Finite Group Databasebeta

← C2×#11739982 #14217893

Subgroups — C2×#11739982 #14217893

Order 1792.

2946 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#518C211yesmaximal, characteristic, complemented
2C22×#6495C211yesmaximal, characteristic
3C2×#90214C211yesmaximal, characteristic, complemented
4C22×#6406C211yesmaximal, characteristic, complemented
5#11739982C2116yesmaximal, direct product factor
6C2×C4×#1142C212yesmaximal, complemented
7C2×#89786C212yesmaximal, complemented
8C2×#89790C212yesmaximal, complemented
9C2×C4×#1141C212yesmaximal, complemented
10C2×#89774C211yesmaximal, characteristic, complemented
11C2×#89767C211yesmaximal, characteristic, complemented
12C2×#89769C211yesmaximal, characteristic, complemented
13C23×C7×D4C2211yescharacteristic
14C22×#1157C2211yescharacteristic
15C7×#518—24no—
16C7×#518C2218yescomplemented
17C2×C4×C7×D4—21no—
18C2×C4×C7×D4—21no—
19C2×C4×C7×D4C2212yes—
20C2×C4×C7×D4C2212yes—
21C2×C7×#117C2211yescharacteristic
22C2×C7×#117C2211yescharacteristic
23C22×C7×C22⋊C4—22no—
24C22×#1142C2212yes—
25C2×#6495C4116yescomplemented
26C2×#6495C2218yes—
27C22×#1141C2212yes—
28C22×C4⋊Dic7C2211yescharacteristic
29C22×#1136C2211yescharacteristic
30C23×C7⋊C8C2211yescharacteristic
31#90214—24no—
32#90214C2218yescomplemented
33C2×#6455—21no—
34C2×D7×C4⋊C4—21no—
35C2×(C22⋊D7)⋊C4—22no—
36C2×C4×D28C2212yescomplemented
37C2×C4×Dic14C2212yescomplemented
38C2×#6406C2212yes—
39C2×#6406C2212yes—
40C2×#6406C2218yescomplemented
41#89790C22116yescomplemented
42C4×#1142C22116yescomplemented
43#89786C22116yescomplemented
44C4×#1141C22116yescomplemented
45#89774C2218yescomplemented
46#89769C2218yescomplemented
47#89767C2218yescomplemented
48C2×#6384C2211yescharacteristic, complemented
49C2×#6384C2211yescharacteristic, complemented
50C2×#6383C2211yescharacteristic, complemented
51C2×#6383C2211yescharacteristic, complemented
52C2×#6382C2212yescomplemented
53C2×#6381C2212yescomplemented
54C2×#6377C2212yescomplemented
55C2×C4×C7⋊C8C2212yescomplemented
56C2×#2946—71nomaximal, Sylow
57C25×C7—21no—
58C22×C7×D4—21no—
59C22×C7×D4—22no—
60C22×C7×D4—24no—
61C22×C7×D4C2×C418yescomplemented
62C22×C7×D4C2312yes—
63C22×C7×D4C2314yes—
64C23×C4×C7—22no—
65C23×C4×C7—22no—
66C23×C4×C7C2311yescharacteristic
67C22×C22⋊D7—21no—
68C23×Dic7—21no—
69C2×#1157—22no—
70C2×#1157—24no—
71C2×#1157C2×C418yescomplemented
72C2×#1157C2314yes—
73C22×D28C2311yescharacteristic
74C22×C4×D7—21no—
75C22×C4×D7—22no—
76C22×Dic14C2311yescharacteristic
77C4×C7×D4—28no—
78C4×C7×D4—28no—
79C4×C7×D4—24no—
80C4×C7×D4—24no—
81C4×C7×D4C2318yes—
82C4×C7×D4C2318yes—
83C7×#117—22no—
84C7×#117D414yes—
85C7×#117C2314yes—
86C7×#117C2314yes—
87C2×C7×C4⋊C4D411yescharacteristic
88C2×C7×C4⋊C4D411yescharacteristic
89C2×C7×C4⋊C4C2311yescharacteristic
90C2×C7×C4⋊C4C2311yescharacteristic
91C2×C7×C22⋊C4—21no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—216no—
95C2×C7×C22⋊C4D412yes—
96C2×C42×C7—21no—
97C2×C42×C7C2312yes—
98C2×#1142C2×C4116yescomplemented
99C2×#1142C2318yes—
100#6495C2×C4164yescomplemented
101C2×#1141C2×C4116yescomplemented
102C2×#1141C2318yes—
103C2×(C2×D7)⋊C4—22no—
104C2×C4⋊Dic7—21no—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7C2312yes—
107C2×C4⋊Dic7C2314yes—
108C2×Dic7⋊C4—22no—
109C2×C4×Dic7—22no—
110C2×#1136C2×C418yescomplemented
111C2×#1136C2314yes—
112C22×C7⋊C8—24no—
113C22×C7⋊C8C2311yescharacteristic
114C22×C7⋊C8C2311yescharacteristic
115C22×C7⋊C8C2314yes—
116C22×C7⋊C8C2312yes—
117#6455—28no—
118D7×C4⋊C4—28no—
119(C22⋊D7)⋊C4—216no—
120C4×D28—24no—
121C4×D28C2318yescomplemented
122C4×Dic14—24no—
123C4×Dic14C2318yescomplemented
124#6406C2318yes—
125#6406C2318yes—
126#6384C2314yescomplemented
127#6384C2314yescomplemented
128#6383C2314yescomplemented
129#6383C2314yescomplemented
130#6382C2318yescomplemented
131#6381C2318yescomplemented
132#6377C2318yescomplemented
133C4×C7⋊C8C2318yescomplemented
134C22×AGL(1,ℤ/8)—71no—
135C2×#520—71no—
136C2×#518D711yescharacteristic, complemented
137#2946—716no—
138C2×#442—72no—
139C2×#440—72no—
140C2×C4×SD16—72no—
141C2×C4×D8—72no—
142C2×#428—71no—
143C2×#416—71no—
144C22×#102—71no—
145C2×#405—71no—
146C24×C7—22no—
147C24×C7—28no—
148C24×C7—24no—
149C24×C7—82no—
150C24×C7—82no—
151C24×C7C2×D411yescharacteristic
152C23×D7—21no—
153C2×C7×D4—28no—
154C2×C7×D4—216no—
155C2×C7×D4—24no—
156C2×C7×D4—22no—
157C2×C7×D4—24no—
158C2×C7×D4—28no—
159C2×C7×D4C22×C418yes—
160C2×C7×D4C22×C4116yescomplemented
161C2×C7×D4C2414yes—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—28no—
165C22×C4×C7—28no—
166C22×C4×C7—84no—
167C22×C4×C7—84no—
168C22×C4×C7C22×C414yes—
169C22×C4×C7C2×D412yes—
170C22×C4×C7C2×D412yes—
171C22×C4×C7C2×D411yescharacteristic
172C22×C4×C7C2×D412yes—
173C22×C4×C7#4114yes—
174C22×C4×C7C2411yescharacteristic
175C22×C4×C7C2412yes—
176C2×C22⋊D7—28no—
177C2×C22⋊D7—24no—
178C22×Dic7—21no—
179C22×Dic7—22no—
180C22×Dic7—24no—
181C22×Dic7—82no—
182#1157—216no—
183#1157—28no—
184#1157C22×C4116yescomplemented
185C2×D28—21no—
186C2×D28—22no—
187C2×D28C22×C414yes—
188C2×D28C2412yes—
189C2×C4×D7—28no—
190C2×C4×D7—24no—
191C2×C4×D7—28no—
192C2×C4×D7—84no—
193C2×Dic14—21no—
194C2×Dic14—22no—
195C2×Dic14C22×C414yes—
196C2×Dic14C2412yes—
197C7×C4⋊C4—21no—
198C7×C4⋊C4—21no—
199C7×C4⋊C4C2×D414yes—
200C7×C4⋊C4C2×D414yes—
201C7×C4⋊C4C2412yes—
202C7×C4⋊C4C2412yes—
203C7×C22⋊C4—24no—
204C7×C22⋊C4—28no—
205C7×C22⋊C4—28no—
206C7×C22⋊C4C2×D418yes—
207C42×C7—24no—
208C42×C7C2×D414yes—
209C42×C7C2414yes—
210#1142C22×C4132yescomplemented
211#1141C22×C4132yescomplemented
212(C2×D7)⋊C4—28no—
213C4⋊Dic7—22no—
214C4⋊Dic7—24no—
215C4⋊Dic7C2414yes—
216Dic7⋊C4—28no—
217C4×Dic7—28no—
218#1136C22×C4116yescomplemented
219C2×C7⋊C8—22no—
220C2×C7⋊C8—22no—
221C2×C7⋊C8—28no—
222C2×C7⋊C8C22×C418yes—
223C2×C7⋊C8C2412yes—
224C2×C7⋊C8C2412yes—
225C2×C7⋊C8C2414yes—
226C22×#41—71no—
227C23×D4C2×D711yescharacteristic
228C2×AGL(1,ℤ/8)—716no—
229C2×AGL(1,ℤ/8)—78no—
230C22×SD16—72no—
231C22×D8—72no—
232C22×M16—71no—
233C23×C8—71no—
234#520—78no—
235#520—144no—
236#518—24no—
237#518C2×D718yescomplemented
238C2×C4×Q8—72no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4—72no—
242C2×C4×D4—142no—
243C2×C4×D4C2×D712yes—
244C2×C4×D4C2×D712yes—
245C2×#117—141no—
246C2×#117C2×D711yescharacteristic
247C2×#117C2×D711yescharacteristic
248C22×C4⋊C4—71no—
249C22×C4⋊C4—141no—
250C22×C22⋊C4—22no—
251#442—716no—
252#440—716no—
253C4×SD16—716no—
254C4×D8—716no—
255#428—78no—
256C2×#107—72no—
257C2×#106—72no—
258#416—78no—
259C2×#103—71no—
260C2×#103—71no—
261C2×#102—72no—
262C2×#102—72no—
263C2×#102—78no—
264C2×#102—71no—
265C2×#102—71no—
266#405—78no—
267C2×#97—72no—
268C2×C4×C8—72no—
269C23×C7—22no—
270C23×C7—22no—
271C23×C7—28no—
272C23×C7—24no—
273C23×C7—216no—
274C23×C7—44no—
275C23×C7—44no—
276C23×C7—816no—
277C23×C7—84no—
278C23×C7—84no—
279C23×C7C4×D414yes—
280C23×C7C22×D412yes—
281C23×C7C22×D411yescharacteristic
282C22×D7—24no—
283C22×D7—22no—
284C22×D7—42no—
285C22×D7—42no—
286C7×D4—28no—
287C7×D4—216no—
288C7×D4—24no—
289C7×D4C23×C418yes—
290C2×C4×C7—24no—
291C2×C4×C7—24no—
292C2×C4×C7—22no—
293C2×C4×C7—22no—
294C2×C4×C7—42no—
295C2×C4×C7—42no—
296C2×C4×C7—88no—
297C2×C4×C7—88no—
298C2×C4×C7C4×D414yes—
299C2×C4×C7C4×D418yes—
300C2×C4×C7C23×C412yes—
301C2×C4×C7C23×C414yes—
302C2×C4×C7C22×D414yes—
303C2×C4×C7C22×D414yes—
304C2×C4×C7C22×D412yes—
305C2×C4×C7C22×D411yescharacteristic
306C2×C4×C7C2×#4112yes—
307C2×C4×C7C2×#4114yes—
308C2×C4×C7C2511yescharacteristic
309C22⋊D7—216no—
310C2×Dic7—24no—
311C2×Dic7—22no—
312C2×Dic7—24no—
313C2×Dic7—44no—
314C2×Dic7—84no—
315D28—24no—
316D28—22no—
317D28C23×C414yes—
318C4×D7—216no—
319C4×D7—88no—
320Dic14—24no—
321Dic14—22no—
322Dic14C23×C414yes—
323C7⋊C8—22no—
324C7⋊C8—22no—
325C7⋊C8C23×C418yes—
326C25—21no—
327C2×#41—78no—
328C2×#41—74no—
329C2×#41—144no—
330C2×#41—142no—
331C22×Q8—71no—
332C22×D4—24no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—71no—
336C22×D4—141no—
337C22×D4C4×D718yescomplemented
338C22×D4C22×D712yes—
339C22×D4C22×D714yes—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—141no—
343C23×C4—141no—
344C23×C4—142no—
345C23×C4C22×D711yescharacteristic
346AGL(1,ℤ/8)—764no—
347C2×SD16—716no—
348C2×SD16—78no—
349C2×D8—716no—
350C2×D8—78no—
351C2×M16—78no—
352C2×M16—74no—
353C22×C8—72no—
354C22×C8—71no—
355C22×C8—71no—
356C22×C8—74no—
357C22×C8—144no—
358C4×Q8—78no—
359C4×Q8—144no—
360C4×D4—28no—
361C4×D4—28no—
362C4×D4—24no—
363C4×D4—24no—
364C4×D4—78no—
365C4×D4—1416no—
366C4×D4—144no—
367C4×D4C22×D718yes—
368C4×D4C22×D718yes—
369#117—22no—
370#117—148no—
371#117C22⋊D714yes—
372#117C22×D714yes—
373#117C22×D714yes—
374C2×C4⋊C4—72no—
375C2×C4⋊C4—74no—
376C2×C4⋊C4—141no—
377C2×C4⋊C4—142no—
378C2×C4⋊C4—142no—
379C2×C4⋊C4—148no—
380C2×C4⋊C4C22⋊D711yescharacteristic
381C2×C4⋊C4C22⋊D711yescharacteristic
382C2×C4⋊C4C22×D711yescharacteristic
383C2×C4⋊C4C22×D711yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—216no—
388C2×C22⋊C4—142no—
389C2×C22⋊C4C22⋊D712yes—
390C2×C42—21no—
391C2×C42—142no—
392C2×C42C22×D712yes—
393#107—78no—
394#106—78no—
395#103—74no—
396#103—74no—
397#102—78no—
398#102—78no—
399#102—74no—
400#102—74no—
401#97—78no—
402C4×C8—78no—
403C22×C7—28no—
404C22×C7—22no—
405C22×C7—22no—
406C22×C7—28no—
407C22×C7—416no—
408C22×C7—44no—
409C22×C7—44no—
410C22×C7—816no—
411C22×C7C2×C4×D414yes—
412C22×C7C2×C4×D412yes—
413C22×C7#57612yes—
414C22×C7#57712yes—
415C22×C7C23×D411yescharacteristic
416C2×D7—24no—
417C2×D7—48no—
418C2×D7—42no—
419C2×D7—42no—
420C4×C7—24no—
421C4×C7—24no—
422C4×C7—42no—
423C4×C7—42no—
424C4×C7C2×C4×D412yes—
425C4×C7C2×C4×D414yes—
426C4×C7C24×C411yescharacteristic
427C4×C7C22×#4111yescharacteristic
428Dic7—24no—
429Dic7—44no—
430C24—22no—
431C24—28no—
432C24—24no—
433C24—82no—
434C24—82no—
435C24—141no—
436C24C2×C22⋊D711yescharacteristic
437#41—716no—
438#41—1416no—
439#41—148no—
440C2×Q8—74no—
441C2×Q8—72no—
442C2×Q8—142no—
443C2×Q8—141no—
444C2×D4—28no—
445C2×D4—216no—
446C2×D4—24no—
447C2×D4—28no—
448C2×D4—24no—
449C2×D4—22no—
450C2×D4—74no—
451C2×D4—72no—
452C2×D4—148no—
453C2×D4—144no—
454C2×D4—142no—
455C2×D4—141no—
456C2×D4C2×C4×D718yes—
457C2×D4C2×C4×D7116yescomplemented
458C2×D4C23×D714yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—84no—
464C22×C4—84no—
465C22×C4—141no—
466C22×C4—148no—
467C22×C4—144no—
468C22×C4—142no—
469C22×C4—144no—
470C22×C4—148no—
471C22×C4—564no—
472C22×C4—562no—
473C22×C4C2×C4×D714yes—
474C22×C4#115714yes—
475C22×C4C2×C22⋊D712yes—
476C22×C4C2×C22⋊D712yes—
477C22×C4C2×C22⋊D712yes—
478C22×C4C2×C22⋊D711yescharacteristic
479C22×C4C23×D712yes—
480C22×C4C23×D711yescharacteristic
481SD16—732no—
482D8—732no—
483M16—716no—
484C2×C8—78no—
485C2×C8—74no—
486C2×C8—72no—
487C2×C8—72no—
488C2×C8—142no—
489C2×C8—142no—
490C2×C8—148no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—74no—
494C4⋊C4—148no—
495C4⋊C4—144no—
496C4⋊C4—142no—
497C4⋊C4C2×C22⋊D714yes—
498C4⋊C4C2×C22⋊D714yes—
499C4⋊C4C23×D712yes—
500C4⋊C4C23×D712yes—
501C22⋊C4—24no—
502C22⋊C4—28no—
503C22⋊C4—28no—
504C22⋊C4—148no—
505C22⋊C4C2×C22⋊D718yes—
506C42—24no—
507C42—148no—
508C42C2×C22⋊D714yes—
509C42C23×D714yes—
510C2×C7—24no—
511C2×C7—48no—
512C2×C7#294614yescomplemented
513C2×C7C22×C4×D411yescharacteristic
514C2×C7C2×#57611yescharacteristic
515C2×C7C2×#57711yescharacteristic
516D7—44no—
517C23—22no—
518C23—22no—
519C23—28no—
520C23—24no—
521C23—216no—
522C23—44no—
523C23—44no—
524C23—816no—
525C23—84no—
526C23—84no—
527C23—144no—
528C23—142no—
529C23—282no—
530C23—282no—
531C23C4×C22⋊D714yes—
532C23C22×C22⋊D712yes—
533C23C22×C22⋊D711yescharacteristic
534Q8—74no—
535Q8—144no—
536Q8—142no—
537D4—28no—
538D4—216no—
539D4—24no—
540D4—74no—
541D4—1416no—
542D4—144no—
543D4—142no—
544D4C22×C4×D718yes—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—88no—
552C2×C4—88no—
553C2×C4—144no—
554C2×C4—142no—
555C2×C4—1416no—
556C2×C4—144no—
557C2×C4—284no—
558C2×C4—568no—
559C2×C4—564no—
560C2×C4C4×C22⋊D714yes—
561C2×C4C4×C22⋊D718yes—
562C2×C4C22×C4×D712yes—
563C2×C4C22×C4×D714yes—
564C2×C4C2×#115712yes—
565C2×C4C2×#115714yes—
566C2×C4C22×C22⋊D714yes—
567C2×C4C22×C22⋊D714yes—
568C2×C4C22×C22⋊D712yes—
569C2×C4C22×C22⋊D711yescharacteristic
570C2×C4C24×D711yescharacteristic
571C8—78no—
572C8—142no—
573C8—142no—
574C7C2×#294611yescharacteristic, complemented, Sylow
575C22—28no—
576C22—22no—
577C22—22no—
578C22—28no—
579C22—416no—
580C22—44no—
581C22—44no—
582C22—816no—
583C22—144no—
584C22—288no—
585C22—282no—
586C22—282no—
587C22C2×C4×C22⋊D714yes—
588C22C2×C4×C22⋊D712yes—
589C22#9052612yes—
590C22#9052712yes—
591C22C23×C22⋊D711yescharacteristic
592C4—24no—
593C4—24no—
594C4—42no—
595C4—42no—
596C4—144no—
597C4—284no—
598C4C2×C4×C22⋊D714yes—
599C4C2×C4×C22⋊D712yes—
600C4C23×C4×D711yescharacteristic
601C4C22×#115711yescharacteristic
602C2—24no—
603C2—48no—
604C2—284no—
605C2#1173998214yesdirect product factor
606C2C22×C4×C22⋊D711yescharacteristic
607C2C2×#9052611yescharacteristic
608C2C2×#9052711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC4×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C7×#518C2
socleC23×C7C22×D4
prime radicalC22×#6495C2
cosocleC2×C4×C7C25
hypercenterC2×#518D7
hypocenterC7C2×#2946
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
1. C2×C7×#518C2semidirect
3. C2×#90214C2semidirect
4. C22×#6406C2semidirect
5. #11739982C2direct (N × H)
6. C2×C4×#1142C2semidirect
7. C2×#89786C2semidirect
8. C2×#89790C2semidirect
9. C2×C4×#1141C2semidirect
10. C2×#89774C2semidirect
11. C2×#89767C2semidirect
12. C2×#89769C2semidirect
16. C7×#518C22semidirect
25. C2×#6495C4semidirect
32. #90214C22semidirect
36. C2×C4×D28C22semidirect
37. C2×C4×Dic14C22semidirect
40. C2×#6406C22semidirect
41. #89790C22semidirect
42. C4×#1142C22semidirect
43. #89786C22semidirect
44. C4×#1141C22semidirect
45. #89774C22semidirect
46. #89769C22semidirect
47. #89767C22semidirect
48. C2×#6384C22semidirect
49. C2×#6384C22semidirect
50. C2×#6383C22semidirect
51. C2×#6383C22semidirect
52. C2×#6382C22semidirect
53. C2×#6381C22semidirect
54. C2×#6377C22semidirect
55. C2×C4×C7⋊C8C22semidirect
61. C22×C7×D4C2×C4semidirect
71. C2×#1157C2×C4semidirect
98. C2×#1142C2×C4semidirect
100. #6495C2×C4semidirect
101. C2×#1141C2×C4semidirect
110. C2×#1136C2×C4semidirect
121. C4×D28C23semidirect
123. C4×Dic14C23semidirect
126. #6384C23semidirect
127. #6384C23semidirect
128. #6383C23semidirect
129. #6383C23semidirect
130. #6382C23semidirect
131. #6381C23semidirect
132. #6377C23semidirect
133. C4×C7⋊C8C23semidirect
136. C2×#518D7semidirect
160. C2×C7×D4C22×C4semidirect
184. #1157C22×C4semidirect
210. #1142C22×C4semidirect
211. #1141C22×C4semidirect
218. #1136C22×C4semidirect
237. #518C2×D7semidirect
337. C22×D4C4×D7semidirect
457. C2×D4C2×C4×D7semidirect
512. C2×C7#2946semidirect
574. C7C2×#2946semidirect
605. C2#11739982direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5182
C22×#64952
C2×#902142
C22×#64062
#117399822
C2×C4×#11422
C2×#897862
C2×#897902
C2×C4×#11412
C2×#897742
C2×#897672
C2×#897692
C2×#29467