Finite Group Databasebeta

← #33102777

Subgroups — #33102777

Order 18688.

1074 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989306C211yesmaximal, characteristic
2C2×C8×Dic146C211yesmaximal, characteristic, complemented
3#22612883C211yesmaximal, characteristic, complemented
4#22610864C211yesmaximal, characteristic
5#22610862C211yesmaximal, characteristic
6#22610852C211yesmaximal, characteristic, complemented
7#22610741C211yesmaximal, characteristic
8#22610731C211yesmaximal, characteristic, complemented
9#22609944C211yesmaximal, characteristic, complemented
10#22609943C211yesmaximal, characteristic, complemented
11#22609929C211yesmaximal, characteristic
12#103×Dic73C211yesmaximal, characteristic, complemented
13C4×#14556516C211yesmaximal, characteristic, complemented
14#102×Dic73C211yesmaximal, characteristic
15C73×#1958C211yesmaximal, characteristic
16#17989306—24no—
17#17989306C418yescomplemented
18C2×#14556589C2211yescharacteristic
19C2×#14556584—21no—
20C2×#14556584—21no—
21C2×#14556578C2211yescharacteristic
22C2×#14556568—21no—
23C2×Q8×Dic73C2211yescharacteristic
24C2×C4×Dic146C2211yescharacteristic
25C2×C4×Dic146C2211yescharacteristic
26C2×D4×Dic73C2211yescharacteristic
27C2×#14556547—21no—
28C8×Dic146—24no—
29C2×C4⋊#10596831C2211yescharacteristic
30C2×#14556520C2211yescharacteristic
31C2×#14556520C2211yescharacteristic
32C2×#14556516C2211yescharacteristic
33C2×#14556516C2211yescharacteristic
34C2×#14556515C2211yescharacteristic
35C2×#14556515C2211yescharacteristic
36C2×#14556514C2211yescharacteristic
37C2×#14556514C2211yescharacteristic
38C2×#14556512C2211yescharacteristic
39C2×#14556512C2211yescharacteristic
40C2×C8×Dic73C2211yescharacteristic
41C2×C8×Dic73C2211yescharacteristic
42#17988491—21no—
43#17988472—21no—
44#17988469—21no—
45#17988456C2211yescharacteristic
46#17988452C2211yescharacteristic
47C4⋊C4×Dic73C2211yescharacteristic
48C4⋊C4×Dic73C2211yescharacteristic
49C4×C4⋊Dic73C2211yescharacteristic
50#17988438—21no—
51#17988350C2211yescharacteristic
52#17988350C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55C2×#124×C73C2211yescharacteristic
56C2×#103×C73C2211yescharacteristic
57C2×#103×C73C2211yescharacteristic
58C2×#102×C73C2211yescharacteristic
59C2×#102×C73C2211yescharacteristic
60C2×C4×C8×C73C2211yescharacteristic
61#382×C73C2211yescharacteristic
62C22×Dic146D411yescharacteristic
63C22×Dic146C2311yescharacteristic
64C23×Dic73—21no—
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67#14556589—22no—
68#14556589C2×C414yes—
69#14556584—28no—
70#14556584—28no—
71#14556578—22no—
72#14556578C2×C414yes—
73#14556568—28no—
74Q8×Dic73—22no—
75Q8×Dic73C2×C414yes—
76C4×Dic146—22no—
77C4×Dic146C2×C414yes—
78C4×Dic146C2×C414yes—
79C4×Dic146D414yes—
80D4×Dic73—22no—
81D4×Dic73C2×C414yes—
82#14556547—28no—
83C2×C4⋊Dic73—21no—
84C2×C4⋊Dic73D411yescharacteristic
85C2×C4⋊Dic73C2311yescharacteristic
86C2×C4⋊Dic73C2311yescharacteristic
87C2×C4⋊Dic73C2311yescharacteristic
88C2×#11924007—21no—
89C2×#11924007—21no—
90C2×#11924007—21no—
91C2×#11924007—21no—
92C2×#11924007—21no—
93C2×#11924007D411yescharacteristic
94C2×#11924007D411yescharacteristic
95C2×C22⋊Dic73—21no—
96C2×C22⋊Dic73—21no—
97C2×C22⋊Dic73—21no—
98C2×C4×Dic73—21no—
99C2×C4×Dic73—21no—
100C2×C4×Dic73—21no—
101C2×C4×Dic73—21no—
102C2×C4×Dic73—21no—
103C2×C4×Dic73C2311yescharacteristic
104C2×C4×Dic73C2311yescharacteristic
105C4⋊#10596831—22no—
106#14556520—22no—
107#14556520—22no—
108#14556516—22no—
109#14556516—22no—
110#14556515—22no—
111#14556515—41no—
112#14556514—41no—
113#14556514—41no—
114#14556512—22no—
115#14556512—41no—
116C8×Dic73—22no—
117C8×Dic73—22no—
118#14556498—21no—
119#14556498—21no—
120#14556498—21no—
121#14556498—21no—
122#14556498—21no—
123C22×Q8×C73C2311yescharacteristic
124C22×D4×C73C2311yescharacteristic
125C22×C8×C73C2311yescharacteristic
126C22×C8×C73C2311yescharacteristic
127#124×C73—22no—
128#124×C73C2×C414yes—
129C2×C4⋊C4×C73C2311yescharacteristic
130C2×C4⋊C4×C73C2311yescharacteristic
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C42×C73C2311yescharacteristic
134#103×C73—22no—
135#103×C73—41no—
136#102×C73—22no—
137#102×C73—41no—
138C4×C8×C73—22no—
139#95×C73—21no—
140#95×C73—21no—
141C2×Dic146—22no—
142C2×Dic146—22no—
143C2×Dic146—21no—
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147C2×Dic146—21no—
148C2×Dic146C22⋊C414yes—
149C2×Dic146C22×C412yes—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73—24no—
154C22×Dic73—21no—
155C22×Dic73—42no—
156C22×Dic73—42no—
157C22×Dic73C2×D411yescharacteristic
158C22×Dic73C2×D411yescharacteristic
159C22×Dic73C2×D411yescharacteristic
160C22×Dic73C2×D411yescharacteristic
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—24no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73C22⋊C414yes—
173C4⋊Dic73C22×C412yes—
174C4⋊Dic73#4112yes—
175#11924007—24no—
176#11924007—24no—
177#11924007—24no—
178#11924007—42no—
179#11924007—81no—
180#11924007C22⋊C414yes—
181#11924007C22⋊C414yes—
182C22⋊Dic73—24no—
183C22⋊Dic73—24no—
184C22⋊Dic73—24no—
185C4×Dic73—24no—
186C4×Dic73—24no—
187C4×Dic73—42no—
188C4×Dic73—81no—
189C4×Dic73—81no—
190C4×Dic73C22×C412yes—
191C4×Dic73C22×C412yes—
192C4×Dic73C2×D412yes—
193C4×Dic73C2×D412yes—
194C24×C73—21no—
195C2×Q8×C73—21no—
196C2×Q8×C73—21no—
197C2×Q8×C73—21no—
198C2×Q8×C73—21no—
199C2×Q8×C73—21no—
200C2×Q8×C73C22×C412yes—
201C2×D4×C73—21no—
202C2×D4×C73—21no—
203C2×D4×C73—21no—
204C2×D4×C73—21no—
205C2×D4×C73—21no—
206C2×D4×C73C22×C412yes—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2×D411yescharacteristic
212C22×C4×C73C2411yescharacteristic
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73#4112yes—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C22⋊C4×C73—24no—
224C22⋊C4×C73—24no—
225C42×C73C22×C412yes—
226C42×C73C2×D412yes—
227C23×C73—22no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73C22×D411yescharacteristic
235Q8×C73—22no—
236Q8×C73—22no—
237Q8×C73—41no—
238Q8×C73—41no—
239D4×C73—22no—
240D4×C73—22no—
241D4×C73—41no—
242D4×C73—41no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—22no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—41no—
255C2×C4×C73—41no—
256C2×C4×C73C2×C22⋊C412yes—
257C2×C4×C73C2×C22⋊C412yes—
258C2×C4×C73C23×C411yescharacteristic
259C2×C4×C73C22×D411yescharacteristic
260C2×C4×C73C2×#4111yescharacteristic
261C2×C4×C73C2×#4111yescharacteristic
262C2×C4×C73H(5,𝔽2)11yescharacteristic
263C2×C4×C732−1+411yescharacteristic
264C2×Dic73—21no—
265C2×Dic73—21no—
266C2×Dic73—21no—
267C2×Dic73—21no—
268C2×Dic73—21no—
269C2×Dic73—21no—
270C2×Dic73—22no—
271C2×Dic73—22no—
272C2×Dic73—22no—
273C2×Dic73—41no—
274C2×Dic73—41no—
275C2×Dic73—41no—
276C2×Dic73—41no—
277C2×Dic73—41no—
278C2×Dic73—41no—
279C2×Dic73—48no—
280C2×Dic73—41no—
281C2×Dic73—41no—
282C2×Dic73—41no—
283C2×Dic73C2×C22⋊C412yes—
284C2×Dic73C2×C22⋊C412yes—
285C2×Dic73C2×C22⋊C412yes—
286C2×Dic73C2×C22⋊C412yes—
287C2×Dic73#13512yes—
288C2×Dic73#13512yes—
289Dic146—28no—
290Dic146—22no—
291Dic146—22no—
292Dic146—41no—
293Dic146—41no—
294C8×C73—22no—
295C8×C73—41no—
296#10596831—41no—
297#10596831—41no—
298C22×C73—42no—
299C22×C73—42no—
300C22×C73—42no—
301C22×C73—81no—
302C22×C73—81no—
303C22×C73—81no—
304C22×C73—81no—
305C22×C73C22×C22⋊C411yescharacteristic
306C22×C73#54811yescharacteristic
307C22×C73#55011yescharacteristic
308C22×C73C2×#13511yescharacteristic
309C22×C73C2×#13511yescharacteristic
310C22×C73#57711yescharacteristic
311C22×C73#57811yescharacteristic
312C4×C73—22no—
313C4×C73—22no—
314C4×C73—42no—
315C4×C73—81no—
316C4×C73—81no—
317C4×C73C4×#4111yescharacteristic
318C4×C73#52011yescharacteristic
319C4×C73#54811yescharacteristic
320C4×C73#55011yescharacteristic
321Dic73—22no—
322Dic73—22no—
323Dic73—22no—
324Dic73—42no—
325Dic73—42no—
326Dic73—42no—
327Dic73—81no—
328Dic73#41614yes—
329#22541—731nomaximal, Sylow
330C2×C73—82no—
331C2×C73#234111yescharacteristic
332C2×C73C2×#41611yescharacteristic
333C2×C73#289811yescharacteristic
334C2×C73#336011yescharacteristic
335C2×C73#336411yescharacteristic
336C2×C73#339311yescharacteristic
337C2×C73#339411yescharacteristic
338C2×#556—731no—
339C2×C8×Q8—731no—
340#2355—731no—
341#1983—731no—
342#1983—731no—
343#1981—731no—
344#1958—731no—
345#1958D7311yescharacteristic
346#1956—731no—
347#1805—731no—
348#1805—731no—
349#1802—731no—
350C4×#103—731no—
351C4×#103—731no—
352C4×#102—731no—
353C73#2254111yescharacteristic, complemented, Sylow
354#556—738no—
355#556—1464no—
356C2×C4⋊Q8—731no—
357C2×#126—1461no—
358C2×#126—1461no—
359C2×#124—731no—
360C2×#124C2×D7311yescharacteristic
361C2×C22⋊Q8—1461no—
362C2×C4×Q8—731no—
363C2×C4×Q8—731no—
364C2×C4×Q8—731no—
365C2×C4×D4—731no—
366C2×#117—1461no—
367C8×Q8—1464no—
368C2×C4⋊C8—731no—
369C2×C4⋊C8—731no—
370C2×C4⋊C8—731no—
371C2×#103—731no—
372C2×#103—731no—
373C2×#103—731no—
374C2×#103—731no—
375C2×#103—731no—
376C2×#103—731no—
377C2×#103C2×D7311yescharacteristic
378C2×#103C2×D7311yescharacteristic
379C2×#102—731no—
380C2×#102—731no—
381C2×#102C2×D7311yescharacteristic
382C2×#102C2×D7311yescharacteristic
383C2×C4×C8—731no—
384C2×C4×C8—731no—
385C2×C4×C8C2×D7311yescharacteristic
386#391—1461no—
387#387—1461no—
388#387—1461no—
389#384—731no—
390#382—731no—
391#382C2×D7311yescharacteristic
392C4×C4⋊C4—731no—
393C4×C4⋊C4—731no—
394C4×C4⋊C4—731no—
395C4×C4⋊C4—1461no—
396#340—731no—
397#340—731no—
398#340—731no—
399#340—731no—
400C22×Q8—731no—
401C22×Q8—731no—
402C22×Q8C22×D7311yescharacteristic
403C22×D4C22×D7311yescharacteristic
404C23×C4—1461no—
405C22×C8—731no—
406C22×C8—731no—
407C22×C8C22×D7311yescharacteristic
408C22×C8C22×D7311yescharacteristic
409C4⋊Q8—734no—
410C4⋊Q8—1462no—
411#126—1468no—
412#126—1468no—
413#124—22no—
414#124—734no—
415#124—1462no—
416#124C4×D7314yes—
417C22⋊Q8—1468no—
418C4×Q8—734no—
419C4×Q8—734no—
420C4×Q8—734no—
421C4×Q8—734no—
422C4×Q8—1462no—
423C4×Q8—1462no—
424C4×D4—734no—
425C4×D4—1462no—
426#117—1468no—
427C2×C4⋊C4—731no—
428C2×C4⋊C4—731no—
429C2×C4⋊C4—731no—
430C2×C4⋊C4—731no—
431C2×C4⋊C4—731no—
432C2×C4⋊C4—731no—
433C2×C4⋊C4—1461no—
434C2×C4⋊C4—1461no—
435C2×C4⋊C4—1461no—
436C2×C4⋊C4—1461no—
437C2×C4⋊C4—1461no—
438C2×C4⋊C4—1461no—
439C2×C4⋊C4C22×D7311yescharacteristic
440C2×C4⋊C4C22×D7311yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—1461no—
444C2×C22⋊C4—1461no—
445C2×C22⋊C4—1461no—
446C2×C42—731no—
447C2×C42—731no—
448C2×C42—1461no—
449C2×C42—1461no—
450C2×C42—1461no—
451C2×C42—1461no—
452C2×C42—1461no—
453C2×C42C22×D7311yescharacteristic
454C4⋊C8—1462no—
455C4⋊C8—1462no—
456C4⋊C8—1462no—
457#103—22no—
458#103—41no—
459#103—2921no—
460#103—2921no—
461#103—2921no—
462#103—1462no—
463#103—1462no—
464#103—1462no—
465#102—22no—
466#102—41no—
467#102—2921no—
468#102—1462no—
469C4×C8—22no—
470C4×C8—1462no—
471C4×C8—1462no—
472#95—21no—
473#95—21no—
474#95—1461no—
475#95—1461no—
476#95—1461no—
477#95—1461no—
478#95—1461no—
479C24—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—734no—
486C2×Q8—732no—
487C2×Q8—1462no—
488C2×Q8—1462no—
489C2×Q8—1461no—
490C2×Q8—1461no—
491C2×Q8—1461no—
492C2×Q8—1461no—
493C2×Q8—1461no—
494C2×Q8C2×C4×D7312yes—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4C2×C4×D7312yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—2922no—
505C22×C4—2922no—
506C22×C4—731no—
507C22×C4—731no—
508C22×C4—731no—
509C22×C4—731no—
510C22×C4—1461no—
511C22×C4—1464no—
512C22×C4—1461no—
513C22×C4—1461no—
514C22×C4—1461no—
515C22×C4D4×D7311yescharacteristic
516C22×C4D4×D7311yescharacteristic
517C22×C4C23×D7311yescharacteristic
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—1461no—
524C2×C8—1461no—
525C2×C8—1461no—
526C2×C8—1461no—
527C2×C8—1461no—
528C2×C8—1461no—
529C2×C8#1192402712yes—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—2922no—
535C4⋊C4—5841no—
536C4⋊C4—734no—
537C4⋊C4—734no—
538C4⋊C4—734no—
539C4⋊C4—732no—
540C4⋊C4—732no—
541C4⋊C4—1464no—
542C4⋊C4—1464no—
543C4⋊C4—1464no—
544C4⋊C4—1461no—
545C4⋊C4—1461no—
546C4⋊C4—1464no—
547C4⋊C4—1461no—
548C4⋊C4—1461no—
549C22⋊C4—24no—
550C22⋊C4—24no—
551C22⋊C4—1464no—
552C22⋊C4—1464no—
553C22⋊C4—1464no—
554C42—2922no—
555C42—5841no—
556C42—5841no—
557C42—732no—
558C42—732no—
559C42—732no—
560C42—732no—
561C42—1464no—
562C42—1464no—
563C42C2×C4×D7312yes—
564C42D4×D7312yes—
565C23—22no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C2×D4×D7311yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577Q8—2921no—
578Q8—2921no—
579Q8—1468no—
580Q8—1462no—
581Q8—1462no—
582D4—22no—
583D4—22no—
584D4—41no—
585D4—41no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—2921no—
600C2×C4—2921no—
601C2×C4—2921no—
602C2×C4—2921no—
603C2×C4—2921no—
604C2×C4—2921no—
605C2×C4—2928no—
606C2×C4—2921no—
607C2×C4—2921no—
608C2×C4—2921no—
609C2×C4—732no—
610C2×C4—732no—
611C2×C4—732no—
612C2×C4—732no—
613C2×C4—732no—
614C2×C4—732no—
615C2×C4—1462no—
616C2×C4—1462no—
617C2×C4—1462no—
618C2×C4—1461no—
619C2×C4—1461no—
620C2×C4—1461no—
621C2×C4—1461no—
622C2×C4—1461no—
623C2×C4—1461no—
624C2×C4C22⋊C4×D7312yes—
625C2×C4C22⋊C4×D7312yes—
626C2×C4C22×C4×D7311yescharacteristic
627C2×C4C2×D4×D7311yescharacteristic
628C2×C4#41×D7311yescharacteristic
629C2×C4C2×#1192402711yescharacteristic
630C2×C4#1455663611yescharacteristic
631C2×C4#1455663811yescharacteristic
632C8—22no—
633C8—41no—
634C8—2921no—
635C8—2921no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22C2×C22⋊C4×D7311yescharacteristic
644C22#1798924511yescharacteristic
645C22#1798925711yescharacteristic
646C22#135×D7311yescharacteristic
647C22#135×D7311yescharacteristic
648C22#1798939411yescharacteristic
649C22#1798940111yescharacteristic
650C4—22no—
651C4—22no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4—2922no—
656C4—2922no—
657C4—2922no—
658C4—5841no—
659C4—734no—
660C4—1462no—
661C4—1462no—
662C4—1462no—
663C4C4×#1192402711yescharacteristic
664C4#1798906611yescharacteristic
665C4#1798924311yescharacteristic
666C4#1798925511yescharacteristic
667C2—82no—
668C2#2261277011yescharacteristic
669C2#416×D7311yescharacteristic
670C2#2261846011yescharacteristic
671C2#2262257711yescharacteristic
672C2#2262261311yescharacteristic
673C2#2262291611yescharacteristic
674C2#2262292411yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1958C2
socleC23×C73C22×D4
prime radicalC22×D4×C73C23
cosocleC22×C4×C73C24
hypercenter#1958D73
hypocenterC73#22541
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1958

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic146C2semidirect
3. #22612883C2semidirect
6. #22610852C2semidirect
8. #22610731C2semidirect
9. #22609944C2semidirect
10. #22609943C2semidirect
12. #103×Dic73C2semidirect
13. C4×#14556516C2semidirect
17. #17989306C4semidirect
353. C73#22541semidirect

Maximal subgroups

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

subgroupindex
C2×#179893062
C2×C8×Dic1462
#226128832
#226108642
#226108622
#226108522
#226107412
#226107312
#226099442
#226099432
#226099292
#103×Dic732
C4×#145565162
#102×Dic732
C73×#19582
#2254173