Finite Group Databasebeta

← #34022343

Subgroups — #34022343

Order 18688.

868 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×#17989611C211yesmaximal, characteristic, complemented
2C2×#17989603C211yesmaximal, characteristic, complemented
3#22626055C211yesmaximal, characteristic
4#22626052C211yesmaximal, characteristic
5#22626031C211yesmaximal, characteristic, complemented
6#22626030C211yesmaximal, characteristic, complemented
7#22626005C211yesmaximal, characteristic, complemented
8#22626005C211yesmaximal, characteristic, complemented
9#22626001C211yesmaximal, characteristic, complemented
10#22626000C211yesmaximal, characteristic, complemented
11#22625719C211yesmaximal, characteristic, complemented
12#22625661C211yesmaximal, characteristic, complemented
13#22625657C211yesmaximal, characteristic, complemented
14#22625588C211yesmaximal, characteristic, complemented
15#22612371C211yesmaximal, characteristic
16#17989611—24no—
17#17989603—24no—
18C2×#14556658C2211yescharacteristic
19C2×#14556658C2211yescharacteristic
20C2×C4⋊#10596833C2211yescharacteristic
21C2×C4⋊#10596833C2211yescharacteristic
22C2×C4⋊#10596833C2211yescharacteristic
23C2×C4⋊#10596833C2211yescharacteristic
24C2×C22⋊#10596833C2211yescharacteristic
25C2×C22⋊#10596833C2211yescharacteristic
26C2×C22⋊#10596833C2211yescharacteristic
27C2×C22⋊#10596833C2211yescharacteristic
28C2×C22⋊#10596833C2211yescharacteristic
29C2×C22⋊#10596833C2211yescharacteristic
30C2×C22⋊#10596833C2211yescharacteristic
31C2×C22⋊#10596833C2211yescharacteristic
32C2×#14556646C2211yescharacteristic
33C2×#14556646C2211yescharacteristic
34C2×#14556646C2211yescharacteristic
35C2×#14556646C2211yescharacteristic
36C2×C4×#10596833C2211yescharacteristic
37C2×C4×#10596833C2211yescharacteristic
38C2×C4×#10596833C2211yescharacteristic
39C2×C4×#10596833C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44#17989453C2211yescharacteristic
45#17989453C2211yescharacteristic
46C2×D4×Dic73C2211yescharacteristic
47C2×#14556547C2211yescharacteristic
48C22×C4×Dic73C2211yescharacteristic
49#17988481C411yescharacteristic
50#17988475C411yescharacteristic
51#17988472C411yescharacteristic
52#17988470C411yescharacteristic
53#17988467C411yescharacteristic
54#17988460C411yescharacteristic
55#17988459C411yescharacteristic
56#17988438C2211yescharacteristic
57C22⋊C4×Dic73C2211yescharacteristic
58C22⋊C4×Dic73C2211yescharacteristic
59#17988432C2211yescharacteristic
60#386×C73C411yescharacteristic
61C22×#10596833C2311yescharacteristic
62C22×#10596833C2311yescharacteristic
63C22×#10596833C2311yescharacteristic
64C22×#10596833C2311yescharacteristic
65C22×#10596833C2311yescharacteristic
66C22×#10596833C2311yescharacteristic
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69#14556658—22no—
70#14556658—22no—
71C4⋊#10596833—22no—
72C4⋊#10596833—22no—
73C4⋊#10596833—22no—
74C4⋊#10596833—22no—
75C22⋊#10596833—22no—
76C22⋊#10596833—22no—
77C22⋊#10596833—22no—
78C22⋊#10596833—22no—
79C22⋊#10596833—22no—
80C22⋊#10596833—22no—
81C22⋊#10596833—22no—
82C22⋊#10596833—22no—
83#14556646—22no—
84#14556646—22no—
85#14556646—22no—
86#14556646—22no—
87C4×#10596833—22no—
88C4×#10596833—22no—
89C4×#10596833—22no—
90C4×#10596833D414yescomplemented
91C23×Dic73C2×C411yescharacteristic
92C23×Dic73C2311yescharacteristic
93C23×Dic73C2311yescharacteristic
94D4×Dic73—22no—
95D4×Dic73—22no—
96#14556547—22no—
97#14556547—22no—
98C2×C4⋊Dic73C2×C411yescharacteristic
99C2×#11924007C2×C411yescharacteristic
100C2×#11924007C2×C411yescharacteristic
101C2×#11924007C2×C411yescharacteristic
102C2×#11924007C2×C411yescharacteristic
103C2×C22⋊Dic73C2×C411yescharacteristic
104C2×C22⋊Dic73C2×C411yescharacteristic
105C2×C22⋊Dic73C2×C411yescharacteristic
106C2×C22⋊Dic73C2×C411yescharacteristic
107C2×C22⋊Dic73C2×C411yescharacteristic
108C2×C4×Dic73—22no—
109C2×C4×Dic73—22no—
110C2×C4×Dic73C2×C411yescharacteristic
111C2×C4×Dic73C2×C411yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113C2×C4×Dic73C2311yescharacteristic
114C2×C4×Dic73C2311yescharacteristic
115C2×C4×Dic73C2311yescharacteristic
116C2×C4×Dic73C2311yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120#14556498C2×C411yescharacteristic
121#14556498C2×C411yescharacteristic
122#14556498C2×C411yescharacteristic
123#14556498C2×C411yescharacteristic
124#14556498C2×C411yescharacteristic
125C22×D4×C73C2×C411yescharacteristic
126C23×C4×C73C2×C411yescharacteristic
127C2×C22⋊C4×C73C2×C411yescharacteristic
128C2×C22⋊C4×C73C2×C411yescharacteristic
129C2×C22⋊C4×C73C2×C411yescharacteristic
130#95×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
132C2×#10596833—21no—
133C2×#10596833—21no—
134C2×#10596833—21no—
135C2×#10596833—21no—
136C2×#10596833—21no—
137C2×#10596833—21no—
138C2×#10596833—21no—
139C2×#10596833—21no—
140C2×#10596833—21no—
141C2×#10596833—21no—
142C2×#10596833—21no—
143C2×#10596833—21no—
144C2×#10596833—21no—
145C2×#10596833—21no—
146C2×#10596833—21no—
147C2×#10596833—21no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—21no—
152C2×#10596833C2×D412yes—
153C2×#10596833C2×D412yes—
154C2×#10596833#4112yes—
155C2×#10596833#4112yes—
156C22×Dic73—22no—
157C22×Dic73—21no—
158C22×Dic73—21no—
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73—41no—
170C22×Dic73—41no—
171C22×Dic73C22×C411yescharacteristic
172C22×Dic73C22×C411yescharacteristic
173C22×Dic73C22×C411yescharacteristic
174C22×Dic73C22×C411yescharacteristic
175C22×Dic73C22×C411yescharacteristic
176C22×Dic73C22×C411yescharacteristic
177C22×Dic73C22×C411yescharacteristic
178C22×Dic73C2411yescharacteristic
179C4⋊Dic73—22no—
180#11924007—22no—
181#11924007—22no—
182#11924007—22no—
183#11924007—41no—
184C22⋊Dic73—22no—
185C22⋊Dic73—22no—
186C22⋊Dic73—22no—
187C22⋊Dic73—22no—
188C22⋊Dic73—41no—
189C4×Dic73—22no—
190C4×Dic73—22no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196C4×Dic73—21no—
197C4×Dic73C2×D412yes—
198C4×Dic73#4112yes—
199C4×Dic73#4112yes—
200C4×Dic73#4112yes—
201C24×C73C22×C411yescharacteristic
202C24×C73C22×C411yescharacteristic
203C2×D4×C73—22no—
204C2×D4×C73—22no—
205C2×D4×C73—41no—
206C22×C4×C73—22no—
207C22×C4×C73—22no—
208C22×C4×C73—22no—
209C22×C4×C73C22×C411yescharacteristic
210C22×C4×C73C22×C411yescharacteristic
211C22×C4×C73C22×C411yescharacteristic
212C22×C4×C73C22×C411yescharacteristic
213C22×C4×C73C22×C411yescharacteristic
214C22⋊C4×C73—22no—
215C22⋊C4×C73—22no—
216C22⋊C4×C73—41no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73#13112yes—
231C23×C73C23×C411yescharacteristic
232D4×C73—44no—
233C2×C4×C73—28no—
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#11712yes—
247C2×C4×C73C4×D412yes—
248C2×C4×C73#13112yes—
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—
265C2×Dic73—21no—
266C2×Dic73—21no—
267C2×Dic73—21no—
268C2×Dic73—44no—
269C2×Dic73—41no—
270C2×Dic73—41no—
271C2×Dic73—41no—
272C2×Dic73—41no—
273C2×Dic73—41no—
274C2×Dic73—41no—
275C2×Dic73—41no—
276C2×Dic73—41no—
277C2×Dic73#11712yes—
278C2×Dic73C4×D412yes—
279C2×Dic73C22×D411yescharacteristic
280C2×Dic73C2×#4111yescharacteristic
281C2×Dic73C2×#4111yescharacteristic
282C2×Dic73C2×#4111yescharacteristic
283C2×Dic73C2×#4111yescharacteristic
284C2×Dic73C2×#4111yescharacteristic
285#10596833—22no—
286#10596833—22no—
287#10596833—22no—
288#10596833—22no—
289#10596833—41no—
290#10596833—41no—
291#10596833—41no—
292#10596833—41no—
293C22×C73—22no—
294C22×C73—22no—
295C22×C73—22no—
296C22×C73—41no—
297C22×C73—41no—
298C22×C73—41no—
299C22×C73—41no—
300C22×C73—41no—
301C22×C73—41no—
302C22×C73—41no—
303C22×C73—41no—
304C22×C73—41no—
305C22×C73—41no—
306C22×C73—41no—
307C22×C73C2×#11711yescharacteristic
308C22×C73C2×C4×D411yescharacteristic
309C22×C73C4×#4111yescharacteristic
310C22×C73C2×#13111yescharacteristic
311C22×C73C2×#13111yescharacteristic
312C22×C73#56811yescharacteristic
313C22×C73#56811yescharacteristic
314C4×C73—22no—
315C4×C73—22no—
316C4×C73—22no—
317C4×C73—41no—
318C4×C73—41no—
319Dic73—22no—
320Dic73—22no—
321Dic73—41no—
322Dic73—41no—
323Dic73—41no—
324Dic73—41no—
325Dic73—41no—
326Dic73#52911yescharacteristic
327Dic73#52911yescharacteristic
328Dic73#53211yescharacteristic
329Dic73#53211yescharacteristic
330#21272—731nomaximal, Sylow
331C2×C73—42no—
332C2×C73—81no—
333C2×C73#229311yescharacteristic
334C2×C73#292411yescharacteristic
335C2×C73#292511yescharacteristic
336C2×C73#292911yescharacteristic
337C2×C73#293011yescharacteristic
338C2×C73#296811yescharacteristic
339C2×C73#296911yescharacteristic
340C2×#433—731no—
341C2×#431—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#1923—731no—
351#1768—731no—
352#1750—731no—
353#1749—731no—
354#1726—731no—
355C73#2127211yescharacteristic, complemented, Sylow
356C2×C4×D4—731no—
357C2×#117—731no—
358C22×C42—731no—
359#433—1464no—
360#431—1464no—
361C2×C4⋊C8—731no—
362C2×C4⋊C8—731no—
363C2×C4⋊C8—731no—
364C2×C4⋊C8—731no—
365C2×C4⋊C8—731no—
366C2×C4⋊C8—731no—
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⋊C8—731no—
374C2×C22⋊C8—731no—
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×C8—731no—
383#388—731no—
384#388—731no—
385#387—731no—
386#387—731no—
387#386—731no—
388#386#6440811yescharacteristic
389#385—731no—
390#385—731no—
391C4×C4⋊C4—731no—
392C4×C22⋊C4—731no—
393C4×C22⋊C4—731no—
394#376—731no—
395#336—731no—
396#336—731no—
397#336—731no—
398#336—731no—
399#336—731no—
400#336—731no—
401C22×D4C2×#6440811yescharacteristic
402C23×C4—731no—
403C23×C4—731no—
404C23×C4—731no—
405C23×C4C2×#6440811yescharacteristic
406C22×C8—731no—
407C22×C8—731no—
408C22×C8—731no—
409C22×C8—731no—
410C22×C8—731no—
411C22×C8—731no—
412C22×C8—731no—
413C22×C8—731no—
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⋊C4C2×#6440811yescharacteristic
429C2×C22⋊C4C2×#6440811yescharacteristic
430C2×C22⋊C4C2×#6440811yescharacteristic
431C2×C42—731no—
432C2×C42—731no—
433C2×C42—731no—
434C2×C42—731no—
435C2×C42—731no—
436C2×C42—731no—
437C2×C42—731no—
438C2×C42—1462no—
439C2×C42—1462no—
440C4⋊C8—1462no—
441C4⋊C8—1462no—
442C4⋊C8—1462no—
443C4⋊C8—1462no—
444C4⋊C8—1462no—
445C4⋊C8—1462no—
446C22⋊C8—1462no—
447C22⋊C8—1462no—
448C22⋊C8—1462no—
449C22⋊C8—1462no—
450C22⋊C8—1462no—
451C22⋊C8—1462no—
452C22⋊C8—1462no—
453C22⋊C8—1462no—
454#97—1462no—
455#97—1462no—
456#97—1462no—
457#97—1462no—
458C4×C8—734no—
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#95C2×#6440811yescharacteristic
471#95C2×#6440811yescharacteristic
472C24C22×#6440811yescharacteristic
473C24C22×#6440811yescharacteristic
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—41no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—2921no—
481C22×C4—2921no—
482C22×C4—731no—
483C22×C4—731no—
484C22×C4—731no—
485C22×C4—731no—
486C22×C4—731no—
487C22×C4—731no—
488C22×C4—731no—
489C22×C4—731no—
490C22×C4—1461no—
491C22×C4—1461no—
492C22×C4—1461no—
493C22×C4—1461no—
494C22×C4—1461no—
495C22×C4—1461no—
496C22×C4—1461no—
497C22×C4—1462no—
498C22×C4—1461no—
499C22×C4—1461no—
500C22×C4—1461no—
501C22×C4—1461no—
502C22×C4—1461no—
503C22×C4C22×#6440811yescharacteristic
504C22×C4C22×#6440811yescharacteristic
505C22×C4C22×#6440811yescharacteristic
506C22×C4C22×#6440811yescharacteristic
507C22×C4C22×#6440811yescharacteristic
508C2×C8—732no—
509C2×C8—732no—
510C2×C8—732no—
511C2×C8—732no—
512C2×C8—1461no—
513C2×C8—1461no—
514C2×C8—1461no—
515C2×C8—1461no—
516C2×C8—1461no—
517C2×C8—1461no—
518C2×C8—1461no—
519C2×C8—1461no—
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×C8—1461no—
531C2×C8—1461no—
532C4⋊C4—2921no—
533C4⋊C4—1462no—
534C4⋊C4—1462no—
535C4⋊C4—1462no—
536C4⋊C4—1462no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—41no—
540C22⋊C4—2921no—
541C22⋊C4—1462no—
542C22⋊C4—1462no—
543C22⋊C4—1462no—
544C22⋊C4—1462no—
545C42—732no—
546C42—732no—
547C42—732no—
548C42—732no—
549C42—1461no—
550C42—1461no—
551C42—1461no—
552C42—1461no—
553C42—1461no—
554C42—1462no—
555C42—1461no—
556C42—1462no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23#1455667812yes—
571C23C23×#6440811yescharacteristic
572D4—44no—
573C2×C4—28no—
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—2921no—
587C2×C4—2921no—
588C2×C4—2921no—
589C2×C4—2921no—
590C2×C4—2921no—
591C2×C4—2921no—
592C2×C4—2921no—
593C2×C4—2921no—
594C2×C4—2924no—
595C2×C4—731no—
596C2×C4—731no—
597C2×C4—731no—
598C2×C4—731no—
599C2×C4—731no—
600C2×C4—731no—
601C2×C4—732no—
602C2×C4—732no—
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—1461no—
619C2×C4—1461no—
620C2×C4—1461no—
621C2×C4—1461no—
622C2×C4#1455667012yes—
623C2×C4D4×#6440812yes—
624C2×C4#1455667812yes—
625C8—2921no—
626C8—2921no—
627C8—2921no—
628C8—2921no—
629C8—1462no—
630C8—1462no—
631C8—1462no—
632C8—1462no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22C2×#1455667011yescharacteristic
648C22C2×D4×#6440811yescharacteristic
649C22#41×#6440811yescharacteristic
650C22C2×#1455667811yescharacteristic
651C22C2×#1455667811yescharacteristic
652C22#1798966511yescharacteristic
653C22#1798966611yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—41no—
658C4—41no—
659C4—2921no—
660C4—2921no—
661C4—2921no—
662C4—2921no—
663C4—2921no—
664C4—731no—
665C4—731no—
666C4—731no—
667C4—731no—
668C4—1462no—
669C4—1462no—
670C2—42no—
671C2—81no—
672C2#2262638811yescharacteristic
673C2#2262662011yescharacteristic
674C2#2262662711yescharacteristic
675C2#2262664611yescharacteristic
676C2#2262664911yescharacteristic
677C2#2262675811yescharacteristic
678C2#2262676211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#386×C73C4
prime radicalC22×D4×C73C2×C4
cosocleC22×Dic73C24
hypercenter#386#64408
hypocenterC73#21272
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#17989611C2semidirect
2. C2×#17989603C2semidirect
5. #22626031C2semidirect
6. #22626030C2semidirect
7. #22626005C2semidirect
8. #22626005C2semidirect
9. #22626001C2semidirect
10. #22626000C2semidirect
11. #22625719C2semidirect
12. #22625661C2semidirect
13. #22625657C2semidirect
14. #22625588C2semidirect
90. C4×#10596833D4semidirect
355. C73#21272semidirect

Maximal subgroups

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

subgroupindex
C2×#179896112
C2×#179896032
#226260552
#226260522
#226260312
#226260302
#226260052
#226260012
#226260002
#226257192
#226256612
#226256572
#226255882
#226123712
#2127273