Finite Group Databasebeta

← #34021123

Subgroups — #34021123

Order 18688.

1426 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989610C211yesmaximal, characteristic, complemented
2C2×#17989606C211yesmaximal, characteristic, complemented
3#22625823C212yesmaximal, complemented
4#22625790C212yesmaximal, complemented
5#22625789C212yesmaximal, complemented
6#22625754C212yesmaximal
7#22625661C212yesmaximal, complemented
8#22625660C212yesmaximal, complemented
9C2×#117×D73C211yesmaximal, characteristic
10#17989610—24no—
11#17989606—24no—
12C2×#14556658C2212yescomplemented
13C2×C4⋊#10596833C2212yescomplemented
14C2×#14556648C2212yes—
15C2×#14556648C2212yes—
16C2×#14556648C2214yes—
17C2×C22⋊#10596833C2214yes—
18C2×#14556646C2212yescomplemented
19C2×C4×#10596833C2212yescomplemented
20#17989453C2214yescomplemented
21#17989453C2214yescomplemented
22C23×C4×D73C2211yescharacteristic
23C2×#14556550C411yescharacteristic
24C2×#14556549C2211yescharacteristic
25C2×#14556549C2211yescharacteristic
26C2×#14556548C411yescharacteristic
27C2×#14556548C411yescharacteristic
28C2×#14556547C2211yescharacteristic
29C2×#14556547C2211yescharacteristic
30#117×D73—24no—
31#117×D73—24no—
32C2×C4⋊C4×D73C411yescharacteristic
33C2×C4⋊C4×D73C411yescharacteristic
34C2×C22⋊C4×D73C411yescharacteristic
35C2×C22⋊C4×D73C411yescharacteristic
36C2×C42×D73C2211yescharacteristic
37C2×C42×D73C2211yescharacteristic
38C2×#117×C73C411yescharacteristic
39C22×#10596833C2314yes—
40C22×#10596833C2314yes—
41#14556658—24no—
42C4⋊#10596833—24no—
43#14556648—24no—
44#14556648—24no—
45#14556648—28no—
46C22⋊#10596833—28no—
47#14556646—24no—
48C4×#10596833—24no—
49C24×D73C2×C411yescharacteristic
50C23×Dic73C2311yescharacteristic
51C22×C4×D73—24no—
52C22×C4×D73—22no—
53C22×C4×D73—22no—
54C22×C4×D73—24no—
55C22×C4×D73C2×C411yescharacteristic
56C22×C4×D73C2×C411yescharacteristic
57C22×C4×D73C2×C411yescharacteristic
58C22×C4×D73C2×C411yescharacteristic
59C22×C4×D73C2×C411yescharacteristic
60C22×C4×D73C2×C411yescharacteristic
61C22×C4×D73C2311yescharacteristic
62C22×C4×D73C2311yescharacteristic
63#14556550—24no—
64#14556549—22no—
65#14556549—22no—
66#14556549—22no—
67#14556549—22no—
68#14556548—24no—
69#14556548—24no—
70#14556547—22no—
71#14556547—22no—
72#14556547—22no—
73#14556547—22no—
74C2×C4⋊Dic73C2×C411yescharacteristic
75C2×C4⋊Dic73C2×C411yescharacteristic
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×#11924007C2×C411yescharacteristic
80C4⋊C4×D73—24no—
81C4⋊C4×D73—24no—
82C2×C22⋊Dic73C2×C411yescharacteristic
83C2×C22⋊Dic73C2×C411yescharacteristic
84C2×#11924005C2×C411yescharacteristic
85C2×#11924005C2×C411yescharacteristic
86C2×#11924005C2×C411yescharacteristic
87C2×#11924005C2×C411yescharacteristic
88C22⋊C4×D73—24no—
89C22⋊C4×D73—24no—
90C2×C4×Dic73C2×C411yescharacteristic
91C2×C4×Dic73C2×C411yescharacteristic
92C2×C4×Dic73C2311yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96C42×D73—22no—
97C42×D73—22no—
98C42×D73D414yes—
99C42×D73D414yes—
100C23×C4×C73C2×C411yescharacteristic
101#117×C73—24no—
102C2×C4⋊C4×C73C2×C411yescharacteristic
103C2×C4⋊C4×C73C2×C411yescharacteristic
104C2×C22⋊C4×C73C2×C411yescharacteristic
105C2×C22⋊C4×C73C2×C411yescharacteristic
106C2×C42×C73C2×C411yescharacteristic
107C2×C42×C73C2×C411yescharacteristic
108C2×#10596833—24no—
109C2×#10596833—24no—
110C2×#10596833—24no—
111C2×#10596833—24no—
112C2×#10596833—24no—
113C2×#10596833—24no—
114C23×D73—22no—
115C23×D73—22no—
116C23×D73—22no—
117C23×D73—24no—
118C23×D73—42no—
119C23×D73C22×C411yescharacteristic
120C23×D73C22×C411yescharacteristic
121C22×Dic73—21no—
122C22×Dic73—21no—
123C22×Dic73—22no—
124C22×Dic73C22×C411yescharacteristic
125C22×Dic73C22×C411yescharacteristic
126C22×Dic73C22×C411yescharacteristic
127C22×Dic73C22×C411yescharacteristic
128C22×Dic73C22×C411yescharacteristic
129C22×Dic73#4114yes—
130C22×Dic73C2411yescharacteristic
131C2×C4×D73—216no—
132C2×C4×D73—216no—
133C2×C4×D73—22no—
134C2×C4×D73—22no—
135C2×C4×D73—24no—
136C2×C4×D73—22no—
137C2×C4×D73—22no—
138C2×C4×D73—22no—
139C2×C4×D73—22no—
140C2×C4×D73—21no—
141C2×C4×D73—21no—
142C2×C4×D73—22no—
143C2×C4×D73—22no—
144C2×C4×D73—22no—
145C2×C4×D73—22no—
146C2×C4×D73—22no—
147C2×C4×D73—24no—
148C2×C4×D73—42no—
149C2×C4×D73—42no—
150C2×C4×D73C22⋊C414yes—
151C2×C4×D73C22⋊C414yes—
152C2×C4×D73C2×D412yes—
153C2×C4×D73C2×D412yes—
154C2×C4×D73#4114yes—
155C4⋊Dic73—22no—
156C4⋊Dic73—22no—
157#11924007—22no—
158#11924007—22no—
159#11924007—22no—
160#11924007—22no—
161C22⋊Dic73—22no—
162C22⋊Dic73—22no—
163#11924005—22no—
164#11924005—22no—
165#11924005—22no—
166#11924005—22no—
167C4×Dic73—22no—
168C4×Dic73—21no—
169C4×Dic73—21no—
170C4×Dic73—21no—
171C4×Dic73—21no—
172C4×Dic73C22⋊C414yes—
173C4×Dic73C2×D412yes—
174C4×Dic73C2×D412yes—
175C4×Dic73C2×D412yes—
176C4×Dic73C2×D412yes—
177C24×C73C22×C411yescharacteristic
178C22×C4×C73—22no—
179C22×C4×C73—22no—
180C22×C4×C73—22no—
181C22×C4×C73C22×C411yescharacteristic
182C22×C4×C73C22×C411yescharacteristic
183C22×C4×C73C22×C411yescharacteristic
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C22×C411yescharacteristic
187C4⋊C4×C73—22no—
188C4⋊C4×C73—22no—
189C22⋊C4×C73—22no—
190C22⋊C4×C73—22no—
191C42×C73—22no—
192C42×C73C22⋊C414yes—
193C23×C73—21no—
194C23×C73—21no—
195C23×C73—22no—
196C23×C73—22no—
197C23×C73#11712yes—
198C23×C73C23×C411yescharacteristic
199C22×D73—21no—
200C22×D73—21no—
201C22×D73—22no—
202C22×D73—28no—
203C22×D73—21no—
204C22×D73—21no—
205C22×D73—22no—
206C22×D73—22no—
207C22×D73—48no—
208C22×D73—48no—
209C22×D73—44no—
210C22×D73—44no—
211C22×D73C2×C22⋊C412yes—
212C22×D73#11712yes—
213C22×D73#13114yes—
214C2×C4×C73—28no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—22no—
220C2×C4×C73—22no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—22no—
224C2×C4×C73—22no—
225C2×C4×C73C2×C22⋊C412yes—
226C2×C4×C73C2×C22⋊C412yes—
227C2×C4×C73C2×C22⋊C412yes—
228C2×C4×C73#11712yes—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—22no—
232C2×Dic73—22no—
233C2×Dic73—24no—
234C2×Dic73—24no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—22no—
238C2×Dic73—22no—
239C2×Dic73C2×C22⋊C412yes—
240C2×Dic73C2×C22⋊C412yes—
241C2×Dic73#11712yes—
242C2×Dic73C22×D411yescharacteristic
243C2×Dic73C22×D411yescharacteristic
244C2×Dic73C2×#4112yes—
245C2×Dic73C2×#4112yes—
246C4×D73—28no—
247C4×D73—28no—
248C4×D73—28no—
249C4×D73—24no—
250C4×D73—24no—
251C4×D73—24no—
252C4×D73—24no—
253C4×D73—44no—
254C4×D73—44no—
255C4×D73—44no—
256#10596833—44no—
257#10596833—44no—
258C22×C73—24no—
259C22×C73—22no—
260C22×C73—41no—
261C22×C73—41no—
262C22×C73—42no—
263C22×C73C22×C22⋊C411yescharacteristic
264C22×C73C2×#11711yescharacteristic
265C22×C73C2×#11711yescharacteristic
266C22×C73C2×#13112yes—
267C22×C73#56812yes—
268C2×D73—22no—
269C2×D73—24no—
270C2×D73—24no—
271C2×D73—22no—
272C2×D73—24no—
273C2×D73—22no—
274C2×D73—416no—
275C2×D73—41no—
276C2×D73—41no—
277C2×D73—42no—
278C2×D73#40814yes—
279C4×C73—22no—
280C4×C73—22no—
281C4×C73—22no—
282C4×C73—22no—
283C4×C73—41no—
284C4×C73—41no—
285Dic73—22no—
286Dic73—22no—
287Dic73—22no—
288Dic73—41no—
289Dic73—41no—
290Dic73#52512yes—
291Dic73#52512yes—
292#20717—731nomaximal, Sylow
293C2×C73—42no—
294C2×C73#228011yescharacteristic
295C2×C73C2×#40811yescharacteristic
296C2×C73#287911yescharacteristic
297C2×C73#292412yes—
298C2×C73#292412yes—
299D73—24no—
300D73—42no—
301C22×#117—731no—
302C2×#432—731no—
303C2×#431—731no—
304#1817—732no—
305#1798—732no—
306#1798—732no—
307#1779—732no—
308#1750—732no—
309#1750—732no—
310C73#2071711yescharacteristic, complemented, Sylow
311C24×C4—731no—
312C2×#117—731no—
313C2×#117—731no—
314C2×#117—731no—
315C2×#117—731no—
316C2×#117—731no—
317C2×#117—731no—
318C2×#117—731no—
319C2×#117—1464no—
320C2×#117—1464no—
321C2×#117#6440811yescharacteristic
322C22×C4⋊C4—731no—
323C22×C4⋊C4—731no—
324C22×C22⋊C4—731no—
325C22×C22⋊C4—731no—
326C22×C42—731no—
327C22×C42—731no—
328#432—1464no—
329#431—1464no—
330C2×C4⋊C8—732no—
331C2×C4⋊C8—732no—
332C2×C22⋊C8—734no—
333C2×C22⋊C8—734no—
334C2×C22⋊C8—732no—
335C2×C22⋊C8—732no—
336C2×#97—732no—
337C2×C4×C8—732no—
338#336—734no—
339#336—734no—
340C25—731no—
341C23×C4—731no—
342C23×C4—731no—
343C23×C4—731no—
344C23×C4—731no—
345C23×C4—731no—
346C23×C4—731no—
347C23×C4—731no—
348C23×C4—731no—
349C23×C4—731no—
350C23×C4—1462no—
351C23×C4—1462no—
352C23×C4—1464no—
353C23×C4—1464no—
354C23×C4C2×#6440811yescharacteristic
355C22×C8—734no—
356C22×C8—734no—
357#117—24no—
358#117—1464no—
359#117—1462no—
360#117—1462no—
361#117—1462no—
362#117—1462no—
363#117—1462no—
364#117—1462no—
365#117—1462no—
366#117—1462no—
367#117—1464no—
368#117—1464no—
369C2×C4⋊C4—731no—
370C2×C4⋊C4—731no—
371C2×C4⋊C4—731no—
372C2×C4⋊C4—731no—
373C2×C4⋊C4—731no—
374C2×C4⋊C4—731no—
375C2×C4⋊C4—1464no—
376C2×C4⋊C4—1464no—
377C2×C4⋊C4C2×#6440811yescharacteristic
378C2×C4⋊C4C2×#6440811yescharacteristic
379C2×C22⋊C4—731no—
380C2×C22⋊C4—731no—
381C2×C22⋊C4—731no—
382C2×C22⋊C4—731no—
383C2×C22⋊C4—731no—
384C2×C22⋊C4—731no—
385C2×C22⋊C4—1464no—
386C2×C22⋊C4—1464no—
387C2×C22⋊C4C2×#6440811yescharacteristic
388C2×C22⋊C4C2×#6440811yescharacteristic
389C2×C42—731no—
390C2×C42—731no—
391C2×C42—731no—
392C2×C42—734no—
393C2×C42—734no—
394C2×C42—731no—
395C2×C42—731no—
396C2×C42—731no—
397C2×C42—1462no—
398C2×C42—1462no—
399C2×C42C2×#6440811yescharacteristic
400C2×C42C2×#6440811yescharacteristic
401C4⋊C8—1464no—
402C4⋊C8—1464no—
403C22⋊C8—1464no—
404C22⋊C8—1464no—
405C22⋊C8—1468no—
406C22⋊C8—1468no—
407#97—1464no—
408C4×C8—1464no—
409C24—2922no—
410C24—731no—
411C24—731no—
412C24—1464no—
413C24—1462no—
414C24—1462no—
415C24—1462no—
416C24C22×#6440811yescharacteristic
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—2922no—
421C22×C4—2922no—
422C22×C4—734no—
423C22×C4—731no—
424C22×C4—731no—
425C22×C4—731no—
426C22×C4—731no—
427C22×C4—734no—
428C22×C4—734no—
429C22×C4—732no—
430C22×C4—732no—
431C22×C4—734no—
432C22×C4—731no—
433C22×C4—731no—
434C22×C4—1462no—
435C22×C4—1462no—
436C22×C4—1464no—
437C22×C4—1461no—
438C22×C4—1461no—
439C22×C4—1462no—
440C22×C4—1462no—
441C22×C4—1462no—
442C22×C4—1462no—
443C22×C4—1462no—
444C22×C4—1462no—
445C22×C4—1464no—
446C22×C4—1462no—
447C22×C4—14616no—
448C22×C4—14616no—
449C22×C4—1461no—
450C22×C4—1461no—
451C22×C4—1462no—
452C22×C4—1462no—
453C22×C4—1462no—
454C22×C4C22×#6440811yescharacteristic
455C22×C4C22×#6440811yescharacteristic
456C22×C4C22×#6440811yescharacteristic
457C22×C4C22×#6440811yescharacteristic
458C22×C4C22×#6440811yescharacteristic
459C22×C4C22×#6440811yescharacteristic
460C2×C8—1464no—
461C2×C8—1464no—
462C2×C8—1464no—
463C2×C8—1464no—
464C2×C8—1464no—
465C2×C8—1464no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—1462no—
469C4⋊C4—1462no—
470C4⋊C4—1462no—
471C4⋊C4—1462no—
472C4⋊C4—1462no—
473C4⋊C4—1462no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—1462no—
477C22⋊C4—1462no—
478C22⋊C4—1462no—
479C22⋊C4—1462no—
480C22⋊C4—1462no—
481C22⋊C4—1462no—
482C42—22no—
483C42—734no—
484C42—732no—
485C42—732no—
486C42—732no—
487C42—732no—
488C42—1461no—
489C42—1461no—
490C42—1461no—
491C42—1461no—
492C42—1462no—
493C42C22⋊#6440814yes—
494C23—21no—
495C23—21no—
496C23—22no—
497C23—22no—
498C23—2928no—
499C23—2924no—
500C23—2924no—
501C23—2928no—
502C23—732no—
503C23—734no—
504C23—732no—
505C23—1468no—
506C23—1461no—
507C23—1461no—
508C23—1462no—
509C23—1462no—
510C23—1461no—
511C23—1461no—
512C23—1462no—
513C23#1455667012yes—
514C23C23×#6440811yescharacteristic
515C2×C4—28no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—2924no—
527C2×C4—2924no—
528C2×C4—2924no—
529C2×C4—731no—
530C2×C4—731no—
531C2×C4—732no—
532C2×C4—732no—
533C2×C4—732no—
534C2×C4—732no—
535C2×C4—732no—
536C2×C4—1464no—
537C2×C4—1464no—
538C2×C4—1464no—
539C2×C4—1464no—
540C2×C4—1468no—
541C2×C4—1468no—
542C2×C4—1468no—
543C2×C4—1461no—
544C2×C4—1461no—
545C2×C4—1462no—
546C2×C4—1462no—
547C2×C4—1464no—
548C2×C4—1464no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4—1462no—
552C2×C4—1462no—
553C2×C4C2×C22⋊#6440812yes—
554C2×C4C2×C22⋊#6440812yes—
555C2×C4C2×C22⋊#6440812yes—
556C2×C4#1455667012yes—
557C8—2924no—
558C8—2924no—
559C22—24no—
560C22—22no—
561C22—42no—
562C22—41no—
563C22—41no—
564C22—29216no—
565C22—2922no—
566C22—2921no—
567C22—2921no—
568C22—734no—
569C22—1464no—
570C22—1462no—
571C22—1464no—
572C22—1464no—
573C22—1462no—
574C22—1462no—
575C22C22×C22⋊#6440811yescharacteristic
576C22C2×#1455667011yescharacteristic
577C22C2×#1455667011yescharacteristic
578C22D73⋊#13112yes—
579C22#1798966612yes—
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—2921no—
587C4—2921no—
588C4—732no—
589C4—732no—
590C4—1462no—
591C4—1462no—
592C4—1462no—
593C2—42no—
594C2—2922no—
595C2—1464no—
596C2#2262637511yescharacteristic
597C2D73⋊#40811yescharacteristic
598C2#2262651611yescharacteristic
599C2#2262662312yes—
600C2#2262662512yes—
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
FittingC2×#117×C73C4
prime radicalC24×D73C2×C4
cosocleC22×Dic73C24
hypercenterC2×#117#64408
hypocenterC73#20717
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#17989610C2semidirect
2. C2×#17989606C2semidirect
3. #22625823C2semidirect
4. #22625790C2semidirect
5. #22625789C2semidirect
7. #22625661C2semidirect
8. #22625660C2semidirect
12. C2×#14556658C22semidirect
13. C2×C4⋊#10596833C22semidirect
18. C2×#14556646C22semidirect
19. C2×C4×#10596833C22semidirect
20. #17989453C22semidirect
21. #17989453C22semidirect
310. C73#20717semidirect

Maximal subgroups

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

subgroupindex
C2×#179896102
C2×#179896062
#226258232
#226257902
#226257892
#226257542
#226256612
#226256602
C2×#117×D732
#2071773