Finite Group Databasebeta

← #34026933

Subgroups — #34026933

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×#17989616C212yesmaximal
2C2×#17989591C211yesmaximal, characteristic, complemented
3C22×C4⋊#10596833C211yesmaximal, characteristic, complemented
4#22626031C212yesmaximal, complemented
5#22625877C212yesmaximal, complemented
6#22625874C212yesmaximal, complemented
7#22625863C211yesmaximal, characteristic, complemented
8#22625786C211yesmaximal, characteristic, complemented
9#22625785C211yesmaximal, characteristic, complemented
10#22625717C211yesmaximal, characteristic, complemented
11C4×#14556551C211yesmaximal, characteristic
12C22×#11924038C2212yes—
13C23×#10596833C2212yes—
14#17989616—28no—
15#17989591—24no—
16C2×C4⋊#10596833—24no—
17C2×C4⋊#10596833C2211yescharacteristic
18C2×C4⋊#10596833C2212yes—
19C2×C4⋊#10596833C2211yescharacteristic
20C2×C4⋊#10596833C2212yes—
21C2×C4⋊#10596833C2212yes—
22C2×C4⋊#10596833C2211yescharacteristic
23C2×C4⋊#10596833C2212yes—
24C2×C4⋊#10596833C2211yescharacteristic
25C2×#14556648C2212yes—
26C2×C22⋊#10596833C2212yes—
27C2×#14556646C2212yes—
28#17989453C2212yes—
29#17989453C2212yes—
30#17989453C2212yes—
31C2×C4×C22⋊D73C411yescharacteristic
32C2×#14556551C411yescharacteristic
33C2×#14556551C2211yescharacteristic
34C22×C4×Dic73C2211yescharacteristic
35C2×C42×D73C2211yescharacteristic
36C4×#11924007C411yescharacteristic
37#17988438C411yescharacteristic
38#17988438C2211yescharacteristic
39C22⋊C4×Dic73C411yescharacteristic
40C22⋊C4×Dic73C2211yescharacteristic
41C4×#11924005C411yescharacteristic
42#17988434C411yescharacteristic
43#17988434C2211yescharacteristic
44C42×Dic73C2211yescharacteristic
45C4×C22⋊C4×C73C411yescharacteristic
46C2×#11924038—24no—
47C2×#11924038—24no—
48C2×#11924038—42no—
49C22×#10596833—24no—
50C22×#10596833—24no—
51C22×#10596833—42no—
52C22×#10596833C2312yes—
53C22×#10596833C2312yes—
54C22×#10596833C2312yes—
55C22×#10596833C2312yes—
56C4⋊#10596833—24no—
57C4⋊#10596833—24no—
58C4⋊#10596833—22no—
59C4⋊#10596833—22no—
60C4⋊#10596833—24no—
61C4⋊#10596833—22no—
62C4⋊#10596833—42no—
63C4⋊#10596833D414yescomplemented
64#14556648—24no—
65C22⋊#10596833—24no—
66#14556646—24no—
67C22×C22⋊D73C2×C411yescharacteristic
68C23×Dic73C2×C411yescharacteristic
69C23×Dic73C2311yescharacteristic
70C22×C4×D73C2×C411yescharacteristic
71C22×C4×D73C2×C411yescharacteristic
72C22×C4×D73C2311yescharacteristic
73C4×C22⋊D73—24no—
74#14556551—24no—
75#14556551D414yes—
76#14556551Q814yes—
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×#11924007C2×C411yescharacteristic
80C2×C22⋊Dic73C2×C411yescharacteristic
81C2×#11924005C2×C411yescharacteristic
82C2×#11924005C2×C411yescharacteristic
83C2×#11924005C2×C411yescharacteristic
84C2×C4×Dic73—22no—
85C2×C4×Dic73—22no—
86C2×C4×Dic73C2×C411yescharacteristic
87C2×C4×Dic73C2×C411yescharacteristic
88C2×C4×Dic73C2×C411yescharacteristic
89C2×C4×Dic73C2×C411yescharacteristic
90C2×C4×Dic73C2×C411yescharacteristic
91C2×C4×Dic73C2×C411yescharacteristic
92C2×C4×Dic73C2311yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C42×D73—22no—
98C42×D73—22no—
99#14556498C2×C411yescharacteristic
100#14556498C2×C411yescharacteristic
101#14556498C2×C411yescharacteristic
102#14556498C2×C411yescharacteristic
103C23×C4×C73C2×C411yescharacteristic
104C2×C22⋊C4×C73C2×C411yescharacteristic
105C2×C22⋊C4×C73C2×C411yescharacteristic
106C2×C42×C73C2×C411yescharacteristic
107C2×C42×C73C2×C411yescharacteristic
108#95×C73C2×C411yescharacteristic
109#95×C73C2×C411yescharacteristic
110#11924038—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—
124C23×D73C22×C411yescharacteristic
125C2×C22⋊D73—22no—
126C2×C22⋊D73—22no—
127C2×C22⋊D73C4⋊C414yes—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—22no—
133C22×Dic73—22no—
134C22×Dic73—41no—
135C22×Dic73C22×C411yescharacteristic
136C22×Dic73C22×C411yescharacteristic
137C22×Dic73C22×C411yescharacteristic
138C22×Dic73C22×C411yescharacteristic
139C22×Dic73C22×C411yescharacteristic
140C22×Dic73C22×C411yescharacteristic
141C22×Dic73C2×D412yes—
142C22×Dic73C2×Q812yes—
143C22×Dic73C2411yescharacteristic
144C2×C4×D73—21no—
145C2×C4×D73—21no—
146C2×C4×D73—21no—
147C2×C4×D73—21no—
148C2×C4×D73—22no—
149C2×C4×D73—22no—
150C2×C4×D73—22no—
151C2×C4×D73—22no—
152C2×C4×D73—22no—
153C2×C4×D73—41no—
154C2×C4×D73C2×D412yes—
155C2×C4×D73C2×Q812yes—
156#11924007—22no—
157#11924007—22no—
158#11924007C4⋊C414yes—
159C22⋊Dic73—22no—
160#11924005—22no—
161#11924005—22no—
162#11924005C4⋊C414yes—
163C4×Dic73—22no—
164C4×Dic73—22no—
165C4×Dic73—22no—
166C4×Dic73—22no—
167C4×Dic73—22no—
168C4×Dic73—21no—
169C4×Dic73—21no—
170C4×Dic73—21no—
171C4×Dic73—21no—
172C4×Dic73—21no—
173C4×Dic73—21no—
174C4×Dic73—41no—
175C4×Dic73C2×D412yes—
176C4×Dic73C2×D412yes—
177C4×Dic73C2×Q812yes—
178C4×Dic73#4112yes—
179C24×C73C22×C411yescharacteristic
180C22×C4×C73—22no—
181C22×C4×C73—22no—
182C22×C4×C73M1614yescomplemented
183C22×C4×C73C22×C411yescharacteristic
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C22×C411yescharacteristic
189C22⋊C4×C73C4⋊C414yes—
190C22⋊C4×C73M1614yescomplemented
191C42×C73—22no—
192C42×C73—22no—
193C23×C73—21no—
194C23×C73—21no—
195C23×C73—21no—
196C23×C73—21no—
197C23×C73C2×C4⋊C412yes—
198C23×C73C2×M1612yes—
199C23×C73C2×M1612yes—
200C23×C73C23×C411yescharacteristic
201C22×D73—21no—
202C22×D73—21no—
203C22×D73—21no—
204C22×D73—21no—
205C22×D73—21no—
206C22×D73—21no—
207C22×D73C2×C4⋊C412yes—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
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—28no—
219C2×C4×C73C2×C4⋊C412yes—
220C2×C4×C73C2×C4⋊C412yes—
221C2×C4×C73C4×D412yes—
222C2×C4×C73C2×M1612yes—
223C2×C4×C73C2×M1612yes—
224C2×C4×C73C2×M1612yes—
225C2×C4×C73C2×M1612yes—
226C2×C4×C73#13112yes—
227C22⋊D73—28no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—22no—
235C2×Dic73—22no—
236C2×Dic73—22no—
237C2×Dic73—22no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—44no—
248C2×Dic73C2×C4⋊C412yes—
249C2×Dic73C2×C4⋊C412yes—
250C2×Dic73C4×D412yes—
251C2×Dic73C22×D411yescharacteristic
252C2×Dic73C22×D411yescharacteristic
253C2×Dic73C22×Q811yescharacteristic
254C2×Dic73C2×#4111yescharacteristic
255C2×Dic73H(5,𝔽2)11yescharacteristic
256C2×Dic732−1+411yescharacteristic
257C4×D73—22no—
258C4×D73—22no—
259C4×D73—22no—
260C4×D73—22no—
261C4×D73—44no—
262C4×D73—44no—
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#42314yescomplemented
274C22×C73C22×C4⋊C411yescharacteristic
275C22×C73C2×C4×D411yescharacteristic
276C22×C73#52011yescharacteristic
277C22×C73C22×M1611yescharacteristic
278C22×C73C22×M1611yescharacteristic
279C22×C73C2×#13111yescharacteristic
280C22×C73#56811yescharacteristic
281C2×D73—22no—
282C2×D73—22no—
283C2×D73—22no—
284C2×D73—41no—
285C2×D73—41no—
286C2×D73—41no—
287C2×D73—41no—
288C4×C73—22no—
289C4×C73—22no—
290C4×C73—22no—
291C4×C73—22no—
292C4×C73—22no—
293C4×C73#43514yescomplemented
294Dic73—22no—
295Dic73—22no—
296Dic73—22no—
297Dic73—41no—
298Dic73—41no—
299Dic73—41no—
300Dic73D4211yescharacteristic
301Dic73#54711yescharacteristic
302Dic73D4×Q811yescharacteristic
303Dic73#55411yescharacteristic
304#22648—731nomaximal, Sylow
305C2×C73—24no—
306C2×C73D4×C4⋊C411yescharacteristic
307C2×C73C2×#42311yescharacteristic
308C2×C73#290611yescharacteristic
309C2×C73C2×#43511yescharacteristic
310C2×C73D4×M1611yescharacteristic
311C2×C73#298911yescharacteristic
312C2×C73#299011yescharacteristic
313D73—42no—
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—731no—
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#6440811yescharacteristic
356C43—731no—
357#336—732no—
358#336—732no—
359#336—732no—
360C22×D4—731no—
361C23×C4—731no—
362C23×C4—731no—
363C23×C4—731no—
364C23×C4—731no—
365C23×C4—731no—
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—734no—
378C4×D4—734no—
379C4×D4—1464no—
380C4×D4—1464no—
381C2×C4⋊C4—731no—
382C2×C4⋊C4—731no—
383C2×C4⋊C4—731no—
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—1462no—
402C2×C42—1462no—
403C2×C42—1462no—
404C2×C42—1462no—
405C2×C42C2×#6440811yescharacteristic
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#95C2×#6440811yescharacteristic
423#95C2×#6440811yescharacteristic
424C24—731no—
425C24C22×#6440811yescharacteristic
426C2×D4—734no—
427C2×D4—1462no—
428C2×D4—1462no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—2921no—
432C22×C4—2921no—
433C22×C4—731no—
434C22×C4—731no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—732no—
438C22×C4—732no—
439C22×C4—732no—
440C22×C4—732no—
441C22×C4—731no—
442C22×C4—731no—
443C22×C4—731no—
444C22×C4—1462no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4—1461no—
448C22×C4—1461no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4—1462no—
452C22×C4—1462no—
453C22×C4—1462no—
454C22×C4—1462no—
455C22×C4—1461no—
456C22×C4—1461no—
457C22×C4—1461no—
458C22×C4—1461no—
459C22×C4#1192403814yescomplemented
460C22×C4C22×#6440811yescharacteristic
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—734no—
481C4⋊C4—1462no—
482C4⋊C4—1462no—
483C22⋊C4—734no—
484C22⋊C4—1462no—
485C22⋊C4—1462no—
486C22⋊C4—1462no—
487C22⋊C4C4⋊#6440814yes—
488C22⋊C4#1192403814yescomplemented
489C42—22no—
490C42—22no—
491C42—2921no—
492C42—732no—
493C42—732no—
494C42—732no—
495C42—732no—
496C42—1461no—
497C42—1461no—
498C42—1461no—
499C42—1461no—
500C42—1461no—
501C42—1462no—
502C42—1461no—
503C42—1462no—
504C42—1462no—
505C42—1462no—
506C42—1462no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—732no—
512C23—1461no—
513C23—1461no—
514C23—1461no—
515C23—1461no—
516C23—1461no—
517C23—1461no—
518C23C2×C4⋊#6440812yes—
519C23C2×#1192403812yes—
520C23C2×#1192403812yes—
521C23C23×#6440811yescharacteristic
522D4—1468no—
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—28no—
534C2×C4—2924no—
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—1462no—
547C2×C4—1462no—
548C2×C4—1462no—
549C2×C4—1462no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4—1461no—
556C2×C4—1461no—
557C2×C4—1461no—
558C2×C4—1461no—
559C2×C4—1462no—
560C2×C4—1462no—
561C2×C4—1462no—
562C2×C4—1462no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4—1461no—
569C2×C4C2×C4⋊#6440812yes—
570C2×C4C2×C4⋊#6440812yes—
571C2×C4D4×#6440812yes—
572C2×C4C2×#1192403812yes—
573C2×C4C2×#1192403812yes—
574C2×C4C2×#1192403812yes—
575C2×C4C2×#1192403812yes—
576C2×C4#1455667812yes—
577C8—2922no—
578C8—2922no—
579C8—2922no—
580C8—1464no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—2921no—
588C22—2921no—
589C22—2921no—
590C22—2921no—
591C22—1462no—
592C22—1462no—
593C22—1462no—
594C22#1798959114yescomplemented
595C22C22×C4⋊#6440811yescharacteristic
596C22C2×D4×#6440811yescharacteristic
597C22#1798965611yescharacteristic
598C22C22×#1192403811yescharacteristic
599C22C22×#1192403811yescharacteristic
600C22C2×#1455667811yescharacteristic
601C22#1798966611yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—22no—
606C4—22no—
607C4—2921no—
608C4—2921no—
609C4—2921no—
610C4—731no—
611C4—731no—
612C4—731no—
613C4—731no—
614C4—1462no—
615C4—1462no—
616C4—1462no—
617C4#1798961614yescomplemented
618C2—24no—
619C2—2922no—
620C2D4×C4⋊#6440811yescharacteristic
621C2C2×#1798959111yescharacteristic
622C2#2262657611yescharacteristic
623C2C2×#1798961611yescharacteristic
624C2D4×#1192403811yescharacteristic
625C2#2262685211yescharacteristic
626C2#2262685911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
FittingC4×C22⋊C4×C73C4
prime radicalC22×C22⋊D73C2×C4
cosocleC22×Dic73C24
hypercenterC4×C22⋊C4#64408
hypocenterC73#22648
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#17989591C2semidirect
3. C22×C4⋊#10596833C2semidirect
4. #22626031C2semidirect
5. #22625877C2semidirect
6. #22625874C2semidirect
7. #22625863C2semidirect
8. #22625786C2semidirect
9. #22625785C2semidirect
10. #22625717C2semidirect
63. C4⋊#10596833D4semidirect
182. C22×C4×C73M16semidirect
190. C22⋊C4×C73M16semidirect
273. C22×C73#423semidirect
293. C4×C73#435semidirect
325. C73#22648semidirect
459. C22×C4#11924038semidirect
488. C22⋊C4#11924038semidirect
594. C22#17989591semidirect
617. C4#17989616semidirect

Maximal subgroups

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

subgroupindex
C2×#179896162
C2×#179895912
C22×C4⋊#105968332
#226260312
#226258772
#226258742
#226258632
#226257862
#226257852
#226257172
C4×#145565512
#2264873