Finite Group Databasebeta

← #33103789

Subgroups — #33103789

Order 18688.

868 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
1C4×C4⋊C4×D73C211yesmaximal, characteristic
2#22610654C211yesmaximal, characteristic, complemented
3#22610652C211yesmaximal, characteristic, complemented
4#22610495C211yesmaximal, characteristic, complemented
5#22610493C211yesmaximal, characteristic, complemented
6#22610488C211yesmaximal, characteristic, complemented
7#22610486C211yesmaximal, characteristic, complemented
8#22609910C211yesmaximal, characteristic
9#22609910C211yesmaximal, characteristic
10#22609908C211yesmaximal, characteristic
11#22609806C211yesmaximal, characteristic, complemented
12#22609694C211yesmaximal, characteristic
13#22609694C211yesmaximal, characteristic
14C4×#14556503C211yesmaximal, characteristic
15C73×#1771C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D73C411yescharacteristic
17C2×C4⋊C4×D73C411yescharacteristic
18C2×C42×D73C2211yescharacteristic
19C2×C42×D73C2211yescharacteristic
20C2×C42×D73C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×#14556520C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556502C2211yescharacteristic
31C2×#14556502C2211yescharacteristic
32C2×C4×#10596831C2211yescharacteristic
33C4⋊C4×Dic73C411yescharacteristic
34C4⋊C4×Dic73C411yescharacteristic
35C4×#11924007C2211yescharacteristic
36C4×#11924007C2211yescharacteristic
37C4×C4⋊Dic73C2211yescharacteristic
38#17988438C411yescharacteristic
39#17988438C411yescharacteristic
40#95×D73C411yescharacteristic
41#95×D73C411yescharacteristic
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
54C2×#97×C73C2211yescharacteristic
55C2×C4×C8×C73C2211yescharacteristic
56C4×C4⋊C4×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×C4×D73C2×C411yescharacteristic
60C22×C4×D73C2×C411yescharacteristic
61C22×C4×D73C2×C411yescharacteristic
62C22×C4×D73C2×C411yescharacteristic
63C22×C4×D73C2×C411yescharacteristic
64C22×C4×D73C2×C411yescharacteristic
65C22×C4×D73C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C2×C4⋊Dic73C2×C411yescharacteristic
71C2×C4⋊Dic73C2×C411yescharacteristic
72C2×#11924007C2×C411yescharacteristic
73C2×#11924007C2×C411yescharacteristic
74C2×#11924007C2×C411yescharacteristic
75C2×#11924007C2×C411yescharacteristic
76C4⋊C4×D73—24no—
77C4⋊C4×D73—24no—
78C2×C4×Dic73C2×C411yescharacteristic
79C2×C4×Dic73C2×C411yescharacteristic
80C2×C4×Dic73C2×C411yescharacteristic
81C2×C4×Dic73C2×C411yescharacteristic
82C2×C4×Dic73C2×C411yescharacteristic
83C2×C4×Dic73C2×C411yescharacteristic
84C2×C4×Dic73C2311yescharacteristic
85C2×C4×Dic73C2311yescharacteristic
86C2×C4×Dic73C2311yescharacteristic
87C42×D73—22no—
88C42×D73—22no—
89C42×D73—41no—
90C42×D73—41no—
91C42×D73—41no—
92C42×D73—41no—
93C4⋊#10596831—22no—
94#14556520—41no—
95#14556520—41no—
96#14556520—41no—
97#14556520—41no—
98#14556503—22no—
99#14556503—22no—
100#14556503—22no—
101#14556503Q814yes—
102#14556502—22no—
103#14556502—41no—
104C4×#10596831—41no—
105#14556498C2×C411yescharacteristic
106#14556498C2×C411yescharacteristic
107#14556498C2×C411yescharacteristic
108#14556498C2×C411yescharacteristic
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111C22×C8×C73C2311yescharacteristic
112C22×C8×C73C2311yescharacteristic
113C22×C8×C73C2311yescharacteristic
114C22×C8×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2×C411yescharacteristic
116C2×C4⋊C4×C73C2×C411yescharacteristic
117C2×C42×C73C2311yescharacteristic
118C2×C42×C73C2311yescharacteristic
119C2×C42×C73C2311yescharacteristic
120C4⋊C8×C73—22no—
121#97×C73—22no—
122#97×C73—41no—
123C4×C8×C73—41no—
124#95×C73C2×C411yescharacteristic
125#95×C73C2×C411yescharacteristic
126C23×D73C22×C411yescharacteristic
127C22×Dic73C22×C411yescharacteristic
128C22×Dic73C22×C411yescharacteristic
129C22×Dic73C22×C411yescharacteristic
130C22×Dic73C22×C411yescharacteristic
131C22×Dic73C22×C411yescharacteristic
132C22×Dic73C22×C411yescharacteristic
133C22×Dic73C22×C411yescharacteristic
134C2×C4×D73—22no—
135C2×C4×D73—22no—
136C2×C4×D73—21no—
137C2×C4×D73—21no—
138C2×C4×D73—21no—
139C2×C4×D73—21no—
140C2×C4×D73—22no—
141C2×C4×D73—22no—
142C2×C4×D73—22no—
143C2×C4×D73—22no—
144C2×C4×D73—22no—
145C2×C4×D73—22no—
146C2×C4×D73—22no—
147C2×C4×D73—22no—
148C2×C4×D73—41no—
149C2×C4×D73—41no—
150C2×C4×D73—41no—
151C2×C4×D73—41no—
152C2×C4×D73—41no—
153C2×C4×D73—41no—
154C2×C4×D73—41no—
155C2×C4×D73M1614yes—
156C2×C4×D73C2×Q812yes—
157C2×C4×D73#4112yes—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831C2×Q812yes—
170C4⋊Dic73—22no—
171C4⋊Dic73—22no—
172#11924007—22no—
173#11924007—22no—
174#11924007—22no—
175#11924007M1614yes—
176C4×Dic73—22no—
177C4×Dic73—22no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—41no—
185C4×Dic73—41no—
186C4×Dic73—41no—
187C4×Dic73—41no—
188C22×C4×C73C22×C411yescharacteristic
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C22×C411yescharacteristic
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C22×C411yescharacteristic
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C2411yescharacteristic
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73C2×Q812yes—
207C4⋊C4×C73—22no—
208C4⋊C4×C73—22no—
209C42×C73—21no—
210C42×C73—21no—
211C42×C73—21no—
212C42×C73—21no—
213C42×C73#4112yes—
214C42×C73#4112yes—
215C23×C73C23×C411yescharacteristic
216C22×D73—21no—
217C22×D73—21no—
218C22×D73—21no—
219C22×D73—21no—
220C22×D73C4×Q812yes—
221C22×D73C2×M1612yes—
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#11712yes—
238C2×C4×C73#11712yes—
239C2×C4×C73C2×M1612yes—
240C2×C4×C73C2×M1612yes—
241C2×C4×C73C22×Q811yescharacteristic
242C2×C4×C73C2×#4111yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C2×C4×C73H(5,𝔽2)11yescharacteristic
246C2×C4×C73H(5,𝔽2)11yescharacteristic
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×Dic73C4×Q812yes—
265C2×Dic73C2×M1612yes—
266C2×Dic73C2×M1612yes—
267C2×Dic73C2×M1612yes—
268C4×D73—28no—
269C4×D73—22no—
270C4×D73—22no—
271C4×D73—22no—
272C4×D73—22no—
273C4×D73—44no—
274C4×D73—44no—
275C4×D73—44no—
276C4×D73—44no—
277C4×D73—44no—
278C8×C73—22no—
279C8×C73—41no—
280C8×C73—41no—
281C8×C73—41no—
282#10596831—22no—
283#10596831—41no—
284#10596831—41no—
285#10596831—41no—
286C22×C73C2×#11711yescharacteristic
287C22×C73C2×C4×Q811yescharacteristic
288C22×C73#51811yescharacteristic
289C22×C73C22×M1611yescharacteristic
290C22×C73C22×M1611yescharacteristic
291C22×C73C2×#13111yescharacteristic
292C22×C73#56811yescharacteristic
293C2×D73—22no—
294C2×D73—22no—
295C2×D73—22no—
296C2×D73—22no—
297C2×D73—22no—
298C2×D73—22no—
299C2×D73#44614yes—
300C4×C73—22no—
301C4×C73—22no—
302C4×C73—22no—
303C4×C73—22no—
304C4×C73—41no—
305C4×C73—41no—
306C4×C73#55311yescharacteristic
307C4×C73#55311yescharacteristic
308C4×C73#55411yescharacteristic
309C4×C73#55411yescharacteristic
310Dic73—22no—
311Dic73—22no—
312Dic73—22no—
313Dic73—22no—
314Dic73—41no—
315Dic73—41no—
316Dic73—41no—
317#22627—731nomaximal, Sylow
318C2×C73#234511yescharacteristic
319C2×C73#292011yescharacteristic
320C2×C73#292411yescharacteristic
321C2×C73C2×#44611yescharacteristic
322C2×C73Q8×M1611yescharacteristic
323C2×C73#297311yescharacteristic
324C2×C73#297411yescharacteristic
325D73—24no—
326C2×C4×C4⋊C4—731no—
327#1940—731no—
328#1940—731no—
329#1917—731no—
330#1917—731no—
331#1916—731no—
332#1916—731no—
333#1797—731no—
334#1797—731no—
335#1797—731no—
336#1771—731no—
337#1771D7311yescharacteristic, complemented
338#1749—731no—
339#1749—731no—
340C4×C22⋊C8—731no—
341C73#2262711yescharacteristic, complemented, Sylow
342C22×C4⋊C4—731no—
343C22×C4⋊C4—731no—
344C22×C42—731no—
345C22×C42—731no—
346C22×C42—731no—
347C2×C4⋊C8—731no—
348C2×C4⋊C8—731no—
349C2×C4⋊C8—731no—
350C2×C4⋊C8—731no—
351C2×C4⋊C8—731no—
352C2×C4⋊C8C2×D7311yescharacteristic
353C2×C22⋊C8—731no—
354C2×C22⋊C8—731no—
355C2×C22⋊C8—731no—
356C2×C22⋊C8—731no—
357C2×#97—731no—
358C2×#97—731no—
359C2×#97C2×D7311yescharacteristic
360C2×#97C2×D7311yescharacteristic
361C2×C4×C8—731no—
362C2×C4×C8C2×D7311yescharacteristic
363C4×C4⋊C4—731no—
364C4×C4⋊C4—731no—
365C4×C4⋊C4—731no—
366C4×C4⋊C4—731no—
367C4×C4⋊C4—731no—
368C4×C4⋊C4—731no—
369C4×C4⋊C4—731no—
370C4×C4⋊C4C2×D7311yescharacteristic
371C2×#95—731no—
372C2×#95—731no—
373#336—731no—
374#336—731no—
375#336—731no—
376#336—731no—
377#336—731no—
378#336—731no—
379#336—731no—
380#336—731no—
381#336—731no—
382#336—731no—
383#336C2×D7311yescharacteristic
384#336C2×D7311yescharacteristic
385C23×C4—731no—
386C23×C4—731no—
387C23×C4—731no—
388C23×C4—731no—
389C23×C4—731no—
390C23×C4—731no—
391C23×C4—731no—
392C22×C8—731no—
393C22×C8—731no—
394C22×C8—731no—
395C22×C8—731no—
396C22×C8C22×D7311yescharacteristic
397C22×C8C22×D7311yescharacteristic
398C22×C8C22×D7311yescharacteristic
399C22×C8C22×D7311yescharacteristic
400C2×C4⋊C4—731no—
401C2×C4⋊C4—731no—
402C2×C4⋊C4—731no—
403C2×C4⋊C4—731no—
404C2×C4⋊C4—731no—
405C2×C4⋊C4—731no—
406C2×C4⋊C4—1464no—
407C2×C4⋊C4—1464no—
408C2×C4⋊C4C4×D7311yescharacteristic
409C2×C4⋊C4C4×D7311yescharacteristic
410C2×C42—2921no—
411C2×C42—2921no—
412C2×C42—2921no—
413C2×C42—2921no—
414C2×C42—731no—
415C2×C42—731no—
416C2×C42—731no—
417C2×C42—731no—
418C2×C42—731no—
419C2×C42—731no—
420C2×C42—731no—
421C2×C42—731no—
422C2×C42—731no—
423C2×C42—1462no—
424C2×C42—1462no—
425C2×C42C22×D7311yescharacteristic
426C2×C42C22×D7311yescharacteristic
427C2×C42C22×D7311yescharacteristic
428C4⋊C8—22no—
429C4⋊C8—2921no—
430C4⋊C8—2921no—
431C4⋊C8—2921no—
432C4⋊C8—2921no—
433C4⋊C8—1462no—
434C22⋊C8—734no—
435C22⋊C8—1462no—
436C22⋊C8—1462no—
437C22⋊C8—1462no—
438#97—22no—
439#97—41no—
440#97—2921no—
441#97—1462no—
442C4×C8—41no—
443C4×C8—2921no—
444#95—731no—
445#95—731no—
446#95—731no—
447#95—731no—
448#95—731no—
449#95—731no—
450#95C4×D7311yescharacteristic
451#95C4×D7311yescharacteristic
452C24—731no—
453C22×C4—2921no—
454C22×C4—2921no—
455C22×C4—2921no—
456C22×C4—2921no—
457C22×C4—2921no—
458C22×C4—2921no—
459C22×C4—2921no—
460C22×C4—734no—
461C22×C4—731no—
462C22×C4—731no—
463C22×C4—731no—
464C22×C4—731no—
465C22×C4—732no—
466C22×C4—732no—
467C22×C4—731no—
468C22×C4—731no—
469C22×C4—731no—
470C22×C4—1462no—
471C22×C4—1462no—
472C22×C4—1462no—
473C22×C4—1462no—
474C22×C4—1462no—
475C22×C4—1462no—
476C22×C4—1462no—
477C22×C4—1462no—
478C22×C4—1462no—
479C22×C4—1462no—
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×C4C2×C4×D7311yescharacteristic
490C22×C4C23×D7311yescharacteristic
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—732no—
503C2×C8—1461no—
504C2×C8—1461no—
505C2×C8—1461no—
506C2×C8—1461no—
507C2×C8—1461no—
508C2×C8—1461no—
509C2×C8—1461no—
510C2×C8—1461no—
511C2×C8—1461no—
512C2×C8—1461no—
513C2×C8—1461no—
514C2×C8Q8×D7312yes—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—734no—
518C4⋊C4—1462no—
519C4⋊C4—1462no—
520C4⋊C4—1462no—
521C4⋊C4—1462no—
522C4⋊C4—1462no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—2921no—
528C42—2921no—
529C42—2921no—
530C42—2921no—
531C42—1462no—
532C42—1462no—
533C42—1461no—
534C42—1461no—
535C42—1461no—
536C42—1461no—
537C42—1461no—
538C42—1461no—
539C42#1192402812yes—
540C42#1192402812yes—
541C23—732no—
542C23—732no—
543C23—732no—
544C23—1461no—
545C23—1461no—
546C23—1461no—
547C23—1461no—
548C23C22×C4×D7311yescharacteristic
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
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—2924no—
564C2×C4—2924no—
565C2×C4—2924no—
566C2×C4—2924no—
567C2×C4—2924no—
568C2×C4—732no—
569C2×C4—732no—
570C2×C4—732no—
571C2×C4—732no—
572C2×C4—1468no—
573C2×C4—1461no—
574C2×C4—1461no—
575C2×C4—1461no—
576C2×C4—1461no—
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—1462no—
591C2×C4—1462no—
592C2×C4—1462no—
593C2×C4—1462no—
594C2×C4#1455654812yes—
595C2×C4#1455654812yes—
596C2×C4M16×D7312yes—
597C2×C4M16×D7312yes—
598C2×C4C2×Q8×D7311yescharacteristic
599C2×C4#41×D7311yescharacteristic
600C2×C4C2×#1192402811yescharacteristic
601C2×C4C2×#1192402811yescharacteristic
602C2×C4#1455663611yescharacteristic
603C2×C4#1455663711yescharacteristic
604C8—22no—
605C8—41no—
606C8—41no—
607C8—41no—
608C8—2921no—
609C8—2921no—
610C8—2921no—
611C8—1462no—
612C22—734no—
613C22—1462no—
614C22—1462no—
615C22—1462no—
616C22—1462no—
617C22—1462no—
618C22—1462no—
619C22C2×#1455654811yescharacteristic
620C22C4×Q8×D7311yescharacteristic
621C22#1798905911yescharacteristic
622C22C2×M16×D7311yescharacteristic
623C22C2×M16×D7311yescharacteristic
624C22#131×D7311yescharacteristic
625C22#1798935211yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—22no—
630C4—41no—
631C4—41no—
632C4—2921no—
633C4—2921no—
634C4—2921no—
635C4—1462no—
636C4—1462no—
637C4—1462no—
638C4—1462no—
639C4#1798928111yescharacteristic
640C4#1798928711yescharacteristic
641C4#1798929211yescharacteristic
642C4#1798929711yescharacteristic
643C2—1464no—
644C2#2261280411yescharacteristic
645C2#2261856211yescharacteristic
646C2#2261858611yescharacteristic
647C2#446×D7311yescharacteristic
648C2#2261888311yescharacteristic
649C2#2261895611yescharacteristic
650C2#2261896111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1771C2
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenter#1771D73
hypocenterC73#22627
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. #22610654C2semidirect
3. #22610652C2semidirect
4. #22610495C2semidirect
5. #22610493C2semidirect
6. #22610488C2semidirect
7. #22610486C2semidirect
11. #22609806C2semidirect
15. C73×#1771C2semidirect
337. #1771D73semidirect
341. C73#22627semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊C4×D732
#226106542
#226106522
#226104952
#226104932
#226104882
#226104862
#226099102
#226099082
#226098062
#226096942
C4×#145565032
C73×#17712
#2262773