Finite Group Databasebeta

← #33090177

Subgroups — #33090177

Order 18688.

860 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988645C211yesmaximal, characteristic, complemented
2C2×#17988643C211yesmaximal, characteristic, complemented
3#22612377C211yesmaximal, characteristic
4#22610727C211yesmaximal, characteristic
5#22610723C211yesmaximal, characteristic
6#22610651C211yesmaximal, characteristic, complemented
7#22610648C211yesmaximal, characteristic, complemented
8#22610546C211yesmaximal, characteristic, complemented
9#22610542C211yesmaximal, characteristic, complemented
10#22610537C211yesmaximal, characteristic, complemented
11#22609787C211yesmaximal, characteristic, complemented
12#22609699C211yesmaximal, characteristic, complemented
13#22609688C211yesmaximal, characteristic, complemented
14#22609617C211yesmaximal, characteristic, complemented
15C73×#1923C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊D73C2211yescharacteristic
17C2×#14556550C2211yescharacteristic
18C2×C42×D73C2211yescharacteristic
19#17988645—24no—
20#17988643—24no—
21C2×C4⋊#10596831C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×#14556520C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556502C2211yescharacteristic
33C2×#14556501C2211yescharacteristic
34C2×#14556501C2211yescharacteristic
35C2×#14556501C2211yescharacteristic
36C2×C8×Dic73C2211yescharacteristic
37C2×C8×Dic73C2211yescharacteristic
38C2×C8×Dic73C2211yescharacteristic
39#17988481C411yescharacteristic
40#17988481C411yescharacteristic
41#17988474C411yescharacteristic
42#17988474C411yescharacteristic
43#17988463C411yescharacteristic
44#17988463C411yescharacteristic
45#17988461C411yescharacteristic
46#17988461C411yescharacteristic
47C4×#11924007C2211yescharacteristic
48C4×#11924005C2211yescharacteristic
49#17988433C2211yescharacteristic
50#17988342C2211yescharacteristic
51#17988342C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57C2×C4×C8×C73C2211yescharacteristic
58C4×C22⋊C4×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×C22⋊D73C2×C411yescharacteristic
62C22×C4×D73C2×C411yescharacteristic
63C22×C4×D73C2×C411yescharacteristic
64C22×C4×D73C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C4×C22⋊D73—22no—
70C4×C22⋊D73—22no—
71#14556550—22no—
72#14556550—22no—
73C2×C4⋊Dic73C2×C411yescharacteristic
74C2×C4⋊Dic73C2×C411yescharacteristic
75C2×#11924007C2×C411yescharacteristic
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×C22⋊Dic73C2×C411yescharacteristic
79C2×C22⋊Dic73C2×C411yescharacteristic
80C2×C22⋊Dic73C2×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—22no—
90C42×D73—22no—
91C4⋊#10596831—22no—
92#14556520—22no—
93#14556520—22no—
94#14556520—22no—
95#14556520—22no—
96C22⋊#10596831—22no—
97C22⋊#10596831—22no—
98#14556503—22no—
99#14556503—22no—
100#14556503—22no—
101#14556503—22no—
102#14556502—22no—
103#14556501—22no—
104#14556501—22no—
105#14556501D414yescomplemented
106C8×Dic73—22no—
107C8×Dic73—22no—
108C8×Dic73—22no—
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117C23×C4×C73C2311yescharacteristic
118C22×C8×C73C2311yescharacteristic
119C22×C8×C73C2311yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122C2×C22⋊C4×C73C2×C411yescharacteristic
123C2×C22⋊C4×C73C2×C411yescharacteristic
124C2×C42×C73C2311yescharacteristic
125C2×C42×C73C2311yescharacteristic
126C4⋊C8×C73—22no—
127C22⋊C8×C73—22no—
128C22⋊C8×C73—22no—
129C4×C8×C73—22no—
130#95×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
132C23×D73C22×C411yescharacteristic
133C2×C22⋊D73—22no—
134C2×C22⋊D73—22no—
135C2×C22⋊D73—41no—
136C22×Dic73C22×C411yescharacteristic
137C22×Dic73C22×C411yescharacteristic
138C22×Dic73C22×C411yescharacteristic
139C22×Dic73C22×C411yescharacteristic
140C22×Dic73C22×C411yescharacteristic
141C22×Dic73C22×C411yescharacteristic
142C22×Dic73C22×C411yescharacteristic
143C2×C4×D73—22no—
144C2×C4×D73—22no—
145C2×C4×D73—21no—
146C2×C4×D73—21no—
147C2×C4×D73—21no—
148C2×C4×D73—21no—
149C2×C4×D73—21no—
150C2×C4×D73—21no—
151C2×C4×D73—22no—
152C2×C4×D73—22no—
153C2×C4×D73—41no—
154C2×C4×D73—41no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831C2×D412yes—
166C2×#10596831#4112yes—
167C4⋊Dic73—22no—
168C4⋊Dic73—22no—
169#11924007—22no—
170#11924007—22no—
171#11924007—41no—
172C22⋊Dic73—22no—
173C22⋊Dic73—22no—
174C22⋊Dic73—22no—
175#11924005—22no—
176#11924005—22no—
177#11924005—41no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—22no—
181C4×Dic73—22no—
182C4×Dic73C2×D412yes—
183C4×Dic73#4112yes—
184C4×Dic73#4112yes—
185C4×Dic73#4112yes—
186C24×C73C22×C411yescharacteristic
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C22×C411yescharacteristic
195C22×C4×C73C22×C411yescharacteristic
196C22×C4×C73C22×C411yescharacteristic
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C2411yescharacteristic
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×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73C2×D412yes—
210C2×C8×C73#4112yes—
211C22⋊C4×C73—22no—
212C22⋊C4×C73—41no—
213C42×C73—21no—
214C42×C73—21no—
215C42×C73—21no—
216C42×C73—21no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73C23×C411yescharacteristic
225C22×D73—21no—
226C22×D73—21no—
227C22×D73—21no—
228C22×D73—21no—
229C22×D73—21no—
230C22×D73—21no—
231C22×D73#13112yes—
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—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73#13112yes—
251C2×C4×C73C22×D411yescharacteristic
252C2×C4×C73C2×#4111yescharacteristic
253C2×C4×C73C2×#4111yescharacteristic
254C2×C4×C73C2×#4111yescharacteristic
255C2×C4×C73C2×#4111yescharacteristic
256C2×C4×C73C2×#4111yescharacteristic
257C22⋊D73—44no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—21no—
263C2×Dic73—21no—
264C2×Dic73—21no—
265C2×Dic73—21no—
266C2×Dic73—21no—
267C2×Dic73—21no—
268C2×Dic73—21no—
269C2×Dic73—21no—
270C2×Dic73—21no—
271C2×Dic73—21no—
272C2×Dic73—21no—
273C2×Dic73—21no—
274C2×Dic73—21no—
275C2×Dic73#11712yes—
276C2×Dic73#11712yes—
277C2×Dic73C4×D412yes—
278C2×Dic73C4×D412yes—
279C4×D73—44no—
280C4×D73—44no—
281C4×D73—41no—
282C4×D73—41no—
283C4×D73—41no—
284C4×D73—41no—
285C8×C73—22no—
286C8×C73—22no—
287C8×C73—41no—
288C8×C73—41no—
289#10596831—22no—
290#10596831—22no—
291#10596831—41no—
292#10596831—41no—
293C22×C73—41no—
294C22×C73—41no—
295C22×C73—41no—
296C22×C73—41no—
297C22×C73—41no—
298C22×C73—41no—
299C22×C73—41no—
300C22×C73C2×#11711yescharacteristic
301C22×C73C2×C4×D411yescharacteristic
302C22×C73C4×#4111yescharacteristic
303C22×C73C2×#13111yescharacteristic
304C22×C73C2×#13111yescharacteristic
305C22×C73#56811yescharacteristic
306C22×C73#56811yescharacteristic
307C2×D73—22no—
308C2×D73—22no—
309C2×D73—22no—
310C2×D73—41no—
311C2×D73—41no—
312C2×D73—41no—
313C2×D73—41no—
314C4×C73—22no—
315C4×C73—41no—
316C4×C73—41no—
317C4×C73—41no—
318C4×C73—41no—
319C4×C73#52911yescharacteristic
320C4×C73#52911yescharacteristic
321C4×C73#53211yescharacteristic
322C4×C73#53211yescharacteristic
323Dic73—22no—
324Dic73—22no—
325Dic73—22no—
326Dic73—22no—
327Dic73—41no—
328Dic73—41no—
329Dic73—41no—
330#21273—731nomaximal, Sylow
331C2×C73—81no—
332C2×C73#229311yescharacteristic
333C2×C73#292411yescharacteristic
334C2×C73#292511yescharacteristic
335C2×C73#293311yescharacteristic
336C2×C73#293311yescharacteristic
337C2×C73#296611yescharacteristic
338C2×C73#296711yescharacteristic
339D73—42no—
340C2×#433—731no—
341C2×#432—731no—
342#2290—731no—
343#1955—731no—
344#1954—731no—
345#1940—731no—
346#1939—731no—
347#1924—731no—
348#1924—731no—
349#1923—731no—
350#1923D7311yescharacteristic, complemented
351#1768—731no—
352#1750—731no—
353C4×C22⋊C8—731no—
354#1726—731no—
355C73#2127311yescharacteristic, complemented, Sylow
356C2×C4×D4—731no—
357C2×#117—731no—
358C22×C42—731no—
359#433—1464no—
360#432—1464no—
361C2×C4⋊C8—731no—
362C2×C4⋊C8—731no—
363C2×C4⋊C8—731no—
364C2×C4⋊C8—731no—
365C2×C4⋊C8—731no—
366C2×C4⋊C8C2×D7311yescharacteristic
367C2×C22⋊C8—731no—
368C2×C22⋊C8—731no—
369C2×C22⋊C8—731no—
370C2×C22⋊C8—731no—
371C2×C22⋊C8—731no—
372C2×C22⋊C8—731no—
373C2×C22⋊C8C2×D7311yescharacteristic
374C2×C22⋊C8C2×D7311yescharacteristic
375C2×#97—731no—
376C2×#97—731no—
377C2×#97—731no—
378C2×#97—731no—
379C2×C4×C8—731no—
380C2×C4×C8—731no—
381C2×C4×C8—731no—
382C2×C4×C8C2×D7311yescharacteristic
383#388—731no—
384#388—731no—
385#387—731no—
386#387—731no—
387#386—731no—
388#386—731no—
389#385—731no—
390#385—731no—
391C4×C4⋊C4—731no—
392C4×C22⋊C4—731no—
393C4×C22⋊C4C2×D7311yescharacteristic
394#376—731no—
395#336—731no—
396#336—731no—
397#336—731no—
398#336—731no—
399#336C2×D7311yescharacteristic
400#336C2×D7311yescharacteristic
401C22×D4—731no—
402C23×C4—731no—
403C23×C4—731no—
404C23×C4—731no—
405C23×C4C22×D7311yescharacteristic
406C22×C8—731no—
407C22×C8—731no—
408C22×C8—731no—
409C22×C8—731no—
410C22×C8C22×D7311yescharacteristic
411C22×C8C22×D7311yescharacteristic
412C22×C8C22×D7311yescharacteristic
413C22×C8C22×D7311yescharacteristic
414C4×D4—1462no—
415C4×D4—1462no—
416#117—1462no—
417#117—1462no—
418C2×C4⋊C4—731no—
419C2×C4⋊C4—731no—
420C2×C4⋊C4—731no—
421C2×C4⋊C4—731no—
422C2×C4⋊C4—731no—
423C2×C22⋊C4—731no—
424C2×C22⋊C4—731no—
425C2×C22⋊C4—731no—
426C2×C22⋊C4—731no—
427C2×C22⋊C4—731no—
428C2×C22⋊C4—731no—
429C2×C22⋊C4C4×D7311yescharacteristic
430C2×C22⋊C4C4×D7311yescharacteristic
431C2×C42—731no—
432C2×C42—731no—
433C2×C42—731no—
434C2×C42—731no—
435C2×C42—731no—
436C2×C42—1462no—
437C2×C42—1462no—
438C2×C42C22×D7311yescharacteristic
439C2×C42C22×D7311yescharacteristic
440C4⋊C8—22no—
441C4⋊C8—1462no—
442C4⋊C8—1462no—
443C4⋊C8—1462no—
444C4⋊C8—1462no—
445C4⋊C8—1462no—
446C22⋊C8—22no—
447C22⋊C8—22no—
448C22⋊C8—1462no—
449C22⋊C8—1462no—
450C22⋊C8—1462no—
451C22⋊C8—1462no—
452C22⋊C8—1462no—
453C22⋊C8—1462no—
454#97—734no—
455#97—1462no—
456#97—1462no—
457#97—1462no—
458C4×C8—22no—
459C4×C8—1462no—
460C4×C8—1462no—
461C4×C8—1462no—
462#95—731no—
463#95—731no—
464#95—731no—
465#95—731no—
466#95—731no—
467#95—731no—
468#95—731no—
469#95—731no—
470#95C4×D7311yescharacteristic
471#95C4×D7311yescharacteristic
472C24—731no—
473C24C2×C4×D7311yescharacteristic
474C2×D4—2921no—
475C2×D4—1462no—
476C2×D4—1462no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—2921no—
484C22×C4—2921no—
485C22×C4—731no—
486C22×C4—731no—
487C22×C4—731no—
488C22×C4—731no—
489C22×C4—731no—
490C22×C4—731no—
491C22×C4—731no—
492C22×C4—1462no—
493C22×C4—1462no—
494C22×C4—1462no—
495C22×C4—1462no—
496C22×C4—1461no—
497C22×C4—1461no—
498C22×C4—1461no—
499C22×C4—1461no—
500C22×C4—1461no—
501C22×C4—1461no—
502C22×C4C2×C4×D7311yescharacteristic
503C22×C4C2×C4×D7311yescharacteristic
504C22×C4C2×C4×D7311yescharacteristic
505C22×C4C2×C4×D7311yescharacteristic
506C22×C4C2×C4×D7311yescharacteristic
507C22×C4C23×D7311yescharacteristic
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—732no—
519C2×C8—732no—
520C2×C8—1461no—
521C2×C8—1461no—
522C2×C8—1461no—
523C2×C8—1461no—
524C2×C8—1461no—
525C2×C8—1461no—
526C2×C8—1461no—
527C2×C8—1461no—
528C2×C8—1461no—
529C2×C8—1461no—
530C2×C8D4×D7312yes—
531C2×C8#1192402712yes—
532C4⋊C4—2921no—
533C4⋊C4—1462no—
534C4⋊C4—1462no—
535C4⋊C4—1462no—
536C4⋊C4—1462no—
537C22⋊C4—22no—
538C22⋊C4—41no—
539C22⋊C4—2921no—
540C22⋊C4—1462no—
541C22⋊C4—1462no—
542C22⋊C4—1462no—
543C22⋊C4—1462no—
544C22⋊C4—1462no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—732no—
550C42—732no—
551C42—732no—
552C42—732no—
553C42—1462no—
554C42—1462no—
555C42—1461no—
556C42—1461no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—732no—
565C23—1461no—
566C23—1461no—
567C23—1461no—
568C23—1461no—
569C23—1461no—
570C23—1461no—
571C23C22×C4×D7311yescharacteristic
572D4—2924no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—2924no—
592C2×C4—2924no—
593C2×C4—2921no—
594C2×C4—2921no—
595C2×C4—2921no—
596C2×C4—2921no—
597C2×C4—732no—
598C2×C4—732no—
599C2×C4—732no—
600C2×C4—732no—
601C2×C4—1461no—
602C2×C4—1461no—
603C2×C4—1461no—
604C2×C4—1461no—
605C2×C4—1461no—
606C2×C4—1461no—
607C2×C4—1461no—
608C2×C4—1461no—
609C2×C4—1461no—
610C2×C4—1461no—
611C2×C4—1461no—
612C2×C4—1461no—
613C2×C4—1461no—
614C2×C4—1461no—
615C2×C4—1461no—
616C2×C4—1461no—
617C2×C4—1461no—
618C2×C4#1455659712yes—
619C2×C4C2×D4×D7311yescharacteristic
620C2×C4#41×D7311yescharacteristic
621C2×C4#41×D7311yescharacteristic
622C2×C4#41×D7311yescharacteristic
623C2×C4#41×D7311yescharacteristic
624C2×C4C2×#1192402711yescharacteristic
625C8—22no—
626C8—22no—
627C8—41no—
628C8—41no—
629C8—2921no—
630C8—2921no—
631C8—1462no—
632C8—1462no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—2921no—
641C22—2921no—
642C22—2921no—
643C22—2921no—
644C22—1462no—
645C22—1462no—
646C22—1462no—
647C22#117×D7311yescharacteristic
648C22C4×D4×D7311yescharacteristic
649C22C4×#1192402711yescharacteristic
650C22#131×D7311yescharacteristic
651C22C2×#1455659711yescharacteristic
652C22#1798935211yescharacteristic
653C22#1798935311yescharacteristic
654C4—22no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—2921no—
660C4—2921no—
661C4—2921no—
662C4—1462no—
663C4—1462no—
664C4—1462no—
665C4—1462no—
666C4#1798911411yescharacteristic
667C4#1798912011yescharacteristic
668C4#1798913211yescharacteristic
669C4#1798913611yescharacteristic
670C2—81no—
671C2—2922no—
672C2#2261239111yescharacteristic
673C2#2261858711yescharacteristic
674C2#2261859211yescharacteristic
675C2#2261865111yescharacteristic
676C2#2261866011yescharacteristic
677C2#2261890311yescharacteristic
678C2#2261891311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1923C2
prime radicalC22×C22⋊D73C2×C4
cosocleC22×C4×C73C24
hypercenter#1923D73
hypocenterC73#21273
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#17988645C2semidirect
2. C2×#17988643C2semidirect
6. #22610651C2semidirect
7. #22610648C2semidirect
8. #22610546C2semidirect
9. #22610542C2semidirect
10. #22610537C2semidirect
11. #22609787C2semidirect
12. #22609699C2semidirect
13. #22609688C2semidirect
14. #22609617C2semidirect
15. C73×#1923C2semidirect
105. #14556501D4semidirect
350. #1923D73semidirect
355. C73#21273semidirect

Maximal subgroups

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

subgroupindex
C2×#179886452
C2×#179886432
#226123772
#226107272
#226107232
#226106512
#226106482
#226105462
#226105422
#226105372
#226097872
#226096992
#226096882
#226096172
C73×#19232
#2127373