Finite Group Databasebeta

← #33093982

Subgroups — #33093982

Order 18688.

818 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988942C211yesmaximal, characteristic
2#22612672C211yesmaximal, characteristic, complemented
3#22612642C211yesmaximal, characteristic
4#22610900C211yesmaximal, characteristic, complemented
5#22610747C211yesmaximal, characteristic
6#22610628C211yesmaximal, characteristic
7#22610621C211yesmaximal, characteristic, complemented
8#22610614C211yesmaximal, characteristic
9#22610607C211yesmaximal, characteristic, complemented
10#22610059C211yesmaximal, characteristic, complemented
11#22609762C211yesmaximal, characteristic, complemented
12#22609757C211yesmaximal, characteristic
13C4×#14556516C211yesmaximal, characteristic, complemented
14C4×#14556513C211yesmaximal, characteristic
15C73×#1726C211yesmaximal, characteristic, complemented
16C2×#14556583C2211yescharacteristic
17C2×#14556579C2211yescharacteristic
18C2×C4×Dic146C2211yescharacteristic
19C2×C4×D292C2211yescharacteristic
20#17988942C418yescomplemented
21C2×#14556516C2211yescharacteristic
22C2×#14556516C2211yescharacteristic
23C2×#14556516C2211yescharacteristic
24C2×#14556516C2211yescharacteristic
25C2×#14556513C2211yescharacteristic
26C2×#14556513C2211yescharacteristic
27C2×#14556513C2211yescharacteristic
28C2×#14556513C2211yescharacteristic
29#17988493C2211yescharacteristic
30#17988489C2211yescharacteristic
31#17988485C2211yescharacteristic
32#17988485C2211yescharacteristic
33#17988484—21no—
34#17988484—21no—
35#17988479—21no—
36#17988479—21no—
37#17988474—21no—
38#17988474—21no—
39#17988461—21no—
40#17988461—21no—
41#17988457C2211yescharacteristic
42#17988457C2211yescharacteristic
43C4×C4⋊Dic73C2211yescharacteristic
44C4×C4⋊Dic73C2211yescharacteristic
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988350C2211yescharacteristic
51#17988350C2211yescharacteristic
52#17988350C2211yescharacteristic
53C2×#97×C73C2211yescharacteristic
54C2×#97×C73C2211yescharacteristic
55C2×#97×C73C2211yescharacteristic
56C2×C4×C8×C73C2211yescharacteristic
57C2×C4×C8×C73C2211yescharacteristic
58C2×C4×C8×C73C2211yescharacteristic
59#376×C73C2211yescharacteristic
60C22×Dic146C2311yescharacteristic
61C22×D292C2311yescharacteristic
62C22×C4×D73—21no—
63#14556583—22no—
64#14556583C2×C414yescomplemented
65#14556579—22no—
66#14556579C2×C414yes—
67C4×Dic146—22no—
68C4×Dic146—22no—
69C4×D292—22no—
70C4×D292—22no—
71C2×C4⋊Dic73—21no—
72C2×C4⋊Dic73—21no—
73C2×C4⋊Dic73—21no—
74C2×C4⋊Dic73—21no—
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C4⋊Dic73C2311yescharacteristic
77C2×C4⋊Dic73C2311yescharacteristic
78C2×C4⋊Dic73C2311yescharacteristic
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C4⋊Dic73C2311yescharacteristic
81C2×#11924007—21no—
82C2×#11924007—21no—
83C2×#11924007—21no—
84C2×#11924007—21no—
85C2×#11924007—21no—
86C2×#11924005—21no—
87C2×#11924005—21no—
88C2×#11924005—21no—
89C2×#11924005—21no—
90C2×#11924005—21no—
91C2×C4×Dic73—21no—
92C2×C4×Dic73—21no—
93C2×C4×Dic73—21no—
94#14556516—22no—
95#14556516—22no—
96#14556516C2×C414yescomplemented
97#14556516C2×C414yescomplemented
98#14556513—22no—
99#14556513—22no—
100#14556513C2×C414yes—
101#14556513C2×C414yes—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108C22×C8×C73C2311yescharacteristic
109C22×C8×C73C2311yescharacteristic
110C22×C8×C73C2311yescharacteristic
111C22×C8×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115#97×C73—22no—
116#97×C73—22no—
117#97×C73—22no—
118C4×C8×C73—22no—
119C4×C8×C73—22no—
120C4×C8×C73C2×C414yescomplemented
121#95×C73D411yescharacteristic
122#95×C73D411yescharacteristic
123#95×C73D411yescharacteristic
124#95×C73D411yescharacteristic
125C23×D73—21no—
126C2×Dic146—21no—
127C2×Dic146—21no—
128C2×Dic146—21no—
129C2×Dic146—21no—
130C2×Dic146—21no—
131C2×Dic146C22×C412yes—
132C2×D292—21no—
133C2×D292—21no—
134C2×D292—21no—
135C2×D292—21no—
136C2×D292—21no—
137C2×D292C22×C412yes—
138C22×Dic73—21no—
139C22×Dic73—21no—
140C22×Dic73—21no—
141C22×Dic73—21no—
142C22×Dic73—21no—
143C22×Dic73—21no—
144C22×Dic73—21no—
145C2×C4×D73—42no—
146C2×C4×D73—81no—
147C2×C4×D73—81no—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73—21no—
155C4⋊Dic73—21no—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—81no—
159C4⋊Dic73—81no—
160C4⋊Dic73—81no—
161C4⋊Dic73—81no—
162C4⋊Dic73C22×C412yes—
163C4⋊Dic73C22×C412yes—
164#11924007—24no—
165#11924007—24no—
166#11924007—42no—
167#11924007—81no—
168#11924007—81no—
169#11924005—24no—
170#11924005—24no—
171#11924005—42no—
172#11924005—81no—
173#11924005—81no—
174C4×Dic73—42no—
175C4×Dic73—81no—
176C4×Dic73—81no—
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2411yescharacteristic
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73C22×C412yes—
193C2×C8×C73C22×C412yes—
194C2×C8×C73#4112yes—
195C2×C8×C73#4112yes—
196C42×C73—21no—
197C42×C73—21no—
198C42×C73C22×C412yes—
199C42×C73#4112yes—
200C42×C73#4112yes—
201C42×C73#4112yes—
202C23×C73C22×D411yescharacteristic
203C22×D73—22no—
204C22×D73—41no—
205C22×D73—41no—
206C22×D73—41no—
207C22×D73—41no—
208C22×D73—41no—
209C22×D73—41no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73C4×D412yes—
225C2×C4×C73C4×D412yes—
226C2×C4×C73#12412yes—
227C2×C4×C73#12412yes—
228C2×C4×C73C23×C411yescharacteristic
229C2×C4×C73C2×#4111yescharacteristic
230C2×C4×C73C2×#4111yescharacteristic
231C2×C4×C73C2×#4111yescharacteristic
232C2×C4×C73C2×#4111yescharacteristic
233C2×C4×C73C2×#4111yescharacteristic
234C2×Dic73—22no—
235C2×Dic73—22no—
236C2×Dic73—22no—
237C2×Dic73—41no—
238C2×Dic73—41no—
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253C2×Dic73—41no—
254C2×Dic73—41no—
255D292—22no—
256D292—22no—
257D292—41no—
258D292—41no—
259C4×D73—84no—
260Dic146—22no—
261Dic146—22no—
262Dic146—41no—
263Dic146—41no—
264C8×C73—22no—
265C8×C73—22no—
266C8×C73—22no—
267C8×C73—22no—
268C22×C73C2×C4×D411yescharacteristic
269C22×C73C2×#12411yescharacteristic
270C22×C73#53211yescharacteristic
271C22×C73#57611yescharacteristic
272C22×C73#57711yescharacteristic
273C22×C73#57711yescharacteristic
274C22×C73#57811yescharacteristic
275C2×D73—42no—
276C2×D73—42no—
277C2×D73—42no—
278C2×D73—81no—
279C2×D73—81no—
280C2×D73—81no—
281C2×D73—81no—
282C4×C73—22no—
283C4×C73—22no—
284C4×C73—22no—
285C4×C73—22no—
286C4×C73—41no—
287C4×C73—41no—
288C4×C73C4×#4111yescharacteristic
289C4×C73C4×#4111yescharacteristic
290C4×C73#52911yescharacteristic
291C4×C73#52911yescharacteristic
292Dic73—42no—
293Dic73—42no—
294Dic73—42no—
295Dic73—81no—
296Dic73—81no—
297Dic73—81no—
298Dic73—81no—
299#21643—731nomaximal, Sylow
300C2×C73C4×#12411yescharacteristic
301C2×C73#295111yescharacteristic
302C2×C73#295211yescharacteristic
303C2×C73#313611yescharacteristic
304C2×C73#313711yescharacteristic
305C2×C73#317811yescharacteristic
306C2×C73#317911yescharacteristic
307D73—82no—
308C2×#488—731no—
309#2330—731no—
310#2326—731no—
311#1992—731no—
312#1959—731no—
313#1936—731no—
314#1935—731no—
315#1934—731no—
316#1933—731no—
317#1834—731no—
318#1763—731no—
319#1762—731no—
320C4×#103—731no—
321C4×#102—731no—
322#1726D7311yescharacteristic, complemented
323C73#2164311yescharacteristic, complemented, Sylow
324C2×#125—731no—
325C2×#124—731no—
326C2×C4×Q8—731no—
327C2×C4×D4—731no—
328#488—738no—
329C2×#103—731no—
330C2×#103—731no—
331C2×#103—731no—
332C2×#103—731no—
333C2×#102—731no—
334C2×#102—731no—
335C2×#102—731no—
336C2×#102—731no—
337C2×#97C2×D7311yescharacteristic
338C2×#97C2×D7311yescharacteristic
339C2×#97C2×D7311yescharacteristic
340C2×C4×C8C2×D7311yescharacteristic
341C2×C4×C8C2×D7311yescharacteristic
342C2×C4×C8C2×D7311yescharacteristic
343#391—731no—
344#390—731no—
345#389—731no—
346#389—731no—
347#389—1461no—
348#389—1461no—
349#388—1461no—
350#388—1461no—
351#387—1461no—
352#387—1461no—
353#385—1461no—
354#385—1461no—
355#384—731no—
356#384—731no—
357C4×C4⋊C4—731no—
358C4×C4⋊C4—731no—
359#376C2×D7311yescharacteristic
360#340—731no—
361#340—731no—
362#340—731no—
363#340—731no—
364#340—731no—
365#340—731no—
366#340—731no—
367#340—731no—
368C22×Q8—731no—
369C22×D4—731no—
370C23×C4—1461no—
371C22×C8C22×D7311yescharacteristic
372C22×C8C22×D7311yescharacteristic
373C22×C8C22×D7311yescharacteristic
374C22×C8C22×D7311yescharacteristic
375#125—734no—
376#125—1462no—
377#124—734no—
378#124—1462no—
379C4×Q8—1462no—
380C4×Q8—1462no—
381C4×D4—1462no—
382C4×D4—1462no—
383C2×C4⋊C4—731no—
384C2×C4⋊C4—731no—
385C2×C4⋊C4—731no—
386C2×C4⋊C4—731no—
387C2×C4⋊C4—731no—
388C2×C4⋊C4—731no—
389C2×C4⋊C4—1461no—
390C2×C4⋊C4—1461no—
391C2×C4⋊C4—1461no—
392C2×C4⋊C4—1461no—
393C2×C4⋊C4—1461no—
394C2×C4⋊C4—1461no—
395C2×C4⋊C4—1461no—
396C2×C4⋊C4—1461no—
397C2×C4⋊C4—1461no—
398C2×C22⋊C4—1461no—
399C2×C22⋊C4—1461no—
400C2×C22⋊C4—1461no—
401C2×C22⋊C4—1461no—
402C2×C22⋊C4—1461no—
403C2×C42—1461no—
404C2×C42—1461no—
405C2×C42—1461no—
406C2×C42C22×D7311yescharacteristic
407C2×C42C22×D7311yescharacteristic
408C2×C42C22×D7311yescharacteristic
409#103—734no—
410#103—734no—
411#103—1462no—
412#103—1462no—
413#102—734no—
414#102—734no—
415#102—1462no—
416#102—1462no—
417#97—22no—
418#97—22no—
419#97—22no—
420C4×C8—22no—
421C4×C8—22no—
422C4×C8C4×D7314yescomplemented
423#95—1461no—
424#95—1461no—
425#95—1461no—
426#95—1461no—
427#95—1461no—
428#95—1461no—
429#95D29211yescharacteristic
430#95D29211yescharacteristic
431#95D29211yescharacteristic
432#95D29211yescharacteristic
433C24—1461no—
434C2×Q8—732no—
435C2×Q8—1461no—
436C2×Q8—1461no—
437C2×Q8—1461no—
438C2×Q8—1461no—
439C2×Q8—1461no—
440C2×D4—732no—
441C2×D4—1461no—
442C2×D4—1461no—
443C2×D4—1461no—
444C2×D4—1461no—
445C2×D4—1461no—
446C22×C4—2922no—
447C22×C4—5841no—
448C22×C4—5841no—
449C22×C4—1461no—
450C22×C4—1461no—
451C22×C4—1461no—
452C22×C4—1461no—
453C22×C4—1461no—
454C22×C4—1461no—
455C22×C4—1461no—
456C22×C4C2×D29211yescharacteristic
457C22×C4C2×D29211yescharacteristic
458C22×C4C2×D29211yescharacteristic
459C22×C4C2×D29211yescharacteristic
460C22×C4C2×D29211yescharacteristic
461C22×C4C2×D29211yescharacteristic
462C22×C4C23×D7311yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8C2×C4×D7312yes—
472C2×C8C2×C4×D7312yes—
473C2×C8#1192402812yes—
474C2×C8#1192402812yes—
475C4⋊C4—2922no—
476C4⋊C4—5841no—
477C4⋊C4—5841no—
478C4⋊C4—5841no—
479C4⋊C4—5841no—
480C4⋊C4—5841no—
481C4⋊C4—5841no—
482C4⋊C4—732no—
483C4⋊C4—732no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4—1461no—
487C4⋊C4—1461no—
488C4⋊C4—1461no—
489C4⋊C4—1461no—
490C4⋊C4—1461no—
491C4⋊C4—1461no—
492C4⋊C4—1464no—
493C4⋊C4—1464no—
494C4⋊C4—1461no—
495C4⋊C4—1461no—
496C22⋊C4—2922no—
497C22⋊C4—5841no—
498C22⋊C4—5841no—
499C22⋊C4—1464no—
500C22⋊C4—1464no—
501C42—21no—
502C42—21no—
503C42—2922no—
504C42—5841no—
505C42—5841no—
506C42C2×C4×D7312yes—
507C42#1192402812yes—
508C42#1192402812yes—
509C42#1192402812yes—
510C23—2921no—
511C23—2921no—
512C23—2921no—
513C23—2921no—
514C23—2921no—
515C23—2921no—
516C23—1462no—
517C23C22×D29211yescharacteristic
518Q8—2921no—
519Q8—2921no—
520Q8—1462no—
521Q8—1462no—
522D4—2921no—
523D4—2921no—
524D4—1462no—
525D4—1462no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—2921no—
551C2×C4—2921no—
552C2×C4—2921no—
553C2×C4—2921no—
554C2×C4—2921no—
555C2×C4—2921no—
556C2×C4—2921no—
557C2×C4—2921no—
558C2×C4—5844no—
559C2×C4—1462no—
560C2×C4—1462no—
561C2×C4—1462no—
562C2×C4C4×D29212yes—
563C2×C4C4×D29212yes—
564C2×C4#1455657912yes—
565C2×C4#1455657912yes—
566C2×C4C22×C4×D7311yescharacteristic
567C2×C4C2×#1192402811yescharacteristic
568C2×C4C2×#1192402811yescharacteristic
569C2×C4C2×#1192402811yescharacteristic
570C2×C4C2×#1192402811yescharacteristic
571C2×C4C2×#1192402811yescharacteristic
572C8—22no—
573C8—22no—
574C8—22no—
575C8—22no—
576C22—2922no—
577C22—2922no—
578C22—2922no—
579C22—5841no—
580C22—5841no—
581C22—5841no—
582C22—5841no—
583C22C2×C4×D29211yescharacteristic
584C22C2×#1455657911yescharacteristic
585C22#1798913711yescharacteristic
586C22#1798939211yescharacteristic
587C22#1798939911yescharacteristic
588C22#1798939911yescharacteristic
589C22#1798940411yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—2922no—
597C4—2922no—
598C4—2922no—
599C4—5841no—
600C4—5841no—
601C4—5841no—
602C4—5841no—
603C4C4×#1192402811yescharacteristic
604C4C4×#1192402811yescharacteristic
605C4#1798912111yescharacteristic
606C4#1798912111yescharacteristic
607C2—5842no—
608C2C4×#1455657911yescharacteristic
609C2#2261880811yescharacteristic
610C2#2261881611yescharacteristic
611C2#2262028711yescharacteristic
612C2#2262029811yescharacteristic
613C2#2262059911yescharacteristic
614C2#2262061411yescharacteristic
subgroupG/H
centerC23C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1726C2
socleC23×C73C22×D4
prime radicalC22×D292C23
cosocleC22×C4×C73C24
hypercenter#1726D73
hypocenterC73#21643
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ #376 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #22612672C2semidirect
4. #22610900C2semidirect
7. #22610621C2semidirect
9. #22610607C2semidirect
10. #22610059C2semidirect
11. #22609762C2semidirect
13. C4×#14556516C2semidirect
15. C73×#1726C2semidirect
20. #17988942C4semidirect
64. #14556583C2×C4semidirect
96. #14556516C2×C4semidirect
97. #14556516C2×C4semidirect
120. C4×C8×C73C2×C4semidirect
322. #1726D73semidirect
323. C73#21643semidirect
422. C4×C8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179889422
#226126722
#226126422
#226109002
#226107472
#226106282
#226106212
#226106142
#226106072
#226100592
#226097622
#226097572
C4×#145565162
C4×#145565132
C73×#17262
#2164373