Finite Group Databasebeta

← #2085×D73 #33114948

Subgroups — #2085×D73 #33114948

Order 18688.

998 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D73C211yesmaximal, characteristic
2C2×#106×D73C211yesmaximal, characteristic
3#389×D73C211yesmaximal, characteristic
4#382×D73C211yesmaximal, characteristic
5#22611418C211yesmaximal, characteristic, complemented
6#22611417C211yesmaximal, characteristic, complemented
7#22611416C211yesmaximal, characteristic, complemented
8#22611415C211yesmaximal, characteristic, complemented
9#22611414C211yesmaximal, characteristic, complemented
10#22611413C211yesmaximal, characteristic, complemented
11#22611412C211yesmaximal, characteristic, complemented
12#340×D73C211yesmaximal, characteristic
13#340×D73C211yesmaximal, characteristic
14#336×D73C211yesmaximal, characteristic
15C73×#2085C211yesmaximal, characteristic, complemented
16C22×C8×D73C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×C4⋊C4×D73—21no—
19C2×C4⋊C4×D73C2211yescharacteristic
20C2×C4⋊C4×D73C2211yescharacteristic
21C2×C4⋊C4×D73C2211yescharacteristic
22C2×C4⋊C4×D73C2211yescharacteristic
23C2×C42×D73C2211yescharacteristic
24C2×#14556525C2211yescharacteristic
25C2×#14556524C2211yescharacteristic
26C2×#14556524C2211yescharacteristic
27#107×D73—24no—
28C2×#14556523C2211yescharacteristic
29C2×#14556522C2211yescharacteristic
30C2×#14556522C2211yescharacteristic
31#106×D73—24no—
32#17988486C2211yescharacteristic
33#17988485C2211yescharacteristic
34#17988484—21no—
35#17988483C2211yescharacteristic
36#17988482—21no—
37#17988453C2211yescharacteristic
38#17988452C2211yescharacteristic
39#17988452C2211yescharacteristic
40#17988451—21no—
41#17988451—21no—
42#95×D73—21no—
43#95×D73—21no—
44#95×D73—21no—
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988342C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C2×#107×C73C2211yescharacteristic
55C2×#106×C73C2211yescharacteristic
56#389×C73C2211yescharacteristic
57#382×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×C4×D73—21no—
62C22×C4×D73—21no—
63C22×C4×D73—21no—
64C22×C4×D73—21no—
65C22×C4×D73D411yescharacteristic
66C22×C4×D73D411yescharacteristic
67C22×C4×D73C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C2×C8×D73—22no—
71C2×C8×D73—22no—
72C2×C8×D73—22no—
73C2×C8×D73—22no—
74C2×C8×D73Q814yes—
75C2×C8×D73Q814yes—
76C2×C4⋊Dic73—21no—
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×#11924007—21no—
87C4⋊C4×D73—22no—
88C4⋊C4×D73—22no—
89C4⋊C4×D73—22no—
90C4⋊C4×D73—22no—
91C4⋊C4×D73—22no—
92C4⋊C4×D73—22no—
93C4⋊C4×D73—22no—
94C4⋊C4×D73—44no—
95C4⋊C4×D73D414yes—
96C2×C4×Dic73D411yescharacteristic
97C2×C4×Dic73D411yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99C42×D73—22no—
100C42×D73—22no—
101#14556525—22no—
102#14556524—22no—
103#14556524—22no—
104#14556523—22no—
105#14556522—22no—
106#14556522—22no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110#14556498—21no—
111#14556498—21no—
112#14556498—21no—
113#14556498—21no—
114#14556498—21no—
115#14556498—21no—
116C22×C8×C73C2311yescharacteristic
117C22×C8×C73C2311yescharacteristic
118C2×C4⋊C4×C73—21no—
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C42×C73C2311yescharacteristic
124#107×C73—22no—
125#106×C73—22no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129C23×D73C2×D411yescharacteristic
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73C2×D411yescharacteristic
135C22×Dic73C2×D411yescharacteristic
136C22×Dic73C2×D411yescharacteristic
137C2×C4×D73—24no—
138C2×C4×D73—22no—
139C2×C4×D73—22no—
140C2×C4×D73—22no—
141C2×C4×D73—22no—
142C2×C4×D73—22no—
143C2×C4×D73—22no—
144C2×C4×D73—42no—
145C2×C4×D73—42no—
146C2×C4×D73—42no—
147C2×C4×D73—42no—
148C2×C4×D73—42no—
149C2×C4×D73—42no—
150C2×C4×D73—42no—
151C2×C4×D73—42no—
152C2×C4×D73—42no—
153C2×C4×D73—42no—
154C2×C4×D73—42no—
155C2×C4×D73C2×D412yes—
156C2×C4×D73C2×Q812yes—
157C2×C4×D73C2×Q812yes—
158C2×C4×D73#4112yes—
159C2×C4×D73#4112yes—
160C2×C4×D73#4112yes—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831C2×Q812yes—
166C2×#10596831C2×Q812yes—
167C8×D73—28no—
168C8×D73—28no—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73—21no—
175C4⋊Dic73—21no—
176C4⋊Dic73—42no—
177C4⋊Dic73C2×D412yes—
178#11924007—24no—
179#11924007—42no—
180#11924007—42no—
181#11924007—42no—
182#11924007—42no—
183#11924007—42no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—22no—
187C4×Dic73—22no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2411yescharacteristic
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73C2×Q812yes—
200C2×C8×C73C2×Q812yes—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—42no—
209C4⋊C4×C73C2×D412yes—
210C42×C73—21no—
211C42×C73—21no—
212C23×C73C22×D411yescharacteristic
213C22×D73#12112yes—
214C22×D73#12312yes—
215C22×D73C4⋊Q812yes—
216C22×D73#13512yes—
217C22×D73#13512yes—
218C22×D73AGL(1,ℤ/8)12yes—
219C22×D73#13712yes—
220C2×C4×C73—22no—
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—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73C22×D411yescharacteristic
239C2×C4×C73C22×Q811yescharacteristic
240C2×C4×C73C22×Q811yescharacteristic
241C2×C4×C73C2×#4111yescharacteristic
242C2×C4×C73C2×#4111yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×Dic73—22no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73—21no—
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#12112yes—
263C2×Dic73#12312yes—
264C2×Dic73C4⋊Q812yes—
265C4×D73—48no—
266C4×D73—44no—
267C4×D73—44no—
268C4×D73—84no—
269C4×D73—84no—
270C4×D73—84no—
271C4×D73C22⋊Q814yes—
272C4×D73C22⋊Q814yes—
273C4×D73#12514yes—
274C4×D73#12514yes—
275C8×C73—22no—
276C8×C73—22no—
277#10596831—22no—
278#10596831—22no—
279C22×C73C2×#12111yescharacteristic
280C22×C73C2×#12311yescharacteristic
281C22×C73C2×C4⋊Q811yescharacteristic
282C22×C73C2×#13511yescharacteristic
283C22×C73C2×#13511yescharacteristic
284C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C73C2×#13711yescharacteristic
286C2×D73#39814yes—
287C2×D73#46314yes—
288C2×D73#46414yes—
289C2×D73#48214yes—
290C2×D73#48514yes—
291C2×D73#49914yes—
292C2×D73#50114yes—
293C4×C73—41no—
294C4×C73—41no—
295C4×C73—42no—
296C4×C73—81no—
297C4×C73—81no—
298C4×C73—81no—
299C4×C73C2×C22⋊Q811yescharacteristic
300C4×C73C2×C22⋊Q811yescharacteristic
301C4×C73C2×#12511yescharacteristic
302C4×C73C2×#12511yescharacteristic
303Dic73—41no—
304Dic73—41no—
305Dic73—42no—
306Dic73—81no—
307Dic73—81no—
308Dic73—81no—
309Dic73#39814yes—
310C2×#2085—731nomaximal, Sylow
311C2×C73C2×#39811yescharacteristic
312C2×C73C2×#46311yescharacteristic
313C2×C73C2×#46411yescharacteristic
314C2×C73C2×#48211yescharacteristic
315C2×C73C2×#48511yescharacteristic
316C2×C73C2×#49911yescharacteristic
317C2×C73C2×#50111yescharacteristic
318D73#208518yesdirect product factor
319C22×#107—731no—
320C22×#106—731no—
321C2×#389—731no—
322C2×#382—731no—
323#2085—731no—
324#2085—731no—
325#2085—731no—
326#2085—731no—
327#2085—731no—
328#2085—731no—
329#2085—731no—
330#2085D7311yescharacteristic, direct product factor
331C2×#340—731no—
332C2×#340—731no—
333C2×#336—731no—
334C73C2×#208511yescharacteristic, complemented, Sylow
335C23×C8—731no—
336C23×C8—731no—
337C22×C4⋊C4—731no—
338C22×C4⋊C4—731no—
339C22×C4⋊C4—731no—
340C22×C4⋊C4—731no—
341C22×C4⋊C4—1461no—
342C22×C42—731no—
343C2×#107—731no—
344C2×#107—731no—
345C2×#107—731no—
346C2×#107—1464no—
347C2×#107C2×D7311yescharacteristic
348C2×#106—731no—
349C2×#106—731no—
350C2×#106—731no—
351C2×#106—1464no—
352C2×#106C2×D7311yescharacteristic
353#389—731no—
354#389—731no—
355#389—731no—
356#389—1461no—
357#389—1461no—
358#389C2×D7311yescharacteristic
359#382—731no—
360#382—731no—
361#382—731no—
362#382—1461no—
363#382—1461no—
364#382C2×D7311yescharacteristic
365C2×#95—1461no—
366C2×#95—1461no—
367C2×#95—1461no—
368#340—731no—
369#340—731no—
370#340—731no—
371#340—731no—
372#340—731no—
373#340—731no—
374#340C2×D7311yescharacteristic
375#340C2×D7311yescharacteristic
376#336—731no—
377#336—731no—
378#336—731no—
379#336C2×D7311yescharacteristic
380C23×C4—731no—
381C23×C4—731no—
382C23×C4—731no—
383C23×C4—1461no—
384C23×C4—1461no—
385C23×C4—1461no—
386C23×C4—1461no—
387C22×C8—731no—
388C22×C8—731no—
389C22×C8—734no—
390C22×C8—734no—
391C22×C8—1462no—
392C22×C8—1462no—
393C22×C8—1462no—
394C22×C8—1462no—
395C22×C8C22×D7311yescharacteristic
396C22×C8C22×D7311yescharacteristic
397C2×C4⋊C4—21no—
398C2×C4⋊C4—2924no—
399C2×C4⋊C4—731no—
400C2×C4⋊C4—734no—
401C2×C4⋊C4—731no—
402C2×C4⋊C4—731no—
403C2×C4⋊C4—731no—
404C2×C4⋊C4—1462no—
405C2×C4⋊C4—1462no—
406C2×C4⋊C4—1462no—
407C2×C4⋊C4—1462no—
408C2×C4⋊C4—1462no—
409C2×C4⋊C4—1462no—
410C2×C4⋊C4—1462no—
411C2×C4⋊C4—1461no—
412C2×C4⋊C4—1461no—
413C2×C4⋊C4—1461no—
414C2×C4⋊C4—1461no—
415C2×C4⋊C4—1461no—
416C2×C4⋊C4—1461no—
417C2×C4⋊C4—1461no—
418C2×C4⋊C4C22×D7311yescharacteristic
419C2×C4⋊C4C22×D7311yescharacteristic
420C2×C4⋊C4C22×D7311yescharacteristic
421C2×C4⋊C4C22×D7311yescharacteristic
422C2×C42—731no—
423C2×C42—731no—
424C2×C42—731no—
425C2×C42—1462no—
426C2×C42—1462no—
427C2×C42C22×D7311yescharacteristic
428#107—22no—
429#107—1462no—
430#107—1462no—
431#107—1462no—
432#106—22no—
433#106—1462no—
434#106—1462no—
435#106—1462no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—1461no—
440#95—1461no—
441#95—1461no—
442#95—1461no—
443#95—1461no—
444#95—1461no—
445#95—1461no—
446#95—1461no—
447#95—1461no—
448C24—731no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—2922no—
454C22×C4—2922no—
455C22×C4—2922no—
456C22×C4—2922no—
457C22×C4—2922no—
458C22×C4—2922no—
459C22×C4—2922no—
460C22×C4—2922no—
461C22×C4—2922no—
462C22×C4—2922no—
463C22×C4—2922no—
464C22×C4—731no—
465C22×C4—732no—
466C22×C4—732no—
467C22×C4—732no—
468C22×C4—732no—
469C22×C4—732no—
470C22×C4—732no—
471C22×C4—731no—
472C22×C4—731no—
473C22×C4—1462no—
474C22×C4—1462no—
475C22×C4—1462no—
476C22×C4—1464no—
477C22×C4—1462no—
478C22×C4—1462no—
479C22×C4—1462no—
480C22×C4—1461no—
481C22×C4—1461no—
482C22×C4—1461no—
483C22×C4—1461no—
484C22×C4D4×D7311yescharacteristic
485C22×C4D4×D7311yescharacteristic
486C22×C4C23×D7311yescharacteristic
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—732no—
492C2×C8—732no—
493C2×C8—1468no—
494C2×C8—1468no—
495C2×C8—1461no—
496C2×C8—1461no—
497C2×C8—1461no—
498C2×C8—1461no—
499C2×C8Q8×D7312yes—
500C2×C8Q8×D7312yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—2922no—
510C4⋊C4—2922no—
511C4⋊C4—2922no—
512C4⋊C4—2922no—
513C4⋊C4—2922no—
514C4⋊C4—2922no—
515C4⋊C4—732no—
516C4⋊C4—1464no—
517C4⋊C4—1461no—
518C4⋊C4—1461no—
519C4⋊C4—1461no—
520C4⋊C4—1461no—
521C4⋊C4—1461no—
522C4⋊C4—1461no—
523C4⋊C4—1461no—
524C4⋊C4D4×D7312yes—
525C42—21no—
526C42—21no—
527C42—1462no—
528C42—1462no—
529C42—1461no—
530C42—1461no—
531C23—732no—
532C23—732no—
533C23—732no—
534C23—732no—
535C23—732no—
536C23—732no—
537C23—732no—
538C23C2×D4×D7311yescharacteristic
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
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—2928no—
558C2×C4—2924no—
559C2×C4—2924no—
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—2921no—
569C2×C4—2921no—
570C2×C4—2921no—
571C2×C4—5844no—
572C2×C4—5844no—
573C2×C4—5844no—
574C2×C4—732no—
575C2×C4—732no—
576C2×C4—732no—
577C2×C4—734no—
578C2×C4—734no—
579C2×C4—734no—
580C2×C4—734no—
581C2×C4—1461no—
582C2×C4—1462no—
583C2×C4—1461no—
584C2×C4—1461no—
585C2×C4—1461no—
586C2×C4—1461no—
587C2×C4—1461no—
588C2×C4C2×D4×D7311yescharacteristic
589C2×C4C2×Q8×D7311yescharacteristic
590C2×C4C2×Q8×D7311yescharacteristic
591C2×C4#41×D7311yescharacteristic
592C2×C4#41×D7311yescharacteristic
593C2×C4#41×D7311yescharacteristic
594C8—22no—
595C8—22no—
596C8—1462no—
597C8—1462no—
598C22—734no—
599C22—734no—
600C22—734no—
601C22—734no—
602C22—734no—
603C22—734no—
604C22—734no—
605C22#121×D7311yescharacteristic
606C22#123×D7311yescharacteristic
607C22C4⋊Q8×D7311yescharacteristic
608C22#135×D7311yescharacteristic
609C22#135×D7311yescharacteristic
610C22AGL(1,ℤ/8)×D7311yescharacteristic
611C22#137×D7311yescharacteristic
612C4—41no—
613C4—41no—
614C4—42no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—2921no—
619C4—2921no—
620C4—2922no—
621C4—5841no—
622C4—5841no—
623C4—5841no—
624C4—734no—
625C4C22⋊Q8×D7311yescharacteristic
626C4C22⋊Q8×D7311yescharacteristic
627C4#125×D7311yescharacteristic
628C4#125×D7311yescharacteristic
629C2—738no—
630C2#398×D7311yescharacteristic
631C2#463×D7311yescharacteristic
632C2#464×D7311yescharacteristic
633C2#482×D7311yescharacteristic
634C2#485×D7311yescharacteristic
635C2#499×D7311yescharacteristic
636C2#501×D7311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2085C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
hypercenter#2085D73
hypocenterC73C2×#2085
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2085

Complements

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

NH ≅ G/Ntype
5. #22611418C2semidirect
6. #22611417C2semidirect
7. #22611416C2semidirect
8. #22611415C2semidirect
9. #22611414C2semidirect
10. #22611413C2semidirect
11. #22611412C2semidirect
15. C73×#2085C2semidirect
318. D73#2085direct (N × H)
330. #2085D73direct (N × H)
334. C73C2×#2085semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D732
C2×#106×D732
#389×D732
#382×D732
#226114182
#226114172
#226114162
#226114152
#226114142
#226114132
#226114122
#340×D732
#336×D732
C73×#20852
C2×#208573