Finite Group Databasebeta

← C2×#22627043 #34034494

Subgroups — C2×#22627043 #34034494

Order 18688.

1390 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989700C212yesmaximal, complemented
2#22627043C218yesmaximal, direct product factor
3C2×#17989673C212yesmaximal, complemented
4C2×#17989672C212yesmaximal
5C22×#14556670C211yesmaximal, characteristic
6#17989700—24no—
7#17989700C2218yescomplemented
8C2×C4⋊#10596842—22no—
9C2×C22⋊#10596842C2214yes—
10C2×C4×#10596842—22no—
11#17989673C2218yescomplemented
12#17989672C2218yes—
13C2×#14556670—22no—
14C2×#14556670—22no—
15C2×#14556670—24no—
16C2×#14556670C414yes—
17C2×#14556670C2214yes—
18C22×C4⋊#64408C411yescharacteristic
19C22×C4⋊#64408C2211yescharacteristic
20C22×C22⋊#64408C411yescharacteristic
21C22×C22⋊#64408C2211yescharacteristic
22C22×C4×#64408C411yescharacteristic
23C22×C4×#64408C2211yescharacteristic
24C23×C4×D73C411yescharacteristic
25C22×#10596842—24no—
26C4⋊#10596842—28no—
27C22⋊#10596842—24no—
28C22⋊#10596842C2318yes—
29C4×#10596842—28no—
30C23×#64408C2×C411yescharacteristic
31C23×#64408C2×C411yescharacteristic
32C23×#64408C2×C411yescharacteristic
33C23×#64408C2311yescharacteristic
34#14556670—28no—
35#14556670—28no—
36#14556670—28no—
37#14556670—28no—
38C2×C4⋊#64408—22no—
39C2×C4⋊#64408—22no—
40C2×C4⋊#64408—22no—
41C2×C4⋊#64408—22no—
42C2×C4⋊#64408C2×C414yes—
43C2×C4⋊#64408C2×C412yes—
44C2×C4⋊#64408C2312yes—
45C2×C22⋊#64408—22no—
46C2×C22⋊#64408—22no—
47C2×C22⋊#64408—22no—
48C2×C22⋊#64408—22no—
49C2×C22⋊#64408C2×C414yes—
50C2×C22⋊#64408C2×C412yes—
51C2×C22⋊#64408C2312yes—
52C2×C4×#64408—22no—
53C2×C4×#64408—21no—
54C2×C4×#64408—21no—
55C2×C4×#64408C2×C414yes—
56C2×C4×#64408C2×C412yes—
57C2×C4×#64408D412yes—
58C2×C4×#64408D412yes—
59C2×C4×#64408D414yes—
60C2×C4×#64408C2312yes—
61C24×D73C2×C411yescharacteristic
62C23×Dic73C811yescharacteristic, complemented
63C22×C4×D73—22no—
64C22×C4×D73—21no—
65C22×C4×D73—21no—
66C22×C4×D73—22no—
67C22×C4×D73—21no—
68C22×C4×D73—21no—
69C22×C4×D73C811yescharacteristic, complemented
70C22×C4×D73C811yescharacteristic, complemented
71C22×C4×D73C814yescomplemented
72C22×C4×D73C2×C411yescharacteristic
73C22×C4×D73C2×C411yescharacteristic
74C22×C4×D73C2×C414yes—
75C23×C4×C73C811yescharacteristic, complemented
76C2×#10596842—28no—
77C2×#10596842—48no—
78C22×#64408—21no—
79C22×#64408—21no—
80C22×#64408—21no—
81C22×#64408—21no—
82C22×#64408—42no—
83C22×#64408—42no—
84C22×#64408—42no—
85C22×#64408—42no—
86C22×#64408C22⋊C412yes—
87C22×#64408C22⋊C412yes—
88C22×#64408C22×C412yes—
89C22×#64408C22×C412yes—
90C22×#64408C22×C412yes—
91C22×#64408C22×C411yescharacteristic
92C22×#64408C2×D412yes—
93C22×#64408C2×D412yes—
94C22×#64408C2411yescharacteristic
95C4⋊#64408—24no—
96C4⋊#64408—28no—
97C4⋊#64408—24no—
98C22⋊#64408—24no—
99C22⋊#64408—28no—
100C22⋊#64408—24no—
101C4×#64408—24no—
102C4×#64408—24no—
103C4×#64408C22⋊C414yes—
104C4×#64408C22⋊C414yes—
105C4×#64408C2×D414yes—
106C4×#64408C2×D414yes—
107C23×D73—21no—
108C23×D73—21no—
109C23×D73—21no—
110C23×D73—21no—
111C23×D73—42no—
112C23×D73—42no—
113C23×D73C2×C811yescharacteristic
114C23×D73C2×C812yes—
115C23×D73C22×C411yescharacteristic
116C23×D73C22×C412yes—
117C22×Dic73—22no—
118C22×Dic73—21no—
119C22×Dic73—21no—
120C22×Dic73C2×C811yescharacteristic
121C22×Dic73C2×C811yescharacteristic
122C22×Dic73C2×C814yescomplemented
123C2×C4×D73—21no—
124C2×C4×D73—21no—
125C2×C4×D73—21no—
126C2×C4×D73—21no—
127C2×C4×D73—22no—
128C2×C4×D73—21no—
129C2×C4×D73—21no—
130C2×C4×D73—22no—
131C2×C4×D73—21no—
132C2×C4×D73—21no—
133C2×C4×D73—24no—
134C2×C4×D73—24no—
135C2×C4×D73—24no—
136C2×C4×D73—24no—
137C2×C4×D73—24no—
138C2×C4×D73—24no—
139C2×C4×D73—24no—
140C2×C4×D73—24no—
141C2×C4×D73C22⋊C412yes—
142C2×C4×D73C22⋊C411yescharacteristic
143C2×C4×D73C22⋊C411yescharacteristic
144C2×C4×D73C2×C812yes—
145C2×C4×D73C2×C812yes—
146C2×C4×D73C2×C814yescomplemented
147C2×C4×D73C2×C814yescomplemented
148C2×C4×D73M1611yescharacteristic
149C2×C4×D73M1612yes—
150C2×C4×D73M1611yescharacteristic
151C2×C4×D73C22×C412yes—
152C2×C4×D73C22×C412yes—
153C24×C73C2×C811yescharacteristic
154C22×C4×C73—22no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73C2×C811yescharacteristic
158C22×C4×C73C2×C811yescharacteristic
159C22×C4×C73C2×C814yescomplemented
160C23×C73—21no—
161C23×C73—21no—
162C23×C73—42no—
163C23×C73C22×C811yescharacteristic
164C23×C73C22×C812yes—
165C22×D73—22no—
166C22×D73—22no—
167C22×D73—21no—
168C22×D73—21no—
169C22×D73—22no—
170C22×D73—22no—
171C22×D73—22no—
172C22×D73—22no—
173C22×D73—44no—
174C22×D73—42no—
175C22×D73—42no—
176C22×D73—44no—
177C22×D73—44no—
178C22×D73—42no—
179C22×D73—42no—
180C22×D73—42no—
181C22×D73—42no—
182C22×D73—42no—
183C22×D73C2×C22⋊C411yescharacteristic
184C22×D73C2×C22⋊C411yescharacteristic
185C22×D73C22×C811yescharacteristic
186C22×D73C22×C812yes—
187C22×D73C2×M1611yescharacteristic
188C22×D73C2×M1611yescharacteristic
189C22×D73C23×C411yescharacteristic
190C2×#64408—24no—
191C2×#64408—24no—
192C2×#64408—22no—
193C2×#64408—22no—
194C2×#64408—42no—
195C2×#64408—41no—
196C2×#64408—42no—
197C2×#64408—42no—
198C2×#64408—41no—
199C2×#64408—42no—
200C2×#64408—42no—
201C2×#64408—42no—
202C2×#64408—42no—
203C2×#64408—42no—
204C2×#64408—42no—
205C2×#64408C2×C22⋊C412yes—
206C2×#64408C2×C22⋊C414yes—
207C2×#64408C22×D412yes—
208#10596842—48no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—24no—
212C2×C4×C73—24no—
213C2×C4×C73C22⋊C812yes—
214C2×C4×C73C22⋊C811yescharacteristic
215C2×C4×C73C22⋊C811yescharacteristic
216C2×C4×C73C22×C812yes—
217C2×C4×C73C22×C812yes—
218C2×Dic73—21no—
219C2×Dic73—21no—
220C2×Dic73—24no—
221C2×Dic73—24no—
222C2×Dic73C22⋊C812yes—
223C2×Dic73C22⋊C811yescharacteristic
224C2×Dic73C22⋊C811yescharacteristic
225C2×Dic73C22×C812yes—
226C2×Dic73C22×C812yes—
227C4×D73—22no—
228C4×D73—22no—
229C4×D73—22no—
230C4×D73—22no—
231C4×D73—24no—
232C4×D73—24no—
233C4×D73—24no—
234C4×D73—24no—
235C4×D73C22⋊C812yes—
236C4×D73C22⋊C812yes—
237C4×D73C22⋊C812yes—
238C4×D73C22⋊C812yes—
239C4×D73C2×C22⋊C412yes—
240C4×D73C2×C22⋊C412yes—
241C4×D73C2×M1612yes—
242C4×D73C2×M1612yes—
243C22×C73—22no—
244C22×C73—22no—
245C22×C73—42no—
246C22×C73—42no—
247C22×C73—42no—
248C22×C73C2×C22⋊C811yescharacteristic
249C22×C73C2×C22⋊C811yescharacteristic
250C22×C73C23×C811yescharacteristic
251C2×D73—22no—
252C2×D73—21no—
253C2×D73—21no—
254C2×D73—21no—
255C2×D73—21no—
256C2×D73—22no—
257C2×D73—22no—
258C2×D73—22no—
259C2×D73—44no—
260C2×D73—44no—
261C2×D73—42no—
262C2×D73—42no—
263C2×D73—42no—
264C2×D73—42no—
265C2×D73—44no—
266C2×D73—42no—
267C2×D73C2×C22⋊C811yescharacteristic
268C2×D73C2×C22⋊C811yescharacteristic
269C2×D73#41012yes—
270C2×D73#41312yes—
271C2×D73C22×C22⋊C411yescharacteristic
272C2×D73C22×M1611yescharacteristic
273#64408—22no—
274#64408—22no—
275#64408—24no—
276#64408—42no—
277#64408—42no—
278C4×C73—22no—
279C4×C73C2×C22⋊C812yes—
280C4×C73C2×C22⋊C812yes—
281Dic73—22no—
282Dic73C2×C22⋊C812yes—
283Dic73C2×C22⋊C812yes—
284C2×#1458—731nomaximal, Sylow
285C2×C73—21no—
286C2×C73—21no—
287C2×C73—42no—
288C2×C73#145812yescomplemented
289C2×C73C22×C22⋊C811yescharacteristic
290D73—21no—
291D73—21no—
292D73—42no—
293D73#145812yescomplemented
294D73C2×#41011yescharacteristic
295D73C2×#41311yescharacteristic
296C22×#117—731no—
297C2×#431—732no—
298#1458—738no—
299C2×#324—732no—
300C2×#323—732no—
301C73C2×#145811yescharacteristic, complemented, Sylow
302C24×C4—731no—
303C2×#117—734no—
304C2×#117—734no—
305C2×#117—1462no—
306C2×#117—1462no—
307C2×#117—1464no—
308C22×C4⋊C4—731no—
309C22×C4⋊C4—731no—
310C22×C22⋊C4—731no—
311C22×C22⋊C4—731no—
312C22×C42—731no—
313C22×C42—731no—
314#431—738no—
315#431—1464no—
316C2×C4⋊C8—1462no—
317C2×C22⋊C8—734no—
318C2×C4×C8—1462no—
319#324—738no—
320#323—738no—
321C25—731no—
322C23×C4—731no—
323C23×C4—731no—
324C23×C4—731no—
325C23×C4—731no—
326C23×C4—731no—
327C23×C4—731no—
328C23×C4—731no—
329C23×C4—731no—
330C23×C4—731no—
331C23×C4—734no—
332C23×C4—734no—
333C23×C4—1461no—
334C23×C4—1462no—
335C23×C4—1461no—
336C23×C4—1462no—
337C23×C4—1461no—
338C23×C4—1461no—
339C23×C4#1059684211yescharacteristic, complemented
340C22×C8—1464no—
341#117—1468no—
342#117—1468no—
343#117—1468no—
344#117—1468no—
345C2×C4⋊C4—732no—
346C2×C4⋊C4—734no—
347C2×C4⋊C4—732no—
348C2×C4⋊C4—1462no—
349C2×C4⋊C4—1462no—
350C2×C4⋊C4—1462no—
351C2×C4⋊C4—1462no—
352C2×C22⋊C4—732no—
353C2×C22⋊C4—734no—
354C2×C22⋊C4—732no—
355C2×C22⋊C4—1462no—
356C2×C22⋊C4—1462no—
357C2×C22⋊C4—1462no—
358C2×C22⋊C4—1462no—
359C2×C42—732no—
360C2×C42—732no—
361C2×C42—732no—
362C2×C42—732no—
363C2×C42—734no—
364C2×C42—734no—
365C2×C42—1461no—
366C2×C42—1462no—
367C2×C42—1461no—
368C4⋊C8—1468no—
369C22⋊C8—738no—
370C22⋊C8—1464no—
371C4×C8—1468no—
372C24—2922no—
373C24—2922no—
374C24—731no—
375C24—732no—
376C24—732no—
377C24—731no—
378C24—1461no—
379C24—1461no—
380C24—1461no—
381C24—1461no—
382C24C2×#1059684211yescharacteristic
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—2922no—
387C22×C4—2922no—
388C22×C4—2922no—
389C22×C4—2922no—
390C22×C4—732no—
391C22×C4—732no—
392C22×C4—731no—
393C22×C4—732no—
394C22×C4—731no—
395C22×C4—732no—
396C22×C4—732no—
397C22×C4—731no—
398C22×C4—731no—
399C22×C4—732no—
400C22×C4—732no—
401C22×C4—731no—
402C22×C4—731no—
403C22×C4—731no—
404C22×C4—732no—
405C22×C4—732no—
406C22×C4—732no—
407C22×C4—732no—
408C22×C4—731no—
409C22×C4—734no—
410C22×C4—732no—
411C22×C4—734no—
412C22×C4—734no—
413C22×C4—732no—
414C22×C4—1464no—
415C22×C4—1464no—
416C22×C4—1462no—
417C22×C4—1461no—
418C22×C4—1461no—
419C22×C4—1464no—
420C22×C4—1464no—
421C22×C4—1464no—
422C22×C4—1464no—
423C22×C4—1464no—
424C22×C4—1464no—
425C22×C4—1461no—
426C22×C4—1461no—
427C22×C4—1461no—
428C22×C4—1461no—
429C22×C4—1461no—
430C22×C4—1461no—
431C22×C4—1461no—
432C22×C4—1461no—
433C22×C4—1462no—
434C22×C4—1461no—
435C22×C4—1461no—
436C22×C4—1462no—
437C22×C4—1461no—
438C22×C4—1461no—
439C22×C4C2×#1059684211yescharacteristic
440C22×C4C2×#1059684211yescharacteristic
441C22×C4C2×#1059684214yescomplemented
442C2×C8—2928no—
443C2×C8—1468no—
444C4⋊C4—1464no—
445C4⋊C4—1464no—
446C4⋊C4—1468no—
447C22⋊C4—1464no—
448C22⋊C4—1464no—
449C22⋊C4—1468no—
450C42—734no—
451C42—734no—
452C42—734no—
453C42—734no—
454C42—1464no—
455C42—1464no—
456C23—21no—
457C23—21no—
458C23—42no—
459C23—2922no—
460C23—2922no—
461C23—2922no—
462C23—2922no—
463C23—2922no—
464C23—2924no—
465C23—2924no—
466C23—2922no—
467C23—2922no—
468C23—2924no—
469C23—732no—
470C23—731no—
471C23—731no—
472C23—731no—
473C23—731no—
474C23—731no—
475C23—731no—
476C23—1462no—
477C23—1462no—
478C23—1462no—
479C23—1462no—
480C23—1462no—
481C23—1462no—
482C23—1461no—
483C23—1461no—
484C23C22×#1059684211yescharacteristic
485C23C22×#1059684212yes—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—2922no—
491C2×C4—2922no—
492C2×C4—2922no—
493C2×C4—2922no—
494C2×C4—2922no—
495C2×C4—2922no—
496C2×C4—2921no—
497C2×C4—2922no—
498C2×C4—2922no—
499C2×C4—2921no—
500C2×C4—2922no—
501C2×C4—732no—
502C2×C4—731no—
503C2×C4—731no—
504C2×C4—732no—
505C2×C4—732no—
506C2×C4—732no—
507C2×C4—732no—
508C2×C4—732no—
509C2×C4—732no—
510C2×C4—732no—
511C2×C4—732no—
512C2×C4—732no—
513C2×C4—732no—
514C2×C4—732no—
515C2×C4—734no—
516C2×C4—732no—
517C2×C4—1464no—
518C2×C4—1464no—
519C2×C4—1462no—
520C2×C4—1462no—
521C2×C4—1462no—
522C2×C4—1462no—
523C2×C4—1462no—
524C2×C4—1462no—
525C2×C4—1464no—
526C2×C4—1464no—
527C2×C4—1464no—
528C2×C4—1464no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4—1464no—
532C2×C4—1464no—
533C2×C4C22⋊#1059684211yescharacteristic
534C2×C4C22⋊#1059684212yes—
535C2×C4C22⋊#1059684211yescharacteristic
536C2×C4C22×#1059684212yes—
537C2×C4C22×#1059684212yes—
538C8—2928no—
539C22—22no—
540C22—22no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—2922no—
545C22—2922no—
546C22—2922no—
547C22—2922no—
548C22—2924no—
549C22—2924no—
550C22—2924no—
551C22—2922no—
552C22—731no—
553C22—731no—
554C22—732no—
555C22—732no—
556C22—731no—
557C22—731no—
558C22—1461no—
559C22—1461no—
560C22—1461no—
561C22—1461no—
562C22—1462no—
563C22—1462no—
564C22—1462no—
565C22—1462no—
566C22C2×C22⋊#1059684211yescharacteristic
567C22C2×C22⋊#1059684211yescharacteristic
568C22C23×#1059684211yescharacteristic
569C4—22no—
570C4—2922no—
571C4—2922no—
572C4—732no—
573C4—732no—
574C4—1462no—
575C4—1462no—
576C4—1464no—
577C4—1462no—
578C4C2×C22⋊#1059684212yes—
579C4C2×C22⋊#1059684212yes—
580C2—21no—
581C2—21no—
582C2—42no—
583C2—2922no—
584C2—731no—
585C2—731no—
586C2—732no—
587C2—1461no—
588C2—1461no—
589C2#2262704312yesdirect product factor
590C2C22×C22⋊#1059684211yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10596842
commutatorC22×C73C23×C8
FrattiniC22C23×#10596842
FittingC23×C4×C73C8
socleC22×C73C2×C22⋊C8
prime radicalC24×D73C2×C4
cosocleC22×#64408C24
hypercenterC23×C4#10596842
hypocenterC73C2×#1458
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#17989700C2semidirect
2. #22627043C2direct (N × H)
3. C2×#17989673C2semidirect
7. #17989700C22semidirect
11. #17989673C22semidirect
62. C23×Dic73C8semidirect
69. C22×C4×D73C8semidirect
70. C22×C4×D73C8semidirect
71. C22×C4×D73C8semidirect
75. C23×C4×C73C8semidirect
122. C22×Dic73C2×C8semidirect
146. C2×C4×D73C2×C8semidirect
147. C2×C4×D73C2×C8semidirect
159. C22×C4×C73C2×C8semidirect
288. C2×C73#1458semidirect
293. D73#1458semidirect
301. C73C2×#1458semidirect
339. C23×C4#10596842semidirect
441. C22×C4C2×#10596842semidirect
589. C2#22627043direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179897002
#226270432
C2×#179896732
C2×#179896722
C22×#145566702
C2×#145873