Finite Group Databasebeta

← #33115075

Subgroups — #33115075

Order 18688.

950 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988626C211yesmaximal, characteristic
2C2×#17988609C211yesmaximal, characteristic
3#22612412C211yesmaximal, characteristic
4#389×D73C211yesmaximal, characteristic
5#22611435C211yesmaximal, characteristic, complemented
6#22611432C211yesmaximal, characteristic, complemented
7#22611430C211yesmaximal, characteristic, complemented
8#22611427C211yesmaximal, characteristic, complemented
9#22611424C211yesmaximal, characteristic, complemented
10#22611423C211yesmaximal, characteristic, complemented
11#22611421C211yesmaximal, characteristic, complemented
12#22609649C211yesmaximal, characteristic
13#22609649C211yesmaximal, characteristic
14#22609649C211yesmaximal, characteristic
15C73×#2088C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C2×#14556549C2211yescharacteristic
19C2×#14556549C2211yescharacteristic
20C2×C4⋊C4×D73—21no—
21C2×C4⋊C4×D73C2211yescharacteristic
22C2×C4⋊C4×D73C2211yescharacteristic
23C2×C42×D73C2211yescharacteristic
24#17988626—24no—
25C2×#14556525C2211yescharacteristic
26C2×#14556524C2211yescharacteristic
27C2×#14556522C2211yescharacteristic
28#17988609—24no—
29C2×C4⋊#10596831C2211yescharacteristic
30C2×#14556520C2211yescharacteristic
31C2×#14556520C2211yescharacteristic
32#17988486C2211yescharacteristic
33#17988486C2211yescharacteristic
34#17988485C2211yescharacteristic
35#17988485C2211yescharacteristic
36#17988484—21no—
37#17988483C2211yescharacteristic
38#17988483C2211yescharacteristic
39#17988482—21no—
40#17988461—21no—
41#17988458—21no—
42C4⋊C4×Dic73—21no—
43#17988438—21no—
44#95×D73—21no—
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54C2×#106×C73C2211yescharacteristic
55C2×C4⋊C8×C73C2211yescharacteristic
56#389×C73C2211yescharacteristic
57#389×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61C22×C4×D73—21no—
62C22×C4×D73—21no—
63C22×C4×D73D411yescharacteristic
64C22×C4×D73D411yescharacteristic
65C22×C4×D73C2311yescharacteristic
66C2×#11924011—22no—
67C2×#11924011—22no—
68C2×#11924011—22no—
69C2×#11924011—22no—
70C2×#11924011—22no—
71C2×#11924011D414yes—
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74#14556549—22no—
75#14556549—22no—
76#14556549—22no—
77#14556549Q814yes—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73—21no—
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×#11924007—21no—
85C2×#11924007—21no—
86C2×#11924007—21no—
87C2×#11924007—21no—
88C2×#11924007—21no—
89C2×#11924007—21no—
90C4⋊C4×D73—22no—
91C4⋊C4×D73—22no—
92C4⋊C4×D73—22no—
93C4⋊C4×D73—44no—
94C4⋊C4×D73Q814yes—
95C2×#11924005—21no—
96C2×#11924005—21no—
97C2×C4×Dic73—21no—
98C2×C4×Dic73—21no—
99C2×C4×Dic73D411yescharacteristic
100C2×C4×Dic73D411yescharacteristic
101C2×C4×Dic73C2311yescharacteristic
102C42×D73—22no—
103C42×D73—22no—
104#14556525—22no—
105#14556524—22no—
106#14556522—22no—
107C4⋊#10596831—22no—
108#14556520—22no—
109#14556520—22no—
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×C73—21no—
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C42×C73C2311yescharacteristic
125#106×C73—22no—
126C4⋊C8×C73—22no—
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—22no—
138C2×C4×D73—22no—
139C2×C4×D73—24no—
140C2×C4×D73—22no—
141C2×C4×D73—22no—
142C2×C4×D73—41no—
143C2×C4×D73—41no—
144C2×C4×D73—42no—
145C2×C4×D73—42no—
146C2×C4×D73—42no—
147C2×C4×D73—42no—
148C2×C4×D73—42no—
149C2×C4×D73C2×D412yes—
150C2×C4×D73C2×Q812yes—
151C2×C4×D73C2×Q812yes—
152C2×C4×D73#4112yes—
153C2×C4×D73#4112yes—
154C2×C4×D73#4112yes—
155#11924011—28no—
156#11924011—44no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831C2×D412yes—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—42no—
170C4⋊Dic73—42no—
171C4⋊Dic73C2×Q812yes—
172C4⋊Dic73C2×Q812yes—
173#11924007—24no—
174#11924007—42no—
175#11924007—42no—
176#11924007—42no—
177#11924007—42no—
178#11924007—42no—
179#11924005—24no—
180#11924005—42no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—22no—
184C4×Dic73—22no—
185C4×Dic73—24no—
186C4×Dic73—42no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73C2×D411yescharacteristic
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73C2411yescharacteristic
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73C2×D412yes—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—42no—
207C4⋊C4×C73—42no—
208C4⋊C4×C73C2×Q812yes—
209C4⋊C4×C73C2×Q812yes—
210C42×C73—21no—
211C42×C73—21no—
212C23×C73C22×D411yescharacteristic
213C22×D73—21no—
214C22×D73—21no—
215C22×D73—21no—
216C22×D73—21no—
217C22×D73#12112yes—
218C22×D73C22⋊Q812yes—
219C22×D73C22⋊Q812yes—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—22no—
224C2×C4×C73—22no—
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#13712yes—
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—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—22no—
248C2×Dic73—22no—
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#12112yes—
262C2×Dic73C22⋊Q812yes—
263C2×Dic73C22⋊Q812yes—
264C2×Dic73AGL(1,ℤ/8)12yes—
265C4×D73—44no—
266C4×D73—44no—
267C4×D73—48no—
268C4×D73—84no—
269C4×D73#12314yes—
270C4×D73#12514yes—
271C4×D73#12514yes—
272C4×D73C4⋊Q814yes—
273C8×C73—22no—
274C8×C73—41no—
275#10596831—22no—
276#10596831—41no—
277C22×C73C2×#12111yescharacteristic
278C22×C73C2×C22⋊Q811yescharacteristic
279C22×C73C2×C22⋊Q811yescharacteristic
280C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C73C2×#13711yescharacteristic
282C22×C73#57511yescharacteristic
283C22×C73#57511yescharacteristic
284C2×D73—22no—
285C2×D73—22no—
286C2×D73—22no—
287C2×D73—22no—
288C2×D73—22no—
289C2×D73—22no—
290C2×D73#39814yes—
291C4×C73—22no—
292C4×C73—42no—
293C4×C73—42no—
294C4×C73—41no—
295C4×C73—81no—
296C4×C73—81no—
297C4×C73C2×#12311yescharacteristic
298C4×C73C2×#12511yescharacteristic
299C4×C73C2×#12511yescharacteristic
300C4×C73C2×C4⋊Q811yescharacteristic
301Dic73—22no—
302Dic73—42no—
303Dic73—42no—
304Dic73—41no—
305Dic73—81no—
306Dic73—81no—
307Dic73#39814yes—
308#23670—731nomaximal, Sylow
309C2×C73C2×#39811yescharacteristic
310C2×C73#305511yescharacteristic
311C2×C73#305611yescharacteristic
312C2×C73#307711yescharacteristic
313C2×C73#307811yescharacteristic
314C2×C73#307911yescharacteristic
315C2×C73#308011yescharacteristic
316D73—24no—
317C2×#428—731no—
318C2×#423—731no—
319#2296—731no—
320C2×#389—731no—
321#2088—731no—
322#2088—731no—
323#2088—731no—
324#2088D7311yescharacteristic, complemented
325#2087—731no—
326#2087—731no—
327#2086—731no—
328#2086—731no—
329#1736—731no—
330#1736—731no—
331#1736—731no—
332C73#2367011yescharacteristic, complemented, Sylow
333C22×M16—731no—
334C22×M16—731no—
335C2×#117—731no—
336C2×#117—731no—
337C22×C4⋊C4—731no—
338C22×C4⋊C4—731no—
339C22×C4⋊C4—1461no—
340C22×C42—731no—
341#428—1464no—
342C2×#107—731no—
343C2×#107—731no—
344C2×#106—731no—
345C2×#106C2×D7311yescharacteristic
346#423—1464no—
347C2×C4⋊C8—731no—
348C2×C4⋊C8—731no—
349C2×C4⋊C8—731no—
350C2×C4⋊C8C2×D7311yescharacteristic
351#389—731no—
352#389—731no—
353#389—731no—
354#389—731no—
355#389—731no—
356#389—731no—
357#389—1461no—
358#389—1461no—
359#389C2×D7311yescharacteristic
360#389C2×D7311yescharacteristic
361#385—1461no—
362#385—1461no—
363C4×C4⋊C4—1461no—
364C4×C4⋊C4—1461no—
365C2×#95—1461no—
366#340—731no—
367#340—731no—
368#340—731no—
369#340—731no—
370#340—731no—
371#340—731no—
372#340—731no—
373#340—731no—
374#340—731no—
375#340C2×D7311yescharacteristic
376#340C2×D7311yescharacteristic
377#340C2×D7311yescharacteristic
378C23×C4—731no—
379C23×C4—731no—
380C23×C4—731no—
381C23×C4—1461no—
382C23×C4—1461no—
383C2×M16—734no—
384C2×M16—1462no—
385C2×M16—1462no—
386C2×M16—1462no—
387C2×M16—1462no—
388C2×M16—1462no—
389C22×C8—731no—
390C22×C8—731no—
391C22×C8C22×D7311yescharacteristic
392C22×C8C22×D7311yescharacteristic
393#117—734no—
394#117—1462no—
395#117—1462no—
396#117—1462no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—2924no—
400C2×C4⋊C4—731no—
401C2×C4⋊C4—731no—
402C2×C4⋊C4—734no—
403C2×C4⋊C4—731no—
404C2×C4⋊C4—731no—
405C2×C4⋊C4—1462no—
406C2×C4⋊C4—1462no—
407C2×C4⋊C4—1462no—
408C2×C4⋊C4—1461no—
409C2×C4⋊C4—1461no—
410C2×C4⋊C4—1461no—
411C2×C4⋊C4—1461no—
412C2×C4⋊C4—1461no—
413C2×C4⋊C4—1461no—
414C2×C4⋊C4—1461no—
415C2×C4⋊C4—1461no—
416C2×C4⋊C4C22×D7311yescharacteristic
417C2×C4⋊C4C22×D7311yescharacteristic
418C2×C4⋊C4C22×D7311yescharacteristic
419C2×C4⋊C4C22×D7311yescharacteristic
420C2×C22⋊C4—1461no—
421C2×C22⋊C4—1461no—
422C2×C42—731no—
423C2×C42—731no—
424C2×C42—731no—
425C2×C42—1462no—
426C2×C42—1462no—
427C2×C42—1461no—
428C2×C42—1461no—
429C2×C42C22×D7311yescharacteristic
430#107—1462no—
431#107—1462no—
432#106—22no—
433#106—1462no—
434C4⋊C8—22no—
435C4⋊C8—1462no—
436C4⋊C8—1462no—
437C4⋊C8—1462no—
438#95—21no—
439#95—21no—
440#95—1461no—
441#95—1461no—
442#95—1461no—
443#95—1461no—
444#95—1461no—
445#95—1461no—
446C24—731no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—2921no—
452C22×C4—2921no—
453C22×C4—2922no—
454C22×C4—2922no—
455C22×C4—2922no—
456C22×C4—2922no—
457C22×C4—2922no—
458C22×C4—731no—
459C22×C4—732no—
460C22×C4—732no—
461C22×C4—732no—
462C22×C4—732no—
463C22×C4—732no—
464C22×C4—732no—
465C22×C4—731no—
466C22×C4—731no—
467C22×C4—1462no—
468C22×C4—1462no—
469C22×C4—1462no—
470C22×C4—1464no—
471C22×C4—1461no—
472C22×C4—1461no—
473C22×C4—1461no—
474C22×C4—1461no—
475C22×C4—1462no—
476C22×C4D4×D7311yescharacteristic
477C22×C4D4×D7311yescharacteristic
478C22×C4C23×D7311yescharacteristic
479M16—2924no—
480M16—1468no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—732no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8—1461no—
492C2×C8D4×D7312yes—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—2922no—
502C4⋊C4—2922no—
503C4⋊C4—2922no—
504C4⋊C4—2922no—
505C4⋊C4—2922no—
506C4⋊C4—2922no—
507C4⋊C4—2922no—
508C4⋊C4—732no—
509C4⋊C4—732no—
510C4⋊C4—1464no—
511C4⋊C4—1461no—
512C4⋊C4—1461no—
513C4⋊C4—1461no—
514C4⋊C4—1461no—
515C4⋊C4—1461no—
516C4⋊C4—1461no—
517C4⋊C4Q8×D7312yes—
518C4⋊C4Q8×D7312yes—
519C22⋊C4—2922no—
520C22⋊C4—1464no—
521C42—21no—
522C42—21no—
523C42—2922no—
524C42—1462no—
525C42—1462no—
526C42—1464no—
527C42—1461no—
528C42—1461no—
529C23—732no—
530C23—732no—
531C23—732no—
532C23—1461no—
533C23—1461no—
534C23—1461no—
535C23—1461no—
536C23C2×D4×D7311yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
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—2924no—
555C2×C4—2928no—
556C2×C4—2924no—
557C2×C4—2921no—
558C2×C4—2921no—
559C2×C4—2921no—
560C2×C4—2921no—
561C2×C4—2921no—
562C2×C4—2921no—
563C2×C4—2921no—
564C2×C4—2921no—
565C2×C4—2921no—
566C2×C4—2921no—
567C2×C4—5844no—
568C2×C4—732no—
569C2×C4—732no—
570C2×C4—732no—
571C2×C4—734no—
572C2×C4—734no—
573C2×C4—734no—
574C2×C4—734no—
575C2×C4—732no—
576C2×C4—1461no—
577C2×C4—1461no—
578C2×C4—1461no—
579C2×C4—1462no—
580C2×C4—1462no—
581C2×C4—1461no—
582C2×C4—1461no—
583C2×C4#1455662012yes—
584C2×C4C2×D4×D7311yescharacteristic
585C2×C4C2×Q8×D7311yescharacteristic
586C2×C4C2×Q8×D7311yescharacteristic
587C2×C4#41×D7311yescharacteristic
588C2×C4#41×D7311yescharacteristic
589C2×C4#41×D7311yescharacteristic
590C8—22no—
591C8—41no—
592C8—2921no—
593C8—1462no—
594C22—734no—
595C22—1462no—
596C22—1462no—
597C22—1462no—
598C22—1462no—
599C22—1462no—
600C22—1462no—
601C22#121×D7311yescharacteristic
602C22C22⋊Q8×D7311yescharacteristic
603C22C22⋊Q8×D7311yescharacteristic
604C22AGL(1,ℤ/8)×D7311yescharacteristic
605C22C2×#1455662011yescharacteristic
606C22#1798938411yescharacteristic
607C22#1798938611yescharacteristic
608C4—22no—
609C4—42no—
610C4—42no—
611C4—41no—
612C4—81no—
613C4—81no—
614C4—2922no—
615C4—2922no—
616C4—2921no—
617C4—5841no—
618C4—5841no—
619C4—734no—
620C4—1462no—
621C4#123×D7311yescharacteristic
622C4#125×D7311yescharacteristic
623C4#125×D7311yescharacteristic
624C4C4⋊Q8×D7311yescharacteristic
625C2—1464no—
626C2#398×D7311yescharacteristic
627C2#2261954511yescharacteristic
628C2#2261955411yescharacteristic
629C2#2261972611yescharacteristic
630C2#2261973111yescharacteristic
631C2#2261974311yescharacteristic
632C2#2261975011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2088C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
hypercenter#2088D73
hypocenterC73#23670
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2088

Complements

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

NH ≅ G/Ntype
5. #22611435C2semidirect
6. #22611432C2semidirect
7. #22611430C2semidirect
8. #22611427C2semidirect
9. #22611424C2semidirect
10. #22611423C2semidirect
11. #22611421C2semidirect
15. C73×#2088C2semidirect
324. #2088D73semidirect
332. C73#23670semidirect

Maximal subgroups

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

subgroupindex
C2×#179886262
C2×#179886092
#226124122
#389×D732
#226114352
#226114322
#226114302
#226114272
#226114242
#226114232
#226114212
#226096492
C73×#20882
#2367073