Finite Group Databasebeta

← C2×#11739980 #14221934

Subgroups — C2×#11739980 #14221934

Order 1792.

2150 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×C4×C7×#41C211yesmaximal, characteristic
2C2×#90161C211yesmaximal, characteristic, complemented
3C2×#90011C212yesmaximal
4#11739980C2116yesmaximal, direct product factor
5C2×#89803C211yesmaximal, characteristic, complemented
6C2×#89793C211yesmaximal, characteristic, complemented
7C2×#89802C212yesmaximal, complemented
8C2×#89791C211yesmaximal, characteristic, complemented
9C2×#89780C211yesmaximal, characteristic, complemented
10C2×#89790C212yesmaximal, complemented
11C2×#89768C212yesmaximal, complemented
12C2×#89698C211yesmaximal, characteristic, complemented
13C22×C7×#41C2211yescharacteristic
14C4×C7×#41—24no—
15C4×C7×#41C2218yes—
16C2×C4×C7×Q8C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×C7×D4—21no—
19C2×C4×C7×D4—21no—
20C2×C4×C7×D4C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C2×C7×#117—21no—
23C2×C7×#117C2211yescharacteristic
24C22×C42×C7—21no—
25C22×C42×C7C2211yescharacteristic
26C22×#1144C2212yes—
27C22×#1142C2212yes—
28C2×#6489—21no—
29C2×#6487—21no—
30C2×#6487C2212yes—
31#90161—24no—
32#90161C2218yescomplemented
33C2×#6433—21no—
34C2×#6432C2211yescharacteristic
35C2×#6432C2211yescharacteristic
36C2×C4×Dic14—21no—
37C2×C4×Dic14C2212yes—
38#90011C22116yes—
39C2×#6409C2212yes—
40C2×#6406C2212yes—
41C2×C22⋊(C7⋊C8)C2212yes—
42#89803C2218yescomplemented
43#89802C22116yescomplemented
44#89793C2218yescomplemented
45#89791C2218yescomplemented
46#89790C22116yescomplemented
47#89780C2218yescomplemented
48#89768C22116yescomplemented
49C2×#6384C2212yes—
50C2×#6384C2212yes—
51C2×#6382C2212yes—
52C2×#6381C2212yes—
53#89698C2218yescomplemented
54C2×C4⋊(C7⋊C8)C2211yescharacteristic
55C2×C4⋊(C7⋊C8)C2211yescharacteristic
56C2×#6377C2212yes—
57C2×#3116—71nomaximal, Sylow
58C2×C7×#41—24no—
59C2×C7×#41—24no—
60C2×C7×#41—22no—
61C2×C7×#41C2314yes—
62C22×C7×Q8C2311yescharacteristic
63C22×C7×D4—21no—
64C22×C7×D4C2311yescharacteristic
65C23×C4×C7—21no—
66C23×C4×C7—21no—
67C23×C4×C7—21no—
68C23×C4×C7D411yescharacteristic
69C23×C4×C7D411yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C22×Dic14—21no—
72C22×Dic14C2312yes—
73C4×C7×Q8—22no—
74C4×C7×Q8—22no—
75C4×C7×Q8C2314yes—
76C4×C7×Q8C2314yes—
77C4×C7×D4—28no—
78C4×C7×D4—28no—
79C4×C7×D4—22no—
80C4×C7×D4—22no—
81C4×C7×D4C2314yes—
82C4×C7×D4C2314yes—
83C7×#117—22no—
84C7×#117—28no—
85C7×#117C2314yes—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—21no—
88C2×C7×C4⋊C4C2311yescharacteristic
89C2×C7×C4⋊C4C2311yescharacteristic
90C2×C7×C22⋊C4—21no—
91C2×C7×C22⋊C4—21no—
92C2×C7×C22⋊C4—21no—
93C2×C42×C7—21no—
94C2×C42×C7—21no—
95C2×C42×C7—21no—
96C2×C42×C7—28no—
97C2×C42×C7D411yescharacteristic
98C2×C42×C7D411yescharacteristic
99C2×C42×C7D414yes—
100C2×C42×C7C2311yescharacteristic
101C2×C42×C7C2311yescharacteristic
102C2×C42×C7C2314yes—
103C2×C22⋊Dic7—22no—
104C2×#1144—28no—
105C2×#1144C2318yes—
106C2×#1142—28no—
107C2×#1142C2318yes—
108#6489—28no—
109C2×C4⋊Dic7—21no—
110C2×C4⋊Dic7—21no—
111C2×C4⋊Dic7—21no—
112C2×C4⋊Dic7C2312yes—
113#6487—24no—
114#6487—28no—
115#6487C2318yes—
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—22no—
118C2×C4×Dic7—22no—
119C22×C7⋊C8C2312yes—
120C22×C7⋊C8C2312yes—
121#6433—28no—
122#6432—22no—
123#6432—22no—
124#6432C2314yes—
125#6432C2314yes—
126C4×Dic14—28no—
127C4×Dic14—24no—
128C4×Dic14C2318yes—
129#6409C2318yes—
130#6406C2318yes—
131C22⋊(C7⋊C8)C2318yes—
132#6384C2318yes—
133#6384C2318yes—
134#6382C2318yes—
135#6381C2318yes—
136C4⋊(C7⋊C8)C2314yes—
137C4⋊(C7⋊C8)C2314yes—
138#6377C2318yes—
139C2×#533—71no—
140C2×C4×#41D711yescharacteristic
141#3116—716no—
142C2×#485—72no—
143C2×#477—71no—
144C2×#476—71no—
145C2×#462—71no—
146C2×#461—71no—
147C2×#452—72no—
148C2×#441—72no—
149C2×#440—72no—
150C2×#432—71no—
151C24×C7—21no—
152C24×C7C2×D411yescharacteristic
153C7×#41—216no—
154C7×#41—28no—
155C7×#41—28no—
156C2×C7×Q8—21no—
157C2×C7×Q8—22no—
158C2×C7×Q8#4114yes—
159C2×C7×Q8C2412yes—
160C2×C7×D4—28no—
161C2×C7×D4—24no—
162C2×C7×D4—21no—
163C2×C7×D4—22no—
164C2×C7×D4#4114yes—
165C2×C7×D4C2412yes—
166C22×C4×C7—28no—
167C22×C4×C7—21no—
168C22×C4×C7—24no—
169C22×C4×C7—24no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—24no—
175C22×C4×C7—24no—
176C22×C4×C7—42no—
177C22×C4×C7—44no—
178C22×C4×C7—44no—
179C22×C4×C7C2×D411yescharacteristic
180C22×C4×C7C2×D411yescharacteristic
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2×D412yes—
183C22×C4×C7C2×D411yescharacteristic
184C22×C4×C7C2×D414yes—
185C22×C4×C7C2×D414yes—
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7C2412yes—
188C22×C4×C7C2411yescharacteristic
189C22×Dic7—22no—
190C22×Dic7—22no—
191C2×Dic14—24no—
192C2×Dic14—24no—
193C2×Dic14—22no—
194C2×Dic14—24no—
195C2×Dic14—44no—
196C2×Dic14C2414yes—
197C7×C4⋊C4—24no—
198C7×C4⋊C4—24no—
199C7×C4⋊C4—21no—
200C7×C4⋊C4—21no—
201C7×C4⋊C4C2412yes—
202C7×C4⋊C4C2412yes—
203C7×C22⋊C4—24no—
204C7×C22⋊C4—24no—
205C7×C22⋊C4—24no—
206C42×C7—24no—
207C42×C7—24no—
208C42×C7—24no—
209C42×C7C2×D414yes—
210C42×C7C2×D412yes—
211C42×C7C2×D412yes—
212C42×C7C2×D414yes—
213C42×C7C2412yes—
214C42×C7C2412yes—
215C22⋊Dic7—28no—
216#1144—216no—
217#1142—216no—
218C4⋊Dic7—22no—
219C4⋊Dic7—24no—
220C4⋊Dic7—24no—
221C4⋊Dic7—24no—
222C4⋊Dic7C2414yes—
223Dic7⋊C4—28no—
224Dic7⋊C4—28no—
225C4×Dic7—28no—
226C2×C7⋊C8—24no—
227C2×C7⋊C8—24no—
228C2×C7⋊C8C2414yes—
229C2×C7⋊C8C2414yes—
230C22×#41C2×D711yescharacteristic
231C22×Q16—72no—
232C22×SD16—72no—
233#533—78no—
234#533—144no—
235C2×C4⋊Q8—71no—
236C2×C4⋊Q8—71no—
237C2×#125—141no—
238C2×C22⋊Q8—72no—
239C2×C22⋊Q8—141no—
240C4×#41—24no—
241C4×#41C2×D718yes—
242C2×C4×Q8—72no—
243C2×C4×Q8—141no—
244C2×C4×Q8C2×D711yescharacteristic
245C2×C4×Q8C2×D711yescharacteristic
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4C2×D711yescharacteristic
249C2×C4×D4C2×D711yescharacteristic
250C2×#117—21no—
251C2×#117—141no—
252C2×#117C2×D711yescharacteristic
253C22×C42—21no—
254C22×C42C2×D711yescharacteristic
255#485—716no—
256#477—78no—
257#476—78no—
258#462—78no—
259#461—78no—
260#452—716no—
261#441—716no—
262#440—716no—
263#432—78no—
264C2×#107—72no—
265C2×#106—72no—
266C2×C4⋊C8—71no—
267C2×C4⋊C8—71no—
268C2×#103—72no—
269C2×#103—72no—
270C2×#103—72no—
271C2×#102—72no—
272C2×C22⋊C8—72no—
273C2×#97—72no—
274C23×C7—22no—
275C23×C7—24no—
276C23×C7—22no—
277C23×C7—22no—
278C23×C7—22no—
279C23×C7—42no—
280C23×C7—42no—
281C23×C7C22×D412yes—
282C23×C7C22×D411yescharacteristic
283C7×Q8—24no—
284C7×Q8—22no—
285C7×Q8C2×#4114yes—
286C7×D4—216no—
287C7×D4—24no—
288C7×D4—22no—
289C7×D4C2×#4114yes—
290C2×C4×C7—216no—
291C2×C4×C7—22no—
292C2×C4×C7—24no—
293C2×C4×C7—22no—
294C2×C4×C7—22no—
295C2×C4×C7—22no—
296C2×C4×C7—22no—
297C2×C4×C7—24no—
298C2×C4×C7—28no—
299C2×C4×C7—22no—
300C2×C4×C7—22no—
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—44no—
304C2×C4×C7—48no—
305C2×C4×C7—42no—
306C2×C4×C7—42no—
307C2×C4×C7—48no—
308C2×C4×C7#13714yes—
309C2×C4×C7C22×D412yes—
310C2×C4×C7C22×D412yes—
311C2×C4×C7C22×D412yes—
312C2×C4×C7C22×D412yes—
313C2×C4×C7C22×D411yescharacteristic
314C2×C4×C7C22×D412yes—
315C2×C4×C7C2×#4112yes—
316C2×C4×C7C2×#4112yes—
317C2×C4×C7C2511yescharacteristic
318C2×Dic7—24no—
319C2×Dic7—24no—
320C2×Dic7—44no—
321C2×Dic7—44no—
322Dic14—24no—
323Dic14—24no—
324Dic14—48no—
325Dic14—44no—
326C7⋊C8—24no—
327C7⋊C8—24no—
328C2×#41—24no—
329C2×#41—24no—
330C2×#41—22no—
331C2×#41C22×D714yes—
332C22×Q8—72no—
333C22×Q8—141no—
334C22×Q8C22×D711yescharacteristic
335C22×D4—21no—
336C22×D4C22×D711yescharacteristic
337C23×C4—21no—
338C23×C4—21no—
339C23×C4—21no—
340C23×C4C22⋊D711yescharacteristic
341C23×C4C22⋊D711yescharacteristic
342C23×C4C22×D711yescharacteristic
343C2×Q16—78no—
344C2×Q16—148no—
345C2×SD16—78no—
346C2×SD16—148no—
347C22×C8—72no—
348C22×C8—72no—
349C4⋊Q8—74no—
350C4⋊Q8—74no—
351C4⋊Q8—142no—
352C4⋊Q8—142no—
353#125—148no—
354C22⋊Q8—78no—
355C22⋊Q8—144no—
356C22⋊Q8—148no—
357C4×Q8—22no—
358C4×Q8—22no—
359C4×Q8—78no—
360C4×Q8—144no—
361C4×Q8—148no—
362C4×Q8C22×D714yes—
363C4×Q8C22×D714yes—
364C4×D4—28no—
365C4×D4—28no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4C22×D714yes—
369C4×D4C22×D714yes—
370#117—22no—
371#117—28no—
372#117—148no—
373#117C22×D714yes—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—72no—
377C2×C4⋊C4—141no—
378C2×C4⋊C4—141no—
379C2×C4⋊C4—142no—
380C2×C4⋊C4—142no—
381C2×C4⋊C4—141no—
382C2×C4⋊C4C22×D711yescharacteristic
383C2×C4⋊C4C22×D711yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—142no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—28no—
392C2×C42—142no—
393C2×C42C22⋊D711yescharacteristic
394C2×C42C22⋊D714yes—
395C2×C42C22⋊D711yescharacteristic
396C2×C42C22×D711yescharacteristic
397C2×C42C22×D711yescharacteristic
398C2×C42C22×D714yes—
399#107—78no—
400#106—78no—
401C4⋊C8—74no—
402C4⋊C8—74no—
403#103—78no—
404#103—78no—
405#103—78no—
406#102—78no—
407C22⋊C8—78no—
408#97—78no—
409C22×C7—22no—
410C22×C7—24no—
411C22×C7—22no—
412C22×C7—22no—
413C22×C7—44no—
414C22×C7—48no—
415C22×C7—42no—
416C22×C7—42no—
417C22×C7#52512yes—
418C22×C7C2×#13712yes—
419C22×C7#57512yes—
420C22×C7C23×D411yescharacteristic
421C4×C7—22no—
422C4×C7—24no—
423C4×C7—22no—
424C4×C7—22no—
425C4×C7—22no—
426C4×C7—42no—
427C4×C7—42no—
428C4×C7#52512yes—
429C4×C7C2×#13714yes—
430C4×C7C22×#4111yescharacteristic
431C4×C7C22×#4111yescharacteristic
432Dic7—44no—
433Dic7—44no—
434C24—21no—
435C24C2×C22⋊D711yescharacteristic
436#41—216no—
437#41—28no—
438#41—28no—
439C2×Q8—22no—
440C2×Q8—21no—
441C2×Q8—74no—
442C2×Q8—144no—
443C2×Q8—142no—
444C2×Q8—144no—
445C2×Q8—144no—
446C2×Q8—284no—
447C2×Q8#115714yes—
448C2×Q8C23×D712yes—
449C2×D4—28no—
450C2×D4—24no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4#115714yes—
454C2×D4C23×D712yes—
455C22×C4—28no—
456C22×C4—21no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—42no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—142no—
469C22×C4—142no—
470C22×C4C2×C22⋊D712yes—
471C22×C4C2×C22⋊D714yes—
472C22×C4C2×C22⋊D711yescharacteristic
473C22×C4C2×C22⋊D711yescharacteristic
474C22×C4C2×C22⋊D711yescharacteristic
475C22×C4C2×C22⋊D711yescharacteristic
476C22×C4C2×C22⋊D714yes—
477C22×C4C2×C22⋊D711yescharacteristic
478C22×C4C23×D712yes—
479C22×C4C23×D711yescharacteristic
480Q16—1416no—
481SD16—1416no—
482C2×C8—74no—
483C2×C8—74no—
484C2×C8—144no—
485C2×C8—144no—
486C4⋊C4—24no—
487C4⋊C4—24no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—74no—
491C4⋊C4—148no—
492C4⋊C4—148no—
493C4⋊C4—142no—
494C4⋊C4—144no—
495C4⋊C4—144no—
496C4⋊C4—144no—
497C4⋊C4C23×D712yes—
498C4⋊C4C23×D712yes—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—24no—
502C22⋊C4—148no—
503C42—24no—
504C42—24no—
505C42—24no—
506C42—148no—
507C42C2×C22⋊D714yes—
508C42C2×C22⋊D714yes—
509C42C2×C22⋊D712yes—
510C42C2×C22⋊D712yes—
511C42C23×D712yes—
512C42C23×D712yes—
513C2×C7—42no—
514C2×C7—44no—
515C2×C7#311614yescomplemented
516C2×C7C2×#52511yescharacteristic
517C2×C7C22×#13711yescharacteristic
518C2×C7C2×#57511yescharacteristic
519C23—22no—
520C23—24no—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—42no—
525C23—42no—
526C23C22×C22⋊D712yes—
527C23C22×C22⋊D711yescharacteristic
528Q8—24no—
529Q8—22no—
530Q8—144no—
531Q8—144no—
532Q8—288no—
533Q8—284no—
534Q8C2×#115714yes—
535D4—216no—
536D4—24no—
537D4—22no—
538D4C2×#115714yes—
539C2×C4—216no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—28no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—44no—
553C2×C4—48no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—48no—
557C2×C4—144no—
558C2×C4—144no—
559C2×C4—284no—
560C2×C4—284no—
561C2×C4#651414yes—
562C2×C4C2×#115712yes—
563C2×C4C2×#115712yes—
564C2×C4C22×C22⋊D712yes—
565C2×C4C22×C22⋊D712yes—
566C2×C4C22×C22⋊D712yes—
567C2×C4C22×C22⋊D712yes—
568C2×C4C22×C22⋊D711yescharacteristic
569C2×C4C22×C22⋊D712yes—
570C2×C4C24×D711yescharacteristic
571C8—144no—
572C8—144no—
573C7C2×#311611yescharacteristic, complemented, Sylow
574C22—22no—
575C22—24no—
576C22—22no—
577C22—22no—
578C22—42no—
579C22—42no—
580C22—44no—
581C22—48no—
582C22#9048212yes—
583C22#9051312yes—
584C22C2×#651412yes—
585C22C23×C22⋊D711yescharacteristic
586C4—22no—
587C4—24no—
588C4—22no—
589C4—22no—
590C4—22no—
591C4—42no—
592C4—42no—
593C4—284no—
594C4—284no—
595C4#9048212yes—
596C4C2×#651414yes—
597C4C22×#115711yescharacteristic
598C4C22×#115711yescharacteristic
599C2—42no—
600C2—44no—
601C2#1173998014yesdirect product factor
602C2C2×#9048211yescharacteristic
603C2C2×#9051311yescharacteristic
604C2C22×#651411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C4×C7×#41C2
socleC23×C7C22×D4
prime radicalC22×C7×#41C22
hypercenterC2×C4×#41D7
hypocenterC7C2×#3116
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×#90161C2semidirect
4. #11739980C2direct (N × H)
5. C2×#89803C2semidirect
6. C2×#89793C2semidirect
7. C2×#89802C2semidirect
8. C2×#89791C2semidirect
9. C2×#89780C2semidirect
10. C2×#89790C2semidirect
11. C2×#89768C2semidirect
12. C2×#89698C2semidirect
32. #90161C22semidirect
42. #89803C22semidirect
43. #89802C22semidirect
44. #89793C22semidirect
45. #89791C22semidirect
46. #89790C22semidirect
47. #89780C22semidirect
48. #89768C22semidirect
53. #89698C22semidirect
515. C2×C7#3116semidirect
573. C7C2×#3116semidirect
601. C2#11739980direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C7×#412
C2×#901612
C2×#900112
#117399802
C2×#898032
C2×#897932
C2×#898022
C2×#897912
C2×#897802
C2×#897902
C2×#897682
C2×#896982
C2×#31167