Finite Group Databasebeta

← #33089471

Subgroups — #33089471

Order 18688.

990 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988628C211yesmaximal, characteristic
2C2×#107×D73C211yesmaximal, characteristic
3C2×#17988612C211yesmaximal, characteristic
4#22612552C211yesmaximal, characteristic
5#22612285C211yesmaximal, characteristic
6#22610701C211yesmaximal, characteristic, complemented
7#22610699C211yesmaximal, characteristic, complemented
8#22610698C211yesmaximal, characteristic, complemented
9#22610696C211yesmaximal, characteristic, complemented
10#22610688C211yesmaximal, characteristic, complemented
11#22610687C211yesmaximal, characteristic, complemented
12#22610686C211yesmaximal, characteristic, complemented
13#22609649C211yesmaximal, characteristic
14#22609646C211yesmaximal, characteristic
15C73×#1947C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×#14556549C2211yescharacteristic
19C2×#14556549C2211yescharacteristic
20C2×#14556548C2211yescharacteristic
21C2×C4⋊C4×D73C2211yescharacteristic
22C2×C4⋊C4×D73C2211yescharacteristic
23#17988628—24no—
24C2×#14556525C2211yescharacteristic
25C2×#14556524C2211yescharacteristic
26C2×#14556524C2211yescharacteristic
27C2×#14556524C2211yescharacteristic
28#107×D73—24no—
29C2×#14556523C2211yescharacteristic
30C2×#14556522C2211yescharacteristic
31#17988612C418yescomplemented
32C2×C4⋊#10596831C2211yescharacteristic
33C2×#14556520C2211yescharacteristic
34C2×#14556520C2211yescharacteristic
35#17988482—21no—
36#17988482—21no—
37#17988458—21no—
38#17988458—21no—
39#17988456C2211yescharacteristic
40#17988453C2211yescharacteristic
41#17988452C2211yescharacteristic
42C4⋊C4×Dic73C2211yescharacteristic
43C4⋊C4×Dic73C2211yescharacteristic
44C4×#11924007—21no—
45C4×C4⋊Dic73C2211yescharacteristic
46#17988438—21no—
47C4×#11924005—21no—
48#17988434—21no—
49#17988350C2211yescharacteristic
50#17988350C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55C2×#107×C73C2211yescharacteristic
56C2×#107×C73C2211yescharacteristic
57C2×C4⋊C8×C73C2211yescharacteristic
58#384×C73C2211yescharacteristic
59C4×C4⋊C4×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C22×C4×D73—21no—
63C22×C4×D73—21no—
64C22×C4×D73C2311yescharacteristic
65C2×#11924011—22no—
66C2×#11924011—22no—
67C2×#11924011C2×C414yes—
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C2×C8×D73—22no—
71C2×C8×D73—22no—
72C2×C8×D73C2×C414yes—
73#14556549—22no—
74#14556549—22no—
75#14556549—22no—
76#14556549Q814yes—
77#14556548C2×C414yes—
78#14556548Q814yes—
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×#11924007—21no—
84C2×#11924007—21no—
85C2×#11924007—21no—
86C2×#11924007—21no—
87C2×#11924007D411yescharacteristic
88C2×#11924007D411yescharacteristic
89C4⋊C4×D73—22no—
90C4⋊C4×D73—22no—
91C4⋊C4×D73—22no—
92C4⋊C4×D73D414yes—
93C2×#11924005—21no—
94C2×#11924005—21no—
95C2×#11924005D411yescharacteristic
96C2×#11924005D411yescharacteristic
97C2×C4×Dic73—21no—
98C2×C4×Dic73—21no—
99C2×C4×Dic73—21no—
100C2×C4×Dic73—21no—
101C2×C4×Dic73—21no—
102C2×C4×Dic73C2311yescharacteristic
103#14556525—22no—
104#14556524—22no—
105#14556524—22no—
106#14556524—22no—
107#14556523—22no—
108#14556522—22no—
109C4⋊#10596831C2×C414yescomplemented
110#14556520C2×C414yescomplemented
111#14556520C2×C414yescomplemented
112#14556498—21no—
113#14556498—21no—
114#14556498—21no—
115#14556498—21no—
116#14556498—21no—
117#14556498—21no—
118#14556498—21no—
119C22×C8×C73C2311yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C2×C4⋊C4×C73—21no—
122C2×C4⋊C4×C73—21no—
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C4⋊C4×C73C2311yescharacteristic
125C2×C4⋊C4×C73C2311yescharacteristic
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C42×C73—21no—
128C2×C42×C73C2311yescharacteristic
129#107×C73—22no—
130#107×C73—22no—
131C4⋊C8×C73C2×C414yescomplemented
132#95×C73—21no—
133C23×D73C2×D411yescharacteristic
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—21no—
137C22×Dic73—21no—
138C22×Dic73C2×D411yescharacteristic
139C22×Dic73C2×D411yescharacteristic
140C22×Dic73C2×D411yescharacteristic
141C2×C4×D73—24no—
142C2×C4×D73—42no—
143C2×C4×D73—81no—
144C2×C4×D73—81no—
145C2×C4×D73—81no—
146C2×C4×D73—81no—
147C2×C4×D73C22×C412yes—
148C2×C4×D73C2×D412yes—
149C2×C4×D73C2×Q812yes—
150C2×C4×D73C2×Q812yes—
151C2×C4×D73#4112yes—
152C2×C4×D73#4112yes—
153#11924011—28no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831C22×C412yes—
159C2×#10596831C22×C412yes—
160C8×D73—28no—
161C4⋊Dic73—21no—
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73C2×D412yes—
168C4⋊Dic73C2×Q812yes—
169#11924007—24no—
170#11924007—42no—
171#11924007—81no—
172#11924007—81no—
173#11924007C4⋊C414yes—
174#11924007C4⋊C414yes—
175#11924005—24no—
176#11924005—42no—
177#11924005C4⋊C414yes—
178#11924005C4⋊C414yes—
179C4×Dic73—24no—
180C4×Dic73—42no—
181C4×Dic73—81no—
182C4×Dic73—81no—
183C4×Dic73—81no—
184C4×Dic73C22×C412yes—
185C4×Dic73C2×Q812yes—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73C2×D411yescharacteristic
192C22×C4×C73C2411yescharacteristic
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73C22×C412yes—
198C2×C8×C73C22×C412yes—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—81no—
206C4⋊C4×C73—81no—
207C4⋊C4×C73C2×D412yes—
208C4⋊C4×C73C2×Q812yes—
209C42×C73—81no—
210C42×C73C22×C412yes—
211C42×C73C2×Q812yes—
212C23×C73C22×D411yescharacteristic
213C22×D73—21no—
214C22×D73—21no—
215C22×D73—21no—
216C22×D73—21no—
217C22×D73C2×C4⋊C412yes—
218C22×D73#12112yes—
219C22×D73C22⋊Q812yes—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—22no—
225C2×C4×C73—22no—
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×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73C2×C4⋊C412yes—
237C2×C4×C73C2×C4⋊C412yes—
238C2×C4×C73C23×C411yescharacteristic
239C2×C4×C73C22×D411yescharacteristic
240C2×C4×C73C22×Q811yescharacteristic
241C2×C4×C73C22×Q811yescharacteristic
242C2×C4×C73C2×#4111yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—22no—
249C2×Dic73—22no—
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×Dic73C2×C4⋊C412yes—
261C2×Dic73C2×C4⋊C412yes—
262C2×Dic73C2×C4⋊C412yes—
263C2×Dic73#12112yes—
264C2×Dic73C22⋊Q812yes—
265C4×D73—84no—
266C4×D73—84no—
267C4×D73C4×D414yes—
268C4×D73C4×Q814yes—
269C4×D73#12514yes—
270C4×D73C4⋊Q814yes—
271C8×C73—22no—
272C8×C73—22no—
273#10596831—22no—
274#10596831—22no—
275C22×C73C22×C4⋊C411yescharacteristic
276C22×C73C2×#12111yescharacteristic
277C22×C73C2×C22⋊Q811yescharacteristic
278C22×C73#57611yescharacteristic
279C22×C73#57611yescharacteristic
280C22×C73#57811yescharacteristic
281C22×C73#57811yescharacteristic
282C2×D73—22no—
283C2×D73—22no—
284C2×D73—22no—
285C2×D73—22no—
286C2×D73—22no—
287C2×D73—22no—
288C2×D73#38914yes—
289C4×C73—22no—
290C4×C73—22no—
291C4×C73—42no—
292C4×C73—42no—
293C4×C73—81no—
294C4×C73—81no—
295C4×C73C2×C4×D411yescharacteristic
296C4×C73C2×C4×Q811yescharacteristic
297C4×C73C2×#12511yescharacteristic
298C4×C73C2×C4⋊Q811yescharacteristic
299Dic73—22no—
300Dic73—22no—
301Dic73—42no—
302Dic73—42no—
303Dic73—81no—
304Dic73—81no—
305Dic73#38914yes—
306#21173—731nomaximal, Sylow
307C2×C73C2×#38911yescharacteristic
308C2×C73#291311yescharacteristic
309C2×C73#291311yescharacteristic
310C2×C73#304111yescharacteristic
311C2×C73#304411yescharacteristic
312C2×C73#308311yescharacteristic
313C2×C73#308311yescharacteristic
314D73—24no—
315C2×#428—731no—
316C22×#107—731no—
317C2×#424—731no—
318#2317—731no—
319#2274—731no—
320#1949—731no—
321#1949—731no—
322#1949—731no—
323#1949—731no—
324#1947—731no—
325#1947—731no—
326#1947—731no—
327#1947D7311yescharacteristic, complemented
328#1736—731no—
329#1735—731no—
330C73#2117311yescharacteristic, complemented, Sylow
331C22×M16—731no—
332C23×C8—731no—
333C2×#117—731no—
334C2×#117—731no—
335C2×#117—731no—
336C22×C4⋊C4—731no—
337C22×C4⋊C4—731no—
338#428—1464no—
339C2×#107—731no—
340C2×#107—731no—
341C2×#107—731no—
342C2×#107—731no—
343C2×#107—1464no—
344C2×#107C2×D7311yescharacteristic
345C2×#107C2×D7311yescharacteristic
346C2×#106—731no—
347C2×#106—731no—
348#424—738no—
349C2×C4⋊C8—731no—
350C2×C4⋊C8—731no—
351C2×C4⋊C8—731no—
352C2×C4⋊C8C2×D7311yescharacteristic
353#389—1461no—
354#389—1461no—
355#385—1461no—
356#385—1461no—
357#384—731no—
358#384C2×D7311yescharacteristic
359#382—731no—
360#382—731no—
361C4×C4⋊C4—731no—
362C4×C4⋊C4—731no—
363C4×C4⋊C4—731no—
364C4×C4⋊C4—1461no—
365C4×C4⋊C4—1461no—
366C4×C4⋊C4C2×D7311yescharacteristic
367C4×C22⋊C4—1461no—
368C4×C22⋊C4—1461no—
369#340—731no—
370#340—731no—
371#340—731no—
372#340—731no—
373#340—731no—
374#340—731no—
375#340C2×D7311yescharacteristic
376#340C2×D7311yescharacteristic
377C23×C4—731no—
378C23×C4—1461no—
379C23×C4—1461no—
380C2×M16—734no—
381C2×M16—1462no—
382C2×M16—1462no—
383C22×C8—731no—
384C22×C8—731no—
385C22×C8—734no—
386C22×C8—1462no—
387C22×C8—1462no—
388C22×C8C22×D7311yescharacteristic
389C22×C8C22×D7311yescharacteristic
390#117—734no—
391#117—734no—
392#117—734no—
393#117—1462no—
394#117—1462no—
395#117—1462no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—731no—
399C2×C4⋊C4—731no—
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⋊C4C22×D7311yescharacteristic
413C2×C4⋊C4C22×D7311yescharacteristic
414C2×C4⋊C4C22×D7311yescharacteristic
415C2×C4⋊C4C22×D7311yescharacteristic
416C2×C22⋊C4—731no—
417C2×C22⋊C4—731no—
418C2×C22⋊C4—1461no—
419C2×C22⋊C4—1461no—
420C2×C42—21no—
421C2×C42—731no—
422C2×C42—1461no—
423C2×C42—1461no—
424C2×C42—1461no—
425C2×C42—1461no—
426C2×C42—1461no—
427C2×C42C22×D7311yescharacteristic
428#107—22no—
429#107—22no—
430#107—1462no—
431#107—1462no—
432#107—1462no—
433#107—1462no—
434#106—1462no—
435#106—1462no—
436C4⋊C8—734no—
437C4⋊C8—734no—
438C4⋊C8—734no—
439C4⋊C8C4×D7314yescomplemented
440#95—21no—
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—5841no—
455C22×C4—5841no—
456C22×C4—5841no—
457C22×C4—5841no—
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—1464no—
468C22×C4—1461no—
469C22×C4—1461no—
470C22×C4—1461no—
471C22×C4—1461no—
472C22×C4D4×D7311yescharacteristic
473C22×C4D4×D7311yescharacteristic
474C22×C4C23×D7311yescharacteristic
475M16—1468no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—732no—
481C2×C8—732no—
482C2×C8—1468no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8C2×C4×D7312yes—
488C2×C8C2×C4×D7312yes—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4—2922no—
498C4⋊C4—5841no—
499C4⋊C4—5841no—
500C4⋊C4—734no—
501C4⋊C4—734no—
502C4⋊C4—732no—
503C4⋊C4—732no—
504C4⋊C4—1464no—
505C4⋊C4—1461no—
506C4⋊C4—1461no—
507C4⋊C4—1461no—
508C4⋊C4—1461no—
509C4⋊C4—1461no—
510C4⋊C4—1461no—
511C4⋊C4D4×D7312yes—
512C4⋊C4Q8×D7312yes—
513C22⋊C4—2922no—
514C22⋊C4—734no—
515C22⋊C4—734no—
516C22⋊C4—1464no—
517C42—81no—
518C42—2922no—
519C42—5841no—
520C42—5841no—
521C42—5841no—
522C42—732no—
523C42—732no—
524C42—1464no—
525C42C2×C4×D7312yes—
526C42Q8×D7312yes—
527C23—732no—
528C23—732no—
529C23—732no—
530C23—1461no—
531C23—1461no—
532C23—1461no—
533C23—1461no—
534C23C2×D4×D7311yescharacteristic
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—2921no—
552C2×C4—2921no—
553C2×C4—2921no—
554C2×C4—2921no—
555C2×C4—2921no—
556C2×C4—2921no—
557C2×C4—2921no—
558C2×C4—2921no—
559C2×C4—2921no—
560C2×C4—2921no—
561C2×C4—5844no—
562C2×C4—5844no—
563C2×C4—732no—
564C2×C4—732no—
565C2×C4—732no—
566C2×C4—734no—
567C2×C4—734no—
568C2×C4—734no—
569C2×C4—734no—
570C2×C4—732no—
571C2×C4—732no—
572C2×C4—1462no—
573C2×C4—1462no—
574C2×C4—1461no—
575C2×C4—1461no—
576C2×C4—1461no—
577C2×C4—1461no—
578C2×C4C4⋊C4×D7312yes—
579C2×C4C4⋊C4×D7312yes—
580C2×C4C22×C4×D7311yescharacteristic
581C2×C4C2×D4×D7311yescharacteristic
582C2×C4C2×Q8×D7311yescharacteristic
583C2×C4C2×Q8×D7311yescharacteristic
584C2×C4#41×D7311yescharacteristic
585C2×C4#41×D7311yescharacteristic
586C8—22no—
587C8—22no—
588C8—1462no—
589C8—1462no—
590C22—734no—
591C22—1462no—
592C22—1462no—
593C22—1462no—
594C22—1462no—
595C22—1462no—
596C22—1462no—
597C22C2×C4⋊C4×D7311yescharacteristic
598C22#121×D7311yescharacteristic
599C22C22⋊Q8×D7311yescharacteristic
600C22#1798938811yescharacteristic
601C22#1798939111yescharacteristic
602C22#1798940011yescharacteristic
603C22#1798940311yescharacteristic
604C4—22no—
605C4—22no—
606C4—42no—
607C4—42no—
608C4—81no—
609C4—81no—
610C4—2922no—
611C4—2922no—
612C4—5841no—
613C4—5841no—
614C4—734no—
615C4—1462no—
616C4—1462no—
617C4C4×D4×D7311yescharacteristic
618C4C4×Q8×D7311yescharacteristic
619C4#125×D7311yescharacteristic
620C4C4⋊Q8×D7311yescharacteristic
621C2—1464no—
622C2#389×D7311yescharacteristic
623C2#2261852711yescharacteristic
624C2#2261853011yescharacteristic
625C2#2261942911yescharacteristic
626C2#2261945611yescharacteristic
627C2#2261977711yescharacteristic
628C2#2261977911yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1947C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenter#1947D73
hypocenterC73#21173
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
6. #22610701C2semidirect
7. #22610699C2semidirect
8. #22610698C2semidirect
9. #22610696C2semidirect
10. #22610688C2semidirect
11. #22610687C2semidirect
12. #22610686C2semidirect
15. C73×#1947C2semidirect
31. #17988612C4semidirect
109. C4⋊#10596831C2×C4semidirect
110. #14556520C2×C4semidirect
111. #14556520C2×C4semidirect
131. C4⋊C8×C73C2×C4semidirect
327. #1947D73semidirect
330. C73#21173semidirect
439. C4⋊C8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886282
C2×#107×D732
C2×#179886122
#226125522
#226122852
#226107012
#226106992
#226106982
#226106962
#226106882
#226106872
#226106862
#226096492
#226096462
C73×#19472
#2117373