Finite Group Databasebeta

← #34008829

Subgroups — #34008829

Order 18688.

926 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556658C211yesmaximal, characteristic
2C22×#14556646C211yesmaximal, characteristic
3C2×#17989453C211yesmaximal, characteristic
4C2×#17989453C211yesmaximal, characteristic
5C2×#17989453C211yesmaximal, characteristic
6C2×#17989453C211yesmaximal, characteristic
7#95×Dic73C211yesmaximal, characteristic
8C23×#10596833C2211yescharacteristic
9C23×#10596833C2211yescharacteristic
10C23×#10596833C2211yescharacteristic
11C23×#10596833C2211yescharacteristic
12C2×#14556658—22no—
13C2×#14556658—22no—
14C2×#14556658C414yescomplemented
15C2×#14556646—22no—
16C2×#14556646—22no—
17C2×#14556646—22no—
18#17989453—22no—
19#17989453—22no—
20#17989453—22no—
21#17989453C414yescomplemented
22C22×C4×Dic73C2211yescharacteristic
23C22×C4×Dic73C2211yescharacteristic
24C22×C4×Dic73C2211yescharacteristic
25C2×#14556498C411yescharacteristic
26C2×#14556498C411yescharacteristic
27C2×#14556498C411yescharacteristic
28C2×#95×C73C411yescharacteristic
29C22×#10596833—21no—
30C22×#10596833—21no—
31C22×#10596833—21no—
32C22×#10596833—21no—
33C22×#10596833—21no—
34C22×#10596833—21no—
35C22×#10596833—21no—
36C22×#10596833—21no—
37C22×#10596833—21no—
38C22×#10596833—21no—
39C22×#10596833—21no—
40C22×#10596833—21no—
41C22×#10596833—21no—
42C22×#10596833—21no—
43C22×#10596833—21no—
44C22×#10596833—21no—
45C22×#10596833—21no—
46C22×#10596833—21no—
47C22×#10596833—21no—
48C22×#10596833—21no—
49C22×#10596833C2×C412yes—
50C22×#10596833C2×C412yes—
51C22×#10596833C2×C412yes—
52C22×#10596833C2×C412yes—
53C22×#10596833D412yes—
54C22×#10596833D412yes—
55C22×#10596833D412yes—
56C22×#10596833Q812yes—
57#14556658—28no—
58#14556646—28no—
59C23×Dic73C2×C411yescharacteristic
60C23×Dic73C2×C411yescharacteristic
61C23×Dic73C2×C411yescharacteristic
62C23×Dic73C2311yescharacteristic
63C2×C4×Dic73—21no—
64C2×C4×Dic73—21no—
65C2×C4×Dic73—21no—
66C2×C4×Dic73—21no—
67C2×C4×Dic73—21no—
68C2×C4×Dic73—21no—
69C2×C4×Dic73—21no—
70C2×C4×Dic73—21no—
71C2×C4×Dic73—21no—
72C2×C4×Dic73—21no—
73C2×C4×Dic73—21no—
74C2×C4×Dic73—21no—
75C2×C4×Dic73—21no—
76C2×C4×Dic73—21no—
77C2×C4×Dic73C2×C412yes—
78C2×C4×Dic73C2×C412yes—
79C2×C4×Dic73D412yes—
80C2×C4×Dic73Q812yes—
81#14556498—22no—
82#14556498—22no—
83#14556498—22no—
84C23×C4×C73C2×C411yescharacteristic
85C23×C4×C73C2×C411yescharacteristic
86C23×C4×C73C2×C411yescharacteristic
87#95×C73—22no—
88C2×#10596833—22no—
89C2×#10596833—22no—
90C2×#10596833—22no—
91C2×#10596833—22no—
92C2×#10596833—22no—
93C2×#10596833—22no—
94C2×#10596833—22no—
95C2×#10596833—22no—
96C2×#10596833—22no—
97C2×#10596833—22no—
98C2×#10596833—22no—
99C2×#10596833—22no—
100C2×#10596833—22no—
101C2×#10596833—22no—
102C2×#10596833—22no—
103C2×#10596833—22no—
104C2×#10596833—22no—
105C2×#10596833—22no—
106C2×#10596833—41no—
107C2×#10596833—41no—
108C2×#10596833—41no—
109C2×#10596833—41no—
110C2×#10596833—41no—
111C2×#10596833—41no—
112C2×#10596833—41no—
113C2×#10596833—41no—
114C2×#10596833C22⋊C414yes—
115C2×#10596833C4⋊C414yes—
116C22×Dic73—21no—
117C22×Dic73—21no—
118C22×Dic73—21no—
119C22×Dic73—21no—
120C22×Dic73—21no—
121C22×Dic73—21no—
122C22×Dic73—21no—
123C22×Dic73—21no—
124C22×Dic73—21no—
125C22×Dic73—21no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73C4212yes—
133C22×Dic73C4⋊C412yes—
134C22×Dic73M1612yes—
135C22×Dic73M1612yes—
136C22×Dic73M1612yes—
137C22×Dic73C22×C411yescharacteristic
138C22×Dic73C22×C411yescharacteristic
139C22×Dic73C2×D411yescharacteristic
140C22×Dic73C2×D411yescharacteristic
141C22×Dic73C2×D411yescharacteristic
142C22×Dic73C2×D411yescharacteristic
143C22×Dic73C2×Q811yescharacteristic
144C22×Dic73C2×Q811yescharacteristic
145C22×Dic73#4111yescharacteristic
146C22×Dic73#4111yescharacteristic
147C22×Dic73#4111yescharacteristic
148C22×Dic73#4111yescharacteristic
149C22×Dic73#4111yescharacteristic
150C22×Dic73#4111yescharacteristic
151C4×Dic73—22no—
152C4×Dic73—22no—
153C4×Dic73—22no—
154C4×Dic73—22no—
155C4×Dic73—22no—
156C4×Dic73—22no—
157C4×Dic73—22no—
158C4×Dic73—22no—
159C4×Dic73—41no—
160C4×Dic73—41no—
161C4×Dic73—41no—
162C4×Dic73—41no—
163C24×C73C22×C411yescharacteristic
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73C4212yes—
183C22×C4×C73C4⋊C412yes—
184C22×C4×C73M1612yes—
185C23×C73C2×C4211yescharacteristic
186C23×C73C2×C4⋊C411yescharacteristic
187C23×C73#11711yescharacteristic
188C23×C73C4×D411yescharacteristic
189C23×C73C4×D411yescharacteristic
190C23×C73C4×D411yescharacteristic
191C23×C73C4×Q811yescharacteristic
192C23×C73C2×M1611yescharacteristic
193C23×C73C2×M1611yescharacteristic
194C23×C73C2×M1611yescharacteristic
195C23×C73C2×M1611yescharacteristic
196C23×C73#13111yescharacteristic
197C23×C73#13111yescharacteristic
198C23×C73#13111yescharacteristic
199C23×C73#13111yescharacteristic
200C2×C4×C73—22no—
201C2×C4×C73—22no—
202C2×C4×C73—22no—
203C2×C4×C73—22no—
204C2×C4×C73—22no—
205C2×C4×C73—22no—
206C2×C4×C73—22no—
207C2×C4×C73—22no—
208C2×C4×C73—22no—
209C2×C4×C73—41no—
210C2×C4×C73—41no—
211C2×C4×C73—41no—
212C2×C4×C73—41no—
213C2×C4×C73—41no—
214C2×C4×C73—41no—
215C2×C4×C73—41no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×Dic73—22no—
222C2×Dic73—22no—
223C2×Dic73—22no—
224C2×Dic73—22no—
225C2×Dic73—22no—
226C2×Dic73—22no—
227C2×Dic73—22no—
228C2×Dic73—22no—
229C2×Dic73—22no—
230C2×Dic73—22no—
231C2×Dic73—22no—
232C2×Dic73—22no—
233C2×Dic73—41no—
234C2×Dic73—41no—
235C2×Dic73—41no—
236C2×Dic73—41no—
237C2×Dic73—41no—
238C2×Dic73—41no—
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73#9714yescomplemented
242C2×Dic73C2×C22⋊C411yescharacteristic
243C2×Dic73C2×C4⋊C411yescharacteristic
244C2×Dic73#11711yescharacteristic
245C2×Dic73#11711yescharacteristic
246C2×Dic73C4×D411yescharacteristic
247C2×Dic73C4×D411yescharacteristic
248C2×Dic73C4×D411yescharacteristic
249C2×Dic73C4×D411yescharacteristic
250C2×Dic73C4×D411yescharacteristic
251C2×Dic73C4×Q811yescharacteristic
252C2×Dic73C4×Q811yescharacteristic
253C2×Dic73C4×Q811yescharacteristic
254C2×Dic73#12011yescharacteristic
255C2×Dic73#12111yescharacteristic
256C2×Dic73#12111yescharacteristic
257C2×Dic73C22⋊Q811yescharacteristic
258C2×Dic73C22⋊Q811yescharacteristic
259C2×Dic73C22⋊Q811yescharacteristic
260C2×Dic73C22⋊Q811yescharacteristic
261C2×Dic73#12311yescharacteristic
262C2×Dic73#12311yescharacteristic
263C2×Dic73#12311yescharacteristic
264C2×Dic73#12411yescharacteristic
265C2×Dic73#12511yescharacteristic
266C2×Dic73#12511yescharacteristic
267C2×Dic73#12611yescharacteristic
268C2×Dic73#12611yescharacteristic
269C2×Dic73C4⋊Q811yescharacteristic
270#10596833—24no—
271#10596833—24no—
272#10596833—42no—
273#10596833—42no—
274C22×C73C4×C22⋊C411yescharacteristic
275C22×C73C4×C4⋊C411yescharacteristic
276C22×C73C4×C4⋊C411yescharacteristic
277C22×C73#38511yescharacteristic
278C22×C73#38711yescharacteristic
279C22×C73#38811yescharacteristic
280C22×C73#38911yescharacteristic
281C22×C73C2×#9711yescharacteristic
282C22×C73C4×M1611yescharacteristic
283C22×C73#40511yescharacteristic
284C22×C73#40511yescharacteristic
285C22×C73#42311yescharacteristic
286C22×C73#42311yescharacteristic
287C22×C73#42411yescharacteristic
288C22×C73#42411yescharacteristic
289C22×C73#43211yescharacteristic
290C22×C73#43211yescharacteristic
291C22×C73#43311yescharacteristic
292C22×C73#43311yescharacteristic
293C22×C73#43511yescharacteristic
294C22×C73#43511yescharacteristic
295C22×C73#43511yescharacteristic
296C22×C73#43511yescharacteristic
297C22×C73#43511yescharacteristic
298C22×C73#43511yescharacteristic
299C22×C73#43511yescharacteristic
300C22×C73#43511yescharacteristic
301C22×C73#43611yescharacteristic
302C22×C73#43611yescharacteristic
303C22×C73#43611yescharacteristic
304C22×C73#43611yescharacteristic
305C22×C73#44611yescharacteristic
306C22×C73#44611yescharacteristic
307C22×C73#44611yescharacteristic
308C22×C73#44611yescharacteristic
309C4×C73—42no—
310C4×C73—42no—
311C4×C73—42no—
312Dic73—24no—
313Dic73—42no—
314Dic73—42no—
315Dic73#38511yescharacteristic
316Dic73#38611yescharacteristic
317Dic73#38711yescharacteristic
318Dic73#38711yescharacteristic
319Dic73#38711yescharacteristic
320Dic73#38811yescharacteristic
321Dic73#38911yescharacteristic
322Dic73#39111yescharacteristic
323#10877—731nomaximal, Sylow
324C2×C73#143611yescharacteristic
325C2×C73#175211yescharacteristic
326C2×C73#175311yescharacteristic
327C2×C73#176711yescharacteristic
328C2×C73#176811yescharacteristic
329C2×C73#177011yescharacteristic
330C2×C73#177111yescharacteristic
331C2×C73#185111yescharacteristic
332C2×C73#185111yescharacteristic
333C2×C73#191711yescharacteristic
334C2×C73#191711yescharacteristic
335C2×C73#192411yescharacteristic
336C2×C73#192411yescharacteristic
337C2×C73#194011yescharacteristic
338C2×C73#194011yescharacteristic
339C22×C4⋊C8—731no—
340C22×#97—731no—
341C2×#336—731no—
342C2×#336—731no—
343C2×#336—731no—
344C2×#336—731no—
345C4×#95—731no—
346C73#1087711yescharacteristic, complemented, Sylow
347C23×C8—731no—
348C23×C8—731no—
349C23×C8—731no—
350C23×C8—731no—
351C22×C42—731no—
352C22×C42—731no—
353C22×C42—731no—
354C2×C4⋊C8—734no—
355C2×C4⋊C8—1462no—
356C2×C4⋊C8—1462no—
357C2×#97—1462no—
358C2×#97—1462no—
359C2×#97—1462no—
360C2×#95—731no—
361C2×#95—731no—
362C2×#95—731no—
363C2×#95#6440811yescharacteristic
364#336—734no—
365#336—1462no—
366#336—1462no—
367#336—1462no—
368C23×C4—731no—
369C23×C4—731no—
370C23×C4—731no—
371C23×C4—731no—
372C23×C4C2×#6440811yescharacteristic
373C23×C4C2×#6440811yescharacteristic
374C23×C4C2×#6440811yescharacteristic
375C22×C8—732no—
376C22×C8—732no—
377C22×C8—732no—
378C22×C8—732no—
379C22×C8—732no—
380C22×C8—732no—
381C22×C8—732no—
382C22×C8—732no—
383C22×C8—1461no—
384C22×C8—1461no—
385C22×C8—1461no—
386C22×C8—1461no—
387C22×C8—1461no—
388C22×C8—1461no—
389C22×C8—1461no—
390C22×C8—1461no—
391C22×C8—1461no—
392C22×C8—1461no—
393C22×C8—1461no—
394C22×C8—1461no—
395C22×C8—1461no—
396C22×C8—1461no—
397C22×C8—1461no—
398C22×C8—1461no—
399C22×C8—1461no—
400C22×C8—1461no—
401C22×C8—1461no—
402C22×C8—1461no—
403C2×C42—732no—
404C2×C42—732no—
405C2×C42—732no—
406C2×C42—732no—
407C2×C42—1461no—
408C2×C42—1461no—
409C2×C42—1461no—
410C2×C42—1461no—
411C2×C42—1461no—
412C2×C42—1461no—
413C2×C42—1461no—
414C2×C42—1461no—
415C2×C42—1461no—
416C2×C42—1461no—
417C2×C42—1461no—
418C2×C42—1461no—
419C2×C42—1461no—
420C2×C42—1461no—
421C4⋊C8—1468no—
422#97—1468no—
423#95—22no—
424#95—1462no—
425#95—1462no—
426#95—1462no—
427C24C22×#6440811yescharacteristic
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—731no—
447C22×C4—731no—
448C22×C4—731no—
449C22×C4—731no—
450C22×C4—731no—
451C22×C4—731no—
452C22×C4—731no—
453C22×C4—731no—
454C22×C4—731no—
455C22×C4—731no—
456C22×C4—731no—
457C22×C4—731no—
458C22×C4—731no—
459C22×C4—731no—
460C22×C4—732no—
461C22×C4—732no—
462C22×C4—732no—
463C22×C4—732no—
464C22×C4—732no—
465C22×C4—1461no—
466C22×C4—1461no—
467C22×C4—1461no—
468C22×C4—1461no—
469C22×C4—1461no—
470C22×C4—1461no—
471C22×C4—1461no—
472C22×C4—1461no—
473C22×C4—1461no—
474C22×C4—1461no—
475C22×C4—1461no—
476C22×C4—1461no—
477C22×C4—1461no—
478C22×C4—1461no—
479C22×C4—1461no—
480C22×C4—1461no—
481C22×C4C4×#6440812yes—
482C22×C4C4⋊#6440812yes—
483C22×C4#1192403712yes—
484C2×C8—2921no—
485C2×C8—2921no—
486C2×C8—2921no—
487C2×C8—2921no—
488C2×C8—2921no—
489C2×C8—2921no—
490C2×C8—2921no—
491C2×C8—2921no—
492C2×C8—734no—
493C2×C8—734no—
494C2×C8—1462no—
495C2×C8—1462no—
496C2×C8—1462no—
497C2×C8—1462no—
498C2×C8—1462no—
499C2×C8—1462no—
500C2×C8—1462no—
501C2×C8—1462no—
502C2×C8—1462no—
503C2×C8—1462no—
504C2×C8—1462no—
505C2×C8—1462no—
506C2×C8—1462no—
507C2×C8—1462no—
508C2×C8—1462no—
509C2×C8—1462no—
510C2×C8—1462no—
511C2×C8—1462no—
512C42—2921no—
513C42—2921no—
514C42—2921no—
515C42—2921no—
516C42—1462no—
517C42—1462no—
518C42—1462no—
519C42—1462no—
520C42—1462no—
521C42—1462no—
522C42—1462no—
523C42—1462no—
524C23C2×C4×#6440811yescharacteristic
525C23C2×C4⋊#6440811yescharacteristic
526C23#1455667011yescharacteristic
527C23D4×#6440811yescharacteristic
528C23D4×#6440811yescharacteristic
529C23D4×#6440811yescharacteristic
530C23Q8×#6440811yescharacteristic
531C23C2×#1192403711yescharacteristic
532C23D73⋊M1611yescharacteristic
533C23D73⋊M1611yescharacteristic
534C23D73⋊M1611yescharacteristic
535C23#1455667811yescharacteristic
536C23#1455667811yescharacteristic
537C23#1455667811yescharacteristic
538C23#1455667911yescharacteristic
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—2921no—
561C2×C4—2921no—
562C2×C4—2921no—
563C2×C4—2921no—
564C2×C4—2921no—
565C2×C4—2921no—
566C2×C4—2921no—
567C2×C4—2921no—
568C2×C4—731no—
569C2×C4—731no—
570C2×C4—731no—
571C2×C4—731no—
572C2×C4—731no—
573C2×C4—731no—
574C2×C4—731no—
575C2×C4—731no—
576C2×C4—731no—
577C2×C4—731no—
578C2×C4—731no—
579C2×C4—731no—
580C2×C4—731no—
581C2×C4—731no—
582C2×C4—731no—
583C2×C4—731no—
584C2×C4—731no—
585C2×C4—731no—
586C2×C4—731no—
587C2×C4—731no—
588C2×C4—731no—
589C2×C4—731no—
590C2×C4—731no—
591C2×C4—731no—
592C2×C4—731no—
593C2×C4—731no—
594C2×C4—731no—
595C2×C4—731no—
596C2×C4—734no—
597C2×C4—1462no—
598C2×C4—1462no—
599C2×C4—1462no—
600C2×C4—1462no—
601C2×C4—1462no—
602C2×C4—1462no—
603C2×C4—1462no—
604C2×C4—1462no—
605C2×C4—1462no—
606C2×C4—1462no—
607C2×C4—1462no—
608C2×C4—1462no—
609C8—2922no—
610C8—2922no—
611C8—1464no—
612C8—1464no—
613C22C22⋊C4×#6440811yescharacteristic
614C22C4×C4⋊#6440811yescharacteristic
615C22C4⋊C4×#6440811yescharacteristic
616C22#1798953411yescharacteristic
617C22#1798953611yescharacteristic
618C22#1798953711yescharacteristic
619C22#1798953811yescharacteristic
620C22#1798954611yescharacteristic
621C22C4×#1192403711yescharacteristic
622C22#1798955111yescharacteristic
623C22#1798955211yescharacteristic
624C22#1798959011yescharacteristic
625C22#1798959211yescharacteristic
626C22#1798959311yescharacteristic
627C22#1798959411yescharacteristic
628C22#1798960711yescharacteristic
629C22#1798961011yescharacteristic
630C22#1798961111yescharacteristic
631C22#1798961211yescharacteristic
632C22#1798961711yescharacteristic
633C22#1798961711yescharacteristic
634C22#1798961711yescharacteristic
635C22#1798961811yescharacteristic
636C22#1798961811yescharacteristic
637C22#1798961911yescharacteristic
638C22#1798961911yescharacteristic
639C22#1798961911yescharacteristic
640C22#1798962011yescharacteristic
641C22#1798962011yescharacteristic
642C22#1798962011yescharacteristic
643C22#1798962211yescharacteristic
644C22#1798963811yescharacteristic
645C22#1798963911yescharacteristic
646C22#1798963911yescharacteristic
647C22#1798963911yescharacteristic
648C4—42no—
649C4—42no—
650C4—42no—
651C4—2922no—
652C4—2922no—
653C4—731no—
654C4—731no—
655C4—731no—
656C4—731no—
657C4—731no—
658C4—731no—
659C4—731no—
660C4—731no—
661C4—1464no—
662C2#2262511111yescharacteristic
663C2#2262566911yescharacteristic
664C2#2262567311yescharacteristic
665C2#2262571611yescharacteristic
666C2#2262571911yescharacteristic
667C2#2262572611yescharacteristic
668C2#2262573111yescharacteristic
669C2#2262587811yescharacteristic
670C2#2262587911yescharacteristic
671C2#2262599011yescharacteristic
672C2#2262599111yescharacteristic
673C2#2262600411yescharacteristic
674C2#2262600711yescharacteristic
675C2#2262603211yescharacteristic
676C2#2262603311yescharacteristic
subgroupG/H
center, FrattiniC24C22×#64408
commutatorC23×C73C2×C42
FittingC2×#95×C73C4
socle, prime radicalC24×C73C22×C4
cosocleC23×Dic73C23
hypercenterC2×#95#64408
hypocenterC73#10877
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
14. C2×#14556658C4semidirect
21. #17989453C4semidirect
241. C2×Dic73#97semidirect
346. C73#10877semidirect

Maximal subgroups

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

subgroupindex
C22×#145566582
C22×#145566462
C2×#179894532
#95×Dic732
#1087773