Finite Group Databasebeta

← #33007233

Subgroups — #33007233

Order 18688.

2102 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556549C211yesmaximal, characteristic
2C2×#17988446C212yesmaximal
3C2×C4×#11924007C211yesmaximal, characteristic, complemented
4C2×#17988438C211yesmaximal, characteristic, complemented
5#22608169C211yesmaximal, characteristic
6#22608167C212yesmaximal
7#22608167C211yesmaximal, characteristic
8#22608165C212yesmaximal, complemented
9#22608163C211yesmaximal, characteristic, complemented
10#22608159C212yesmaximal, complemented
11C73×#1436C211yesmaximal, characteristic, complemented
12C23×C4×D73C2211yescharacteristic
13C2×#14556549—24no—
14C2×#14556549—24no—
15C2×#14556549C418yescomplemented
16C22×C4⋊Dic73C2211yescharacteristic
17C22×#11924007C2212yes—
18C22×#11924007C2212yes—
19C22×#11924005C2211yescharacteristic
20C22×#11924005C2211yescharacteristic
21C22×#11924005C2212yes—
22C22×#11924005C2212yes—
23C22×C4×Dic73C2211yescharacteristic
24C22×C4×Dic73C2211yescharacteristic
25C22×C4×Dic73C2212yes—
26C22×C4×Dic73C2211yescharacteristic
27#17988446C4116yescomplemented
28C4×#11924007—24no—
29#17988438—24no—
30C2×#14556498C2211yescharacteristic
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C2×#14556498C2212yes—
35C2×#14556498C2212yes—
36C22×C4⋊C4×C73C2211yescharacteristic
37C22×C42×C73C2211yescharacteristic
38C2×#95×C73C2211yescharacteristic
39C2×#95×C73C2212yes—
40C2×#95×C73C2212yes—
41C24×D73C2311yescharacteristic
42C23×Dic73C2312yes—
43C23×Dic73C2312yes—
44C23×Dic73C2311yescharacteristic
45C23×Dic73C2311yescharacteristic
46C23×Dic73C2311yescharacteristic
47C22×C4×D73—22no—
48C22×C4×D73—22no—
49C22×C4×D73—24no—
50C22×C4×D73C2×C418yes—
51C22×C4×D73C2×C414yes—
52#14556549—232no—
53C2×C4⋊Dic73—22no—
54C2×C4⋊Dic73—22no—
55C2×C4⋊Dic73C2×C414yes—
56C2×#11924007—24no—
57C2×#11924007—24no—
58C2×#11924007—24no—
59C2×#11924007—24no—
60C2×#11924007C2×C418yes—
61C2×#11924007C2×C418yes—
62C2×#11924005—22no—
63C2×#11924005—22no—
64C2×#11924005—22no—
65C2×#11924005—22no—
66C2×#11924005—42no—
67C2×#11924005—42no—
68C2×#11924005—42no—
69C2×#11924005—42no—
70C2×#11924005C2×C414yes—
71C2×#11924005C2×C414yes—
72C2×#11924005C2×C418yes—
73C2×#11924005C2×C418yes—
74C2×C4×Dic73—22no—
75C2×C4×Dic73—22no—
76C2×C4×Dic73—24no—
77C2×C4×Dic73—22no—
78C2×C4×Dic73—42no—
79C2×C4×Dic73—42no—
80C2×C4×Dic73—42no—
81C2×C4×Dic73C2×C414yes—
82C2×C4×Dic73C2×C414yes—
83C2×C4×Dic73D414yes—
84C2×C4×Dic73D414yes—
85#14556498—24no—
86#14556498—22no—
87#14556498—42no—
88#14556498—42no—
89#14556498—42no—
90#14556498C2×C418yes—
91C23×C4×C73C2312yes—
92C23×C4×C73C2311yescharacteristic
93C23×C4×C73C2312yes—
94C23×C4×C73C2311yescharacteristic
95C23×C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73—22no—
97C2×C4⋊C4×C73—22no—
98C2×C4⋊C4×C73C2×C414yes—
99C2×C42×C73—22no—
100C2×C42×C73—42no—
101#95×C73—22no—
102#95×C73—42no—
103#95×C73C2×C418yes—
104C23×D73—21no—
105C23×D73—21no—
106C23×D73—22no—
107C23×D73—22no—
108C23×D73—22no—
109C23×D73—22no—
110C23×D73—22no—
111C23×D73C22×C412yes—
112C23×D73C22×C414yes—
113C22×Dic73—22no—
114C22×Dic73—22no—
115C22×Dic73—22no—
116C22×Dic73—22no—
117C22×Dic73—21no—
118C22×Dic73—21no—
119C22×Dic73—22no—
120C22×Dic73—22no—
121C22×Dic73—22no—
122C22×Dic73—22no—
123C22×Dic73—22no—
124C22×Dic73—22no—
125C22×Dic73—22no—
126C22×Dic73—22no—
127C22×Dic73—22no—
128C22×Dic73—22no—
129C22×Dic73—22no—
130C22×Dic73—22no—
131C22×Dic73C22×C414yes—
132C22×Dic73C22×C414yes—
133C22×Dic73C22×C412yes—
134C22×Dic73C22×C412yes—
135C22×Dic73C22×C412yes—
136C22×Dic73C22×C414yes—
137C22×Dic73C2×D412yes—
138C22×Dic73C2×D412yes—
139C22×Dic73C2×D412yes—
140C22×Dic73C2×D412yes—
141C22×Dic73#4114yes—
142C2×C4×D73—28no—
143C2×C4×D73—28no—
144C2×C4×D73—216no—
145C2×C4×D73—216no—
146C2×C4×D73C42116yescomplemented
147C4⋊Dic73—28no—
148#11924007—216no—
149#11924007—216no—
150#11924005—28no—
151#11924005—28no—
152#11924005—48no—
153#11924005—48no—
154C4×Dic73—28no—
155C4×Dic73—48no—
156C4×Dic73—44no—
157C4×Dic73C22⋊C4116yescomplemented
158C24×C73C2411yescharacteristic
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—22no—
162C22×C4×C73—22no—
163C22×C4×C73—22no—
164C22×C4×C73—22no—
165C22×C4×C73—22no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—22no—
169C22×C4×C73—22no—
170C22×C4×C73—22no—
171C22×C4×C73—22no—
172C22×C4×C73—22no—
173C22×C4×C73—22no—
174C22×C4×C73—22no—
175C22×C4×C73—22no—
176C22×C4×C73—22no—
177C22×C4×C73—22no—
178C22×C4×C73—22no—
179C22×C4×C73—22no—
180C22×C4×C73C22×C414yes—
181C22×C4×C73C22×C414yes—
182C22×C4×C73C22×C412yes—
183C22×C4×C73C22×C414yes—
184C22×C4×C73C22×C412yes—
185C22×C4×C73C22×C412yes—
186C22×C4×C73C2×D412yes—
187C22×C4×C73C2×D412yes—
188C4⋊C4×C73—28no—
189C42×C73—44no—
190C23×C73C23×C411yescharacteristic
191C23×C73C23×C412yes—
192C23×C73C22×D411yescharacteristic
193C23×C73C22×D411yescharacteristic
194C23×C73C2×#4112yes—
195C23×C73H(5,𝔽2)12yes—
196C23×C73H(5,𝔽2)12yes—
197C23×C732−1+412yes—
198C23×C732−1+412yes—
199C22×D73—22no—
200C22×D73—22no—
201C22×D73—24no—
202C22×D73—24no—
203C22×D73—24no—
204C22×D73—24no—
205C22×D73—24no—
206C22×D73—24no—
207C22×D73—24no—
208C22×D73—24no—
209C22×D73—41no—
210C22×D73—41no—
211C22×D73—41no—
212C22×D73—41no—
213C22×D73—42no—
214C22×D73—42no—
215C22×D73—42no—
216C22×D73—42no—
217C22×D73—42no—
218C22×D73—42no—
219C22×D73C2×C4214yes—
220C2×C4×C73—22no—
221C2×C4×C73—22no—
222C2×C4×C73—24no—
223C2×C4×C73—24no—
224C2×C4×C73—24no—
225C2×C4×C73—22no—
226C2×C4×C73—22no—
227C2×C4×C73—24no—
228C2×C4×C73—22no—
229C2×C4×C73—24no—
230C2×C4×C73—24no—
231C2×C4×C73—24no—
232C2×C4×C73—24no—
233C2×C4×C73—24no—
234C2×C4×C73—24no—
235C2×C4×C73—24no—
236C2×C4×C73—42no—
237C2×C4×C73—41no—
238C2×C4×C73—42no—
239C2×C4×C73—41no—
240C2×C4×C73—42no—
241C2×C4×C73—42no—
242C2×C4×C73—42no—
243C2×C4×C73—42no—
244C2×C4×C73—42no—
245C2×C4×C73—42no—
246C2×C4×C73—42no—
247C2×C4×C73C2×C4214yes—
248C2×C4×C73C2×C22⋊C414yes—
249C2×Dic73—24no—
250C2×Dic73—22no—
251C2×Dic73—22no—
252C2×Dic73—24no—
253C2×Dic73—22no—
254C2×Dic73—24no—
255C2×Dic73—24no—
256C2×Dic73—24no—
257C2×Dic73—24no—
258C2×Dic73—24no—
259C2×Dic73—24no—
260C2×Dic73—24no—
261C2×Dic73—42no—
262C2×Dic73—42no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—42no—
266C2×Dic73—42no—
267C2×Dic73—42no—
268C2×Dic73—42no—
269C2×Dic73—42no—
270C2×Dic73—42no—
271C2×Dic73—42no—
272C2×Dic73C2×C4214yes—
273C2×Dic73C2×C22⋊C414yes—
274C2×Dic73C2×C22⋊C414yes—
275C2×Dic73#11714yes—
276C2×Dic73C4×D418yes—
277C2×Dic73C4×D418yes—
278C4×D73—232no—
279C22×C73C22×C4211yescharacteristic
280C22×C73C22×C22⋊C411yescharacteristic
281C22×C73C2×#11711yescharacteristic
282C22×C73C2×C4×D412yes—
283C22×C73C2×C4×D412yes—
284C22×C73#51812yes—
285C22×C73#51912yes—
286C22×C73#52012yes—
287C22×C73#52012yes—
288C22×C73#52012yes—
289C22×C73#52012yes—
290C22×C73#53511yescharacteristic
291C22×C73#53511yescharacteristic
292C22×C73#53611yescharacteristic
293C22×C73#53611yescharacteristic
294C22×C73#53712yes—
295C22×C73#53712yes—
296C22×C73#54012yes—
297C22×C73#54112yes—
298C22×C73#54212yes—
299C22×C73#54212yes—
300C2×D73—24no—
301C2×D73—28no—
302C2×D73—42no—
303C2×D73—42no—
304C2×D73—44no—
305C2×D73—44no—
306C2×D73—44no—
307C2×D73—44no—
308C2×D73—44no—
309C4×C73—24no—
310C4×C73—24no—
311C4×C73—42no—
312C4×C73—44no—
313C4×C73—44no—
314Dic73—24no—
315Dic73—42no—
316Dic73—44no—
317Dic73—44no—
318Dic73C4×C22⋊C418yes—
319#13777—731nomaximal, Sylow
320C2×C73C2×C4×C22⋊C411yescharacteristic
321C2×C73#227412yes—
322C2×C73#231111yescharacteristic
323C2×C73#231111yescharacteristic
324C2×C73#231412yes—
325C2×C73#232312yes—
326C2×C73#232312yes—
327C2×C73#232412yes—
328C2×C73#232412yes—
329D73—44no—
330C22×#117—731no—
331C2×#380—732no—
332C2×C4×C4⋊C4—731no—
333C2×C4×C4⋊C4—731no—
334#1437—731no—
335#1437—731no—
336#1437—732no—
337#1436—732no—
338#1436—731no—
339#1436D7311yescharacteristic, complemented
340C4⋊#95—732no—
341C73#1377711yescharacteristic, complemented, Sylow
342C24×C4—731no—
343C2×#117—738no—
344C2×#117—1464no—
345C2×#117—1464no—
346C22×C4⋊C4—731no—
347C22×C4⋊C4—732no—
348C22×C4⋊C4—732no—
349C22×C4⋊C4C2×D7311yescharacteristic
350C22×C22⋊C4—732no—
351C22×C22⋊C4—732no—
352C22×C22⋊C4—731no—
353C22×C22⋊C4—731no—
354C22×C42—732no—
355C22×C42—731no—
356C22×C42—731no—
357C22×C42—731no—
358C22×C42C2×D7311yescharacteristic
359#380—7316no—
360C4×C4⋊C4—1464no—
361C4×C4⋊C4—1464no—
362C2×#95—732no—
363C2×#95—732no—
364C2×#95—732no—
365C2×#95—732no—
366C2×#95—732no—
367C2×#95—731no—
368C2×#95C2×D7311yescharacteristic
369C2×#95C2×D7312yes—
370C2×#95C2×D7312yes—
371C25—731no—
372C23×C4—731no—
373C23×C4—731no—
374C23×C4—734no—
375C23×C4—738no—
376C23×C4—732no—
377C23×C4—732no—
378C23×C4—731no—
379C23×C4—1462no—
380C23×C4—1462no—
381C23×C4—1464no—
382C23×C4C22×D7312yes—
383C23×C4C22×D7312yes—
384C23×C4C22×D7311yescharacteristic
385C23×C4C22×D7311yescharacteristic
386C23×C4C22×D7311yescharacteristic
387#117—14632no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—734no—
391C2×C4⋊C4—738no—
392C2×C4⋊C4—738no—
393C2×C4⋊C4—1462no—
394C2×C4⋊C4—1462no—
395C2×C4⋊C4—1464no—
396C2×C4⋊C4—1464no—
397C2×C4⋊C4—1464no—
398C2×C4⋊C4—1464no—
399C2×C4⋊C4C4×D7314yes—
400C2×C22⋊C4—2922no—
401C2×C22⋊C4—2922no—
402C2×C22⋊C4—2922no—
403C2×C22⋊C4—2922no—
404C2×C22⋊C4—738no—
405C2×C22⋊C4—738no—
406C2×C22⋊C4—734no—
407C2×C22⋊C4—734no—
408C2×C22⋊C4—1462no—
409C2×C22⋊C4—1462no—
410C2×C22⋊C4—1462no—
411C2×C22⋊C4—1462no—
412C2×C42—22no—
413C2×C42—42no—
414C2×C42—2922no—
415C2×C42—2922no—
416C2×C42—2922no—
417C2×C42—734no—
418C2×C42—734no—
419C2×C42—734no—
420C2×C42—734no—
421C2×C42—1464no—
422C2×C42—1462no—
423C2×C42—1462no—
424C2×C42—1462no—
425#95—22no—
426#95—42no—
427#95—2922no—
428#95—2922no—
429#95—2922no—
430#95—738no—
431#95—1464no—
432#95—1462no—
433#95C4×D7318yes—
434C24—732no—
435C24—734no—
436C24—1461no—
437C24—1461no—
438C24—1462no—
439C24—1462no—
440C24—1462no—
441C24—1462no—
442C24—1462no—
443C24C23×D7311yescharacteristic
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—732no—
466C22×C4—734no—
467C22×C4—732no—
468C22×C4—732no—
469C22×C4—734no—
470C22×C4—732no—
471C22×C4—732no—
472C22×C4—732no—
473C22×C4—7316no—
474C22×C4—734no—
475C22×C4—734no—
476C22×C4—732no—
477C22×C4—1468no—
478C22×C4—1468no—
479C22×C4—14616no—
480C22×C4—14616no—
481C22×C4—1462no—
482C22×C4—1462no—
483C22×C4—1461no—
484C22×C4—1461no—
485C22×C4—1462no—
486C22×C4—1462no—
487C22×C4—1462no—
488C22×C4—1462no—
489C22×C4—1462no—
490C22×C4—1462no—
491C22×C4—1462no—
492C22×C4—1462no—
493C22×C4—1462no—
494C22×C4—1462no—
495C22×C4—1462no—
496C22×C4—1462no—
497C22×C4—1462no—
498C22×C4—1462no—
499C22×C4C2×C4×D7314yes—
500C22×C4C2×C4×D7314yes—
501C22×C4C2×C4×D7312yes—
502C22×C4C2×C4×D7314yes—
503C22×C4C2×C4×D7312yes—
504C22×C4C2×C4×D7312yes—
505C22×C4D4×D7312yes—
506C22×C4D4×D7312yes—
507C4⋊C4—28no—
508C4⋊C4—14616no—
509C4⋊C4—14616no—
510C4⋊C4—1468no—
511C22⋊C4—2928no—
512C22⋊C4—2928no—
513C22⋊C4—1468no—
514C22⋊C4—1468no—
515C42—44no—
516C42—2924no—
517C42—2928no—
518C42—7316no—
519C42—1468no—
520C23—2921no—
521C23—2921no—
522C23—2921no—
523C23—2921no—
524C23—2922no—
525C23—2922no—
526C23—2922no—
527C23—2922no—
528C23—2922no—
529C23—2922no—
530C23—734no—
531C23—1462no—
532C23—1462no—
533C23—1464no—
534C23—1464no—
535C23—1464no—
536C23—1464no—
537C23—1464no—
538C23—1464no—
539C23—1464no—
540C23—1464no—
541C23C22×C4×D7311yescharacteristic
542C23C22×C4×D7312yes—
543C23C2×D4×D7311yescharacteristic
544C23C2×D4×D7311yescharacteristic
545C23#41×D7312yes—
546C23#1455663612yes—
547C23#1455663712yes—
548C23#1455663812yes—
549C23#1455663912yes—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—2922no—
578C2×C4—2922no—
579C2×C4—2921no—
580C2×C4—2921no—
581C2×C4—2922no—
582C2×C4—2922no—
583C2×C4—2922no—
584C2×C4—2922no—
585C2×C4—2922no—
586C2×C4—2922no—
587C2×C4—2922no—
588C2×C4—734no—
589C2×C4—734no—
590C2×C4—734no—
591C2×C4—738no—
592C2×C4—738no—
593C2×C4—734no—
594C2×C4—14632no—
595C2×C4—1462no—
596C2×C4—1464no—
597C2×C4—1464no—
598C2×C4—1464no—
599C2×C4—1464no—
600C2×C4—1464no—
601C2×C4—1464no—
602C2×C4—1464no—
603C2×C4—1462no—
604C2×C4—1462no—
605C2×C4—1464no—
606C2×C4—1464no—
607C2×C4C42×D7314yes—
608C2×C4C22⋊C4×D7314yes—
609C22—2922no—
610C22—2922no—
611C22—2924no—
612C22—2924no—
613C22—2924no—
614C22—2924no—
615C22—2924no—
616C22—1464no—
617C22—1468no—
618C22C2×C42×D7311yescharacteristic
619C22C2×C22⋊C4×D7311yescharacteristic
620C22#117×D7311yescharacteristic
621C22C4×D4×D7312yes—
622C22C4×D4×D7312yes—
623C22#1798905912yes—
624C22#1798906312yes—
625C22#1798906612yes—
626C22#1798906712yes—
627C22#1798906812yes—
628C22#1798906912yes—
629C22#1798915211yescharacteristic
630C22#1798915511yescharacteristic
631C22#1798915911yescharacteristic
632C22#1798916211yescharacteristic
633C22#1798916412yes—
634C22#1798916712yes—
635C22#1798918912yes—
636C22#1798919612yes—
637C22#1798920312yes—
638C22#1798920712yes—
639C4—24no—
640C4—24no—
641C4—42no—
642C4—44no—
643C4—44no—
644C4—2922no—
645C4—2924no—
646C4—2924no—
647C4—738no—
648C4—1464no—
649C2—2924no—
650C2C4×C22⋊C4×D7311yescharacteristic
651C2#2261228512yes—
652C2#2261251811yescharacteristic
653C2#2261252211yescharacteristic
654C2#2261253712yes—
655C2#2261260812yes—
656C2#2261261212yes—
657C2#2261261912yes—
658C2#2261262312yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC22×C73C22×C42
FittingC73×#1436C2
socle, cosocleC24×C73C24
prime radicalC24×D73C23
hypercenter#1436D73
hypocenterC73#13777
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11924007C2semidirect
4. C2×#17988438C2semidirect
8. #22608165C2semidirect
9. #22608163C2semidirect
10. #22608159C2semidirect
11. C73×#1436C2semidirect
15. C2×#14556549C4semidirect
27. #17988446C4semidirect
146. C2×C4×D73C42semidirect
157. C4×Dic73C22⋊C4semidirect
339. #1436D73semidirect
341. C73#13777semidirect

Maximal subgroups

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

subgroupindex
C22×#145565492
C2×#179884462
C2×C4×#119240072
C2×#179884382
#226081692
#226081672
#226081652
#226081632
#226081592
C73×#14362
#1377773