Finite Group Databasebeta

← #33137779

Subgroups — #33137779

Order 18688.

756 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988993C211yesmaximal, characteristic, complemented
2C2×#17988887C211yesmaximal, characteristic
3#22613025C211yesmaximal, characteristic, complemented
4#22611413C211yesmaximal, characteristic, complemented
5#22611413C211yesmaximal, characteristic, complemented
6#22611319C211yesmaximal, characteristic
7#22611305C211yesmaximal, characteristic
8#22610884C211yesmaximal, characteristic, complemented
9#22610697C211yesmaximal, characteristic, complemented
10#22610697C211yesmaximal, characteristic, complemented
11#22610655C211yesmaximal, characteristic, complemented
12#22610555C211yesmaximal, characteristic
13#22610548C211yesmaximal, characteristic
14#22609756C211yesmaximal, characteristic
15C73×#2563C211yesmaximal, characteristic
16C2×#14556583C2211yescharacteristic
17#17988993—24no—
18#17988887—24no—
19C2×#14556524C2211yescharacteristic
20C2×#14556524C2211yescharacteristic
21C2×#14556524C2211yescharacteristic
22C2×#14556522C2211yescharacteristic
23C2×#14556522C2211yescharacteristic
24C2×#14556522C2211yescharacteristic
25C2×C4⋊#10596831C2211yescharacteristic
26C2×C4⋊#10596831C2211yescharacteristic
27C2×C4⋊#10596831C2211yescharacteristic
28C2×#14556512C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556512C2211yescharacteristic
32C2×#14556502C2211yescharacteristic
33#17988485C2211yescharacteristic
34#17988485C2211yescharacteristic
35#17988482—21no—
36#17988469—21no—
37#17988468—21no—
38C4×C4⋊Dic73C2211yescharacteristic
39C4×C4⋊Dic73C2211yescharacteristic
40C4×C4⋊Dic73C2211yescharacteristic
41#17988438—21no—
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988342C2211yescharacteristic
49#17988342C2211yescharacteristic
50C2×C4⋊Q8×C73C2211yescharacteristic
51C2×C4×D4×C73C2211yescharacteristic
52#393×C73—21no—
53#393×C73—21no—
54#390×C73C2211yescharacteristic
55#390×C73C2211yescharacteristic
56#382×C73C2211yescharacteristic
57#382×C73C2211yescharacteristic
58#380×C73—21no—
59#380×C73—21no—
60C4×C4⋊C4×C73C2211yescharacteristic
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65#14556583—22no—
66#14556583D414yes—
67C2×C4⋊Dic73C2311yescharacteristic
68C2×C4⋊Dic73C2311yescharacteristic
69C2×C4⋊Dic73C2311yescharacteristic
70C2×C4⋊Dic73C2311yescharacteristic
71C2×#11924007—21no—
72C2×#11924007—21no—
73C2×#11924007—21no—
74C2×#11924007—21no—
75C2×C4×Dic73—21no—
76C2×C4×Dic73—21no—
77C2×C4×Dic73—21no—
78#14556524—22no—
79#14556524—22no—
80#14556524—22no—
81#14556522—22no—
82#14556522—22no—
83#14556522—22no—
84C4⋊#10596831—22no—
85C4⋊#10596831—22no—
86C4⋊#10596831—22no—
87#14556512—22no—
88#14556512—22no—
89#14556512—22no—
90#14556512Q814yescomplemented
91#14556502—22no—
92#14556498—21no—
93#14556498—21no—
94#14556498—21no—
95#14556498—21no—
96#14556498—21no—
97C22×Q8×C73—21no—
98C22×D4×C73C2311yescharacteristic
99C23×C4×C73—21no—
100C4⋊Q8×C73—22no—
101C4⋊Q8×C73—22no—
102C4×D4×C73—22no—
103C4×D4×C73—22no—
104C2×C4⋊C4×C73—21no—
105C2×C4⋊C4×C73D411yescharacteristic
106C2×C4⋊C4×C73D411yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73C2311yescharacteristic
109C2×C4⋊C4×C73C2311yescharacteristic
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73—21no—
113C2×C22⋊C4×C73—21no—
114C2×C22⋊C4×C73—21no—
115C2×C42×C73C2311yescharacteristic
116C2×C42×C73C2311yescharacteristic
117C2×C42×C73C2311yescharacteristic
118#95×C73—21no—
119#95×C73—21no—
120#95×C73—21no—
121#95×C73—21no—
122#95×C73D411yescharacteristic
123#95×C73D411yescharacteristic
124C22×Dic73—21no—
125C22×Dic73—21no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C2×#10596831—21no—
129C2×#10596831—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×#10596831C2×Q812yes—
139C2×#10596831#4112yes—
140C4⋊Dic73—21no—
141C4⋊Dic73—21no—
142C4⋊Dic73—21no—
143C4⋊Dic73—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73C2×D412yes—
146C4⋊Dic73C2×D412yes—
147C4⋊Dic73C2×Q812yes—
148#11924007—24no—
149#11924007—24no—
150#11924007—42no—
151#11924007—81no—
152C4×Dic73—42no—
153C4×Dic73—81no—
154C4×Dic73—81no—
155C24×C73—21no—
156C2×Q8×C73—42no—
157C2×Q8×C73—81no—
158C2×Q8×C73—81no—
159C2×D4×C73—21no—
160C2×D4×C73—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×C73—21no—
164C2×D4×C73C2×Q812yes—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—42no—
169C22×C4×C73—42no—
170C22×C4×C73—42no—
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2411yescharacteristic
178C4⋊C4×C73—21no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—41no—
185C4⋊C4×C73—41no—
186C4⋊C4×C73—42no—
187C22⋊C4×C73—42no—
188C22⋊C4×C73—81no—
189C22⋊C4×C73—81no—
190C22⋊C4×C73—81no—
191C22⋊C4×C73—81no—
192C42×C73—21no—
193C42×C73—21no—
194C42×C73—21no—
195C42×C73—21no—
196C42×C73C2×D412yes—
197C42×C73#4112yes—
198C23×C73—22no—
199C23×C73—41no—
200C23×C73—41no—
201C23×C73—41no—
202C23×C73—41no—
203C23×C73—41no—
204C23×C73—41no—
205C23×C73C22×D411yescharacteristic
206Q8×C73—84no—
207D4×C73—22no—
208D4×C73—22no—
209D4×C73—41no—
210D4×C73—41no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
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—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
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×C73—84no—
237C2×C4×C73#12112yes—
238C2×C4×C73#12112yes—
239C2×C4×C73C22×D411yescharacteristic
240C2×C4×C73C22×Q811yescharacteristic
241C2×C4×C73C2×#4111yescharacteristic
242C2×C4×C73C2×#4111yescharacteristic
243C2×C4×C732−1+411yescharacteristic
244C2×C4×C732−1+411yescharacteristic
245C2×Dic73—22no—
246C2×Dic73—22no—
247C2×Dic73—22no—
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—
257#10596831—22no—
258#10596831—22no—
259#10596831—41no—
260#10596831—41no—
261C22×C73—42no—
262C22×C73—42no—
263C22×C73—42no—
264C22×C73—81no—
265C22×C73—81no—
266C22×C73—81no—
267C22×C73—81no—
268C22×C73C2×#12111yescharacteristic
269C22×C73#54711yescharacteristic
270C22×C73D4×Q811yescharacteristic
271C22×C73#57511yescharacteristic
272C22×C73#57511yescharacteristic
273C22×C73#57611yescharacteristic
274C22×C73#57711yescharacteristic
275C4×C73—22no—
276C4×C73—22no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73—81no—
282C4×C73—81no—
283C4×C73—81no—
284C4×C73#53311yescharacteristic
285C4×C73#54111yescharacteristic
286C4×C73#54811yescharacteristic
287C4×C73D4×Q811yescharacteristic
288Dic73—42no—
289Dic73—42no—
290Dic73—42no—
291Dic73—81no—
292#25466—731nomaximal, Sylow
293C2×C73—82no—
294C2×C73#242911yescharacteristic
295C2×C73#304011yescharacteristic
296C2×C73#304511yescharacteristic
297C2×C73#334711yescharacteristic
298C2×C73#334811yescharacteristic
299C2×C73#338811yescharacteristic
300C2×C73#338911yescharacteristic
301C2×#501—731no—
302C2×#478—731no—
303#2563D7311yescharacteristic
304#2370—731no—
305#2085—731no—
306#2085—731no—
307#2067—731no—
308#2065—731no—
309#1988—731no—
310#1949—731no—
311#1949—731no—
312#1940—731no—
313#1926—731no—
314#1925—731no—
315#1762—731no—
316C73#2546611yescharacteristic, complemented, Sylow
317C2×C4⋊Q8C2×D7311yescharacteristic
318C2×#125—731no—
319C2×C4×D4C2×D7311yescharacteristic
320#501—1464no—
321#478—1464no—
322C2×#107—731no—
323C2×#107—731no—
324C2×#107—731no—
325C2×#106—731no—
326C2×#106—731no—
327C2×#106—731no—
328C2×C4⋊C8—731no—
329C2×C4⋊C8—731no—
330C2×C4⋊C8—731no—
331C2×#102—731no—
332C2×#102—731no—
333C2×#102—731no—
334C2×#102—731no—
335C2×#97—731no—
336#393—21no—
337#393—21no—
338#390C2×D7311yescharacteristic
339#390C2×D7311yescharacteristic
340#389—731no—
341#389—731no—
342#389—1461no—
343#387—1461no—
344#387—1461no—
345#382C2×D7311yescharacteristic
346#382C2×D7311yescharacteristic
347#380—21no—
348#380—21no—
349C4×C4⋊C4—731no—
350C4×C4⋊C4—731no—
351C4×C4⋊C4—731no—
352C4×C4⋊C4—1461no—
353C4×C4⋊C4C2×D7311yescharacteristic
354#340—731no—
355#340—731no—
356#340—731no—
357#340—731no—
358#340—731no—
359#340—731no—
360#336—731no—
361#336—731no—
362C22×Q8—21no—
363C22×D4C22×D7311yescharacteristic
364C23×C4—21no—
365C22×C8—731no—
366C22×C8—731no—
367C22×C8—731no—
368C22×C8—731no—
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371#125—734no—
372#125—1462no—
373C4×D4—22no—
374C4×D4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—731no—
377C2×C4⋊C4—731no—
378C2×C4⋊C4—731no—
379C2×C4⋊C4—731no—
380C2×C4⋊C4—1461no—
381C2×C4⋊C4—1461no—
382C2×C4⋊C4—1461no—
383C2×C4⋊C4—1461no—
384C2×C4⋊C4C22⋊D7311yescharacteristic
385C2×C4⋊C4C22⋊D7311yescharacteristic
386C2×C4⋊C4C22×D7311yescharacteristic
387C2×C4⋊C4C22×D7311yescharacteristic
388C2×C4⋊C4C22×D7311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—1461no—
395C2×C42—1461no—
396C2×C42—1461no—
397C2×C42C22×D7311yescharacteristic
398C2×C42C22×D7311yescharacteristic
399C2×C42C22×D7311yescharacteristic
400#107—1462no—
401#107—1462no—
402#107—1462no—
403#106—1462no—
404#106—1462no—
405#106—1462no—
406C4⋊C8—1462no—
407C4⋊C8—1462no—
408C4⋊C8—1462no—
409#102—734no—
410#102—1462no—
411#102—1462no—
412#102—1462no—
413#97—1462no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—1461no—
419#95—1461no—
420#95—1461no—
421#95—1461no—
422#95—1461no—
423#95C22⋊D7311yescharacteristic
424#95C22⋊D7311yescharacteristic
425C24—21no—
426C2×Q8—42no—
427C2×Q8—81no—
428C2×Q8—81no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4Q8×D7312yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—1461no—
442C22×C4—1461no—
443C22×C4—1461no—
444C22×C4—1461no—
445C22×C4C2×C22⋊D7311yescharacteristic
446C22×C4C2×C22⋊D7311yescharacteristic
447C22×C4C2×C22⋊D7311yescharacteristic
448C22×C4C2×C22⋊D7311yescharacteristic
449C22×C4C2×C22⋊D7311yescharacteristic
450C22×C4C2×C22⋊D7311yescharacteristic
451C22×C4C23×D7311yescharacteristic
452C2×C8—732no—
453C2×C8—732no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8—1461no—
460C2×C8—1461no—
461C2×C8—1461no—
462C2×C8—1461no—
463C2×C8—1461no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—42no—
473C4⋊C4—2922no—
474C4⋊C4—5841no—
475C4⋊C4—732no—
476C4⋊C4—732no—
477C4⋊C4—732no—
478C4⋊C4—1461no—
479C4⋊C4—1461no—
480C4⋊C4—1464no—
481C4⋊C4—1464no—
482C4⋊C4—1461no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C22⋊C4—42no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C22⋊C4—81no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—2922no—
495C42—5841no—
496C42—5841no—
497C42D4×D7312yes—
498C42#1192402712yes—
499C23—22no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23C22×C22⋊D7311yescharacteristic
507Q8—84no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
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—84no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—2921no—
547C2×C4—1462no—
548C2×C4—1462no—
549C2×C4—1462no—
550C2×C4#1455656212yes—
551C2×C4#1455656212yes—
552C2×C4C2×D4×D7311yescharacteristic
553C2×C4C2×Q8×D7311yescharacteristic
554C2×C4#41×D7311yescharacteristic
555C2×C4C2×#1192402711yescharacteristic
556C2×C4#1455663811yescharacteristic
557C2×C4#1455663911yescharacteristic
558C8—2921no—
559C8—2921no—
560C8—1462no—
561C8—1462no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22C2×#1455656211yescharacteristic
570C22#1798923611yescharacteristic
571C22Q8×C22⋊D7311yescharacteristic
572C22#1798938511yescharacteristic
573C22#1798938511yescharacteristic
574C22#1798939011yescharacteristic
575C22#1798939811yescharacteristic
576C4—22no—
577C4—22no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—2922no—
586C4—2922no—
587C4—2922no—
588C4—5841no—
589C4#1798913911yescharacteristic
590C4#1798919711yescharacteristic
591C4#1798924711yescharacteristic
592C4#1798925011yescharacteristic
593C2—82no—
594C2#2261352611yescharacteristic
595C2#2261942111yescharacteristic
596C2#2261946611yescharacteristic
597C2#2262243111yescharacteristic
598C2#2262244611yescharacteristic
599C2#2262287611yescharacteristic
600C2#2262288511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2563C2
socleC23×C73C22×D4
prime radicalC22×D4×C73C23
hypercenter#2563D73
hypocenterC73#25466
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2563

Complements

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

NH ≅ G/Ntype
1. C2×#17988993C2semidirect
3. #22613025C2semidirect
4. #22611413C2semidirect
5. #22611413C2semidirect
8. #22610884C2semidirect
9. #22610697C2semidirect
10. #22610697C2semidirect
11. #22610655C2semidirect
90. #14556512Q8semidirect
316. C73#25466semidirect

Maximal subgroups

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

subgroupindex
C2×#179889932
C2×#179888872
#226130252
#226114132
#226113192
#226113052
#226108842
#226106972
#226106552
#226105552
#226105482
#226097562
C73×#25632
#2546673