Finite Group Databasebeta

← #33114968

Subgroups — #33114968

Order 18688.

898 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988624C211yesmaximal, characteristic
2C2×#17988622C211yesmaximal, characteristic
3#22612412C211yesmaximal, characteristic
4#22612337C211yesmaximal, characteristic
5#22611414C211yesmaximal, characteristic, complemented
6#22611413C211yesmaximal, characteristic, complemented
7#22611412C211yesmaximal, characteristic, complemented
8#22611411C211yesmaximal, characteristic, complemented
9#22611410C211yesmaximal, characteristic, complemented
10#22611406C211yesmaximal, characteristic, complemented
11#22611405C211yesmaximal, characteristic, complemented
12#22609646C211yesmaximal, characteristic
13#22609646C211yesmaximal, characteristic
14#336×D73C211yesmaximal, characteristic
15C73×#2085C211yesmaximal, characteristic, complemented
16C22×C8×D73C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×#14556549C2211yescharacteristic
19C2×#14556549C2211yescharacteristic
20C2×#14556549C2211yescharacteristic
21C2×#14556549C2211yescharacteristic
22C2×C42×D73C2211yescharacteristic
23#17988624—24no—
24#17988622—24no—
25C2×#14556525C2211yescharacteristic
26C2×#14556524C2211yescharacteristic
27C2×#14556524C2211yescharacteristic
28C2×#14556523C2211yescharacteristic
29C2×#14556522C2211yescharacteristic
30C2×#14556522C2211yescharacteristic
31#17988486C2211yescharacteristic
32#17988485C2211yescharacteristic
33#17988483C2211yescharacteristic
34#17988461—21no—
35#17988458—21no—
36#17988456C2211yescharacteristic
37#17988456C2211yescharacteristic
38#17988453C2211yescharacteristic
39#17988446—21no—
40#17988446—21no—
41C4⋊C4×Dic73—21no—
42#17988438—21no—
43#17988438—21no—
44#17988438—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×D73D411yescharacteristic
62C22×C4×D73D411yescharacteristic
63C22×C4×D73C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C2×C8×D73—22no—
67C2×C8×D73—22no—
68C2×C8×D73—22no—
69C2×C8×D73—22no—
70C2×C8×D73Q814yes—
71C2×C8×D73Q814yes—
72#14556549—22no—
73#14556549—22no—
74#14556549—22no—
75#14556549—22no—
76#14556549—22no—
77#14556549—22no—
78#14556549—22no—
79#14556549D414yes—
80C2×C4⋊Dic73—21no—
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×#11924007—21no—
86C2×#11924007—21no—
87C2×#11924007—21no—
88C2×#11924007—21no—
89C2×#11924007—21no—
90C2×#11924007—21no—
91C2×#11924005—21no—
92C2×#11924005—21no—
93C2×#11924005—21no—
94C2×#11924005—21no—
95C2×C4×Dic73—21no—
96C2×C4×Dic73—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#14556524—22no—
107#14556523—22no—
108#14556522—22no—
109#14556522—22no—
110#14556498—21no—
111#14556498—21no—
112#14556498—21no—
113#14556498—21no—
114#14556498—21no—
115C22×C8×C73C2311yescharacteristic
116C22×C8×C73C2311yescharacteristic
117C2×C4⋊C4×C73—21no—
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C42×C73C2311yescharacteristic
123#107×C73—22no—
124#106×C73—22no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128C23×D73C2×D411yescharacteristic
129C22×Dic73—21no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73C2×D411yescharacteristic
134C22×Dic73C2×D411yescharacteristic
135C22×Dic73C2×D411yescharacteristic
136C2×C4×D73—22no—
137C2×C4×D73—22no—
138C2×C4×D73—22no—
139C2×C4×D73—22no—
140C2×C4×D73—41no—
141C2×C4×D73—41no—
142C2×C4×D73C2×D412yes—
143C2×C4×D73C2×Q812yes—
144C2×C4×D73C2×Q812yes—
145C2×C4×D73#4112yes—
146C2×C4×D73#4112yes—
147C2×C4×D73#4112yes—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831C2×Q812yes—
153C2×#10596831C2×Q812yes—
154C8×D73—28no—
155C8×D73—28no—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—21no—
159C4⋊Dic73—21no—
160C4⋊Dic73—21no—
161C4⋊Dic73—21no—
162C4⋊Dic73—21no—
163C4⋊Dic73—42no—
164C4⋊Dic73C2×D412yes—
165#11924007—42no—
166#11924007—42no—
167#11924007—42no—
168#11924007—42no—
169#11924007—42no—
170#11924007—42no—
171#11924005—24no—
172#11924005—42no—
173#11924005—42no—
174#11924005—42no—
175C4×Dic73—21no—
176C4×Dic73—21no—
177C4×Dic73—24no—
178C4×Dic73—22no—
179C4×Dic73—22no—
180C4×Dic73—42no—
181C4×Dic73—42no—
182C4×Dic73—42no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73C2×D411yescharacteristic
189C22×C4×C73C2411yescharacteristic
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73C2×Q812yes—
195C2×C8×C73C2×Q812yes—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—42no—
204C4⋊C4×C73C2×D412yes—
205C42×C73—21no—
206C42×C73—21no—
207C23×C73C22×D411yescharacteristic
208C22×D73—21no—
209C22×D73—21no—
210C22×D73—21no—
211C22×D73—21no—
212C22×D73#12112yes—
213C22×D73#12312yes—
214C22×D73C4⋊Q812yes—
215C2×C4×C73—22no—
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—41no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
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×C73C22×D411yescharacteristic
234C2×C4×C73C22×Q811yescharacteristic
235C2×C4×C73C22×Q811yescharacteristic
236C2×C4×C73C2×#4111yescharacteristic
237C2×C4×C73C2×#4111yescharacteristic
238C2×C4×C73C2×#4111yescharacteristic
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—22no—
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—
255C2×Dic73#12112yes—
256C2×Dic73#12312yes—
257C2×Dic73C4⋊Q812yes—
258C2×Dic73#13512yes—
259C2×Dic73#13512yes—
260C4×D73—44no—
261C4×D73—44no—
262C4×D73C22⋊Q814yes—
263C4×D73C22⋊Q814yes—
264C4×D73#12514yes—
265C4×D73#12514yes—
266C8×C73—22no—
267C8×C73—22no—
268#10596831—22no—
269#10596831—22no—
270C22×C73C2×#12111yescharacteristic
271C22×C73C2×#12311yescharacteristic
272C22×C73C2×C4⋊Q811yescharacteristic
273C22×C73C2×#13511yescharacteristic
274C22×C73C2×#13511yescharacteristic
275C22×C73#57511yescharacteristic
276C22×C73#57511yescharacteristic
277C2×D73—22no—
278C2×D73—22no—
279C2×D73—22no—
280C2×D73—22no—
281C2×D73—22no—
282C2×D73—22no—
283C2×D73#39814yes—
284C4×C73—41no—
285C4×C73—41no—
286C4×C73—42no—
287C4×C73—81no—
288C4×C73—81no—
289C4×C73—81no—
290C4×C73C2×C22⋊Q811yescharacteristic
291C4×C73C2×C22⋊Q811yescharacteristic
292C4×C73C2×#12511yescharacteristic
293C4×C73C2×#12511yescharacteristic
294Dic73—22no—
295Dic73—22no—
296Dic73—42no—
297Dic73—81no—
298Dic73—81no—
299Dic73—81no—
300Dic73#39814yes—
301#23656—731nomaximal, Sylow
302C2×C73C2×#39811yescharacteristic
303C2×C73#303511yescharacteristic
304C2×C73#303511yescharacteristic
305C2×C73#309111yescharacteristic
306C2×C73#309111yescharacteristic
307C2×C73#316011yescharacteristic
308C2×C73#316211yescharacteristic
309D73—24no—
310C2×#427—731no—
311C2×#427—731no—
312#2296—731no—
313#2285—731no—
314#2085—731no—
315#2085—731no—
316#2085—731no—
317#2085D7311yescharacteristic, complemented
318#2084—731no—
319#2084—731no—
320#2083—731no—
321#2083—731no—
322#1735—731no—
323#1735—731no—
324C2×#336—731no—
325C73#2365611yescharacteristic, complemented, Sylow
326C23×C8—731no—
327C23×C8—731no—
328C2×#117—731no—
329C2×#117—731no—
330C2×#117—731no—
331C2×#117—731no—
332C22×C42—731no—
333#427—1464no—
334#427—1464no—
335C2×#107—731no—
336C2×#107—731no—
337C2×#107—731no—
338C2×#107C2×D7311yescharacteristic
339C2×#106—731no—
340C2×#106—731no—
341C2×#106—731no—
342C2×#106C2×D7311yescharacteristic
343#389—731no—
344#389—731no—
345#389—731no—
346#389C2×D7311yescharacteristic
347#385—1461no—
348#385—1461no—
349#384—731no—
350#384—731no—
351#382—731no—
352#382C2×D7311yescharacteristic
353#380—1461no—
354#380—1461no—
355C4×C4⋊C4—1461no—
356C4×C4⋊C4—1461no—
357C4×C4⋊C4—1461no—
358C4×C4⋊C4—1461no—
359#340—731no—
360#340—731no—
361#340—731no—
362#340—731no—
363#340—731no—
364#340—731no—
365#340C2×D7311yescharacteristic
366#340C2×D7311yescharacteristic
367#336—731no—
368#336—731no—
369#336—731no—
370#336C2×D7311yescharacteristic
371C23×C4—731no—
372C23×C4—731no—
373C23×C4—731no—
374C22×C8—731no—
375C22×C8—731no—
376C22×C8—734no—
377C22×C8—734no—
378C22×C8—1462no—
379C22×C8—1462no—
380C22×C8—1462no—
381C22×C8—1462no—
382C22×C8C22×D7311yescharacteristic
383C22×C8C22×D7311yescharacteristic
384#117—734no—
385#117—1462no—
386#117—1462no—
387#117—1462no—
388#117—1462no—
389#117—1462no—
390#117—1462no—
391#117—1462no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—731no—
394C2×C4⋊C4—731no—
395C2×C4⋊C4—731no—
396C2×C4⋊C4—731no—
397C2×C4⋊C4—1461no—
398C2×C4⋊C4—1461no—
399C2×C4⋊C4—1461no—
400C2×C4⋊C4—1461no—
401C2×C4⋊C4—1461no—
402C2×C4⋊C4—1461no—
403C2×C4⋊C4—1461no—
404C2×C4⋊C4C22×D7311yescharacteristic
405C2×C4⋊C4C22×D7311yescharacteristic
406C2×C4⋊C4C22×D7311yescharacteristic
407C2×C4⋊C4C22×D7311yescharacteristic
408C2×C22⋊C4—1461no—
409C2×C22⋊C4—1461no—
410C2×C22⋊C4—1461no—
411C2×C22⋊C4—1461no—
412C2×C42—731no—
413C2×C42—731no—
414C2×C42—731no—
415C2×C42—1462no—
416C2×C42—1462no—
417C2×C42—1461no—
418C2×C42—1461no—
419C2×C42—1461no—
420C2×C42—1461no—
421C2×C42C22×D7311yescharacteristic
422#107—22no—
423#107—1462no—
424#107—1462no—
425#107—1462no—
426#106—22no—
427#106—1462no—
428#106—1462no—
429#106—1462no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—1461no—
434#95—1461no—
435#95—1461no—
436#95—1461no—
437#95—1461no—
438C24—731no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—2921no—
444C22×C4—2921no—
445C22×C4—731no—
446C22×C4—732no—
447C22×C4—732no—
448C22×C4—732no—
449C22×C4—732no—
450C22×C4—732no—
451C22×C4—732no—
452C22×C4—731no—
453C22×C4—731no—
454C22×C4—1462no—
455C22×C4—1462no—
456C22×C4—1462no—
457C22×C4—1462no—
458C22×C4—1461no—
459C22×C4—1461no—
460C22×C4—1461no—
461C22×C4—1461no—
462C22×C4D4×D7311yescharacteristic
463C22×C4D4×D7311yescharacteristic
464C22×C4C23×D7311yescharacteristic
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—732no—
470C2×C8—732no—
471C2×C8—1468no—
472C2×C8—1468no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8—1461no—
477C2×C8Q8×D7312yes—
478C2×C8Q8×D7312yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—2922no—
488C4⋊C4—2922no—
489C4⋊C4—2922no—
490C4⋊C4—2922no—
491C4⋊C4—2922no—
492C4⋊C4—2922no—
493C4⋊C4—2922no—
494C4⋊C4—732no—
495C4⋊C4—1461no—
496C4⋊C4—1461no—
497C4⋊C4—1461no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C4⋊C4—1461no—
501C4⋊C4—1461no—
502C4⋊C4D4×D7312yes—
503C22⋊C4—2922no—
504C22⋊C4—2922no—
505C22⋊C4—2922no—
506C22⋊C4—1464no—
507C42—21no—
508C42—21no—
509C42—2922no—
510C42—2922no—
511C42—2922no—
512C42—1462no—
513C42—1462no—
514C42—1464no—
515C42—1461no—
516C42—1461no—
517C23—732no—
518C23—732no—
519C23—732no—
520C23—1461no—
521C23—1461no—
522C23—1461no—
523C23—1461no—
524C23C2×D4×D7311yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—2924no—
544C2×C4—2924no—
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—732no—
557C2×C4—732no—
558C2×C4—732no—
559C2×C4—734no—
560C2×C4—734no—
561C2×C4—734no—
562C2×C4—734no—
563C2×C4—732no—
564C2×C4—732no—
565C2×C4—1462no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4C2×D4×D7311yescharacteristic
571C2×C4C2×Q8×D7311yescharacteristic
572C2×C4C2×Q8×D7311yescharacteristic
573C2×C4#41×D7311yescharacteristic
574C2×C4#41×D7311yescharacteristic
575C2×C4#41×D7311yescharacteristic
576C8—22no—
577C8—22no—
578C8—1462no—
579C8—1462no—
580C22—734no—
581C22—1462no—
582C22—1462no—
583C22—1462no—
584C22—1462no—
585C22—1462no—
586C22—1462no—
587C22#121×D7311yescharacteristic
588C22#123×D7311yescharacteristic
589C22C4⋊Q8×D7311yescharacteristic
590C22#135×D7311yescharacteristic
591C22#135×D7311yescharacteristic
592C22#1798938311yescharacteristic
593C22#1798938611yescharacteristic
594C4—41no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—2922no—
601C4—5841no—
602C4—5841no—
603C4—5841no—
604C4—734no—
605C4—1462no—
606C4—1462no—
607C4C22⋊Q8×D7311yescharacteristic
608C4C22⋊Q8×D7311yescharacteristic
609C4#125×D7311yescharacteristic
610C4#125×D7311yescharacteristic
611C2—1464no—
612C2#398×D7311yescharacteristic
613C2#2261938311yescharacteristic
614C2#2261938511yescharacteristic
615C2#2261984311yescharacteristic
616C2#2261984911yescharacteristic
617C2#2262044411yescharacteristic
618C2#2262045211yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2085C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
hypercenter#2085D73
hypocenterC73#23656
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. #22611414C2semidirect
6. #22611413C2semidirect
7. #22611412C2semidirect
8. #22611411C2semidirect
9. #22611410C2semidirect
10. #22611406C2semidirect
11. #22611405C2semidirect
15. C73×#2085C2semidirect
317. #2085D73semidirect
325. C73#23656semidirect

Maximal subgroups

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

subgroupindex
C2×#179886242
C2×#179886222
#226124122
#226123372
#226114142
#226114132
#226114122
#226114112
#226114102
#226114062
#226114052
#226096462
#336×D732
C73×#20852
#2365673