Finite Group Databasebeta

← #33115993

Subgroups — #33115993

Order 18688.

796 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×Dic73C211yesmaximal, characteristic
2#22612333C211yesmaximal, characteristic
3#22611492C211yesmaximal, characteristic, complemented
4#22611472C211yesmaximal, characteristic, complemented
5#22611410C211yesmaximal, characteristic, complemented
6#22611367C211yesmaximal, characteristic
7#22611364C211yesmaximal, characteristic
8#22611342C211yesmaximal, characteristic, complemented
9#22611124C211yesmaximal, characteristic
10#106×Dic73C211yesmaximal, characteristic, complemented
11#22609819C211yesmaximal, characteristic, complemented
12#103×Dic73C211yesmaximal, characteristic, complemented
13#103×Dic73C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic73C211yesmaximal, characteristic
15C73×#2035C211yesmaximal, characteristic
16C2×Q8×Dic73C2211yescharacteristic
17C2×#14556547—21no—
18C22×C4×Dic73C2211yescharacteristic
19C2×#14556523C2211yescharacteristic
20C2×#14556522C2211yescharacteristic
21C2×#14556522C2211yescharacteristic
22C2×#14556515C2211yescharacteristic
23C2×#14556515C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C8×Dic73C2211yescharacteristic
26C2×C8×Dic73C2211yescharacteristic
27#17988494C2211yescharacteristic
28#17988486C2211yescharacteristic
29#17988473—21no—
30#17988462—21no—
31#17988456C2211yescharacteristic
32#17988456C2211yescharacteristic
33#17988451—21no—
34#17988447C2211yescharacteristic
35#17988447C2211yescharacteristic
36#17988445—21no—
37C4⋊C4×Dic73—21no—
38C4⋊C4×Dic73C2211yescharacteristic
39C4⋊C4×Dic73C2211yescharacteristic
40C4⋊C4×Dic73C2211yescharacteristic
41#17988438—21no—
42C22⋊C4×Dic73—21no—
43#17988350C2211yescharacteristic
44#17988350C2211yescharacteristic
45#17988350C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C2×C22⋊Q8×C73C2211yescharacteristic
53C2×#106×C73C2211yescharacteristic
54C2×#103×C73C2211yescharacteristic
55C2×#103×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59C23×Dic73D411yescharacteristic
60C23×Dic73D411yescharacteristic
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63Q8×Dic73—22no—
64Q8×Dic73—22no—
65#14556547—44no—
66C2×C4⋊Dic73—21no—
67C2×C4⋊Dic73—21no—
68C2×C4⋊Dic73C2311yescharacteristic
69C2×C4⋊Dic73C2311yescharacteristic
70C2×C4⋊Dic73C2311yescharacteristic
71C2×C4⋊Dic73C2311yescharacteristic
72C2×#11924007—21no—
73C2×#11924007—21no—
74C2×#11924007—21no—
75C2×#11924007—21no—
76C2×C22⋊Dic73—21no—
77C2×C22⋊Dic73—21no—
78C2×C4×Dic73—22no—
79C2×C4×Dic73—22no—
80C2×C4×Dic73—21no—
81C2×C4×Dic73—21no—
82C2×C4×Dic73—21no—
83C2×C4×Dic73—21no—
84C2×C4×Dic73D411yescharacteristic
85C2×C4×Dic73D411yescharacteristic
86C2×C4×Dic73C2311yescharacteristic
87C2×C4×Dic73C2311yescharacteristic
88#14556523—22no—
89#14556522—22no—
90#14556522—22no—
91#14556515—22no—
92#14556515—22no—
93C22⋊#10596831—22no—
94C8×Dic73—22no—
95C8×Dic73—22no—
96#14556498—21no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100#14556498—21no—
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104C22×Q8×C73C2311yescharacteristic
105C23×C4×C73C2311yescharacteristic
106C22×C8×C73C2311yescharacteristic
107C22×C8×C73C2311yescharacteristic
108C22⋊Q8×C73—22no—
109C22⋊Q8×C73—22no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73C2311yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C22⋊C4×C73—21no—
115C2×C22⋊C4×C73—21no—
116#106×C73—22no—
117#103×C73—22no—
118#103×C73—22no—
119C22⋊C8×C73—22no—
120#95×C73—21no—
121C22×Dic73—22no—
122C22×Dic73—22no—
123C22×Dic73—22no—
124C22×Dic73—22no—
125C22×Dic73—21no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—41no—
130C22×Dic73SD1614yes—
131C22×Dic73C2×D411yescharacteristic
132C22×Dic73C2×D411yescharacteristic
133C22×Dic73C2×D411yescharacteristic
134C22×Dic73C2×D411yescharacteristic
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831#4112yes—
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—42no—
150C4⋊Dic73—42no—
151#11924007—42no—
152#11924007—42no—
153#11924007—42no—
154#11924007—42no—
155C22⋊Dic73—42no—
156C22⋊Dic73—42no—
157C4×Dic73—21no—
158C4×Dic73—21no—
159C4×Dic73—22no—
160C4×Dic73—22no—
161C4×Dic73—42no—
162C4×Dic73—42no—
163C4×Dic73—42no—
164C4×Dic73—42no—
165C4×Dic73#4112yes—
166C4×Dic73#4112yes—
167C24×C73C2×D411yescharacteristic
168C2×Q8×C73—21no—
169C2×Q8×C73—21no—
170C2×Q8×C73—21no—
171C2×Q8×C73—21no—
172C2×Q8×C73—21no—
173C2×Q8×C73#4112yes—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73C2411yescharacteristic
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73#4112yes—
192C4⋊C4×C73—24no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73#4112yes—
199C22⋊C4×C73—24no—
200C22⋊C4×C73—42no—
201C23×C73—21no—
202C23×C73—21no—
203C23×C73—21no—
204C23×C73—21no—
205C23×C73—21no—
206C23×C73—21no—
207C23×C73C2×SD1612yes—
208C23×C73C22×D411yescharacteristic
209Q8×C73—22no—
210Q8×C73—22no—
211Q8×C73—41no—
212Q8×C73—41no—
213C2×C4×C73—21no—
214C2×C4×C73—22no—
215C2×C4×C73—22no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
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×C73C2×#4111yescharacteristic
233C2×C4×C73C2×#4111yescharacteristic
234C2×C4×C73C2×#4111yescharacteristic
235C2×C4×C73C2×#4111yescharacteristic
236C2×C4×C73C2×#4111yescharacteristic
237C2×C4×C73C2×#4111yescharacteristic
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—21no—
244C2×Dic73—28no—
245C2×Dic73—44no—
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—41no—
256C2×Dic73—41no—
257C2×Dic73—41no—
258C2×Dic73#12312yes—
259C2×Dic73#12312yes—
260C2×Dic73C2×SD1612yes—
261C2×Dic73C2×SD1612yes—
262C2×Dic73#13512yes—
263C2×Dic73#13712yes—
264C8×C73—22no—
265C8×C73—41no—
266#10596831—22no—
267#10596831—41no—
268C22×C73—22no—
269C22×C73—22no—
270C22×C73—22no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73C2×#12311yescharacteristic
276C22×C73#52511yescharacteristic
277C22×C73#53211yescharacteristic
278C22×C73C22×SD1611yescharacteristic
279C22×C73C2×#13511yescharacteristic
280C22×C73C2×#13711yescharacteristic
281C22×C73#57511yescharacteristic
282C4×C73—42no—
283C4×C73—41no—
284C4×C73—42no—
285C4×C73—81no—
286C4×C73—81no—
287C4×C73#52911yescharacteristic
288C4×C73#52911yescharacteristic
289C4×C73#52911yescharacteristic
290C4×C73#52911yescharacteristic
291Dic73—22no—
292Dic73—22no—
293Dic73—22no—
294Dic73—81no—
295Dic73—81no—
296Dic73—81no—
297Dic73—81no—
298Dic73#48314yes—
299#23756—731nomaximal, Sylow
300C2×C73—42no—
301C2×C73#239511yescharacteristic
302C2×C73C2×#48311yescharacteristic
303C2×C73#309111yescharacteristic
304C2×C73#310311yescharacteristic
305C2×C73#310711yescharacteristic
306C2×C73#316711yescharacteristic
307C2×C73#317211yescharacteristic
308C4×C22⋊Q8—731no—
309#2285—731no—
310#2099—731no—
311#2096—731no—
312#2084—731no—
313#2077—731no—
314#2077—731no—
315#2072—731no—
316#2035—731no—
317#2035D7311yescharacteristic
318C4×#106—731no—
319C4×#106—731no—
320C4×#103—731no—
321C4×#103—731no—
322C4×C22⋊C8—731no—
323C73#2375611yescharacteristic, complemented, Sylow
324C2×C22⋊Q8C2×D7311yescharacteristic
325C2×C4×Q8—731no—
326C2×#117—1461no—
327C22×C42—731no—
328C2×#106—731no—
329C2×#106—731no—
330C2×#106—731no—
331C2×#106C2×D7311yescharacteristic
332C2×#103—731no—
333C2×#103—731no—
334C2×#103C2×D7311yescharacteristic
335C2×#103C2×D7311yescharacteristic
336C2×C22⋊C8—731no—
337C2×C22⋊C8C2×D7311yescharacteristic
338C2×C4×C8—731no—
339C2×C4×C8—731no—
340#391—731no—
341#389—731no—
342#387—1461no—
343#385—1461no—
344#384—731no—
345#384—731no—
346#382—1461no—
347#380—731no—
348#380—731no—
349#380—1461no—
350#380C2×D7311yescharacteristic
351C4×C4⋊C4—731no—
352C4×C4⋊C4—731no—
353C4×C4⋊C4—731no—
354C4×C4⋊C4—1461no—
355C4×C4⋊C4—1461no—
356C4×C22⋊C4—1461no—
357#340—731no—
358#340—731no—
359#340—731no—
360#340—731no—
361#340—731no—
362#340—731no—
363#340—731no—
364#340C2×D7311yescharacteristic
365#336—731no—
366#336—731no—
367C22×Q8C22×D7311yescharacteristic
368C23×C4—731no—
369C23×C4—731no—
370C23×C4C22×D7311yescharacteristic
371C22×C8—731no—
372C22×C8—731no—
373C22×C8C22×D7311yescharacteristic
374C22×C8C22×D7311yescharacteristic
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C4×Q8—1462no—
378C4×Q8—1462no—
379#117—2924no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—731no—
382C2×C4⋊C4—731no—
383C2×C4⋊C4—731no—
384C2×C4⋊C4—731no—
385C2×C4⋊C4—1461no—
386C2×C4⋊C4—1461no—
387C2×C4⋊C4—1461no—
388C2×C4⋊C4—1461no—
389C2×C4⋊C4—1461no—
390C2×C4⋊C4—1461no—
391C2×C4⋊C4C22×D7311yescharacteristic
392C2×C4⋊C4C22×D7311yescharacteristic
393C2×C4⋊C4C22×D7311yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—1461no—
397C2×C22⋊C4—1461no—
398C2×C42—731no—
399C2×C42—731no—
400C2×C42—731no—
401C2×C42—731no—
402C2×C42—1461no—
403C2×C42—1461no—
404C2×C42—1461no—
405C2×C42—1461no—
406C2×C42—1462no—
407C2×C42—1462no—
408#106—22no—
409#106—1462no—
410#106—1462no—
411#106—1462no—
412#103—22no—
413#103—22no—
414#103—1462no—
415#103—1462no—
416C22⋊C8—22no—
417C22⋊C8—1462no—
418C4×C8—1462no—
419C4×C8—1462no—
420#95—21no—
421#95—1461no—
422#95—1461no—
423#95—1461no—
424#95—1461no—
425#95—1461no—
426#95—1461no—
427#95—1461no—
428#95—1461no—
429C24D4×D7311yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8#1192402712yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—2921no—
447C22×C4—731no—
448C22×C4—734no—
449C22×C4—731no—
450C22×C4—731no—
451C22×C4—731no—
452C22×C4—1461no—
453C22×C4—1461no—
454C22×C4—1461no—
455C22×C4—1461no—
456C22×C4—1462no—
457C22×C4—1462no—
458C22×C4—1462no—
459C22×C4—1462no—
460C22×C4D4×D7311yescharacteristic
461C22×C4C23×D7311yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—732no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8#1192402712yes—
474C4⋊C4—24no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—2922no—
481C4⋊C4—2922no—
482C4⋊C4—2922no—
483C4⋊C4—2922no—
484C4⋊C4—2922no—
485C4⋊C4—2922no—
486C4⋊C4—1461no—
487C4⋊C4—1461no—
488C4⋊C4—1461no—
489C4⋊C4—1461no—
490C4⋊C4—1461no—
491C4⋊C4—1461no—
492C4⋊C4—1461no—
493C4⋊C4—1461no—
494C4⋊C4#1192402712yes—
495C22⋊C4—24no—
496C22⋊C4—42no—
497C22⋊C4—2922no—
498C22⋊C4—2922no—
499C42—2922no—
500C42—2922no—
501C42—2922no—
502C42—2922no—
503C42—732no—
504C42—732no—
505C42—1462no—
506C42—1462no—
507C42—1461no—
508C42—1461no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23SD16×D7312yes—
516C23C2×D4×D7311yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
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—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—2921no—
551C2×C4—2921no—
552C2×C4—2924no—
553C2×C4—732no—
554C2×C4—732no—
555C2×C4—732no—
556C2×C4—732no—
557C2×C4—732no—
558C2×C4—732no—
559C2×C4—1468no—
560C2×C4—1461no—
561C2×C4—1461no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4#41×D7311yescharacteristic
567C2×C4#41×D7311yescharacteristic
568C2×C4#41×D7311yescharacteristic
569C2×C4C2×#1192402711yescharacteristic
570C2×C4C2×#1192402711yescharacteristic
571C2×C4C2×#1192402711yescharacteristic
572C8—22no—
573C8—41no—
574C8—2921no—
575C8—1462no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22#123×D7311yescharacteristic
584C22#1798909311yescharacteristic
585C22#1798913211yescharacteristic
586C22C2×SD16×D7311yescharacteristic
587C22#135×D7311yescharacteristic
588C22#137×D7311yescharacteristic
589C22#1798938611yescharacteristic
590C4—42no—
591C4—41no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4—5841no—
596C4—5841no—
597C4—5841no—
598C4—5841no—
599C4—734no—
600C4—1462no—
601C4—1462no—
602C4—1462no—
603C4#1798911411yescharacteristic
604C4#1798911611yescharacteristic
605C4#1798911811yescharacteristic
606C4#1798911811yescharacteristic
607C2—42no—
608C2#2261318711yescharacteristic
609C2#483×D7311yescharacteristic
610C2#2261984911yescharacteristic
611C2#2261995711yescharacteristic
612C2#2261999511yescharacteristic
613C2#2262048511yescharacteristic
614C2#2262053211yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2035C2
socleC23×C73C22×D4
prime radicalC24×C73C2×D4
hypercenter#2035D73
hypocenterC73#23756
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
3. #22611492C2semidirect
4. #22611472C2semidirect
5. #22611410C2semidirect
8. #22611342C2semidirect
10. #106×Dic73C2semidirect
11. #22609819C2semidirect
12. #103×Dic73C2semidirect
13. #103×Dic73C2semidirect
323. C73#23756semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×Dic732
#226123332
#226114922
#226114722
#226114102
#226113672
#226113642
#226113422
#226111242
#106×Dic732
#226098192
#103×Dic732
C22⋊C8×Dic732
C73×#20352
#2375673