Finite Group Databasebeta

← C2×#11727197 #13320888

Subgroups — C2×#11727197 #13320888

Order 1792.

1606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90482C211yesmaximal, characteristic
2C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×C22⋊(C7⋊C8)C211yesmaximal, characteristic, complemented
4#11727197C218yesmaximal, direct product factor
5C2×#89247C212yesmaximal, complemented
6C2×#89246C212yesmaximal, complemented
7C24×C4×C7C2211yescharacteristic
8C22×#1157C411yescharacteristic, complemented
9C22×C7×C22⋊C4—21no—
10C22×C42×C7—21no—
11C2×#6516—21no—
12#90482—22no—
13#90482—22no—
14#90482C414yescomplemented
15#90482C2214yes—
16C2×#6493C411yescharacteristic, complemented
17C2×#6493C2211yescharacteristic
18C2×#6492—21no—
19C2×C4×C22⋊D7—21no—
20C2×C4×C22⋊D7—21no—
21C2×#6489C411yescharacteristic, complemented
22C2×#6487C411yescharacteristic, complemented
23C2×#6487C2211yescharacteristic
24C23×C7⋊C8—21no—
25C4×C7×C22⋊C4—22no—
26C4×C7×C22⋊C4C2214yescomplemented
27C2×C7×#95C2212yes—
28C2×C22⋊(C7⋊C8)—22no—
29C2×C22⋊(C7⋊C8)—21no—
30C2×C22⋊(C7⋊C8)C2212yes—
31C2×C22⋊(C7⋊C8)C2214yescomplemented
32#89247C2218yescomplemented
33#89246C2218yescomplemented
34C2×#1501—71nomaximal, Sylow
35C25×C7D411yescharacteristic
36C23×C4×C7—22no—
37C23×C4×C7—44no—
38C23×C4×C7C2×C411yescharacteristic
39C23×C4×C7C2×C411yescharacteristic
40C23×C4×C7C2×C412yes—
41C23×C4×C7D411yescharacteristic
42C23×C4×C7D411yescharacteristic
43C23×C4×C7D412yes—
44C23×C4×C7D411yescharacteristic
45C23×C4×C7D412yes—
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2312yes—
48C22×C22⋊D7—21no—
49C22×C22⋊D7—21no—
50C22×C22⋊D7—21no—
51C2×#1157—22no—
52C2×#1157—44no—
53C2×#1157C2×C414yescomplemented
54C22×D28C2×C411yescharacteristic
55C22×C4×D7—21no—
56C22×Dic14C2×C411yescharacteristic
57C2×C7×C22⋊C4—28no—
58C2×C7×C22⋊C4—24no—
59C2×C42×C7—24no—
60C2×C42×C7—44no—
61#6516—24no—
62#6516—24no—
63C2×C22⋊Dic7—21no—
64C2×C22⋊Dic7—21no—
65C2×C22⋊Dic7—21no—
66#6493—22no—
67#6493—21no—
68#6493—21no—
69#6493C2×C412yes—
70#6493C2×C414yescomplemented
71#6493C2312yes—
72#6492—24no—
73#6492—24no—
74C4×C22⋊D7—24no—
75C4×C22⋊D7—24no—
76C4×C22⋊D7—24no—
77C4×C22⋊D7—24no—
78C2×(C2×D7)⋊C4—21no—
79C2×(C2×D7)⋊C4—21no—
80#6489—22no—
81#6489C2×C414yescomplemented
82C2×C4⋊Dic7C2×C411yescharacteristic
83C2×C4⋊Dic7C2×C411yescharacteristic
84#6487—22no—
85#6487—21no—
86#6487—21no—
87#6487C2×C412yes—
88#6487C2×C414yescomplemented
89#6487C2312yes—
90C2×Dic7⋊C4—21no—
91C2×Dic7⋊C4—21no—
92C2×C4×Dic7—21no—
93C22×C7⋊C8—22no—
94C22×C7⋊C8—24no—
95C22×C7⋊C8—44no—
96C7×#95—22no—
97C7×#95C2314yes—
98C22⋊(C7⋊C8)—22no—
99C22⋊(C7⋊C8)—24no—
100C22⋊(C7⋊C8)C2314yes—
101C2×#525—71no—
102C22×C22⋊C8—71no—
103C2×C4×C22⋊C4D711yescharacteristic, complemented
104#1501—78no—
105C2×#328—72no—
106C2×#327—72no—
107C24×C7—24no—
108C24×C7—24no—
109C24×C7—42no—
110C24×C7C22⋊C411yescharacteristic
111C24×C7C22⋊C412yes—
112C24×C7C22⋊C411yescharacteristic
113C24×C7C2×D412yes—
114C24×C7C2×D411yescharacteristic
115C23×D7—21no—
116C22×C4×C7—24no—
117C22×C4×C7—24no—
118C22×C4×C7—24no—
119C22×C4×C7—28no—
120C22×C4×C7—24no—
121C22×C4×C7—44no—
122C22×C4×C7—44no—
123C22×C4×C7—44no—
124C22×C4×C7—44no—
125C22×C4×C7—42no—
126C22×C4×C7—42no—
127C22×C4×C7—42no—
128C22×C4×C7—44no—
129C22×C4×C7—44no—
130C22×C4×C7C22⋊C411yescharacteristic
131C22×C4×C7C22⋊C412yes—
132C22×C4×C7C22⋊C412yes—
133C22×C4×C7C22⋊C412yes—
134C22×C4×C7C22⋊C412yes—
135C22×C4×C7C22⋊C412yes—
136C22×C4×C7C22⋊C411yescharacteristic
137C22×C4×C7C22×C411yescharacteristic
138C22×C4×C7C22×C412yes—
139C22×C4×C7C22×C411yescharacteristic
140C22×C4×C7C22×C412yes—
141C22×C4×C7C2×D412yes—
142C22×C4×C7C2×D411yescharacteristic
143C22×C4×C7C2×D412yes—
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2×D412yes—
147C22×C4×C7C2411yescharacteristic
148C2×C22⋊D7—22no—
149C2×C22⋊D7—24no—
150C2×C22⋊D7—24no—
151C2×C22⋊D7—22no—
152C2×C22⋊D7—44no—
153C2×C22⋊D7—44no—
154C2×C22⋊D7—44no—
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—21no—
158#1157—48no—
159#1157—48no—
160C2×D28—21no—
161C2×D28—42no—
162C2×D28C22×C412yes—
163C2×C4×D7—24no—
164C2×C4×D7—44no—
165C2×Dic14—21no—
166C2×Dic14—42no—
167C2×Dic14C22×C412yes—
168C7×C22⋊C4—216no—
169C42×C7—48no—
170C22⋊Dic7—22no—
171C22⋊Dic7—24no—
172C22⋊Dic7—24no—
173C22⋊Dic7—22no—
174(C2×D7)⋊C4—22no—
175(C2×D7)⋊C4—24no—
176(C2×D7)⋊C4—22no—
177C4⋊Dic7—21no—
178C4⋊Dic7—21no—
179C4⋊Dic7C22×C412yes—
180C4⋊Dic7C22×C412yes—
181Dic7⋊C4—22no—
182Dic7⋊C4—24no—
183Dic7⋊C4—22no—
184C4×Dic7—24no—
185C2×C7⋊C8—24no—
186C2×C7⋊C8—44no—
187C2×C7⋊C8—48no—
188C22×#41—71no—
189C24×C4C2×D711yescharacteristic
190C23×C8—141no—
191#525—74no—
192#525—74no—
193#525—142no—
194#525—142no—
195C2×#123—141no—
196C2×C22⋊Q8—71no—
197C2×C22⋊Q8—71no—
198C2×#121—71no—
199C2×#121—71no—
200C2×#120—141no—
201C2×C4×D4—141no—
202C2×C4×D4—141no—
203C2×#117—71no—
204C22×C22⋊C4—21no—
205C22×C42—21no—
206C2×C22⋊C8—72no—
207C2×C22⋊C8—74no—
208C2×C22⋊C8—141no—
209C2×C22⋊C8—142no—
210C4×C22⋊C4—22no—
211C4×C22⋊C4C2×D714yescomplemented
212C2×#95C2×D712yes—
213#328—78no—
214#327—78no—
215C23×C7—22no—
216C23×C7—22no—
217C23×C7—22no—
218C23×C7—22no—
219C23×C7—24no—
220C23×C7—22no—
221C23×C7—24no—
222C23×C7—22no—
223C23×C7—24no—
224C23×C7—24no—
225C23×C7—22no—
226C23×C7—42no—
227C23×C7—42no—
228C23×C7—416no—
229C23×C7#10414yes—
230C23×C7C2×C22⋊C412yes—
231C23×C7C2×C22⋊C411yescharacteristic
232C23×C7C2×C22⋊C412yes—
233C23×C7C2×C22⋊C411yescharacteristic
234C23×C7#13514yes—
235C23×C7C22×D411yescharacteristic
236C22×D7—22no—
237C22×D7—42no—
238C22×D7—42no—
239C22×D7—42no—
240C2×C4×C7—22no—
241C2×C4×C7—22no—
242C2×C4×C7—22no—
243C2×C4×C7—24no—
244C2×C4×C7—24no—
245C2×C4×C7—24no—
246C2×C4×C7—24no—
247C2×C4×C7—24no—
248C2×C4×C7—24no—
249C2×C4×C7—28no—
250C2×C4×C7—42no—
251C2×C4×C7—42no—
252C2×C4×C7—41no—
253C2×C4×C7—42no—
254C2×C4×C7—41no—
255C2×C4×C7—42no—
256C2×C4×C7—41no—
257C2×C4×C7—41no—
258C2×C4×C7—44no—
259C2×C4×C7—416no—
260C2×C4×C7—44no—
261C2×C4×C7#9914yes—
262C2×C4×C7C2×C22⋊C411yescharacteristic
263C2×C4×C7C2×C22⋊C412yes—
264C2×C4×C7C2×C22⋊C411yescharacteristic
265C2×C4×C7C2×C22⋊C412yes—
266C2×C4×C7C23×C411yescharacteristic
267C2×C4×C7C22×D411yescharacteristic
268C22⋊D7—48no—
269C22⋊D7—44no—
270C22⋊D7—44no—
271C22⋊D7—48no—
272C2×Dic7—22no—
273C2×Dic7—22no—
274C2×Dic7—22no—
275C2×Dic7—42no—
276C2×Dic7—42no—
277C2×Dic7—42no—
278D28—42no—
279D28—42no—
280C4×D7—48no—
281Dic14—42no—
282Dic14—42no—
283C7⋊C8—44no—
284C25C22⋊D711yescharacteristic
285C2×#41—74no—
286C2×#41—142no—
287C2×#41—284no—
288C22×Q8—71no—
289C22×D4—71no—
290C22×D4—141no—
291C22×D4—141no—
292C22×D4—141no—
293C23×C4—22no—
294C23×C4—44no—
295C23×C4—141no—
296C23×C4C4×D711yescharacteristic
297C23×C4C4×D711yescharacteristic
298C23×C4C4×D712yes—
299C23×C4D2811yescharacteristic
300C23×C4D2811yescharacteristic
301C23×C4D2812yes—
302C23×C4C22⋊D711yescharacteristic
303C23×C4C22⋊D712yes—
304C23×C4C22×D711yescharacteristic
305C23×C4C22×D712yes—
306C22×C8—142no—
307C22×C8—144no—
308C22×C8—284no—
309#123—144no—
310#123—144no—
311C22⋊Q8—72no—
312C22⋊Q8—74no—
313C22⋊Q8—72no—
314C22⋊Q8—142no—
315C22⋊Q8—141no—
316C22⋊Q8—141no—
317#121—72no—
318#121—74no—
319#121—72no—
320#121—142no—
321#121—141no—
322#121—141no—
323#120—144no—
324#120—144no—
325C4×D4—144no—
326C4×D4—144no—
327C4×D4—144no—
328C4×D4—144no—
329#117—74no—
330#117—142no—
331C2×C4⋊C4—71no—
332C2×C4⋊C4—71no—
333C2×C4⋊C4—141no—
334C2×C4⋊C4—141no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—141no—
338C2×C22⋊C4—141no—
339C2×C22⋊C4—141no—
340C2×C22⋊C4—141no—
341C2×C22⋊C4—141no—
342C2×C42—24no—
343C2×C42—44no—
344C2×C42—141no—
345C22⋊C8—74no—
346C22⋊C8—142no—
347C22⋊C8—144no—
348#95—22no—
349#95C22×D714yes—
350C22×C7—21no—
351C22×C7—21no—
352C22×C7—22no—
353C22×C7—22no—
354C22×C7—21no—
355C22×C7—21no—
356C22×C7—28no—
357C22×C7—28no—
358C22×C7—22no—
359C22×C7—22no—
360C22×C7—22no—
361C22×C7—48no—
362C22×C7—48no—
363C22×C7—44no—
364C22×C7C2×#9912yes—
365C22×C7#41612yes—
366C22×C7#41612yes—
367C22×C7C2×#10414yes—
368C22×C7C2×#10412yes—
369C22×C7C22×C22⋊C411yescharacteristic
370C22×C7C2×#13512yes—
371C2×D7—42no—
372C2×D7—42no—
373C2×D7—42no—
374C2×D7—84no—
375C4×C7—21no—
376C4×C7—21no—
377C4×C7—21no—
378C4×C7—21no—
379C4×C7—22no—
380C4×C7—48no—
381C4×C7C2×#9914yes—
382Dic7—42no—
383Dic7—42no—
384Dic7—42no—
385C24—24no—
386C24—24no—
387C24—42no—
388C24—141no—
389C24(C2×D7)⋊C411yescharacteristic
390C24(C2×D7)⋊C412yes—
391C24(C2×D7)⋊C411yescharacteristic
392C24C2×C22⋊D712yes—
393C24C2×C22⋊D711yescharacteristic
394#41—288no—
395#41—288no—
396C2×Q8—72no—
397C2×Q8—141no—
398C2×Q8—282no—
399C2×D4—72no—
400C2×D4—144no—
401C2×D4—142no—
402C2×D4—144no—
403C2×D4—142no—
404C2×D4—141no—
405C2×D4—282no—
406C2×D4—284no—
407C2×D4—284no—
408C2×D4—284no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—28no—
413C22×C4—24no—
414C22×C4—44no—
415C22×C4—44no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—141no—
424C22×C4—141no—
425C22×C4—141no—
426C22×C4—144no—
427C22×C4—284no—
428C22×C4(C2×D7)⋊C411yescharacteristic
429C22×C4(C2×D7)⋊C412yes—
430C22×C4(C2×D7)⋊C412yes—
431C22×C4(C2×D7)⋊C412yes—
432C22×C4(C2×D7)⋊C412yes—
433C22×C4(C2×D7)⋊C412yes—
434C22×C4(C2×D7)⋊C411yescharacteristic
435C22×C4C2×C4×D711yescharacteristic
436C22×C4C2×C4×D712yes—
437C22×C4C2×C4×D712yes—
438C22×C4C2×C4×D711yescharacteristic
439C22×C4C2×D2811yescharacteristic
440C22×C4C2×D2812yes—
441C22×C4C2×D2811yescharacteristic
442C22×C4C2×D2812yes—
443C22×C4C2×C22⋊D712yes—
444C22×C4C2×C22⋊D711yescharacteristic
445C22×C4C23×D711yescharacteristic
446C2×C8—144no—
447C2×C8—284no—
448C2×C8—288no—
449C4⋊C4—72no—
450C4⋊C4—72no—
451C4⋊C4—142no—
452C4⋊C4—144no—
453C4⋊C4—141no—
454C4⋊C4—141no—
455C4⋊C4—142no—
456C22⋊C4—216no—
457C22⋊C4—144no—
458C22⋊C4—144no—
459C22⋊C4—142no—
460C22⋊C4—142no—
461C22⋊C4—144no—
462C22⋊C4—142no—
463C22⋊C4—142no—
464C42—48no—
465C42—144no—
466C2×C7—22no—
467C2×C7—22no—
468C2×C7—24no—
469C2×C7—42no—
470C2×C7#150114yescomplemented
471C2×C7C22×#9911yescharacteristic
472C2×C7C2×#41611yescharacteristic
473C2×C7C22×#10411yescharacteristic
474D7—82no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—24no—
480C23—24no—
481C23—22no—
482C23—22no—
483C23—24no—
484C23—24no—
485C23—22no—
486C23—42no—
487C23—42no—
488C23—416no—
489C23—142no—
490C23—282no—
491C23—282no—
492C23—282no—
493C23#637914yes—
494C23C2×(C2×D7)⋊C412yes—
495C23C2×(C2×D7)⋊C412yes—
496C23C2×(C2×D7)⋊C411yescharacteristic
497C23C2×(C2×D7)⋊C411yescharacteristic
498C23#651314yes—
499C23C22×C22⋊D711yescharacteristic
500Q8—282no—
501Q8—282no—
502D4—282no—
503D4—282no—
504D4—288no—
505D4—288no—
506D4—284no—
507D4—284no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—28no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—44no—
527C2×C4—416no—
528C2×C4—44no—
529C2×C4—142no—
530C2×C4—142no—
531C2×C4—142no—
532C2×C4—282no—
533C2×C4—282no—
534C2×C4—282no—
535C2×C4—288no—
536C2×C4#638014yes—
537C2×C4C2×(C2×D7)⋊C412yes—
538C2×C4C2×(C2×D7)⋊C411yescharacteristic
539C2×C4C2×(C2×D7)⋊C411yescharacteristic
540C2×C4C2×(C2×D7)⋊C412yes—
541C2×C4C22×C4×D711yescharacteristic
542C2×C4C22×D2811yescharacteristic
543C8—284no—
544C7C2×#150111yescharacteristic, complemented, Sylow
545C22—22no—
546C22—28no—
547C22—28no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—22no—
552C22—21no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—48no—
557C22—48no—
558C22—44no—
559C22—282no—
560C22—282no—
561C22—282no—
562C22—564no—
563C22C2×#637914yes—
564C22C2×#637912yes—
565C22C2×#638012yes—
566C22#8977412yes—
567C22#8977412yes—
568C22C22×(C2×D7)⋊C411yescharacteristic
569C22C2×#651312yes—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—22no—
574C4—21no—
575C4—48no—
576C4—282no—
577C4—282no—
578C4—282no—
579C4C2×#638014yes—
580C2—22no—
581C2—24no—
582C2—22no—
583C2—42no—
584C2—562no—
585C2#1172719714yesdirect product factor
586C2C22×#637911yescharacteristic
587C2C22×#638011yescharacteristic
588C2C2×#8977411yescharacteristic
subgroupG/H
centerC22×C4(C2×D7)⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C4×C7×C22⋊C4C2
socleC23×C7C2×C22⋊C4
prime radicalC2×#90482C2
cosocleC22×C4×C7C24
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C2×#1501
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×C22⋊C4C2semidirect
3. C22×C22⋊(C7⋊C8)C2semidirect
4. #11727197C2direct (N × H)
5. C2×#89247C2semidirect
6. C2×#89246C2semidirect
8. C22×#1157C4semidirect
14. #90482C4semidirect
16. C2×#6493C4semidirect
21. C2×#6489C4semidirect
22. C2×#6487C4semidirect
26. C4×C7×C22⋊C4C22semidirect
31. C2×C22⋊(C7⋊C8)C22semidirect
32. #89247C22semidirect
33. #89246C22semidirect
53. C2×#1157C2×C4semidirect
70. #6493C2×C4semidirect
81. #6489C2×C4semidirect
88. #6487C2×C4semidirect
103. C2×C4×C22⋊C4D7semidirect
211. C4×C22⋊C4C2×D7semidirect
470. C2×C7#1501semidirect
544. C7C2×#1501semidirect
585. C2#11727197direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904822
C2×C4×C7×C22⋊C42
C22×C22⋊(C7⋊C8)2
#117271972
C2×#892472
C2×#892462
C2×#15017