Finite Group Databasebeta

← #33089141

Subgroups — #33089141

Order 18688.

862 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988678C211yesmaximal, characteristic
2#22612568C211yesmaximal, characteristic
3#22612295C211yesmaximal, characteristic, complemented
4#22610560C211yesmaximal, characteristic
5#22610516C211yesmaximal, characteristic, complemented
6#22610514C211yesmaximal, characteristic, complemented
7#22610289C211yesmaximal, characteristic
8#22610283C211yesmaximal, characteristic
9#22610202C211yesmaximal, characteristic, complemented
10#22610196C211yesmaximal, characteristic, complemented
11#106×Dic73C211yesmaximal, characteristic, complemented
12#22609760C211yesmaximal, characteristic, complemented
13#22609758C211yesmaximal, characteristic
14#22609681C211yesmaximal, characteristic, complemented
15C73×#1926C211yesmaximal, characteristic
16C22×#11924016C2211yescharacteristic
17C2×C4×Dic146C2211yescharacteristic
18C2×#14556556C2211yescharacteristic
19C2×#14556556C2211yescharacteristic
20C2×D4×Dic73C2211yescharacteristic
21#17988678C418yescomplemented
22C2×#14556523C2211yescharacteristic
23C2×#14556522C2211yescharacteristic
24C2×#14556516C2211yescharacteristic
25C2×#14556516C2211yescharacteristic
26C2×#14556514C2211yescharacteristic
27C2×#14556512C2211yescharacteristic
28C2×#14556501C2211yescharacteristic
29C2×C8×Dic73C2211yescharacteristic
30#17988490C2211yescharacteristic
31#17988485C2211yescharacteristic
32#17988483C2211yescharacteristic
33#17988481—21no—
34#17988475—21no—
35#17988448—21no—
36#17988445—21no—
37C4⋊C4×Dic73C2211yescharacteristic
38C4⋊C4×Dic73C2211yescharacteristic
39C4⋊C4×Dic73C2211yescharacteristic
40C4×#11924007—21no—
41C4×#11924007—21no—
42#17988438—21no—
43#17988433C2211yescharacteristic
44#17988432—21no—
45#17988350C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988342C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53C2×#106×C73C2211yescharacteristic
54C2×#102×C73C2211yescharacteristic
55C2×#102×C73C2211yescharacteristic
56#390×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60C22×Dic146C2311yescharacteristic
61C23×Dic73—21no—
62C2×#11924016—22no—
63C2×#11924016—22no—
64C2×#11924016C2×C414yes—
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C4×Dic146—22no—
68C4×Dic146—22no—
69#14556556—22no—
70#14556556—22no—
71#14556556—22no—
72#14556556C2×C414yes—
73D4×Dic73—22no—
74D4×Dic73C2×C414yes—
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C4⋊Dic73C2311yescharacteristic
77C2×C4⋊Dic73C2311yescharacteristic
78C2×#11924007—21no—
79C2×#11924007—21no—
80C2×#11924007—21no—
81C2×#11924007—21no—
82C2×#11924007—21no—
83C2×C22⋊Dic73—21no—
84C2×C22⋊Dic73—21no—
85C2×C22⋊Dic73—21no—
86C2×C4×Dic73—21no—
87C2×C4×Dic73—21no—
88C2×C4×Dic73—21no—
89C2×C4×Dic73—21no—
90C2×C4×Dic73—21no—
91C2×C4×Dic73—21no—
92C2×C4×Dic73C2311yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94#14556523—22no—
95#14556522C2×C414yes—
96#14556516—22no—
97#14556516C2×C414yes—
98#14556514—22no—
99#14556512—22no—
100#14556501—22no—
101C8×Dic73C2×C414yes—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498D411yescharacteristic
108#14556498D411yescharacteristic
109#14556498D411yescharacteristic
110#14556498D411yescharacteristic
111C22×D4×C73C2311yescharacteristic
112C22×C8×C73C2311yescharacteristic
113C22×C8×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73—21no—
119C2×C42×C73—21no—
120C2×C42×C73C2311yescharacteristic
121#106×C73—22no—
122#102×C73—22no—
123#102×C73C2×C414yes—
124#95×C73—21no—
125C2×Dic146—21no—
126C2×Dic146—21no—
127C2×Dic146—21no—
128C2×Dic146C22×C412yes—
129C2×Dic146#4112yes—
130C2×Dic146#4112yes—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—24no—
135C22×Dic73—21no—
136C22×Dic73—81no—
137C22×Dic73—81no—
138C22×Dic73C2×D411yescharacteristic
139C22×Dic73C2×D411yescharacteristic
140C22×Dic73C2×D411yescharacteristic
141C22×Dic73C2×D411yescharacteristic
142#11924016—28no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831C22×C412yes—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73C22×C412yes—
154C4⋊Dic73#4112yes—
155#11924007—24no—
156#11924007—24no—
157#11924007—24no—
158#11924007—81no—
159#11924007—81no—
160C22⋊Dic73—24no—
161C22⋊Dic73—81no—
162C22⋊Dic73—81no—
163C4×Dic73—24no—
164C4×Dic73—24no—
165C4×Dic73—21no—
166C4×Dic73—21no—
167C4×Dic73—24no—
168C4×Dic73—81no—
169C4×Dic73—81no—
170C4×Dic73—81no—
171C4×Dic73C22×C412yes—
172C4×Dic73#4112yes—
173C24×C73—21no—
174C2×D4×C73—21no—
175C2×D4×C73—21no—
176C2×D4×C73—21no—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73C22×C412yes—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73C2×D411yescharacteristic
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×C73C22×C412yes—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73C22×C412yes—
197C4⋊C4×C73#4112yes—
198C22⋊C4×C73—81no—
199C22⋊C4×C73—81no—
200C42×C73—21no—
201C42×C73—21no—
202C42×C73—81no—
203C23×C73—22no—
204C23×C73—41no—
205C23×C73—41no—
206C23×C73—41no—
207C23×C73—41no—
208C23×C73—41no—
209C23×C73—41no—
210C23×C73C22×D411yescharacteristic
211D4×C73—22no—
212D4×C73—22no—
213D4×C73—41no—
214D4×C73—41no—
215C2×C4×C73—22no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—22no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
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×C73C23×C411yescharacteristic
231C2×C4×C73C2×#4111yescharacteristic
232C2×C4×C73C2×#4111yescharacteristic
233C2×C4×C73C2×#4111yescharacteristic
234C2×C4×C73C2×#4111yescharacteristic
235C2×C4×C73C2×#4111yescharacteristic
236C2×Dic73—22no—
237C2×Dic73—22no—
238C2×Dic73—22no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—22no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—22no—
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—84no—
259C2×Dic73C4×D412yes—
260C2×Dic73C4×D412yes—
261Dic146—22no—
262Dic146—22no—
263Dic146—22no—
264Dic146#11714yes—
265C8×C73—22no—
266C8×C73—41no—
267#10596831—22no—
268#10596831—41no—
269C22×C73—42no—
270C22×C73—42no—
271C22×C73—42no—
272C22×C73—81no—
273C22×C73—81no—
274C22×C73—81no—
275C22×C73—81no—
276C22×C73C2×C4×D411yescharacteristic
277C22×C73#52511yescharacteristic
278C22×C73#52511yescharacteristic
279C22×C73#57711yescharacteristic
280C22×C73#57711yescharacteristic
281C22×C73#57711yescharacteristic
282C22×C73#57711yescharacteristic
283C4×C73—41no—
284C4×C73—42no—
285C4×C73—41no—
286C4×C73—42no—
287C4×C73—81no—
288C4×C73C2×#11711yescharacteristic
289C4×C73C4×#4111yescharacteristic
290C4×C73#52911yescharacteristic
291C4×C73#52911yescharacteristic
292Dic73—22no—
293Dic73—22no—
294Dic73—24no—
295Dic73—41no—
296Dic73—42no—
297Dic73—41no—
298Dic73—42no—
299Dic73—81no—
300#21131—731nomaximal, Sylow
301C2×C73—82no—
302C2×C73#229011yescharacteristic
303C2×C73#294911yescharacteristic
304C2×C73#295211yescharacteristic
305C2×C73#312511yescharacteristic
306C2×C73#312511yescharacteristic
307C2×C73#312611yescharacteristic
308C2×C73#312611yescharacteristic
309C2×C4×SD16—731no—
310#2319—731no—
311#2276—731no—
312#1926—731no—
313#1926D7311yescharacteristic
314#1920—731no—
315#1920—731no—
316#1880—731no—
317#1880—731no—
318#1865—731no—
319#1865—731no—
320C4×#106—731no—
321#1763—731no—
322#1762—731no—
323#1746—731no—
324C73#2113111yescharacteristic, complemented, Sylow
325C22×SD16—731no—
326C2×C4×Q8—731no—
327C2×C4×Q8—731no—
328C2×C4×Q8—731no—
329C2×C4×D4—731no—
330C4×SD16—738no—
331C2×#106—731no—
332C2×#106—731no—
333C2×#106C2×D7311yescharacteristic
334C2×#103—731no—
335C2×#103—731no—
336C2×#103—731no—
337C2×#102—731no—
338C2×#102C2×D7311yescharacteristic
339C2×#102C2×D7311yescharacteristic
340C2×#97—731no—
341C2×C4×C8—731no—
342#390—731no—
343#390C2×D7311yescharacteristic
344#389—731no—
345#389—731no—
346#388—1461no—
347#388—1461no—
348#381—1461no—
349#380—1461no—
350C4×C4⋊C4—731no—
351C4×C4⋊C4—731no—
352C4×C4⋊C4—731no—
353C4×C4⋊C4—1461no—
354C4×C4⋊C4—1461no—
355C4×C4⋊C4—1461no—
356C4×C4⋊C4C2×D7311yescharacteristic
357#376—731no—
358#376—1461no—
359#340—731no—
360#340—731no—
361#340—731no—
362#340—731no—
363#340—731no—
364#340C2×D7311yescharacteristic
365#336—731no—
366#336—731no—
367#336—731no—
368#336C2×D7311yescharacteristic
369C22×Q8—731no—
370C22×D4C22×D7311yescharacteristic
371C23×C4—1461no—
372C2×SD16—734no—
373C2×SD16—1462no—
374C2×SD16—1462no—
375C22×C8—731no—
376C22×C8—731no—
377C22×C8C22×D7311yescharacteristic
378C22×C8C22×D7311yescharacteristic
379C4×Q8—734no—
380C4×Q8—1462no—
381C4×Q8—1462no—
382C4×Q8—1462no—
383C4×Q8—1462no—
384C4×Q8—1462no—
385C4×D4—734no—
386C4×D4—1462no—
387C2×C4⋊C4—731no—
388C2×C4⋊C4—731no—
389C2×C4⋊C4—731no—
390C2×C4⋊C4—1461no—
391C2×C4⋊C4—1461no—
392C2×C4⋊C4—1461no—
393C2×C4⋊C4—1461no—
394C2×C4⋊C4—1461no—
395C2×C4⋊C4C22×D7311yescharacteristic
396C2×C4⋊C4C22×D7311yescharacteristic
397C2×C4⋊C4C22×D7311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—1461no—
401C2×C22⋊C4—1461no—
402C2×C22⋊C4—1461no—
403C2×C42—21no—
404C2×C42—731no—
405C2×C42—731no—
406C2×C42—1461no—
407C2×C42—1461no—
408C2×C42—1461no—
409C2×C42—1461no—
410C2×C42—1461no—
411C2×C42—1461no—
412C2×C42C22×D7311yescharacteristic
413#106—22no—
414#106—734no—
415#106—1462no—
416#103—734no—
417#103—1462no—
418#103—1462no—
419#102—22no—
420#102—1462no—
421#102C4×D7314yes—
422#97—1462no—
423C4×C8—734no—
424#95—21no—
425#95—731no—
426#95—731no—
427#95—731no—
428#95—731no—
429#95—1461no—
430#95—1461no—
431#95—1461no—
432#95—1461no—
433#95—1461no—
434C24—21no—
435C2×Q8—732no—
436C2×Q8—732no—
437C2×Q8—732no—
438C2×Q8—1461no—
439C2×Q8—1461no—
440C2×Q8—1461no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4C2×C4×D7312yes—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—5841no—
451C22×C4—5841no—
452C22×C4—731no—
453C22×C4—731no—
454C22×C4—731no—
455C22×C4—731no—
456C22×C4—1461no—
457C22×C4—1461no—
458C22×C4—1461no—
459C22×C4—1464no—
460C22×C4—1461no—
461C22×C4D4×D7311yescharacteristic
462C22×C4D4×D7311yescharacteristic
463C22×C4C23×D7311yescharacteristic
464SD16—1468no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—732no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8C2×C4×D7312yes—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—5841no—
482C4⋊C4—5841no—
483C4⋊C4—732no—
484C4⋊C4—732no—
485C4⋊C4—1464no—
486C4⋊C4—1464no—
487C4⋊C4—1464no—
488C4⋊C4—1461no—
489C4⋊C4—1461no—
490C4⋊C4—1461no—
491C4⋊C4—1461no—
492C4⋊C4C2×C4×D7312yes—
493C4⋊C4#1192402712yes—
494C22⋊C4—81no—
495C22⋊C4—81no—
496C22⋊C4—5841no—
497C22⋊C4—5841no—
498C22⋊C4—1464no—
499C42—21no—
500C42—21no—
501C42—81no—
502C42—5841no—
503C42—5841no—
504C42—5841no—
505C42—732no—
506C42—732no—
507C42—1464no—
508C42—1464no—
509C42—1464no—
510C42—1461no—
511C42—1461no—
512C23—22no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23C2×D4×D7311yescharacteristic
520Q8—734no—
521Q8—1462no—
522Q8—1462no—
523Q8—1462no—
524D4—22no—
525D4—22no—
526D4—41no—
527D4—41no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—5844no—
551C2×C4—732no—
552C2×C4—732no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4—1461no—
556C2×C4—1461no—
557C2×C4—1462no—
558C2×C4—1462no—
559C2×C4—1461no—
560C2×C4—1461no—
561C2×C4—1461no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1462no—
566C2×C4—1462no—
567C2×C4—1462no—
568C2×C4C22×C4×D7311yescharacteristic
569C2×C4#41×D7311yescharacteristic
570C2×C4#41×D7311yescharacteristic
571C2×C4#41×D7311yescharacteristic
572C2×C4#41×D7311yescharacteristic
573C2×C4C2×#1192402711yescharacteristic
574C8—22no—
575C8—41no—
576C8—2921no—
577C8—1462no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22C4×D4×D7311yescharacteristic
586C22#1798909511yescharacteristic
587C22#1798909711yescharacteristic
588C22#1798939311yescharacteristic
589C22#1798939411yescharacteristic
590C22#1798939711yescharacteristic
591C22#1798939711yescharacteristic
592C4—42no—
593C4—41no—
594C4—41no—
595C4—42no—
596C4—81no—
597C4—2921no—
598C4—2922no—
599C4—2921no—
600C4—2922no—
601C4—5841no—
602C4—1464no—
603C4—1462no—
604C4—1462no—
605C4#117×D7311yescharacteristic
606C4C4×#1192402711yescharacteristic
607C4#1798911611yescharacteristic
608C4#1798912011yescharacteristic
609C2—82no—
610C2#2261237311yescharacteristic
611C2#2261878511yescharacteristic
612C2#2261881311yescharacteristic
613C2#2262020511yescharacteristic
614C2#2262021111yescharacteristic
615C2#2262021811yescharacteristic
616C2#2262022011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1926C2
socleC23×C73C22×D4
prime radicalC22×D4×C73C23
cosocleC22×C4×C73C24
hypercenter#1926D73
hypocenterC73#21131
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
3. #22612295C2semidirect
5. #22610516C2semidirect
6. #22610514C2semidirect
9. #22610202C2semidirect
10. #22610196C2semidirect
11. #106×Dic73C2semidirect
12. #22609760C2semidirect
14. #22609681C2semidirect
21. #17988678C4semidirect
324. C73#21131semidirect

Maximal subgroups

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

subgroupindex
C2×#179886782
#226125682
#226122952
#226105602
#226105162
#226105142
#226102892
#226102832
#226102022
#226101962
#106×Dic732
#226097602
#226097582
#226096812
C73×#19262
#2113173