Finite Group Databasebeta

← C2×#22589794 #32026374

Subgroups — C2×#22589794 #32026374

Order 18176.

906 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986025C211yesmaximal, characteristic, complemented
2C2×#17986016C211yesmaximal, characteristic
3C2×#17985983C211yesmaximal, characteristic
4#22589794C218yesmaximal, direct product factor
5C2×#17985769C211yesmaximal, characteristic, complemented
6C2×#17985764C211yesmaximal, characteristic, complemented
7C2×#17985755C211yesmaximal, characteristic, complemented
8C2×#416×C71C211yesmaximal, characteristic
9C22×#11765849C2211yescharacteristic
10C22×#11765849C2211yescharacteristic
11C22×#11765849C2211yescharacteristic
12C2×#14556087C2211yescharacteristic
13#17986025—22no—
14#17986025C2214yescomplemented
15C2×Dic71⋊C8—22no—
16#17986016—22no—
17#17986016C2214yes—
18C2×#14556055—22no—
19#17985983—22no—
20#17985983C2214yes—
21C2×#14556047—21no—
22C2×#14556045—21no—
23#17985769C2214yescomplemented
24#17985764C2214yescomplemented
25#17985755C2214yescomplemented
26C22×#41×C71C2211yescharacteristic
27C23×C8×C71C2211yescharacteristic
28C2×#117×C71C2211yescharacteristic
29#416×C71—22no—
30#416×C71C2214yes—
31C2×#103×C71—21no—
32C2×#102×C71—21no—
33C2×#11765849—21no—
34C2×#11765849—21no—
35C2×#11765849—21no—
36C2×#11765849—21no—
37C2×#11765849—21no—
38C2×#11765849—21no—
39C2×#11765849—21no—
40C2×#11765849—21no—
41C2×#11765849—21no—
42C2×#11765849—21no—
43C2×#11765849—21no—
44C2×#11765849—21no—
45C2×#11765849—21no—
46C2×#11765849—21no—
47C2×#11765849—21no—
48C2×#11765849C2312yes—
49C2×#11765849C2312yes—
50C2×#11765849C2312yes—
51C22×C71⋊C8—21no—
52C22×C71⋊C8—21no—
53C22×C71⋊C8—21no—
54#14556087—21no—
55#14556087—21no—
56#14556087D412yes—
57#14556087C2312yes—
58C2×C4⋊Dic71—21no—
59C2×C22⋊Dic71—21no—
60C2×C4×Dic71D412yes—
61Dic71⋊C8—28no—
62#14556055—28no—
63#14556047—24no—
64#14556045—24no—
65C2×#41×C71—21no—
66C2×#41×C71—21no—
67C2×#41×C71—21no—
68C2×#41×C71—21no—
69C2×#41×C71—21no—
70C2×#41×C71—21no—
71C2×#41×C71—21no—
72C2×#41×C71—21no—
73C2×#41×C71—21no—
74C2×#41×C71—21no—
75C2×#41×C71D412yes—
76C2×#41×C71C2312yes—
77C22×Q8×C71D411yescharacteristic
78C22×D4×C71—21no—
79C22×D4×C71D411yescharacteristic
80C23×C4×C71—21no—
81C23×C4×C71C2311yescharacteristic
82C22×C8×C71—21no—
83C22×C8×C71—21no—
84C22×C8×C71—21no—
85C22×C8×C71—21no—
86C22×C8×C71—21no—
87C22×C8×C71—21no—
88C22×C8×C71C2312yes—
89#117×C71—21no—
90#117×C71—21no—
91#117×C71—21no—
92#117×C71C2312yes—
93C2×C4⋊C4×C71—21no—
94C2×C22⋊C4×C71—21no—
95C2×C42×C71—21no—
96#103×C71—24no—
97#102×C71—24no—
98C22×Dic71—22no—
99#11765849—22no—
100#11765849—22no—
101#11765849—22no—
102#11765849—22no—
103#11765849—22no—
104#11765849—22no—
105#11765849—41no—
106#11765849—41no—
107#11765849—41no—
108#11765849—41no—
109#11765849—41no—
110#11765849—41no—
111C2×C71⋊C8—22no—
112C2×C71⋊C8—22no—
113C2×C71⋊C8—22no—
114C2×C71⋊C8—41no—
115C2×C71⋊C8—41no—
116C2×C71⋊C8—41no—
117C2×C71⋊C8—41no—
118C2×C71⋊C8—41no—
119C2×C71⋊C8—41no—
120C4⋊Dic71—22no—
121C4⋊Dic71—22no—
122C22⋊Dic71—22no—
123C22⋊Dic71—22no—
124C4×Dic71—22no—
125C4×Dic71C2×D414yes—
126C24×C71—21no—
127C24×C71#4111yescharacteristic
128#41×C71—22no—
129#41×C71—22no—
130#41×C71—22no—
131#41×C71—22no—
132#41×C71—22no—
133#41×C71—22no—
134#41×C71—22no—
135#41×C71—22no—
136#41×C71—41no—
137#41×C71—41no—
138#41×C71—41no—
139#41×C71—41no—
140#41×C71—41no—
141#41×C71—41no—
142#41×C71—41no—
143#41×C71—41no—
144C2×Q8×C71—21no—
145C2×Q8×C71—21no—
146C2×Q8×C71—21no—
147C2×Q8×C71—21no—
148C2×Q8×C71—21no—
149C2×Q8×C71C2×D412yes—
150C2×D4×C71—22no—
151C2×D4×C71—22no—
152C2×D4×C71—21no—
153C2×D4×C71—21no—
154C2×D4×C71—21no—
155C2×D4×C71—21no—
156C2×D4×C71—21no—
157C2×D4×C71—41no—
158C2×D4×C71—41no—
159C2×D4×C71—41no—
160C2×D4×C71—41no—
161C2×D4×C71C2×D412yes—
162C22×C4×C71—21no—
163C22×C4×C71—22no—
164C22×C4×C71—22no—
165C22×C4×C71—41no—
166C22×C4×C71—41no—
167C22×C4×C71—41no—
168C22×C4×C71—41no—
169C22×C4×C71—41no—
170C22×C4×C71C2×D411yescharacteristic
171C22×C4×C71C2×D411yescharacteristic
172C22×C4×C71C2×D411yescharacteristic
173C22×C4×C71C2×D411yescharacteristic
174C22×C4×C71#4111yescharacteristic
175C22×C4×C71#4111yescharacteristic
176C22×C4×C71#4111yescharacteristic
177C22×C4×C71#4111yescharacteristic
178C22×C4×C71#4111yescharacteristic
179C22×C4×C71#4111yescharacteristic
180C22×C4×C71#4111yescharacteristic
181C22×C4×C71#4111yescharacteristic
182C22×C4×C71#4111yescharacteristic
183C22×C4×C71C2411yescharacteristic
184C2×C8×C71—22no—
185C2×C8×C71—22no—
186C2×C8×C71—22no—
187C2×C8×C71—41no—
188C2×C8×C71—41no—
189C2×C8×C71—41no—
190C2×C8×C71—41no—
191C4⋊C4×C71—22no—
192C4⋊C4×C71—41no—
193C22⋊C4×C71—22no—
194C22⋊C4×C71—41no—
195C42×C71—22no—
196C42×C71—41no—
197C23×C71—22no—
198C23×C71—42no—
199C23×C71—41no—
200C23×C71—41no—
201C23×C71—82no—
202C23×C71#12311yescharacteristic
203C23×C71#12311yescharacteristic
204C23×C71#12311yescharacteristic
205C23×C71#12311yescharacteristic
206C23×C71#12611yescharacteristic
207C23×C71#12611yescharacteristic
208C23×C71C2×#4111yescharacteristic
209Q8×C71—22no—
210Q8×C71—22no—
211Q8×C71—41no—
212Q8×C71—41no—
213D4×C71—22no—
214D4×C71—22no—
215D4×C71—42no—
216D4×C71—42no—
217D4×C71—42no—
218D4×C71—42no—
219D4×C71—41no—
220D4×C71—41no—
221C2×C4×C71—22no—
222C2×C4×C71—41no—
223C2×C4×C71—41no—
224C2×C4×C71—42no—
225C2×C4×C71—42no—
226C2×C4×C71—42no—
227C2×C4×C71—42no—
228C2×C4×C71—42no—
229C2×C4×C71—82no—
230C2×C4×C71#12111yescharacteristic
231C2×C4×C71#12111yescharacteristic
232C2×C4×C71#12111yescharacteristic
233C2×C4×C71#12111yescharacteristic
234C2×C4×C71#12311yescharacteristic
235C2×C4×C71#12311yescharacteristic
236C2×C4×C71#12311yescharacteristic
237C2×C4×C71#12311yescharacteristic
238C2×C4×C71#12311yescharacteristic
239C2×C4×C71#12311yescharacteristic
240C2×C4×C71#12311yescharacteristic
241C2×C4×C71#12311yescharacteristic
242C2×C4×C71#12411yescharacteristic
243C2×C4×C71#12411yescharacteristic
244C2×C4×C71#12411yescharacteristic
245C2×C4×C71#12411yescharacteristic
246C2×C4×C71#12611yescharacteristic
247C2×C4×C71#12611yescharacteristic
248C2×C4×C71#12611yescharacteristic
249C2×C4×C71#12611yescharacteristic
250C2×C4×C71#12611yescharacteristic
251C2×C4×C71#12611yescharacteristic
252C2×C4×C71C22×D411yescharacteristic
253C2×C4×C71C22×D411yescharacteristic
254C2×C4×C71C2×#4111yescharacteristic
255C2×C4×C71C2×#4111yescharacteristic
256C2×C4×C71C2×#4111yescharacteristic
257C2×C4×C71C2×#4111yescharacteristic
258C2×Dic71—24no—
259C2×Dic71—44no—
260C8×C71—42no—
261C71⋊C8—42no—
262C71⋊C8—42no—
263C71⋊C8—42no—
264C22×C71—22no—
265C22×C71—22no—
266C22×C71—22no—
267C22×C71—41no—
268C22×C71—41no—
269C22×C71—41no—
270C22×C71—41no—
271C22×C71—42no—
272C22×C71—82no—
273C22×C71—82no—
274C22×C71—82no—
275C22×C71#39711yescharacteristic
276C22×C71#39711yescharacteristic
277C22×C71#39711yescharacteristic
278C22×C71#39711yescharacteristic
279C22×C71C2×#12311yescharacteristic
280C22×C71C2×#12311yescharacteristic
281C22×C71C2×#12611yescharacteristic
282C4×C71—42no—
283C4×C71—82no—
284C4×C71#39711yescharacteristic
285C4×C71#39711yescharacteristic
286C4×C71#39711yescharacteristic
287C4×C71#39711yescharacteristic
288C4×C71C2×#12111yescharacteristic
289C4×C71C2×#12311yescharacteristic
290C4×C71C2×#12411yescharacteristic
291C4×C71C2×#12611yescharacteristic
292Dic71—44no—
293C2×#2080—711nomaximal, Sylow
294C2×C71—21no—
295C2×C71—21no—
296C2×C71—21no—
297C2×C71—21no—
298C2×C71—21no—
299C2×C71—21no—
300C2×C71—82no—
301C2×C71#208012yescomplemented
302C2×C71C2×#39711yescharacteristic
303C2×#424—711no—
304C2×#421—711no—
305C2×#416D7111yescharacteristic
306C2×#413—711no—
307#2080—718no—
308C2×#344—711no—
309C2×#341—711no—
310C2×H(3,ℤ/4)—711no—
311C71C2×#208011yescharacteristic, complemented, Sylow
312C22×#41C2×D7111yescharacteristic
313C22×M16—711no—
314C22×M16—711no—
315C22×M16—711no—
316C23×C8C2×D7111yescharacteristic
317C2×#117—711no—
318C2×#117C2×D7111yescharacteristic
319#424—714no—
320#424—1422no—
321C2×C4⋊C8—1422no—
322#421—714no—
323#421—1422no—
324C2×#104—1422no—
325#416—22no—
326#416C2×D7114yes—
327C2×#103—21no—
328C2×#102—21no—
329#413—714no—
330#413—1422no—
331C2×#101—1421no—
332C2×#100—1421no—
333#344—714no—
334#341—714no—
335H(3,ℤ/4)—714no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41C22⋊D7112yes—
347C2×#41C22×D7112yes—
348C22×Q8C22⋊D7111yescharacteristic
349C22×D4—21no—
350C22×D4C22⋊D7111yescharacteristic
351C23×C4—21no—
352C23×C4C22×D7111yescharacteristic
353C2×M16—712no—
354C2×M16—712no—
355C2×M16—712no—
356C2×M16—1421no—
357C2×M16—1421no—
358C2×M16—1421no—
359C2×M16—1421no—
360C2×M16—1421no—
361C2×M16—1421no—
362C2×M16—1421no—
363C2×M16—1421no—
364C2×M16—1421no—
365C2×M16—1421no—
366C2×M16—1421no—
367C2×M16—1421no—
368C2×M16—1421no—
369C2×M16—1421no—
370C2×M16—1421no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—1421no—
378C22×C8—1421no—
379C22×C8—1421no—
380C22×C8C22×D7112yes—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—712no—
385#117—712no—
386#117—1421no—
387#117—1421no—
388#117C22×D7112yes—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—1421no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—1421no—
393C2×C42—21no—
394C2×C42—712no—
395C4⋊C8—1428no—
396#104—1428no—
397#103—24no—
398#102—24no—
399#101—1424no—
400#100—1424no—
401C24—21no—
402C24#1176586411yescharacteristic
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8C2×C22⋊D7112yes—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4C2×C22⋊D7112yes—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—1422no—
446C22×C4D4×D7111yescharacteristic
447C22×C4D4×D7111yescharacteristic
448C22×C4C2×C22⋊D7111yescharacteristic
449C22×C4C2×C22⋊D7111yescharacteristic
450C22×C4#1176586411yescharacteristic
451C22×C4#1176586411yescharacteristic
452C22×C4#1176586411yescharacteristic
453C22×C4#1176586411yescharacteristic
454C22×C4#1176586411yescharacteristic
455C22×C4#1176586511yescharacteristic
456C22×C4#1176586511yescharacteristic
457C22×C4#1176586511yescharacteristic
458C22×C4#1176586511yescharacteristic
459C22×C4C23×D7111yescharacteristic
460M16—2841no—
461M16—2841no—
462M16—2841no—
463M16—2841no—
464M16—2841no—
465M16—2841no—
466M16—1422no—
467M16—1422no—
468M16—1422no—
469M16—1422no—
470M16—1422no—
471M16—1422no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—2841no—
480C2×C8—2841no—
481C2×C8—2841no—
482C2×C8—2841no—
483C2×C8—2841no—
484C2×C8—2841no—
485C2×C8—1422no—
486C2×C8—1422no—
487C2×C8—1422no—
488C4⋊C4—22no—
489C4⋊C4—41no—
490C4⋊C4—1422no—
491C4⋊C4—1422no—
492C22⋊C4—22no—
493C22⋊C4—41no—
494C22⋊C4—1422no—
495C22⋊C4—1422no—
496C42—22no—
497C42—41no—
498C42—714no—
499C42—1422no—
500C23—22no—
501C23—42no—
502C23—41no—
503C23—41no—
504C23—82no—
505C23#1455610911yescharacteristic
506C23#1455610911yescharacteristic
507C23#1455611011yescharacteristic
508C23#1455611011yescharacteristic
509C23#1455612111yescharacteristic
510C23#1455612111yescharacteristic
511C23C2×#1176586411yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—41no—
523D4—41no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—82no—
533C2×C4—2844no—
534C2×C4—1424no—
535C2×C4#1455610011yescharacteristic
536C2×C4#1455610011yescharacteristic
537C2×C4#1455610011yescharacteristic
538C2×C4#1455610011yescharacteristic
539C2×C4#1455610911yescharacteristic
540C2×C4#1455610911yescharacteristic
541C2×C4#1455611011yescharacteristic
542C2×C4#1455611011yescharacteristic
543C2×C4#1455611111yescharacteristic
544C2×C4#1455611111yescharacteristic
545C2×C4#1455611111yescharacteristic
546C2×C4#1455611111yescharacteristic
547C2×C4#1455611411yescharacteristic
548C2×C4#1455611411yescharacteristic
549C2×C4#1455611411yescharacteristic
550C2×C4#1455611411yescharacteristic
551C2×C4#1455612111yescharacteristic
552C2×C4#1455612111yescharacteristic
553C2×C4#1455612111yescharacteristic
554C2×C4#1455612111yescharacteristic
555C2×C4#1455612111yescharacteristic
556C2×C4#1455612111yescharacteristic
557C2×C4C2×D4×D7111yescharacteristic
558C2×C4C22×C22⋊D7111yescharacteristic
559C2×C4C2×#1176586411yescharacteristic
560C2×C4C2×#1176586411yescharacteristic
561C2×C4C2×#1176586511yescharacteristic
562C2×C4C2×#1176586511yescharacteristic
563C8—42no—
564C8—2842no—
565C8—2842no—
566C8—2842no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22#1798592711yescharacteristic
579C22#1798592711yescharacteristic
580C22#1798592711yescharacteristic
581C22#1798592711yescharacteristic
582C22C2×#1455610911yescharacteristic
583C22C2×#1455611011yescharacteristic
584C22C2×#1455612111yescharacteristic
585C4—42no—
586C4—82no—
587C4—2844no—
588C4#1798592711yescharacteristic
589C4#1798592711yescharacteristic
590C4#1798592711yescharacteristic
591C4#1798592711yescharacteristic
592C4C2×#1455610011yescharacteristic
593C4C2×#1455611111yescharacteristic
594C4C2×#1455611411yescharacteristic
595C4C2×#1455612111yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—82no—
603C2#2258979412yesdirect product factor
604C2C2×#1798592711yescharacteristic
subgroupG/H
centerC2×C4#14556114
commutator, cosocleC22×C4×C71C24
FrattiniC22×C4C23×D71
FittingC2×#416×C71C2
socleC22×C71#397
prime radicalC22×#41×C71C22
hypercenterC2×#416D71
hypocenterC71C2×#2080
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#17986025C2semidirect
4. #22589794C2direct (N × H)
5. C2×#17985769C2semidirect
6. C2×#17985764C2semidirect
7. C2×#17985755C2semidirect
14. #17986025C22semidirect
23. #17985769C22semidirect
24. #17985764C22semidirect
25. #17985755C22semidirect
301. C2×C71#2080semidirect
311. C71C2×#2080semidirect
603. C2#22589794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179860252
C2×#179860162
C2×#179859832
#225897942
C2×#179857692
C2×#179857642
C2×#179857552
C2×#416×C712
C2×#208071