Finite Group Databasebeta

← #34026932

Subgroups — #34026932

Order 18688.

1116 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989618C212yesmaximal
2C2×#17989590C211yesmaximal, characteristic, complemented
3C22×C4⋊#10596833C211yesmaximal, characteristic, complemented
4#22626033C212yesmaximal, complemented
5#22625878C212yesmaximal, complemented
6#22625875C212yesmaximal, complemented
7#22625864C211yesmaximal, characteristic, complemented
8#22625785C211yesmaximal, characteristic, complemented
9#22625785C211yesmaximal, characteristic, complemented
10#22625717C211yesmaximal, characteristic, complemented
11C4×D4×Dic73C211yesmaximal, characteristic
12C22×#11924037C2212yes—
13C23×#10596833C2212yes—
14#17989618—28no—
15#17989590—24no—
16C2×#14556658C2212yes—
17C2×#14556658C2212yes—
18C2×#14556658C2212yes—
19C2×C4⋊#10596833—24no—
20C2×C4⋊#10596833C2211yescharacteristic
21C2×C4⋊#10596833C2212yes—
22C2×C4⋊#10596833C2211yescharacteristic
23C2×C4⋊#10596833C2211yescharacteristic
24C2×C4⋊#10596833C2211yescharacteristic
25C2×C22⋊#10596833C2212yes—
26C2×C22⋊#10596833C2212yes—
27C2×#14556646C2212yes—
28#17989453C2212yes—
29#17989453C2212yes—
30#17989453C2212yes—
31C2×D4×Dic73C411yescharacteristic
32C2×D4×Dic73C2211yescharacteristic
33C22×C4×Dic73C2211yescharacteristic
34C22×C4×Dic73C2211yescharacteristic
35C4⋊C4×Dic73C411yescharacteristic
36C4⋊C4×Dic73C2211yescharacteristic
37C4×C4⋊Dic73C411yescharacteristic
38C22⋊C4×Dic73C411yescharacteristic
39C22⋊C4×Dic73C411yescharacteristic
40C22⋊C4×Dic73C2211yescharacteristic
41C22⋊C4×Dic73C2211yescharacteristic
42C4×C22⋊Dic73C411yescharacteristic
43C4×C22⋊Dic73C411yescharacteristic
44C42×Dic73C2211yescharacteristic
45C2×C4×D4×C73C411yescharacteristic
46C2×#11924037—24no—
47C2×#11924037—24no—
48C2×#11924037—42no—
49C22×#10596833—24no—
50C22×#10596833—24no—
51C22×#10596833—42no—
52C22×#10596833C2312yes—
53C22×#10596833C2312yes—
54C22×#10596833C2312yes—
55C22×#10596833C2312yes—
56#14556658—24no—
57#14556658—24no—
58#14556658—42no—
59C4⋊#10596833—24no—
60C4⋊#10596833—22no—
61C4⋊#10596833—22no—
62C4⋊#10596833—22no—
63C4⋊#10596833D414yescomplemented
64C22⋊#10596833—24no—
65C22⋊#10596833—24no—
66#14556646—24no—
67C23×Dic73C2×C411yescharacteristic
68C23×Dic73C2×C411yescharacteristic
69C23×Dic73C2311yescharacteristic
70C23×Dic73C2311yescharacteristic
71D4×Dic73—24no—
72D4×Dic73D414yes—
73D4×Dic73Q814yes—
74C2×C4⋊Dic73C2×C411yescharacteristic
75C2×C4⋊Dic73C2×C411yescharacteristic
76C2×C22⋊Dic73C2×C411yescharacteristic
77C2×C22⋊Dic73C2×C411yescharacteristic
78C2×C22⋊Dic73C2×C411yescharacteristic
79C2×C22⋊Dic73C2×C411yescharacteristic
80C2×C4×Dic73—22no—
81C2×C4×Dic73—22no—
82C2×C4×Dic73—22no—
83C2×C4×Dic73—22no—
84C2×C4×Dic73C2×C411yescharacteristic
85C2×C4×Dic73C2×C411yescharacteristic
86C2×C4×Dic73C2×C411yescharacteristic
87C2×C4×Dic73C2×C411yescharacteristic
88C2×C4×Dic73C2×C411yescharacteristic
89C2×C4×Dic73C2×C411yescharacteristic
90C2×C4×Dic73C2×C411yescharacteristic
91C2×C4×Dic73C2311yescharacteristic
92C2×C4×Dic73C2311yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96#14556498C2×C411yescharacteristic
97#14556498C2×C411yescharacteristic
98#14556498C2×C411yescharacteristic
99#14556498C2×C411yescharacteristic
100#14556498C2×C411yescharacteristic
101#14556498C2×C411yescharacteristic
102C22×D4×C73C2×C411yescharacteristic
103C23×C4×C73C2×C411yescharacteristic
104C23×C4×C73C2×C411yescharacteristic
105C4×D4×C73—24no—
106C2×C4⋊C4×C73C2×C411yescharacteristic
107C2×C22⋊C4×C73C2×C411yescharacteristic
108C2×C22⋊C4×C73C2×C411yescharacteristic
109C2×C42×C73C2×C411yescharacteristic
110#11924037—48no—
111C2×#10596833—22no—
112C2×#10596833—22no—
113C2×#10596833—22no—
114C2×#10596833—22no—
115C2×#10596833—22no—
116C2×#10596833—22no—
117C2×#10596833—22no—
118C2×#10596833—22no—
119C2×#10596833—22no—
120C2×#10596833—22no—
121C2×#10596833—22no—
122C2×#10596833—48no—
123C2×#10596833C2×D414yes—
124C22×Dic73—21no—
125C22×Dic73—21no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—22no—
133C22×Dic73—22no—
134C22×Dic73—22no—
135C22×Dic73—22no—
136C22×Dic73—41no—
137C22×Dic73—41no—
138C22×Dic73C22×C411yescharacteristic
139C22×Dic73C22×C411yescharacteristic
140C22×Dic73C22×C411yescharacteristic
141C22×Dic73C22×C411yescharacteristic
142C22×Dic73C22×C411yescharacteristic
143C22×Dic73C22×C411yescharacteristic
144C22×Dic73C22×C411yescharacteristic
145C22×Dic73C2×D412yes—
146C22×Dic73C2×D412yes—
147C22×Dic73C2×Q812yes—
148C22×Dic73C2×Q812yes—
149C22×Dic73C2411yescharacteristic
150C4⋊Dic73—22no—
151C4⋊Dic73C4⋊C414yes—
152C22⋊Dic73—22no—
153C22⋊Dic73C4⋊C414yes—
154C22⋊Dic73C4⋊C414yes—
155C22⋊Dic73M1614yescomplemented
156C4×Dic73—22no—
157C4×Dic73—22no—
158C4×Dic73—22no—
159C4×Dic73—22no—
160C4×Dic73—22no—
161C4×Dic73—22no—
162C4×Dic73—21no—
163C4×Dic73—21no—
164C4×Dic73—21no—
165C4×Dic73—21no—
166C4×Dic73—21no—
167C4×Dic73—21no—
168C4×Dic73—41no—
169C4×Dic73C2×D412yes—
170C4×Dic73C2×D412yes—
171C4×Dic73C2×Q812yes—
172C4×Dic73#4112yes—
173C24×C73C22×C411yescharacteristic
174C24×C73C22×C411yescharacteristic
175C2×D4×C73—22no—
176C2×D4×C73—22no—
177C2×D4×C73C4⋊C414yes—
178C22×C4×C73—22no—
179C22×C4×C73—22no—
180C22×C4×C73—22no—
181C22×C4×C73—22no—
182C22×C4×C73—22no—
183C22×C4×C73M1614yescomplemented
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C22×C411yescharacteristic
189C4⋊C4×C73—22no—
190C22⋊C4×C73—22no—
191C22⋊C4×C73—22no—
192C42×C73—22no—
193C23×C73—21no—
194C23×C73—21no—
195C23×C73—21no—
196C23×C73—21no—
197C23×C73—21no—
198C23×C73—21no—
199C23×C73—21no—
200C23×C73—21no—
201C23×C73—21no—
202C23×C73—21no—
203C23×C73C2×C4⋊C412yes—
204C23×C73C2×C4⋊C412yes—
205C23×C73C2×M1612yes—
206C23×C73C2×M1612yes—
207C23×C73C23×C411yescharacteristic
208D4×C73—28no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—28no—
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—44no—
221C2×C4×C73C2×C4⋊C412yes—
222C2×C4×C73C4×D412yes—
223C2×C4×C73C2×M1612yes—
224C2×C4×C73C2×M1612yes—
225C2×C4×C73#13112yes—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—22no—
239C2×Dic73—22no—
240C2×Dic73—22no—
241C2×Dic73—22no—
242C2×Dic73—22no—
243C2×Dic73—22no—
244C2×Dic73—22no—
245C2×Dic73—22no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—44no—
250C2×Dic73—44no—
251C2×Dic73C2×C4⋊C412yes—
252C2×Dic73C2×C4⋊C412yes—
253C2×Dic73C2×C4⋊C412yes—
254C2×Dic73C4×D412yes—
255C2×Dic73C2×M1612yes—
256C2×Dic73C2×M1612yes—
257C2×Dic73C22×D411yescharacteristic
258C2×Dic73C22×D411yescharacteristic
259C2×Dic73C22×Q811yescharacteristic
260C2×Dic73C2×#4111yescharacteristic
261C2×Dic73H(5,𝔽2)11yescharacteristic
262C2×Dic732−1+411yescharacteristic
263#10596833—24no—
264#10596833—42no—
265#10596833—42no—
266#10596833—42no—
267C22×C73—22no—
268C22×C73—22no—
269C22×C73—22no—
270C22×C73—22no—
271C22×C73—22no—
272C22×C73—22no—
273C22×C73—22no—
274C22×C73—22no—
275C22×C73—22no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73—41no—
279C22×C73—41no—
280C22×C73#42314yescomplemented
281C22×C73C22×C4⋊C411yescharacteristic
282C22×C73C2×C4×D411yescharacteristic
283C22×C73#52011yescharacteristic
284C22×C73C22×M1611yescharacteristic
285C22×C73C22×M1611yescharacteristic
286C22×C73C2×#13111yescharacteristic
287C22×C73#56811yescharacteristic
288C4×C73—22no—
289C4×C73—22no—
290C4×C73—41no—
291C4×C73—41no—
292C4×C73#43514yescomplemented
293Dic73—22no—
294Dic73—22no—
295Dic73—22no—
296Dic73—22no—
297Dic73—22no—
298Dic73—22no—
299Dic73—41no—
300Dic73D4211yescharacteristic
301Dic73#54711yescharacteristic
302Dic73D4×Q811yescharacteristic
303Dic73#55411yescharacteristic
304#22648—731nomaximal, Sylow
305C2×C73—24no—
306C2×C73—42no—
307C2×C73D4×C4⋊C411yescharacteristic
308C2×C73C2×#42311yescharacteristic
309C2×C73#290611yescharacteristic
310C2×C73C2×#43511yescharacteristic
311C2×C73D4×M1611yescharacteristic
312C2×C73#298911yescharacteristic
313C2×C73#299011yescharacteristic
314C2×#435—732no—
315C2×#423—731no—
316C22×C4⋊C8—731no—
317C42×D4—731no—
318#1940—732no—
319#1851—732no—
320#1850—732no—
321#1842—731no—
322#1797—731no—
323#1797—731no—
324#1767—731no—
325C73#2264811yescharacteristic, complemented, Sylow
326C22×M16—732no—
327C23×C8—732no—
328C2×C4×D4—731no—
329C2×C4×D4—731no—
330C2×C4×D4#6440811yescharacteristic
331C22×C42—731no—
332C22×C42—731no—
333#435—1468no—
334#423—1464no—
335C2×C4⋊C8—732no—
336C2×C4⋊C8—731no—
337C2×C4⋊C8—731no—
338C2×C4⋊C8—731no—
339C2×C4⋊C8—731no—
340C2×C4⋊C8—732no—
341C2×C4⋊C8—732no—
342C2×C4⋊C8—732no—
343C2×C4⋊C8—1464no—
344C2×C22⋊C8—732no—
345C2×C22⋊C8—732no—
346C2×#97—732no—
347C4×C4⋊C4—731no—
348C4×C4⋊C4—731no—
349C4×C4⋊C4—731no—
350C4×C22⋊C4—731no—
351C4×C22⋊C4—731no—
352C4×C22⋊C4—731no—
353C4×C22⋊C4—731no—
354C4×C22⋊C4—731no—
355C4×C22⋊C4—731no—
356C43—731no—
357#336—732no—
358#336—732no—
359#336—732no—
360C22×D4C2×#6440811yescharacteristic
361C23×C4—731no—
362C23×C4—731no—
363C23×C4—731no—
364C23×C4—731no—
365C23×C4C2×#6440811yescharacteristic
366C23×C4C2×#6440811yescharacteristic
367C2×M16—2922no—
368C2×M16—1464no—
369C2×M16—1464no—
370C22×C8—2922no—
371C22×C8—732no—
372C22×C8—732no—
373C22×C8—732no—
374C22×C8—732no—
375C22×C8—1464no—
376C22×C8—1464no—
377C4×D4—24no—
378C4×D4—734no—
379C4×D4—734no—
380C4×D4—1464no—
381C2×C4⋊C4—731no—
382C2×C4⋊C4—731no—
383C2×C4⋊C4C2×#6440811yescharacteristic
384C2×C22⋊C4—731no—
385C2×C22⋊C4—731no—
386C2×C22⋊C4—731no—
387C2×C22⋊C4—731no—
388C2×C22⋊C4C2×#6440811yescharacteristic
389C2×C22⋊C4C2×#6440811yescharacteristic
390C2×C42—731no—
391C2×C42—731no—
392C2×C42—731no—
393C2×C42—731no—
394C2×C42—731no—
395C2×C42—731no—
396C2×C42—731no—
397C2×C42—731no—
398C2×C42—731no—
399C2×C42—731no—
400C2×C42—731no—
401C2×C42—731no—
402C2×C42—1462no—
403C2×C42—1462no—
404C2×C42—1462no—
405C2×C42—1462no—
406C2×C42C2×#6440811yescharacteristic
407C4⋊C8—2922no—
408C4⋊C8—734no—
409C4⋊C8—1462no—
410C4⋊C8—1462no—
411C4⋊C8—1464no—
412C4⋊C8—1462no—
413C4⋊C8—1464no—
414C4⋊C8—1464no—
415C22⋊C8—1464no—
416C22⋊C8—1464no—
417#97—1464no—
418#95—731no—
419#95—731no—
420#95—731no—
421#95—731no—
422#95—731no—
423#95—731no—
424C24C22×#6440811yescharacteristic
425C24C22×#6440811yescharacteristic
426C2×D4—22no—
427C2×D4—22no—
428C2×D4C4⋊#6440814yes—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—2921no—
435C22×C4—2921no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4—731no—
441C22×C4—731no—
442C22×C4—731no—
443C22×C4—732no—
444C22×C4—732no—
445C22×C4—732no—
446C22×C4—732no—
447C22×C4—731no—
448C22×C4—1462no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4—1462no—
452C22×C4—1461no—
453C22×C4—1461no—
454C22×C4—1461no—
455C22×C4—1461no—
456C22×C4—1461no—
457C22×C4—1461no—
458C22×C4—1461no—
459C22×C4—1461no—
460C22×C4#1192403714yescomplemented
461C22×C4C22×#6440811yescharacteristic
462C22×C4C22×#6440811yescharacteristic
463C22×C4C22×#6440811yescharacteristic
464C22×C4C22×#6440811yescharacteristic
465C22×C4C22×#6440811yescharacteristic
466M16—2928no—
467C2×C8—2928no—
468C2×C8—734no—
469C2×C8—1462no—
470C2×C8—1462no—
471C2×C8—1462no—
472C2×C8—1462no—
473C2×C8—1462no—
474C2×C8—1462no—
475C2×C8—1462no—
476C2×C8—1462no—
477C2×C8—1462no—
478C2×C8—1462no—
479C2×C8—1462no—
480C4⋊C4—22no—
481C4⋊C4—734no—
482C4⋊C4—1462no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—734no—
486C22⋊C4—734no—
487C22⋊C4—734no—
488C22⋊C4—1462no—
489C42—22no—
490C42—2921no—
491C42—732no—
492C42—732no—
493C42—732no—
494C42—732no—
495C42—1461no—
496C42—1461no—
497C42—1461no—
498C42—1461no—
499C42—1461no—
500C42—1462no—
501C42—1461no—
502C42—1462no—
503C42—1462no—
504C42—1462no—
505C42—1462no—
506C42—1462no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23C2×C4⋊#6440812yes—
518C23C2×C4⋊#6440812yes—
519C23C2×#1192403712yes—
520C23D73⋊M1612yes—
521C23C23×#6440811yescharacteristic
522D4—28no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—28no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—44no—
535C2×C4—2924no—
536C2×C4—2924no—
537C2×C4—731no—
538C2×C4—731no—
539C2×C4—731no—
540C2×C4—731no—
541C2×C4—731no—
542C2×C4—731no—
543C2×C4—732no—
544C2×C4—732no—
545C2×C4—732no—
546C2×C4—732no—
547C2×C4—732no—
548C2×C4—732no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1462no—
553C2×C4—1462no—
554C2×C4—1462no—
555C2×C4—1462no—
556C2×C4—1462no—
557C2×C4—1462no—
558C2×C4—1462no—
559C2×C4—1462no—
560C2×C4—1461no—
561C2×C4—1461no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1461no—
571C2×C4—1461no—
572C2×C4C2×C4⋊#6440812yes—
573C2×C4D4×#6440812yes—
574C2×C4C2×#1192403712yes—
575C2×C4C2×#1192403712yes—
576C2×C4#1455667812yes—
577C8—2922no—
578C8—2922no—
579C8—2922no—
580C8—1464no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22#1798959014yescomplemented
595C22C22×C4⋊#6440811yescharacteristic
596C22C2×D4×#6440811yescharacteristic
597C22#1798965611yescharacteristic
598C22C22×#1192403711yescharacteristic
599C22C2×D73⋊M1611yescharacteristic
600C22C2×#1455667811yescharacteristic
601C22#1798966611yescharacteristic
602C4—22no—
603C4—22no—
604C4—41no—
605C4—41no—
606C4—2921no—
607C4—731no—
608C4—731no—
609C4—731no—
610C4—731no—
611C4—1462no—
612C4—1462no—
613C4—1462no—
614C4—1462no—
615C4—1462no—
616C4—1462no—
617C4#1798961814yescomplemented
618C2—24no—
619C2—42no—
620C2D4×C4⋊#6440811yescharacteristic
621C2C2×#1798959011yescharacteristic
622C2#2262657611yescharacteristic
623C2C2×#1798961811yescharacteristic
624C2#2262667011yescharacteristic
625C2#2262685011yescharacteristic
626C2#2262685611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
FittingC2×C4×D4×C73C4
prime radicalC22×D4×C73C2×C4
cosocleC22×Dic73C24
hypercenterC2×C4×D4#64408
hypocenterC73#22648
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#17989590C2semidirect
3. C22×C4⋊#10596833C2semidirect
4. #22626033C2semidirect
5. #22625878C2semidirect
6. #22625875C2semidirect
7. #22625864C2semidirect
8. #22625785C2semidirect
9. #22625785C2semidirect
10. #22625717C2semidirect
63. C4⋊#10596833D4semidirect
155. C22⋊Dic73M16semidirect
183. C22×C4×C73M16semidirect
280. C22×C73#423semidirect
292. C4×C73#435semidirect
325. C73#22648semidirect
460. C22×C4#11924037semidirect
594. C22#17989590semidirect
617. C4#17989618semidirect

Maximal subgroups

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

subgroupindex
C2×#179896182
C2×#179895902
C22×C4⋊#105968332
#226260332
#226258782
#226258752
#226258642
#226257852
#226257172
C4×D4×Dic732
#2264873