C8—2921no—
436C22⋊C8—2921no—
437C22⋊C8—2921no—
438C22⋊C8—2921no—
439C22⋊C8—2921no—
440C22⋊C8—2921no—
441C22⋊C8—2921no—
442#97—2921no—
443C4×C8—41no—
444C4×C8—2921no—
445#95—731no—
446#95—731no—
447#95—731no—
448#95—731no—
449#95—731no—
450#95—731no—
451#95—731no—
452#95—731no—
453#95C4×D7311yescharacteristic
454#95C4×D7311yescharacteristic
455C24—731no—
456C24—731no—
457C2×D4—2921no—
458C2×D4—1462no—
459C2×D4—1462no—
460C22×C4—731no—
461C22×C4—731no—
462C22×C4—731no—
463C22×C4—731no—
464C22×C4—731no—
465C22×C4—731no—
466C22×C4—1461no—
467C22×C4—1461no—
468C22×C4—1461no—
469C22×C4—1461no—
470C22×C4—1461no—
471C22×C4—1461no—
472C22×C4—1461no—
473C22×C4—1461no—
474C22×C4—1461no—
475C22×C4—1461no—
476C22×C4—1461no—
477C22×C4—1461no—
478C22×C4C2×C4×D7311yescharacteristic
479C22×C4C2×C4×D7311yescharacteristic
480C22×C4C2×C4×D7311yescharacteristic
481C22×C4C2×C4×D7311yescharacteristic
482C22×C4C2×C4×D7311yescharacteristic
483C22×C4C2×C4×D7311yescharacteristic
484C22×C4C23×D7311yescharacteristic
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—2924no—
498C2×C8—1461no—
499C2×C8—1461no—
500C2×C8—1461no—
501C2×C8—1461no—
502C2×C8—1461no—
503C2×C8—1461no—
504C2×C8—1461no—
505C2×C8—1461no—
506C2×C8—1461no—
507C2×C8—1461no—
508C2×C8—1461no—
509C2×C8—1461no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—2921no—
513C4⋊C4—2921no—
514C4⋊C4—2921no—
515C4⋊C4—2921no—
516C4⋊C4—1462no—
517C22⋊C4—2921no—
518C22⋊C4—2921no—
519C22⋊C4—2921no—
520C22⋊C4—2921no—
521C22⋊C4—2921no—
522C22⋊C4—2921no—
523C22⋊C4—1462no—
524C22⋊C4—1462no—
525C22⋊C4—1462no—
526C22⋊C4—1462no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—1461no—
534C42—1461no—
535C42—1461no—
536C42—1461no—
537C23—732no—
538C23—1461no—
539C23—1461no—
540C23—1461no—
541C23—1461no—
542C23—1461no—
543C23—1461no—
544C23—1461no—
545C23—1461no—
546C23—1461no—
547C23—1461no—
548C23—1461no—
549C23—1461no—
550C23—1461no—
551C23C22×C4×D7311yescharacteristic
552D4—2924no—
553C2×C4—21no—
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—21no—
568C2×C4—21no—
569C2×C4—2921no—
570C2×C4—2921no—
571C2×C4—2921no—
572C2×C4—2921no—
573C2×C4—2921no—
574C2×C4—2921no—
575C2×C4—2921no—
576C2×C4—2921no—
577C2×C4—1461no—
578C2×C4—1461no—
579C2×C4—1461no—
580C2×C4—1461no—
581C2×C4—1461no—
582C2×C4—1461no—
583C2×C4—1461no—
584C2×C4—1461no—
585C2×C4—1461no—
586C2×C4—1461no—
587C2×C4—1461no—
588C2×C4—1461no—
589C2×C4—1461no—
590C2×C4—1461no—
591C2×C4—1461no—
592C2×C4—1461no—
593C2×C4—1461no—
594C2×C4—1461no—
595C2×C4#1455659712yes—
596C2×C4#1455659912yes—
597C2×C4#1455663611yescharacteristic
598C2×C4#1455663711yescharacteristic
599C2×C4#1455663711yescharacteristic
600C2×C4#1455663711yescharacteristic
601C2×C4#1455663811yescharacteristic
602C2×C4#1455663911yescharacteristic
603C8—41no—
604C8—41no—
605C8—41no—
606C8—41no—
607C8—2921no—
608C8—2921no—
609C8—2921no—
610C8—2921no—
611C22—2921no—
612C22—2921no—
613C22—2921no—
614C22—2921no—
615C22—2921no—
616C22—2921no—
617C22—2921no—
618C22—2921no—
619C22—2921no—
620C22—2921no—
621C22—2921no—
622C22—1462no—
623C22—1462no—
624C22—1462no—
625C22#1798905911yescharacteristic
626C22#1798906711yescharacteristic
627C22#1798906911yescharacteristic
628C22#131×D7311yescharacteristic
629C22C2×#1455659711yescharacteristic
630C22C2×#1455659911yescharacteristic
631C22#1798935211yescharacteristic
632C4—22no—
633C4—22no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—2921no—
639C4—2921no—
640C4—2921no—
641C4—2921no—
642C4—2921no—
643C4—2921no—
644C4#1798932811yescharacteristic
645C4#1798933311yescharacteristic
646C4#1798933411yescharacteristic
647C4#1798934111yescharacteristic
648C2—2922no—
649C2—5841no—
650C2#2261307811yescharacteristic
651C2#2261898211yescharacteristic
652C2#2261900511yescharacteristic
653C2#2261906511yescharacteristic
654C2#2261908311yescharacteristic
655C2#2261909011yescharacteristic
656C2#2261909311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1916C2
prime radicalC22×D292C2×C4
cosocleC22×C4×C73C24
hypercenter#1916D73
hypocenterC73#23319
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
3. #22610653C2semidirect
4. #22610650C2semidirect
5. #22610545C2semidirect
6. #22610543C2semidirect
7. #22610535C2semidirect
8. #22610535C2semidirect
9. #22610488C2semidirect
11. #22610110C2semidirect
12. #22610110C2semidirect
13. #22609914C2semidirect
14. #22609912C2semidirect
15. C73×#1916C2semidirect
338. #1916D73semidirect
344. C73#23319semidirect

Maximal subgroups

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

subgroupindex
#226131942
#226107252
#226106532
#226106502
#226105452
#226105432
#226105352
#226104882
#226102222
#226101102
#226099142
#226099122
C73×#19162
#2331973