Finite Group Databasebeta

← #34026376

Subgroups — #34026376

Order 18688.

1292 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989639C212yesmaximal, complemented
2#22626104C212yesmaximal, complemented
3#22626103C212yesmaximal, complemented
4#22626102C212yesmaximal, complemented
5#22625787C211yesmaximal, characteristic
6#22625787C211yesmaximal, characteristic
7#22625785C211yesmaximal, characteristic
8#22625657C211yesmaximal, characteristic
9#22625657C211yesmaximal, characteristic
10C4×C22⋊#10596833C211yesmaximal, characteristic
11C22×#14556556C211yesmaximal, characteristic
12#17989639—28no—
13C2×#14556658C2212yes—
14C2×#14556658C2212yes—
15C2×C4⋊#10596833C2212yes—
16C2×C22⋊#10596833C2211yescharacteristic
17C2×C22⋊#10596833C2211yescharacteristic
18C2×C22⋊#10596833C2211yescharacteristic
19C2×C22⋊#10596833C2211yescharacteristic
20C2×#14556646C2212yes—
21C2×#14556646C2212yes—
22C2×C4×#10596833C2212yes—
23#17989453C2212yes—
24#17989453C2212yes—
25#17989453C2212yes—
26#17989453C2212yes—
27#17989453C2212yes—
28#17989453C2212yes—
29C23×Dic146C411yescharacteristic
30C2×#14556556—28no—
31C2×#14556556C411yescharacteristic
32C2×#14556556C411yescharacteristic
33C2×#14556556C411yescharacteristic
34C2×#14556556C411yescharacteristic
35C2×#14556556C2211yescharacteristic
36C2×#14556556C2211yescharacteristic
37C2×#14556556C2211yescharacteristic
38C2×#14556556C2211yescharacteristic
39C22×#11924007C411yescharacteristic
40C22×#11924007C411yescharacteristic
41C22×C4×Dic73C2211yescharacteristic
42C22×C4×Dic73C2211yescharacteristic
43C22×C4×Dic73C2211yescharacteristic
44C22×C4⋊C4×C73C411yescharacteristic
45C22×#10596833C2312yes—
46C22×#10596833C2312yes—
47C22×#10596833C2312yes—
48C22×#10596833C2312yes—
49#14556658—24no—
50#14556658—24no—
51C4⋊#10596833—24no—
52C22⋊#10596833—22no—
53C22⋊#10596833—22no—
54C22⋊#10596833—22no—
55C22⋊#10596833Q814yescomplemented
56#14556646—24no—
57#14556646—24no—
58C4×#10596833—24no—
59C22×Dic146—24no—
60C22×Dic146—24no—
61C22×Dic146—24no—
62C22×Dic146C2×C411yescharacteristic
63C22×Dic146C2×C411yescharacteristic
64C22×Dic146C2×C411yescharacteristic
65C22×Dic146C2×C411yescharacteristic
66C23×Dic73C2×C411yescharacteristic
67C23×Dic73C2×C411yescharacteristic
68C23×Dic73C2×C411yescharacteristic
69C23×Dic73C2311yescharacteristic
70#14556556—24no—
71#14556556—24no—
72#14556556—24no—
73#14556556—24no—
74#14556556—24no—
75#14556556—24no—
76#14556556—24no—
77#14556556D418yes—
78C2×#11924007—24no—
79C2×#11924007—24no—
80C2×#11924007C2×C411yescharacteristic
81C2×#11924007C2×C411yescharacteristic
82C2×#11924007C2×C411yescharacteristic
83C2×#11924007C2×C411yescharacteristic
84C2×#11924007C2×C411yescharacteristic
85C2×#11924007C2×C411yescharacteristic
86C2×#11924007C2×C411yescharacteristic
87C2×#11924007C2×C411yescharacteristic
88C2×C4×Dic73—24no—
89C2×C4×Dic73—24no—
90C2×C4×Dic73—24no—
91C2×C4×Dic73C2×C411yescharacteristic
92C2×C4×Dic73C2×C411yescharacteristic
93C2×C4×Dic73C2×C411yescharacteristic
94C2×C4×Dic73C2×C411yescharacteristic
95C2×C4×Dic73C2×C411yescharacteristic
96C2×C4×Dic73C2×C411yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99C2×C4×Dic73C2311yescharacteristic
100C2×C4×Dic73C2311yescharacteristic
101C2×C4×Dic73C2311yescharacteristic
102C2×C4×Dic73C2311yescharacteristic
103C23×C4×C73C2×C411yescharacteristic
104C23×C4×C73C2×C411yescharacteristic
105C23×C4×C73C2×C411yescharacteristic
106C2×C4⋊C4×C73—24no—
107C2×C4⋊C4×C73C2×C411yescharacteristic
108C2×C4⋊C4×C73C2×C411yescharacteristic
109C2×C4⋊C4×C73C2×C411yescharacteristic
110C2×C4⋊C4×C73C2×C411yescharacteristic
111C2×#10596833—22no—
112C2×#10596833—22no—
113C2×#10596833—22no—
114C2×#10596833—22no—
115C2×#10596833—22no—
116C2×#10596833—22no—
117C2×#10596833—22no—
118C2×#10596833—22no—
119C2×#10596833—22no—
120C2×#10596833—22no—
121C2×#10596833—22no—
122C2×#10596833C2×Q814yescomplemented
123C2×Dic146—232no—
124C2×Dic146—22no—
125C2×Dic146—22no—
126C2×Dic146—22no—
127C2×Dic146—22no—
128C2×Dic146—22no—
129C2×Dic146—22no—
130C2×Dic146—22no—
131C2×Dic146—22no—
132C2×Dic146—22no—
133C2×Dic146—22no—
134C2×Dic146C22⋊C414yes—
135C2×Dic146M1614yes—
136C22×Dic73—22no—
137C22×Dic73—22no—
138C22×Dic73—22no—
139C22×Dic73—22no—
140C22×Dic73—22no—
141C22×Dic73—22no—
142C22×Dic73—22no—
143C22×Dic73—22no—
144C22×Dic73—22no—
145C22×Dic73—41no—
146C22×Dic73M1614yes—
147C22×Dic73C22×C411yescharacteristic
148C22×Dic73C22×C411yescharacteristic
149C22×Dic73C22×C411yescharacteristic
150C22×Dic73C22×C411yescharacteristic
151C22×Dic73C22×C411yescharacteristic
152C22×Dic73C22×C411yescharacteristic
153C22×Dic73C22×C411yescharacteristic
154C22×Dic73C2×Q812yes—
155C22×Dic73#4112yes—
156C22×Dic73C2411yescharacteristic
157#11924007—22no—
158#11924007—22no—
159#11924007—22no—
160#11924007—22no—
161#11924007—22no—
162#11924007—22no—
163#11924007C22⋊C414yes—
164#11924007C22⋊C414yes—
165C4×Dic73—22no—
166C4×Dic73—22no—
167C4×Dic73—22no—
168C4×Dic73—22no—
169C4×Dic73—22no—
170C4×Dic73—22no—
171C4×Dic73—22no—
172C4×Dic73—22no—
173C4×Dic73—22no—
174C4×Dic73C2×D414yes—
175C4×Dic73C2×D414yes—
176C4×Dic73C2×D414yes—
177C24×C73C22×C411yescharacteristic
178C22×C4×C73—22no—
179C22×C4×C73—22no—
180C22×C4×C73—22no—
181C22×C4×C73—22no—
182C22×C4×C73—22no—
183C22×C4×C73—22no—
184C22×C4×C73—22no—
185C22×C4×C73—41no—
186C22×C4×C73—41no—
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C22×C411yescharacteristic
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C22×C411yescharacteristic
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C22×C411yescharacteristic
193C4⋊C4×C73—22no—
194C4⋊C4×C73—22no—
195C4⋊C4×C73—22no—
196C4⋊C4×C73C22⋊C414yes—
197C23×C73—21no—
198C23×C73—21no—
199C23×C73—21no—
200C23×C73—21no—
201C23×C73C4×Q812yes—
202C23×C73C2×M1612yes—
203C23×C73#13112yes—
204C23×C73C23×C411yescharacteristic
205C2×C4×C73—28no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
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—44no—
221C2×C4×C73—44no—
222C2×C4×C73C2×C22⋊C412yes—
223C2×C4×C73C2×C22⋊C412yes—
224C2×C4×C73C2×C22⋊C412yes—
225C2×C4×C73C2×M1612yes—
226C2×Dic73—28no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—24no—
238C2×Dic73—24no—
239C2×Dic73—28no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—44no—
244C2×Dic73C2×C22⋊C412yes—
245C2×Dic73C2×C22⋊C412yes—
246C2×Dic73C2×C22⋊C412yes—
247C2×Dic73C4×Q812yes—
248C2×Dic73C2×M1612yes—
249C2×Dic73C2×M1612yes—
250C2×Dic73C2×M1612yes—
251C2×Dic73C2×M1612yes—
252C2×Dic73C22×D412yes—
253C2×Dic73C22×Q811yescharacteristic
254C2×Dic73C2×#4111yescharacteristic
255C2×Dic732−1+412yes—
256Dic146—28no—
257Dic146—28no—
258Dic146—28no—
259Dic146—28no—
260#10596833—24no—
261#10596833—42no—
262#10596833—42no—
263#10596833—42no—
264C22×C73—22no—
265C22×C73—22no—
266C22×C73—22no—
267C22×C73—22no—
268C22×C73—22no—
269C22×C73—22no—
270C22×C73#44614yescomplemented
271C22×C73C22×C22⋊C411yescharacteristic
272C22×C73C2×C4×Q811yescharacteristic
273C22×C73#51911yescharacteristic
274C22×C73C22×M1611yescharacteristic
275C22×C73C22×M1611yescharacteristic
276C22×C73C2×#13111yescharacteristic
277C22×C73#56811yescharacteristic
278C4×C73—22no—
279C4×C73—22no—
280C4×C73—22no—
281C4×C73—22no—
282C4×C73—41no—
283C4×C73—41no—
284Dic73—22no—
285Dic73—22no—
286Dic73—22no—
287Dic73—22no—
288Dic73—22no—
289Dic73—41no—
290Dic73#40714yes—
291Dic73#54812yes—
292Dic73D4×Q812yes—
293#22510—731nomaximal, Sylow
294C2×C73—24no—
295C2×C73Q8×C22⋊C411yescharacteristic
296C2×C73C2×#40711yescharacteristic
297C2×C73#288011yescharacteristic
298C2×C73C2×#44611yescharacteristic
299C2×C73Q8×M1611yescharacteristic
300C2×C73#298311yescharacteristic
301C2×C73#298411yescharacteristic
302C22×C4×Q8—731no—
303C2×#446—732no—
304#1985—732no—
305#1985—732no—
306#1984—732no—
307#1797—731no—
308#1797—731no—
309#1797—731no—
310#1749—731no—
311#1749—731no—
312C4×C22⋊C8—731no—
313C73#2251011yescharacteristic, complemented, Sylow
314C23×Q8—731no—
315C2×C4×Q8—731no—
316C2×C4×Q8—731no—
317C2×C4×Q8—731no—
318C2×C4×Q8—731no—
319C2×C4×Q8—731no—
320C2×C4×Q8—731no—
321C2×C4×Q8—731no—
322C2×C4×Q8—731no—
323C2×C4×Q8—1468no—
324C22×C4⋊C4—731no—
325C22×C4⋊C4—731no—
326C22×C4⋊C4#6440811yescharacteristic
327C22×C42—731no—
328C22×C42—731no—
329C22×C42—731no—
330#446—1468no—
331C2×C4⋊C8—732no—
332C2×C4⋊C8—732no—
333C2×C4⋊C8—732no—
334C2×C22⋊C8—731no—
335C2×C22⋊C8—731no—
336C2×C22⋊C8—731no—
337C2×C22⋊C8—731no—
338C2×#97—732no—
339C2×#97—732no—
340C2×C4×C8—732no—
341#336—732no—
342#336—732no—
343#336—732no—
344#336—732no—
345#336—732no—
346#336—732no—
347C22×Q8—731no—
348C22×Q8—731no—
349C22×Q8—731no—
350C22×Q8—731no—
351C22×Q8—1464no—
352C22×Q8—1464no—
353C22×Q8—1464no—
354C23×C4—731no—
355C23×C4—731no—
356C23×C4—731no—
357C23×C4—731no—
358C23×C4C2×#6440811yescharacteristic
359C23×C4C2×#6440811yescharacteristic
360C23×C4C2×#6440811yescharacteristic
361C22×C8—732no—
362C22×C8—732no—
363C22×C8—732no—
364C22×C8—732no—
365C4×Q8—738no—
366C4×Q8—1464no—
367C4×Q8—1464no—
368C4×Q8—1464no—
369C4×Q8—1464no—
370C4×Q8—1464no—
371C4×Q8—1464no—
372C4×Q8—1464no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—731no—
375C2×C4⋊C4—731no—
376C2×C4⋊C4—731no—
377C2×C4⋊C4—731no—
378C2×C4⋊C4—731no—
379C2×C4⋊C4—731no—
380C2×C4⋊C4—731no—
381C2×C4⋊C4—731no—
382C2×C4⋊C4—1464no—
383C2×C4⋊C4—1464no—
384C2×C4⋊C4C2×#6440811yescharacteristic
385C2×C4⋊C4C2×#6440811yescharacteristic
386C2×C4⋊C4C2×#6440811yescharacteristic
387C2×C4⋊C4C2×#6440811yescharacteristic
388C2×C42—731no—
389C2×C42—731no—
390C2×C42—731no—
391C2×C42—731no—
392C2×C42—731no—
393C2×C42—731no—
394C2×C42—731no—
395C2×C42—731no—
396C2×C42—731no—
397C2×C42—731no—
398C2×C42—731no—
399C2×C42—731no—
400C2×C42—1464no—
401C2×C42—1464no—
402C2×C42—1464no—
403C4⋊C8—1464no—
404C4⋊C8—1464no—
405C4⋊C8—1464no—
406C22⋊C8—734no—
407C22⋊C8—1462no—
408C22⋊C8—1462no—
409C22⋊C8—1462no—
410#97—1464no—
411#97—1464no—
412C4×C8—1464no—
413C24C22×#6440811yescharacteristic
414C2×Q8—734no—
415C2×Q8—734no—
416C2×Q8—1462no—
417C2×Q8—1462no—
418C2×Q8—1462no—
419C2×Q8—1462no—
420C2×Q8—1462no—
421C2×Q8—1462no—
422C2×Q8—1462no—
423C2×Q8—1462no—
424C2×Q8—14632no—
425C2×Q8—1462no—
426C2×Q8—1462no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—2921no—
437C22×C4—731no—
438C22×C4—731no—
439C22×C4—732no—
440C22×C4—732no—
441C22×C4—734no—
442C22×C4—731no—
443C22×C4—731no—
444C22×C4—731no—
445C22×C4—731no—
446C22×C4—731no—
447C22×C4—731no—
448C22×C4—1462no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4—1462no—
452C22×C4—1462no—
453C22×C4—1462no—
454C22×C4—1462no—
455C22×C4—1462no—
456C22×C4—1462no—
457C22×C4C22×#6440811yescharacteristic
458C22×C4C22×#6440811yescharacteristic
459C22×C4C22×#6440811yescharacteristic
460C22×C4C22×#6440811yescharacteristic
461C22×C4C22×#6440811yescharacteristic
462C22×C4C22×#6440811yescharacteristic
463C2×C8—734no—
464C2×C8—1462no—
465C2×C8—1462no—
466C2×C8—1462no—
467C2×C8—1462no—
468C2×C8—1462no—
469C2×C8—1462no—
470C2×C8—1462no—
471C2×C8—1462no—
472C2×C8—1462no—
473C2×C8—1462no—
474C2×C8—1462no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—734no—
479C4⋊C4—734no—
480C4⋊C4—1462no—
481C4⋊C4—1462no—
482C4⋊C4—1462no—
483C4⋊C4—1462no—
484C4⋊C4—1462no—
485C4⋊C4—1462no—
486C4⋊C4C22⋊#6440814yes—
487C42—734no—
488C42—734no—
489C42—734no—
490C42—1462no—
491C42—1462no—
492C42—1462no—
493C42—1462no—
494C42—1462no—
495C42—1462no—
496C42—1462no—
497C42—1462no—
498C42—1462no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23Q8×#6440812yes—
504C23D73⋊M1612yes—
505C23#1455667812yes—
506C23C23×#6440811yescharacteristic
507Q8—1468no—
508Q8—1468no—
509Q8—1468no—
510Q8—1468no—
511C2×C4—28no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
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—44no—
527C2×C4—44no—
528C2×C4—2924no—
529C2×C4—732no—
530C2×C4—732no—
531C2×C4—731no—
532C2×C4—731no—
533C2×C4—732no—
534C2×C4—732no—
535C2×C4—732no—
536C2×C4—732no—
537C2×C4—732no—
538C2×C4—732no—
539C2×C4—732no—
540C2×C4—732no—
541C2×C4—1461no—
542C2×C4—1461no—
543C2×C4—1461no—
544C2×C4—1468no—
545C2×C4—1464no—
546C2×C4—1464no—
547C2×C4—1468no—
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—1461no—
558C2×C4C2×C22⋊#6440812yes—
559C2×C4C2×C22⋊#6440812yes—
560C2×C4C2×C22⋊#6440812yes—
561C2×C4D73⋊M1612yes—
562C8—2922no—
563C8—2922no—
564C8—2922no—
565C8—1464no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22#1798963914yescomplemented
573C22C22×C22⋊#6440811yescharacteristic
574C22C2×Q8×#6440811yescharacteristic
575C22#1798965511yescharacteristic
576C22C2×D73⋊M1611yescharacteristic
577C22C2×D73⋊M1611yescharacteristic
578C22C2×#1455667811yescharacteristic
579C22#1798966511yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—2921no—
587C4—732no—
588C4—732no—
589C4—734no—
590C4—1462no—
591C4—1462no—
592C4—1462no—
593C4—1462no—
594C4—1462no—
595C2—24no—
596C2Q8×C22⋊#6440811yescharacteristic
597C2D73⋊#40711yescharacteristic
598C2#2262651911yescharacteristic
599C2C2×#1798963911yescharacteristic
600C2#2262673211yescharacteristic
601C2#2262683011yescharacteristic
602C2#2262683111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
FittingC22×C4⋊C4×C73C4
prime radicalC24×C73C22×C4
cosocleC22×Dic73C24
hypercenterC22×C4⋊C4#64408
hypocenterC73#22510
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#17989639C2semidirect
2. #22626104C2semidirect
3. #22626103C2semidirect
4. #22626102C2semidirect
55. C22⋊#10596833Q8semidirect
122. C2×#10596833C2×Q8semidirect
270. C22×C73#446semidirect
313. C73#22510semidirect
572. C22#17989639semidirect

Maximal subgroups

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

subgroupindex
C2×#179896392
#226261042
#226261032
#226261022
#226257872
#226257852
#226256572
C4×C22⋊#105968332
C22×#145565562
#2251073