Finite Group Databasebeta

← #33116020

Subgroups — #33116020

Order 18688.

836 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556565C211yesmaximal, characteristic
2#22612329C211yesmaximal, characteristic, complemented
3#22611500C211yesmaximal, characteristic, complemented
4#22611451C211yesmaximal, characteristic, complemented
5#22611414C211yesmaximal, characteristic, complemented
6#22611364C211yesmaximal, characteristic, complemented
7#22611359C211yesmaximal, characteristic, complemented
8#22611346C211yesmaximal, characteristic, complemented
9#22611121C211yesmaximal, characteristic
10#22611114C211yesmaximal, characteristic
11C4×#14556525C211yesmaximal, characteristic, complemented
12C4×#14556523C211yesmaximal, characteristic, complemented
13C4×#14556513C211yesmaximal, characteristic, complemented
14C4×#14556513C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C73C211yesmaximal, characteristic, complemented
16C2×#14556565C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18C2×C4×C22⋊D73—21no—
19C2×#14556525C2211yescharacteristic
20C2×#14556525C2211yescharacteristic
21C2×#14556523C2211yescharacteristic
22C2×#14556523C2211yescharacteristic
23C2×#14556513C2211yescharacteristic
24C2×#14556513C2211yescharacteristic
25C2×#14556513C2211yescharacteristic
26C2×#14556513C2211yescharacteristic
27#17988489C2211yescharacteristic
28#17988485C2211yescharacteristic
29#17988478—21no—
30#17988466—21no—
31#17988455—21no—
32#17988453C2211yescharacteristic
33#17988453C2211yescharacteristic
34#17988450—21no—
35#17988447C2211yescharacteristic
36#17988447C2211yescharacteristic
37#17988447C2211yescharacteristic
38C4×C4⋊Dic73C2211yescharacteristic
39C4×C4⋊Dic73C2211yescharacteristic
40C4×C4⋊Dic73C2211yescharacteristic
41C4×#11924005—21no—
42C4×C22⋊Dic73—21no—
43#17988433—21no—
44#17988350C2211yescharacteristic
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988350C2211yescharacteristic
51#17988350C2211yescharacteristic
52C22×C42×C73C2211yescharacteristic
53C2×C22⋊C8×C73C2211yescharacteristic
54C2×C22⋊C8×C73C2211yescharacteristic
55C2×C4×C8×C73C2211yescharacteristic
56C2×C4×C8×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×D292C2311yescharacteristic
60C22×C22⋊D73—21no—
61C22×C4×D73—21no—
62#14556565—22no—
63#14556565—22no—
64C4×D292—22no—
65C4×D292—22no—
66C4×C22⋊D73—44no—
67C2×C4⋊Dic73C2311yescharacteristic
68C2×C4⋊Dic73C2311yescharacteristic
69C2×C4⋊Dic73C2311yescharacteristic
70C2×C4⋊Dic73C2311yescharacteristic
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×#11924007—21no—
75C2×C22⋊Dic73—21no—
76C2×C22⋊Dic73—21no—
77C2×C22⋊Dic73—21no—
78C2×#11924005—21no—
79C2×#11924005—21no—
80C2×#11924005—21no—
81C2×#11924005—21no—
82C2×C4×Dic73—21no—
83C2×C4×Dic73—21no—
84C2×C4×Dic73—21no—
85#14556525—22no—
86#14556525—22no—
87#14556523—22no—
88#14556523—22no—
89#14556513—22no—
90#14556513—22no—
91#14556513—22no—
92#14556513—22no—
93#14556498—21no—
94#14556498—21no—
95#14556498—21no—
96#14556498—21no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100#14556498—21no—
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104C23×C4×C73D411yescharacteristic
105C23×C4×C73D411yescharacteristic
106C23×C4×C73C2311yescharacteristic
107C22×C8×C73C2311yescharacteristic
108C22×C8×C73C2311yescharacteristic
109C22×C8×C73C2311yescharacteristic
110C22×C8×C73C2311yescharacteristic
111C2×C42×C73—22no—
112C2×C42×C73—22no—
113C2×C42×C73D411yescharacteristic
114C2×C42×C73D411yescharacteristic
115C2×C42×C73C2311yescharacteristic
116C2×C42×C73C2311yescharacteristic
117C22⋊C8×C73—22no—
118C22⋊C8×C73—22no—
119C4×C8×C73—22no—
120C4×C8×C73—22no—
121C23×D73—21no—
122C2×D292—21no—
123C2×D292—21no—
124C2×D292—21no—
125C2×D292—21no—
126C2×D292—21no—
127C2×D292#4112yes—
128C2×C22⋊D73—24no—
129C2×C22⋊D73—42no—
130C2×C22⋊D73—42no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—21no—
137C22×Dic73—21no—
138C2×C4×D73—42no—
139C2×C4×D73—42no—
140C2×C4×D73—42no—
141C4⋊Dic73—21no—
142C4⋊Dic73—21no—
143C4⋊Dic73—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73#4112yes—
155#11924007—42no—
156C22⋊Dic73—42no—
157C22⋊Dic73—42no—
158C22⋊Dic73—42no—
159#11924005—24no—
160#11924005—42no—
161#11924005—42no—
162#11924005—42no—
163C4×Dic73—42no—
164C4×Dic73—42no—
165C4×Dic73—42no—
166C24×C73C2×D411yescharacteristic
167C22×C4×C73—22no—
168C22×C4×C73—22no—
169C22×C4×C73—22no—
170C22×C4×C73—22no—
171C22×C4×C73—22no—
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—41no—
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2411yescharacteristic
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×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73#4112yes—
196C2×C8×C73#4112yes—
197C42×C73—22no—
198C42×C73—22no—
199C42×C73—21no—
200C42×C73—21no—
201C42×C73#4112yes—
202C42×C73#4112yes—
203C23×C73—21no—
204C23×C73—21no—
205C23×C73—21no—
206C23×C73—21no—
207C23×C73—21no—
208C23×C73—21no—
209C23×C73#13512yes—
210C23×C73C22×D411yescharacteristic
211C22×D73—22no—
212C22×D73—41no—
213C22×D73—41no—
214C22×D73—41no—
215C22×D73—41no—
216C22×D73—41no—
217C22×D73—41no—
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×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—44no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—44no—
235C2×C4×C73#12312yes—
236C2×C4×C73#12312yes—
237C2×C4×C73#13512yes—
238C2×C4×C73AGL(1,ℤ/8)12yes—
239C2×C4×C73C2×#4111yescharacteristic
240C2×C4×C73C2×#4111yescharacteristic
241C2×C4×C73C2×#4111yescharacteristic
242C2×C4×C73C2×#4111yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C22⋊D73—48no—
246C2×Dic73—22no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253C2×Dic73—41no—
254C2×Dic73—41no—
255C2×Dic73—41no—
256C2×Dic73—41no—
257C2×Dic73—41no—
258C2×Dic73—41no—
259C2×Dic73—41no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73—41no—
267D292—22no—
268D292—22no—
269D292—41no—
270D292—41no—
271C4×D73—84no—
272C8×C73—22no—
273C8×C73—22no—
274C8×C73—41no—
275C8×C73—41no—
276C22×C73—22no—
277C22×C73—22no—
278C22×C73—22no—
279C22×C73—41no—
280C22×C73—41no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73C2×#12311yescharacteristic
284C22×C73#52511yescharacteristic
285C22×C73#53211yescharacteristic
286C22×C73C2×#13511yescharacteristic
287C22×C73C2×#13511yescharacteristic
288C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C73#57511yescharacteristic
290C2×D73—42no—
291C2×D73—42no—
292C2×D73—42no—
293C2×D73—81no—
294C2×D73—81no—
295C2×D73—81no—
296C2×D73—81no—
297C4×C73—22no—
298C4×C73—41no—
299C4×C73—41no—
300C4×C73—41no—
301C4×C73#48214yes—
302C4×C73#52911yescharacteristic
303C4×C73#52911yescharacteristic
304C4×C73#52911yescharacteristic
305C4×C73#52911yescharacteristic
306Dic73—42no—
307Dic73—81no—
308Dic73—81no—
309Dic73—81no—
310Dic73—81no—
311Dic73—81no—
312Dic73—81no—
313#23758—731nomaximal, Sylow
314C2×C73—42no—
315C2×C73#239511yescharacteristic
316C2×C73C2×#48211yescharacteristic
317C2×C73#309111yescharacteristic
318C2×C73#310211yescharacteristic
319C2×C73#310511yescharacteristic
320C2×C73#316811yescharacteristic
321C2×C73#317111yescharacteristic
322D73—82no—
323C4×#121—731no—
324#2283—731no—
325#2101—731no—
326#2092—731no—
327#2085—731no—
328#2077—731no—
329#2076—731no—
330#2073—731no—
331#2034—731no—
332#2033—731no—
333C4×#107—731no—
334C4×#106—731no—
335C4×#102—731no—
336C4×#102—731no—
337C4×C22⋊C8D7311yescharacteristic, complemented
338C73#2375811yescharacteristic, complemented, Sylow
339C2×#121—731no—
340C2×C4×D4—731no—
341C2×C4×D4—1461no—
342C22×C42C2×D7311yescharacteristic
343C2×#107—731no—
344C2×#107—731no—
345C2×#106—731no—
346C2×#106—731no—
347C2×#102—731no—
348C2×#102—731no—
349C2×#102—731no—
350C2×#102—731no—
351C2×C22⋊C8C2×D7311yescharacteristic
352C2×C22⋊C8C2×D7311yescharacteristic
353C2×C4×C8C2×D7311yescharacteristic
354C2×C4×C8C2×D7311yescharacteristic
355#390—731no—
356#389—731no—
357#388—1461no—
358#386—1461no—
359#383—1461no—
360#382—731no—
361#382—731no—
362#381—1461no—
363#380—731no—
364#380—731no—
365#380—731no—
366C4×C4⋊C4—731no—
367C4×C4⋊C4—731no—
368C4×C4⋊C4—731no—
369C4×C22⋊C4—1461no—
370C4×C22⋊C4—1461no—
371#376—1461no—
372#340—731no—
373#340—731no—
374#340—731no—
375#340—731no—
376#340—731no—
377#340—731no—
378#340—731no—
379#340—731no—
380#336C2×D7311yescharacteristic
381#336C2×D7311yescharacteristic
382C22×D4—731no—
383C22×D4—1461no—
384C23×C4—1461no—
385C23×C4D29211yescharacteristic
386C23×C4D29211yescharacteristic
387C23×C4C22×D7311yescharacteristic
388C22×C8C22×D7311yescharacteristic
389C22×C8C22×D7311yescharacteristic
390C22×C8C22×D7311yescharacteristic
391C22×C8C22×D7311yescharacteristic
392#121—1462no—
393#121—1462no—
394C4×D4—2924no—
395C4×D4—1462no—
396C4×D4—1462no—
397C2×C4⋊C4—731no—
398C2×C4⋊C4—731no—
399C2×C4⋊C4—731no—
400C2×C4⋊C4—731no—
401C2×C4⋊C4—731no—
402C2×C4⋊C4—731no—
403C2×C4⋊C4—731no—
404C2×C4⋊C4—1461no—
405C2×C22⋊C4—1461no—
406C2×C22⋊C4—1461no—
407C2×C22⋊C4—1461no—
408C2×C22⋊C4—1461no—
409C2×C22⋊C4—1461no—
410C2×C22⋊C4—1461no—
411C2×C22⋊C4—1461no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—1461no—
415C2×C42—1461no—
416C2×C42—1461no—
417C2×C42D29211yescharacteristic
418C2×C42D29211yescharacteristic
419C2×C42C22×D7311yescharacteristic
420C2×C42C22×D7311yescharacteristic
421#107—1462no—
422#107—1462no—
423#106—1462no—
424#106—1462no—
425#102—1462no—
426#102—1462no—
427#102—1462no—
428#102—1462no—
429C22⋊C8—22no—
430C22⋊C8—22no—
431C4×C8—22no—
432C4×C8—22no—
433#95—1461no—
434#95—1461no—
435#95—1461no—
436#95—1461no—
437#95—1461no—
438#95—1461no—
439#95—1461no—
440#95—1461no—
441#95—1461no—
442#95—1461no—
443#95—1461no—
444C24—1461no—
445C24C2×D29211yescharacteristic
446C2×D4—2922no—
447C2×D4—2922no—
448C2×D4—732no—
449C2×D4—1464no—
450C2×D4—1461no—
451C2×D4—1461no—
452C2×D4—1461no—
453C2×D4—1461no—
454C2×D4—1461no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—2922no—
468C22×C4—2922no—
469C22×C4—2922no—
470C22×C4—1461no—
471C22×C4—1461no—
472C22×C4—1461no—
473C22×C4—1461no—
474C22×C4—1461no—
475C22×C4—1461no—
476C22×C4—1461no—
477C22×C4C2×D29211yescharacteristic
478C22×C4C2×D29211yescharacteristic
479C22×C4C2×D29211yescharacteristic
480C22×C4C2×D29211yescharacteristic
481C22×C4C2×D29211yescharacteristic
482C22×C4C23×D7311yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8#1192402812yes—
494C2×C8#1192402812yes—
495C4⋊C4—2922no—
496C4⋊C4—732no—
497C4⋊C4—1461no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C4⋊C4—1461no—
501C4⋊C4—1461no—
502C4⋊C4—1461no—
503C4⋊C4—1461no—
504C4⋊C4—1461no—
505C4⋊C4—1461no—
506C4⋊C4—1461no—
507C4⋊C4—1461no—
508C4⋊C4—1461no—
509C4⋊C4—1461no—
510C22⋊C4—2922no—
511C22⋊C4—2922no—
512C22⋊C4—2922no—
513C22⋊C4—2922no—
514C22⋊C4—2922no—
515C22⋊C4—2922no—
516C22⋊C4—1464no—
517C42—22no—
518C42—22no—
519C42—21no—
520C42—21no—
521C42—2922no—
522C42—2922no—
523C42—2922no—
524C42#1192402712yes—
525C42#1192402712yes—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—2921no—
533C23—2921no—
534C23—2921no—
535C23—2921no—
536C23—2921no—
537C23—2921no—
538C23—1462no—
539C23#1455661312yes—
540C23C22×D29211yescharacteristic
541D4—2928no—
542D4—2921no—
543D4—2921no—
544D4—1462no—
545D4—1462no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—2921no—
564C2×C4—2921no—
565C2×C4—2921no—
566C2×C4—2921no—
567C2×C4—2921no—
568C2×C4—2921no—
569C2×C4—2921no—
570C2×C4—2921no—
571C2×C4—2921no—
572C2×C4—2921no—
573C2×C4—2921no—
574C2×C4—2921no—
575C2×C4—2921no—
576C2×C4—2921no—
577C2×C4—2921no—
578C2×C4—2921no—
579C2×C4—2921no—
580C2×C4—2921no—
581C2×C4—2921no—
582C2×C4—2921no—
583C2×C4—5844no—
584C2×C4—1462no—
585C2×C4#1455657512yes—
586C2×C4#1455657512yes—
587C2×C4#1455661312yes—
588C2×C4#1455661912yes—
589C2×C4#41×D7311yescharacteristic
590C2×C4#41×D7311yescharacteristic
591C2×C4C2×#1192402711yescharacteristic
592C2×C4C2×#1192402711yescharacteristic
593C2×C4C2×#1192402811yescharacteristic
594C2×C4C2×#1192402811yescharacteristic
595C8—22no—
596C8—22no—
597C8—41no—
598C8—41no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—2922no—
607C22—2922no—
608C22—2922no—
609C22—5841no—
610C22—5841no—
611C22—5841no—
612C22—5841no—
613C22C2×#1455657511yescharacteristic
614C22#1798909911yescharacteristic
615C22#1798913711yescharacteristic
616C22C2×#1455661311yescharacteristic
617C22C2×#1455661311yescharacteristic
618C22C2×#1455661911yescharacteristic
619C22#1798938711yescharacteristic
620C4—22no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—2922no—
625C4—5841no—
626C4—5841no—
627C4—5841no—
628C4—5841no—
629C4—5841no—
630C4—5841no—
631C4#1798891214yes—
632C4#1798911711yescharacteristic
633C4#1798911711yescharacteristic
634C4#1798911911yescharacteristic
635C4#1798911911yescharacteristic
636C2—42no—
637C2—5842no—
638C2#2261319111yescharacteristic
639C2C2×#1798891211yescharacteristic
640C2#2261984611yescharacteristic
641C2#2261995111yescharacteristic
642C2#2261998011yescharacteristic
643C2#2262050111yescharacteristic
644C2#2262052611yescharacteristic
subgroupG/H
centerC22×C4C2×D292
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC4×C22⋊C8×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556565C22
hypercenterC4×C22⋊C8D73
hypocenterC73#23758
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #22612329C2semidirect
3. #22611500C2semidirect
4. #22611451C2semidirect
5. #22611414C2semidirect
6. #22611364C2semidirect
7. #22611359C2semidirect
8. #22611346C2semidirect
11. C4×#14556525C2semidirect
12. C4×#14556523C2semidirect
13. C4×#14556513C2semidirect
14. C4×#14556513C2semidirect
15. C4×C22⋊C8×C73C2semidirect
337. C4×C22⋊C8D73semidirect
338. C73#23758semidirect

Maximal subgroups

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

subgroupindex
C4×#145565652
#226123292
#226115002
#226114512
#226114142
#226113642
#226113592
#226113462
#226111212
#226111142
C4×#145565252
C4×#145565232
C4×#145565132
C4×C22⋊C8×C732
#2375873