Finite Group Databasebeta

← #33127366

Subgroups — #33127366

Order 18688.

738 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988894C211yesmaximal, characteristic, complemented
2C2×#17988648C211yesmaximal, characteristic
3#22615761C211yesmaximal, characteristic
4#22611368C211yesmaximal, characteristic
5#22611357C211yesmaximal, characteristic
6#22611131C211yesmaximal, characteristic
7#22611131C211yesmaximal, characteristic
8#22610888C211yesmaximal, characteristic, complemented
9#22610689C211yesmaximal, characteristic, complemented
10#22610666C211yesmaximal, characteristic, complemented
11#22610661C211yesmaximal, characteristic, complemented
12#22610624C211yesmaximal, characteristic, complemented
13#22610610C211yesmaximal, characteristic, complemented
14#22609936C211yesmaximal, characteristic, complemented
15C73×#2323C211yesmaximal, characteristic
16C2×#14556583C2211yescharacteristic
17#17988894—24no—
18#17988648—24no—
19C2×#14556524C2211yescharacteristic
20C2×#14556524C2211yescharacteristic
21C2×#14556524C2211yescharacteristic
22C2×#14556522C2211yescharacteristic
23C2×C4⋊#10596831C2211yescharacteristic
24C2×C4⋊#10596831C2211yescharacteristic
25C2×#14556515C2211yescharacteristic
26C2×#14556515C2211yescharacteristic
27C2×#14556515C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×C22⋊#10596831C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×#14556502C2211yescharacteristic
32C2×C4×#10596831C2211yescharacteristic
33#17988520—21no—
34#17988520—21no—
35#17988510—21no—
36#17988510—21no—
37#17988485C2211yescharacteristic
38#17988485C2211yescharacteristic
39#17988457C2211yescharacteristic
40#17988447C2211yescharacteristic
41#17988447C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50C2×C22⋊Q8×C73C2211yescharacteristic
51C2×C4×Q8×C73C2211yescharacteristic
52C2×#117×C73C2211yescharacteristic
53#391×C73C2211yescharacteristic
54#389×C73—21no—
55#389×C73C2211yescharacteristic
56#388×C73—21no—
57#388×C73—21no—
58#387×C73—21no—
59#380×C73C2211yescharacteristic
60C4×C4⋊C4×C73C2211yescharacteristic
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65#14556583—22no—
66#14556583—22no—
67C2×C4⋊Dic73—21no—
68C2×C4⋊Dic73—21no—
69C2×C4⋊Dic73C2311yescharacteristic
70C2×C4⋊Dic73C2311yescharacteristic
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×#11924007—21no—
74C2×#11924007—21no—
75C2×#11924007—21no—
76C2×#11924007—21no—
77C2×C22⋊Dic73—21no—
78C2×C22⋊Dic73—21no—
79#14556524—22no—
80#14556524—22no—
81#14556524—22no—
82#14556522—22no—
83C4⋊#10596831—22no—
84C4⋊#10596831D414yes—
85#14556515—22no—
86#14556515—22no—
87#14556515—22no—
88#14556515—22no—
89C22⋊#10596831—22no—
90C22⋊#10596831—22no—
91#14556502—22no—
92C4×#10596831—22no—
93#14556498—21no—
94#14556498—21no—
95#14556498—21no—
96#14556498—21no—
97C22×Q8×C73C2311yescharacteristic
98C23×C4×C73C2311yescharacteristic
99C22⋊Q8×C73—22no—
100C22⋊Q8×C73—22no—
101C4×Q8×C73—22no—
102C4×Q8×C73—22no—
103#117×C73—22no—
104#117×C73—22no—
105C2×C4⋊C4×C73—21no—
106C2×C4⋊C4×C73—21no—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73D411yescharacteristic
109C2×C4⋊C4×C73D411yescharacteristic
110C2×C4⋊C4×C73C2311yescharacteristic
111C2×C4⋊C4×C73C2311yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C22⋊C4×C73—21no—
114C2×C22⋊C4×C73—21no—
115C2×C22⋊C4×C73D411yescharacteristic
116C2×C22⋊C4×C73D411yescharacteristic
117C2×C42×C73—21no—
118C2×C42×C73—21no—
119C2×C42×C73C2311yescharacteristic
120C2×C42×C73C2311yescharacteristic
121#95×C73—21no—
122#95×C73—21no—
123#95×C73—21no—
124#95×C73—21no—
125#95×C73—21no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C2×#10596831—21no—
131C2×#10596831—21no—
132C2×#10596831—21no—
133C2×#10596831—21no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831C2×D412yes—
141C2×#10596831C2×D412yes—
142C4⋊Dic73—21no—
143C4⋊Dic73—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—81no—
151C4⋊Dic73—81no—
152#11924007—42no—
153#11924007—42no—
154#11924007—81no—
155#11924007—81no—
156C22⋊Dic73—81no—
157C22⋊Dic73—81no—
158C24×C73C2×D411yescharacteristic
159C2×Q8×C73—21no—
160C2×Q8×C73—21no—
161C2×Q8×C73—21no—
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73#4112yes—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2411yescharacteristic
181C4⋊C4×C73—24no—
182C4⋊C4×C73—22no—
183C4⋊C4×C73—22no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—42no—
190C4⋊C4×C73—81no—
191C4⋊C4×C73#4112yes—
192C22⋊C4×C73—24no—
193C22⋊C4×C73—22no—
194C22⋊C4×C73—22no—
195C22⋊C4×C73—81no—
196C42×C73—21no—
197C42×C73—21no—
198C42×C73—42no—
199C42×C73—81no—
200C42×C73C2×D412yes—
201C42×C73#4112yes—
202C23×C73—21no—
203C23×C73—21no—
204C23×C73—21no—
205C23×C73—21no—
206C23×C73—21no—
207C23×C73—21no—
208C23×C73—21no—
209C23×C73C22×D411yescharacteristic
210Q8×C73—22no—
211Q8×C73—22no—
212Q8×C73—41no—
213Q8×C73—41no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—22no—
222C2×C4×C73—22no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
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—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73#12112yes—
244C2×C4×C73#12112yes—
245C2×C4×C73C22×D411yescharacteristic
246C2×C4×C73C2×#4111yescharacteristic
247C2×C4×C73C2×#4111yescharacteristic
248C2×C4×C73C2×#4111yescharacteristic
249C2×C4×C732−1+411yescharacteristic
250C2×C4×C732−1+411yescharacteristic
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—41no—
262C2×Dic73—41no—
263#10596831—22no—
264#10596831—22no—
265#10596831—41no—
266#10596831—41no—
267C22×C73—41no—
268C22×C73—41no—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73C2×#12111yescharacteristic
275C22×C73#52511yescharacteristic
276C22×C73#53611yescharacteristic
277C22×C73#57611yescharacteristic
278C22×C73#57711yescharacteristic
279C22×C73#57811yescharacteristic
280C22×C73#57811yescharacteristic
281C4×C73—22no—
282C4×C73—22no—
283C4×C73—42no—
284C4×C73—41no—
285C4×C73—42no—
286C4×C73—41no—
287C4×C73—41no—
288C4×C73—81no—
289C4×C73—81no—
290C4×C73#54711yescharacteristic
291C4×C73#54811yescharacteristic
292C4×C73#55211yescharacteristic
293C4×C73#55611yescharacteristic
294Dic73—81no—
295Dic73—81no—
296Dic73—81no—
297Dic73—81no—
298#24715—731nomaximal, Sylow
299C2×C73—81no—
300C2×C73#241511yescharacteristic
301C2×C73#306111yescharacteristic
302C2×C73#306311yescharacteristic
303C2×C73#311911yescharacteristic
304C2×C73#312711yescharacteristic
305C2×C73#324211yescharacteristic
306C2×C73#324311yescharacteristic
307C2×#479—731no—
308C2×#433—731no—
309#2629—731no—
310#2323D7311yescharacteristic
311#2077—731no—
312#2075—731no—
313#2036—731no—
314#2036—731no—
315#1989—731no—
316#1947—731no—
317#1943—731no—
318#1942—731no—
319#1935—731no—
320#1933—731no—
321#1803—731no—
322C73#2471511yescharacteristic, complemented, Sylow
323C2×#125—731no—
324C2×C22⋊Q8C2×D7311yescharacteristic
325C2×C4×Q8C2×D7311yescharacteristic
326C2×#117C2×D7311yescharacteristic
327#479—1464no—
328#433—1464no—
329C2×#107—731no—
330C2×#107—731no—
331C2×#107—731no—
332C2×#106—731no—
333C2×C4⋊C8—731no—
334C2×C4⋊C8—731no—
335C2×#103—731no—
336C2×#103—731no—
337C2×#103—731no—
338C2×#103—731no—
339C2×C22⋊C8—731no—
340C2×C22⋊C8—731no—
341C2×#97—731no—
342C2×C4×C8—731no—
343#398—1461no—
344#398—1461no—
345#396—1461no—
346#396—1461no—
347#391C2×D7311yescharacteristic
348#389—21no—
349#389—731no—
350#389—731no—
351#389C2×D7311yescharacteristic
352#388—21no—
353#388—21no—
354#387—21no—
355#384—731no—
356#380—731no—
357#380—731no—
358#380C2×D7311yescharacteristic
359C4×C4⋊C4C2×D7311yescharacteristic
360#340—731no—
361#340—731no—
362#340—731no—
363#340—731no—
364#340—731no—
365#340—731no—
366#340—731no—
367#340—731no—
368C22×Q8C22×D7311yescharacteristic
369C23×C4C22×D7311yescharacteristic
370C22×C8—731no—
371C22×C8—731no—
372C22×C8—731no—
373C22×C8—731no—
374#125—1462no—
375#125—1462no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C4×Q8—22no—
379C4×Q8—22no—
380#117—22no—
381#117—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—731no—
386C2×C4⋊C4—731no—
387C2×C4⋊C4—731no—
388C2×C4⋊C4—731no—
389C2×C4⋊C4—1461no—
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×C4⋊C4C22×D7311yescharacteristic
399C2×C4⋊C4C22×D7311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—1461no—
403C2×C22⋊C4—1461no—
404C2×C22⋊C4C22⋊D7311yescharacteristic
405C2×C22⋊C4C22⋊D7311yescharacteristic
406C2×C42—21no—
407C2×C42—21no—
408C2×C42C22×D7311yescharacteristic
409C2×C42C22×D7311yescharacteristic
410#107—1462no—
411#107—1462no—
412#107—1462no—
413#106—1462no—
414C4⋊C8—734no—
415C4⋊C8—1462no—
416#103—1462no—
417#103—1462no—
418#103—1462no—
419#103—1462no—
420C22⋊C8—1462no—
421C22⋊C8—1462no—
422#97—1462no—
423C4×C8—1462no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—1461no—
430#95—1461no—
431#95—1461no—
432#95—1461no—
433C24C2×C22⋊D7311yescharacteristic
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8#1192402812yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—1461no—
451C22×C4—1461no—
452C22×C4—1461no—
453C22×C4—1461no—
454C22×C4C2×C22⋊D7311yescharacteristic
455C22×C4C2×C22⋊D7311yescharacteristic
456C22×C4C2×C22⋊D7311yescharacteristic
457C22×C4C2×C22⋊D7311yescharacteristic
458C22×C4C2×C22⋊D7311yescharacteristic
459C22×C4C23×D7311yescharacteristic
460C2×C8—732no—
461C2×C8—732no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1461no—
472C4⋊C4—24no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—81no—
482C4⋊C4—2922no—
483C4⋊C4—2922no—
484C4⋊C4—5841no—
485C4⋊C4—5841no—
486C4⋊C4—5841no—
487C4⋊C4—5841no—
488C4⋊C4—1461no—
489C4⋊C4—1461no—
490C4⋊C4—1461no—
491C4⋊C4—1461no—
492C4⋊C4—1461no—
493C4⋊C4—1461no—
494C4⋊C4—1461no—
495C4⋊C4—1461no—
496C4⋊C4#1192402812yes—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—81no—
501C22⋊C4—5841no—
502C22⋊C4—5841no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—81no—
507C42D4×D7312yes—
508C42#1192402712yes—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23C22×C22⋊D7311yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
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—2921no—
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—2921no—
562C2×C4#1455656312yes—
563C2×C4#1455656312yes—
564C2×C4C2×D4×D7311yescharacteristic
565C2×C4C2×#1192402711yescharacteristic
566C2×C4C2×#1192402811yescharacteristic
567C2×C4C2×#1192402811yescharacteristic
568C2×C4#1455663811yescharacteristic
569C2×C4#1455663811yescharacteristic
570C8—2921no—
571C8—2921no—
572C8—1462no—
573C8—1462no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22C2×#1455656311yescharacteristic
582C22#1798909811yescharacteristic
583C22#1798915811yescharacteristic
584C22#1798939011yescharacteristic
585C22#1798939511yescharacteristic
586C22#1798940211yescharacteristic
587C22#1798940211yescharacteristic
588C4—22no—
589C4—22no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—41no—
594C4—42no—
595C4—81no—
596C4—81no—
597C4—5841no—
598C4—5841no—
599C4—5841no—
600C4—5841no—
601C4#1798924211yescharacteristic
602C4#1798924611yescharacteristic
603C4#1798927711yescharacteristic
604C4#1798930711yescharacteristic
605C2—81no—
606C2#2261336011yescharacteristic
607C2#2261959811yescharacteristic
608C2#2261961811yescharacteristic
609C2#2262013011yescharacteristic
610C2#2262023111yescharacteristic
611C2#2262119311yescharacteristic
612C2#2262120811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2323C2
socleC23×C73C22×D4
prime radicalC24×C73C2×D4
hypercenter#2323D73
hypocenterC73#24715
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
1. C2×#17988894C2semidirect
8. #22610888C2semidirect
9. #22610689C2semidirect
10. #22610666C2semidirect
11. #22610661C2semidirect
12. #22610624C2semidirect
13. #22610610C2semidirect
14. #22609936C2semidirect
322. C73#24715semidirect

Maximal subgroups

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

subgroupindex
C2×#179888942
C2×#179886482
#226157612
#226113682
#226113572
#226111312
#226108882
#226106892
#226106662
#226106612
#226106242
#226106102
#226099362
C73×#23232
#2471573