Finite Group Databasebeta

← C2×#11738715 #14221987

Subgroups — C2×#11738715 #14221987

Order 1792.

2398 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90287C211yesmaximal, characteristic
2C22×#6450C211yesmaximal, characteristic, complemented
3C2×C7×#480C211yesmaximal, characteristic, complemented
4C2×#89812C211yesmaximal, characteristic, complemented
5C2×#89739C211yesmaximal, characteristic, complemented
6#11738715C2116yesmaximal, direct product factor
7C2×#89647C212yesmaximal, complemented
8C2×#89661C212yesmaximal, complemented
9C2×#89534C212yesmaximal, complemented
10C2×#89529C212yesmaximal, complemented
11C2×#89510C211yesmaximal, characteristic, complemented
12C2×#89491C211yesmaximal, characteristic, complemented
13C22×#1159—21no—
14C23×Dic14C2211yescharacteristic
15C2×C7×#121C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C2×#6503C2211yescharacteristic
18C2×#6502—21no—
19C2×D4×Dic7C2211yescharacteristic
20C22×#1142C2212yes—
21C2×#6493C2211yescharacteristic
22C22×Dic7⋊C4—21no—
23C22×C4×Dic7—21no—
24C22×C4×Dic7C2211yescharacteristic
25C22×#1132C2212yes—
26#90287—24no—
27#90287C2218yes—
28C2×#6456C2211yescharacteristic
29C2×#6451C2211yescharacteristic
30C2×#6450—24no—
31C2×#6450—21no—
32C2×#6450—21no—
33C2×#6450C2212yes—
34C2×#6450C2212yes—
35C2×#6450C2218yescomplemented
36C2×#6448—21no—
37C2×(C22⋊D7)⋊C4—21no—
38C7×#480C2218yescomplemented
39C2×C7×#107C2212yes—
40C2×C7×#102C2212yes—
41C2×C7×C22⋊C8C2211yescharacteristic
42C2×C22⋊(C7⋊C8)C2211yescharacteristic
43C2×#6390C2212yes—
44C2×#6389C2212yes—
45C2×Dic7⋊C8C2212yes—
46#89812C2218yescomplemented
47C2×#6384C2212yes—
48#89739C2218yescomplemented
49C2×#6383C2212yes—
50C2×#6381C2212yes—
51#89661C22116yescomplemented
52#89647C22116yescomplemented
53#89534C22116yescomplemented
54#89529C22116yescomplemented
55#89510C2218yescomplemented
56#89491C2218yescomplemented
57C2×#3112—71nomaximal, Sylow
58C22×C7×D4—21no—
59C22×C7×D4C2311yescharacteristic
60C23×C4×C7—21no—
61C23×C4×C7C2311yescharacteristic
62C22×C22⋊D7—21no—
63C22×C22⋊D7—21no—
64C22×C22⋊D7—21no—
65C23×Dic7—21no—
66C23×Dic7—21no—
67C23×Dic7D411yescharacteristic
68C23×Dic7D411yescharacteristic
69C2×#1159—28no—
70C2×#1159—48no—
71C22×D28C2311yescharacteristic
72C22×C4×D7—21no—
73C22×Dic14—21no—
74C22×Dic14—22no—
75C22×Dic14—28no—
76C22×Dic14—21no—
77C22×Dic14C2314yes—
78C22×Dic14C2312yes—
79C22×C7×C8C2312yes—
80C7×#121—22no—
81C7×#121C2314yes—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4C2314yes—
85C2×C7×C4⋊C4C2312yes—
86C2×C7×C4⋊C4C2311yescharacteristic
87C2×C7×C22⋊C4—21no—
88C2×C22⋊Dic7—21no—
89#6503—22no—
90#6503C2314yes—
91#6502—28no—
92D4×Dic7—22no—
93D4×Dic7C2314yes—
94C2×#1142—28no—
95C2×#1142C2318yes—
96#6493—22no—
97#6493C2314yes—
98C2×(C2×D7)⋊C4—21no—
99C2×(C2×D7)⋊C4—21no—
100C2×C4⋊Dic7C2311yescharacteristic
101C2×Dic7⋊C4—21no—
102C2×Dic7⋊C4—22no—
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—28no—
105C2×C4×Dic7—22no—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—28no—
108C2×C4×Dic7D411yescharacteristic
109C2×C4×Dic7D411yescharacteristic
110C2×C4×Dic7D414yes—
111C2×C4×Dic7C2311yescharacteristic
112C2×C4×Dic7C2311yescharacteristic
113C2×C4×Dic7C2314yes—
114C22×C7⋊C8C2312yes—
115C2×#1132—28no—
116C2×#1132C2318yes—
117#6456—22no—
118#6456C2314yes—
119#6451—22no—
120#6451C2314yes—
121#6450—24no—
122#6450—24no—
123#6450—28no—
124#6450—28no—
125#6450C2318yes—
126#6450C2318yes—
127#6448—28no—
128(C22⋊D7)⋊C4—28no—
129C7×#107C2318yes—
130C7×#102C2318yes—
131C7×C22⋊C8C2314yes—
132C22⋊(C7⋊C8)C2314yes—
133#6390C2318yes—
134#6389C2318yes—
135Dic7⋊C8C2318yes—
136#6384C2318yes—
137#6383C2318yes—
138#6381C2318yes—
139C2×#532—71no—
140C22×C4×Q8—71no—
141#3112—716no—
142C2×#480—71no—
143C2×#480D711yescharacteristic, complemented
144C2×#477—72no—
145C2×#460—72no—
146C2×#448—71no—
147C2×#448—71no—
148C2×#440—72no—
149C2×#440—72no—
150C2×#432—71no—
151C24×C7—21no—
152C24×C7C2×D411yescharacteristic
153C23×D7—21no—
154C2×C7×D4—24no—
155C2×C7×D4—21no—
156C2×C7×D4—24no—
157C2×C7×D4—44no—
158C2×C7×D4C2412yes—
159C22×C4×C7—24no—
160C22×C4×C7—24no—
161C22×C4×C7—22no—
162C22×C4×C7—21no—
163C22×C4×C7—44no—
164C22×C4×C7C2×D411yescharacteristic
165C22×C4×C7C2×D412yes—
166C22×C4×C7C2412yes—
167C22×C4×C7C2411yescharacteristic
168C2×C22⋊D7—24no—
169C2×C22⋊D7—24no—
170C2×C22⋊D7—24no—
171C2×C22⋊D7—44no—
172C2×C22⋊D7—44no—
173C2×C22⋊D7—44no—
174C22×Dic7—28no—
175C22×Dic7—24no—
176C22×Dic7—24no—
177C22×Dic7—22no—
178C22×Dic7—24no—
179C22×Dic7—21no—
180C22×Dic7—24no—
181C22×Dic7—44no—
182C22×Dic7C2×D411yescharacteristic
183C22×Dic7C2×D414yes—
184C22×Dic7C2×D411yescharacteristic
185C22×Dic7C2×D411yescharacteristic
186C22×Dic7C2×D414yes—
187C22×Dic7C2×D411yescharacteristic
188#1159—432no—
189C2×D28—24no—
190C2×D28—21no—
191C2×D28C2412yes—
192C2×C4×D7—24no—
193C2×C4×D7—44no—
194C2×Dic14—28no—
195C2×Dic14—216no—
196C2×Dic14—24no—
197C2×Dic14—22no—
198C2×Dic14—24no—
199C2×Dic14—216no—
200C2×Dic14—24no—
201C2×Dic14—44no—
202C2×Dic14#4118yescomplemented
203C2×Dic14C2414yes—
204C2×C7×C8—24no—
205C2×C7×C8C2414yes—
206C7×C4⋊C4—24no—
207C7×C4⋊C4—22no—
208C7×C4⋊C4—21no—
209C7×C4⋊C4C2414yes—
210C7×C4⋊C4C2412yes—
211C7×C22⋊C4—24no—
212C22⋊Dic7—24no—
213#1142—216no—
214(C2×D7)⋊C4—24no—
215(C2×D7)⋊C4—24no—
216C4⋊Dic7—21no—
217C4⋊Dic7C2412yes—
218Dic7⋊C4—24no—
219Dic7⋊C4—28no—
220Dic7⋊C4—28no—
221C4×Dic7—28no—
222C4×Dic7—28no—
223C4×Dic7C2×D414yes—
224C4×Dic7C2×D414yes—
225C4×Dic7C2×D412yes—
226C4×Dic7C2×D412yes—
227C4×Dic7C2412yes—
228C4×Dic7C2412yes—
229C2×C7⋊C8—24no—
230C2×C7⋊C8C2414yes—
231#1132—216no—
232C22×#41—141no—
233C23×Q8—71no—
234C22×SD16—72no—
235C22×SD16—72no—
236#532—78no—
237#532—144no—
238C2×C4⋊Q8—71no—
239C2×#127—71no—
240C2×#124—141no—
241C2×#121—71no—
242C2×#121—141no—
243C2×#121C2×D711yescharacteristic
244C2×C4×Q8—72no—
245C2×C4×Q8—78no—
246C2×C4×Q8—72no—
247C2×C4×Q8—141no—
248C2×C4×Q8—141no—
249C2×C4×Q8—144no—
250C2×C4×D4—71no—
251C2×C4×D4—71no—
252C2×C4×D4—141no—
253C22×C4⋊C4—141no—
254C22×C4⋊C4C2×D711yescharacteristic
255C22×C42—71no—
256C22×C42—141no—
257#480—78no—
258#480C2×D718yescomplemented
259#477—716no—
260#460—716no—
261#448—78no—
262#448—78no—
263#440—716no—
264#440—716no—
265#432—78no—
266C2×#107—72no—
267C2×#107C2×D712yes—
268C2×C4⋊C8—72no—
269C2×#103—72no—
270C2×#103—72no—
271C2×#102—72no—
272C2×#102C2×D712yes—
273C2×C22⋊C8—71no—
274C2×C22⋊C8C2×D711yescharacteristic
275C2×#97—72no—
276C23×C7—22no—
277C23×C7—22no—
278C23×C7—22no—
279C23×C7—42no—
280C23×C7—42no—
281C23×C7—42no—
282C23×C7AGL(1,ℤ/8)14yes—
283C23×C7C22×D412yes—
284C23×C7C22×D411yescharacteristic
285C22×D7—22no—
286C22×D7—42no—
287C22×D7—42no—
288C22×D7—42no—
289C7×D4—24no—
290C7×D4—48no—
291C7×D4—42no—
292C2×C4×C7—22no—
293C2×C4×C7—24no—
294C2×C4×C7—24no—
295C2×C4×C7—24no—
296C2×C4×C7—22no—
297C2×C4×C7—42no—
298C2×C4×C7—48no—
299C2×C4×C7—44no—
300C2×C4×C7C22×D412yes—
301C2×C4×C7C22×D411yescharacteristic
302C2×C4×C7C2×#4114yes—
303C2×C4×C7C2511yescharacteristic
304C22⋊D7—48no—
305C22⋊D7—48no—
306C22⋊D7—48no—
307C2×Dic7—216no—
308C2×Dic7—28no—
309C2×Dic7—22no—
310C2×Dic7—22no—
311C2×Dic7—28no—
312C2×Dic7—22no—
313C2×Dic7—24no—
314C2×Dic7—28no—
315C2×Dic7—22no—
316C2×Dic7—48no—
317C2×Dic7—42no—
318C2×Dic7#13714yes—
319C2×Dic7C22×D412yes—
320C2×Dic7C22×D412yes—
321C2×Dic7C22×D412yes—
322C2×Dic7C22×D412yes—
323D28—24no—
324D28—42no—
325C4×D7—48no—
326Dic14—216no—
327Dic14—28no—
328Dic14—24no—
329Dic14—48no—
330Dic14C2×#4118yescomplemented
331C7×C8—24no—
332C7⋊C8—24no—
333C2×#41—148no—
334C2×#41—288no—
335C22×Q8—72no—
336C22×Q8—74no—
337C22×Q8—141no—
338C22×Q8—148no—
339C22×Q8—142no—
340C22×Q8—141no—
341C22×D4—21no—
342C22×D4—71no—
343C22×D4—141no—
344C22×D4—141no—
345C22×D4—141no—
346C22×D4C22×D711yescharacteristic
347C23×C4—21no—
348C23×C4—71no—
349C23×C4—71no—
350C23×C4—141no—
351C23×C4—141no—
352C23×C4—141no—
353C23×C4C22×D711yescharacteristic
354C2×SD16—78no—
355C2×SD16—78no—
356C2×SD16—148no—
357C2×SD16—148no—
358C22×C8—72no—
359C22×C8C22×D712yes—
360C4⋊Q8—74no—
361C4⋊Q8—142no—
362#127—74no—
363#127—142no—
364#124—148no—
365#121—22no—
366#121—74no—
367#121—148no—
368#121—142no—
369#121C22×D714yes—
370C4×Q8—78no—
371C4×Q8—78no—
372C4×Q8—148no—
373C4×Q8—144no—
374C4×Q8—148no—
375C4×Q8—144no—
376C4×D4—74no—
377C4×D4—74no—
378C4×D4—148no—
379C4×D4—142no—
380C4×D4—142no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—71no—
384C2×C4⋊C4—148no—
385C2×C4⋊C4—142no—
386C2×C4⋊C4—142no—
387C2×C4⋊C4—141no—
388C2×C4⋊C4C22×D712yes—
389C2×C4⋊C4C22×D714yes—
390C2×C4⋊C4C22×D711yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—141no—
393C2×C22⋊C4—141no—
394C2×C22⋊C4—141no—
395C2×C42—71no—
396C2×C42—71no—
397C2×C42—74no—
398C2×C42—71no—
399C2×C42—71no—
400C2×C42—74no—
401C2×C42—148no—
402C2×C42—142no—
403C2×C42—142no—
404#107—78no—
405#107C22×D718yes—
406C4⋊C8—78no—
407#103—78no—
408#103—78no—
409#102—78no—
410#102C22×D718yes—
411C22⋊C8—74no—
412C22⋊C8C22×D714yes—
413#97—78no—
414C22×C7—28no—
415C22×C7—22no—
416C22×C7—22no—
417C22×C7—42no—
418C22×C7—42no—
419C22×C7—42no—
420C22×C7—84no—
421C22×C7#52512yes—
422C22×C7C2×AGL(1,ℤ/8)14yes—
423C22×C7C2×AGL(1,ℤ/8)12yes—
424C22×C7C2×#13712yes—
425C22×C7C23×D411yescharacteristic
426C2×D7—42no—
427C2×D7—42no—
428C2×D7—42no—
429C2×D7—84no—
430C4×C7—22no—
431C4×C7—42no—
432C4×C7—44no—
433C4×C7#52512yes—
434C4×C7C22×#4112yes—
435Dic7—28no—
436Dic7—22no—
437Dic7—22no—
438Dic7—22no—
439Dic7—42no—
440Dic7C2×#13714yes—
441C24—21no—
442C24—141no—
443C24D4×D711yescharacteristic
444#41—2832no—
445C2×Q8—78no—
446C2×Q8—74no—
447C2×Q8—144no—
448C2×Q8—1416no—
449C2×Q8—148no—
450C2×Q8—1416no—
451C2×Q8—144no—
452C2×Q8—142no—
453C2×Q8—144no—
454C2×Q8—284no—
455C2×D4—24no—
456C2×D4—21no—
457C2×D4—24no—
458C2×D4—44no—
459C2×D4—72no—
460C2×D4—144no—
461C2×D4—144no—
462C2×D4—144no—
463C2×D4—141no—
464C2×D4—144no—
465C2×D4—284no—
466C2×D4—284no—
467C2×D4—284no—
468C2×D4C23×D712yes—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—44no—
474C22×C4—71no—
475C22×C4—74no—
476C22×C4—74no—
477C22×C4—71no—
478C22×C4—71no—
479C22×C4—71no—
480C22×C4—144no—
481C22×C4—144no—
482C22×C4—144no—
483C22×C4—148no—
484C22×C4—144no—
485C22×C4—144no—
486C22×C4—142no—
487C22×C4—141no—
488C22×C4—284no—
489C22×C4—284no—
490C22×C4D4×D712yes—
491C22×C4D4×D711yescharacteristic
492C22×C4C23×D712yes—
493C22×C4C23×D711yescharacteristic
494SD16—1416no—
495SD16—1416no—
496C2×C8—24no—
497C2×C8—74no—
498C2×C8—144no—
499C2×C8C23×D714yes—
500C4⋊C4—24no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—72no—
504C4⋊C4—148no—
505C4⋊C4—148no—
506C4⋊C4—144no—
507C4⋊C4—141no—
508C4⋊C4C23×D714yes—
509C4⋊C4C23×D712yes—
510C22⋊C4—24no—
511C22⋊C4—144no—
512C22⋊C4—144no—
513C22⋊C4—144no—
514C42—74no—
515C42—72no—
516C42—74no—
517C42—72no—
518C42—72no—
519C42—72no—
520C42—148no—
521C42—148no—
522C2×C7—24no—
523C2×C7—82no—
524C2×C7#311214yescomplemented
525C2×C7C2×#52511yescharacteristic
526C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
527C2×C7C22×#13711yescharacteristic
528D7—82no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—142no—
536C23—282no—
537C23—282no—
538C23—282no—
539C23#647414yes—
540C23C2×D4×D712yes—
541C23C2×D4×D711yescharacteristic
542Q8—78no—
543Q8—1416no—
544Q8—148no—
545Q8—144no—
546Q8—288no—
547D4—24no—
548D4—48no—
549D4—42no—
550D4—144no—
551D4—288no—
552D4—288no—
553D4—288no—
554D4—282no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—48no—
561C2×C4—44no—
562C2×C4—42no—
563C2×C4—74no—
564C2×C4—72no—
565C2×C4—72no—
566C2×C4—72no—
567C2×C4—72no—
568C2×C4—148no—
569C2×C4—1416no—
570C2×C4—142no—
571C2×C4—142no—
572C2×C4—148no—
573C2×C4—142no—
574C2×C4—148no—
575C2×C4—144no—
576C2×C4—142no—
577C2×C4—288no—
578C2×C4—288no—
579C2×C4—282no—
580C2×C4C2×D4×D712yes—
581C2×C4C2×D4×D711yescharacteristic
582C2×C4D7×#4114yes—
583C2×C4C24×D711yescharacteristic
584C8—24no—
585C8—144no—
586C7C2×#311211yescharacteristic, complemented, Sylow
587C22—22no—
588C22—22no—
589C22—28no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—84no—
594C22—282no—
595C22—282no—
596C22—282no—
597C22—564no—
598C22#9034712yes—
599C22C2×#647414yes—
600C22C2×#647412yes—
601C22D7×#13712yes—
602C22C22×D4×D711yescharacteristic
603C4—22no—
604C4—44no—
605C4—42no—
606C4—74no—
607C4—142no—
608C4—148no—
609C4—142no—
610C4—142no—
611C4—282no—
612C4#9034712yes—
613C4C2×D7×#4112yes—
614C2—24no—
615C2—82no—
616C2—562no—
617C2#1173871514yesdirect product factor
618C2C2×#9034711yescharacteristic
619C2C22×#647411yescharacteristic
620C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#480C2
socleC23×C7C22×D4
prime radicalC2×#90287C2
hypercenterC2×#480D7
hypocenterC7C2×#3112
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C22×#6450C2semidirect
3. C2×C7×#480C2semidirect
4. C2×#89812C2semidirect
5. C2×#89739C2semidirect
6. #11738715C2direct (N × H)
7. C2×#89647C2semidirect
8. C2×#89661C2semidirect
9. C2×#89534C2semidirect
10. C2×#89529C2semidirect
11. C2×#89510C2semidirect
12. C2×#89491C2semidirect
35. C2×#6450C22semidirect
38. C7×#480C22semidirect
46. #89812C22semidirect
48. #89739C22semidirect
51. #89661C22semidirect
52. #89647C22semidirect
53. #89534C22semidirect
54. #89529C22semidirect
55. #89510C22semidirect
56. #89491C22semidirect
143. C2×#480D7semidirect
202. C2×Dic14#41semidirect
258. #480C2×D7semidirect
330. Dic14C2×#41semidirect
524. C2×C7#3112semidirect
586. C7C2×#3112semidirect
617. C2#11738715direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902872
C22×#64502
C2×C7×#4802
C2×#898122
C2×#897392
#117387152
C2×#896472
C2×#896612
C2×#895342
C2×#895292
C2×#895102
C2×#894912
C2×#31127