Finite Group Databasebeta

← C2×#11732438 #13521791

Subgroups — C2×#11732438 #13521791

Order 1792.

2486 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6450C211yesmaximal, characteristic
2C22×#6433C211yesmaximal, characteristic
3C2×C7×#387C211yesmaximal, characteristic
4C2×#89751C211yesmaximal, characteristic
5C2×#89744C211yesmaximal, characteristic
6C2×#89744C211yesmaximal, characteristic
7C2×C4×Dic7⋊C4C211yesmaximal, characteristic
8#11732438C2116yesmaximal, direct product factor
9C2×#89429C211yesmaximal, characteristic
10C2×#89429C211yesmaximal, characteristic
11C2×#89428C211yesmaximal, characteristic
12C2×#89427C211yesmaximal, characteristic
13C2×#89427C211yesmaximal, characteristic
14C2×#89425C211yesmaximal, characteristic
15C2×#89424C211yesmaximal, characteristic
16C2×#89424C211yesmaximal, characteristic
17C23×Dic14C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C22×C4×Dic7C2211yescharacteristic
36C22×C4×Dic7C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C2×#6450—28no—
39C2×#6450C2218yes—
40C2×#6433—28no—
41C2×#6433C2218yes—
42C7×#387C2218yes—
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89751C2218yes—
58#89744C2218yes—
59#89744C2218yes—
60C4×Dic7⋊C4C2218yes—
61#89429C2218yes—
62#89429C2218yes—
63#89428C2218yes—
64#89427C2218yes—
65#89427C2218yes—
66#89425C2218yes—
67#89424C2218yes—
68#89424C2218yes—
69C2×#2462—71nomaximal, Sylow
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C22×Dic14—24no—
86C22×Dic14—24no—
87C22×Dic14—24no—
88C22×Dic14C2314yes—
89C2×C7×C4⋊C4—24no—
90C2×C7×C4⋊C4—24no—
91C2×C7×C4⋊C4C2314yes—
92C2×C7×C4⋊C4C2314yes—
93C2×C42×C7—24no—
94C2×C42×C7C2314yes—
95C2×C4⋊Dic7—24no—
96C2×C4⋊Dic7—24no—
97C2×C4⋊Dic7—24no—
98C2×C4⋊Dic7C2314yes—
99C2×C4⋊Dic7C2314yes—
100C2×C4⋊Dic7C2314yes—
101C2×Dic7⋊C4—24no—
102C2×Dic7⋊C4—24no—
103C2×Dic7⋊C4—24no—
104C2×Dic7⋊C4—24no—
105C2×Dic7⋊C4—24no—
106C2×Dic7⋊C4—24no—
107C2×Dic7⋊C4—24no—
108C2×Dic7⋊C4—24no—
109C2×Dic7⋊C4D418yes—
110C2×Dic7⋊C4Q818yescomplemented
111C2×Dic7⋊C4C2314yes—
112C2×Dic7⋊C4C2314yes—
113C2×Dic7⋊C4C2314yes—
114C2×Dic7⋊C4C2314yes—
115C2×Dic7⋊C4C2314yes—
116C2×Dic7⋊C4C2314yes—
117C2×Dic7⋊C4C2314yes—
118C2×Dic7⋊C4C2314yes—
119C2×Dic7⋊C4C2314yes—
120C2×Dic7⋊C4C2314yes—
121C2×C4×Dic7—24no—
122C2×C4×Dic7—24no—
123C2×C4×Dic7—24no—
124C2×C4×Dic7—24no—
125C2×C4×Dic7C2314yes—
126C2×C4×Dic7C2314yes—
127C2×C4×Dic7C2314yes—
128C2×C4×Dic7C2314yes—
129#6450—232no—
130#6433—232no—
131C7×#95C2314yes—
132C7×#95C2314yes—
133C7×#95C2314yes—
134C7×#95C2314yes—
135C7⋊#95C2314yes—
136C7⋊#95C2314yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C22×#125—71no—
146C22×C4×Q8—71no—
147#2462—716no—
148C2×#398—71no—
149C2×#398—71no—
150C2×#395—71no—
151C2×#395—71no—
152C2×#389—71no—
153C2×#389—71no—
154C2×#387—71no—
155C2×#387—71no—
156C2×#387—71no—
157C2×#387—71no—
158C2×#387—71no—
159C2×#387D711yescharacteristic
160C2×C4×C4⋊C4—71no—
161C24×C7C2411yescharacteristic
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7C2×D414yes—
181C22×C4×C7C2×Q814yes—
182C22×C4×C7#4114yes—
183C22×C4×C7C2412yes—
184C22×C4×C7C2412yes—
185C22×C4×C7C2412yes—
186C22×C4×C7C2412yes—
187C22×C4×C7C2412yes—
188C22×C4×C7C2412yes—
189C22×C4×C7C2412yes—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7C2×D414yes—
209C22×Dic7C2×D414yes—
210C22×Dic7C2×Q814yes—
211C22×Dic7C2×Q814yes—
212C22×Dic7#4114yes—
213C22×Dic7#4114yes—
214C22×Dic7C2412yes—
215C22×Dic7C2412yes—
216C22×Dic7C2412yes—
217C22×Dic7C2412yes—
218C22×Dic7C2412yes—
219C22×Dic7C2412yes—
220C22×Dic7C2412yes—
221C22×Dic7C2412yes—
222C2×Dic14—232no—
223C2×Dic14—28no—
224C2×Dic14—28no—
225C2×Dic14—28no—
226C7×C4⋊C4—28no—
227C7×C4⋊C4—28no—
228C42×C7—28no—
229C4⋊Dic7—28no—
230C4⋊Dic7—28no—
231C4⋊Dic7—28no—
232Dic7⋊C4—28no—
233Dic7⋊C4—28no—
234Dic7⋊C4—28no—
235Dic7⋊C4—28no—
236Dic7⋊C4—28no—
237Dic7⋊C4—28no—
238Dic7⋊C4—28no—
239Dic7⋊C4—28no—
240Dic7⋊C4C2×D4116yes—
241Dic7⋊C4C2×Q8116yescomplemented
242C4×Dic7—28no—
243C4×Dic7—28no—
244C4×Dic7—28no—
245C4×Dic7—28no—
246C23×Q8—71no—
247C2×#125—78no—
248C2×#125—148no—
249C2×C4×Q8—78no—
250C2×C4×Q8—148no—
251C22×C4⋊C4—71no—
252C22×C4⋊C4—71no—
253C22×C4⋊C4—71no—
254C22×C4⋊C4—71no—
255C22×C4⋊C4—71no—
256C22×C4⋊C4—71no—
257C22×C4⋊C4—71no—
258C22×C4⋊C4—71no—
259C22×C4⋊C4—71no—
260C22×C4⋊C4—71no—
261C22×C4⋊C4—71no—
262C22×C4⋊C4—71no—
263C22×C4⋊C4—71no—
264C22×C4⋊C4C2×D711yescharacteristic
265C22×C4⋊C4C2×D711yescharacteristic
266C22×C42—71no—
267C22×C42—71no—
268C22×C42—71no—
269C22×C42—71no—
270C22×C42C2×D711yescharacteristic
271#398—78no—
272#398—78no—
273#395—78no—
274#395—78no—
275#389—78no—
276#389—78no—
277#387—78no—
278#387—78no—
279#387—78no—
280#387—78no—
281#387—78no—
282#387C2×D718yes—
283C4×C4⋊C4—78no—
284C2×#95—71no—
285C2×#95—71no—
286C2×#95—71no—
287C2×#95—71no—
288C2×#95—71no—
289C2×#95—71no—
290C2×#95—71no—
291C2×#95—71no—
292C2×#95—71no—
293C2×#95—71no—
294C2×#95C2×D711yescharacteristic
295C2×#95C2×D711yescharacteristic
296C2×#95C2×D711yescharacteristic
297C2×#95C2×D711yescharacteristic
298C23×C7C22×D412yes—
299C23×C7C22×Q812yes—
300C23×C7C2×#4112yes—
301C23×C7C2×#4112yes—
302C23×C7C2×#4112yes—
303C23×C72−1+412yes—
304C23×C72−1+412yes—
305C23×C7C2511yescharacteristic
306C2×C4×C7—28no—
307C2×C4×C7—28no—
308C2×C4×C7—28no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—44no—
328C2×C4×C7—44no—
329C2×C4×C7—44no—
330C2×C4×C7—44no—
331C2×C4×C7C22×D414yes—
332C2×C4×C7C22×Q814yes—
333C2×C4×C7C2×#4114yes—
334C2×Dic7—28no—
335C2×Dic7—28no—
336C2×Dic7—28no—
337C2×Dic7—28no—
338C2×Dic7—28no—
339C2×Dic7—28no—
340C2×Dic7—22no—
341C2×Dic7—22no—
342C2×Dic7—22no—
343C2×Dic7—22no—
344C2×Dic7—22no—
345C2×Dic7—22no—
346C2×Dic7—22no—
347C2×Dic7—22no—
348C2×Dic7—22no—
349C2×Dic7—22no—
350C2×Dic7—22no—
351C2×Dic7—22no—
352C2×Dic7—22no—
353C2×Dic7—22no—
354C2×Dic7—22no—
355C2×Dic7—22no—
356C2×Dic7—22no—
357C2×Dic7—22no—
358C2×Dic7—44no—
359C2×Dic7—44no—
360C2×Dic7C22×D414yes—
361C2×Dic7C22×D414yes—
362C2×Dic7C22×Q814yes—
363C2×Dic7C22×Q814yes—
364C2×Dic7C2×#4114yes—
365C2×Dic7C2×#4114yes—
366Dic14—232no—
367C22×Q8—74no—
368C22×Q8—144no—
369C22×Q8—144no—
370C22×Q8—144no—
371C23×C4—71no—
372C23×C4—71no—
373C23×C4—71no—
374C23×C4—71no—
375C23×C4—71no—
376C23×C4—71no—
377C23×C4—71no—
378C23×C4—71no—
379C23×C4C22×D711yescharacteristic
380C23×C4C22×D711yescharacteristic
381C23×C4C22×D711yescharacteristic
382C23×C4C22×D711yescharacteristic
383C23×C4C22×D711yescharacteristic
384C23×C4C22×D711yescharacteristic
385C23×C4C22×D711yescharacteristic
386#125—1432no—
387C4×Q8—1432no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—78no—
391C2×C4⋊C4—78no—
392C2×C4⋊C4—74no—
393C2×C4⋊C4—74no—
394C2×C4⋊C4—74no—
395C2×C4⋊C4—74no—
396C2×C4⋊C4—74no—
397C2×C4⋊C4—74no—
398C2×C4⋊C4—74no—
399C2×C4⋊C4—74no—
400C2×C4⋊C4—74no—
401C2×C4⋊C4—74no—
402C2×C4⋊C4—74no—
403C2×C4⋊C4—74no—
404C2×C4⋊C4—74no—
405C2×C4⋊C4—144no—
406C2×C4⋊C4—144no—
407C2×C4⋊C4—144no—
408C2×C4⋊C4—144no—
409C2×C4⋊C4—144no—
410C2×C4⋊C4—144no—
411C2×C4⋊C4—144no—
412C2×C4⋊C4—144no—
413C2×C4⋊C4—144no—
414C2×C4⋊C4—144no—
415C2×C4⋊C4—144no—
416C2×C4⋊C4C22×D714yes—
417C2×C4⋊C4C22×D714yes—
418C2×C42—24no—
419C2×C42—74no—
420C2×C42—74no—
421C2×C42—74no—
422C2×C42—74no—
423C2×C42—144no—
424C2×C42—144no—
425C2×C42—144no—
426C2×C42—144no—
427C2×C42C22×D714yes—
428#95—74no—
429#95—74no—
430#95—74no—
431#95—74no—
432#95—74no—
433#95—74no—
434#95—74no—
435#95—74no—
436#95—74no—
437#95—74no—
438#95C22×D714yes—
439#95C22×D714yes—
440#95C22×D714yes—
441#95C22×D714yes—
442C22×C7#52514yes—
443C22×C7#53314yes—
444C22×C7#54114yes—
445C22×C7#54714yes—
446C22×C7D4×Q814yes—
447C22×C7#55214yes—
448C22×C7#55714yes—
449C22×C7C23×D411yescharacteristic
450C22×C7C23×Q811yescharacteristic
451C22×C7C22×#4111yescharacteristic
452C22×C7C22×#4111yescharacteristic
453C22×C7C22×#4111yescharacteristic
454C22×C7C2×2−1+411yescharacteristic
455C22×C7C2×2−1+411yescharacteristic
456C4×C7—24no—
457C4×C7—24no—
458C4×C7—24no—
459C4×C7—42no—
460C4×C7—42no—
461C4×C7—42no—
462C4×C7—42no—
463Dic7—24no—
464Dic7—24no—
465Dic7—24no—
466Dic7—24no—
467Dic7—24no—
468Dic7—24no—
469Dic7—42no—
470Dic7—42no—
471C24C23×D711yescharacteristic
472C2×Q8—148no—
473C2×Q8—148no—
474C2×Q8—1432no—
475C2×Q8—148no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—74no—
495C22×C4—74no—
496C22×C4—74no—
497C22×C4—74no—
498C22×C4—74no—
499C22×C4—74no—
500C22×C4—72no—
501C22×C4—72no—
502C22×C4—72no—
503C22×C4—72no—
504C22×C4—72no—
505C22×C4—72no—
506C22×C4—72no—
507C22×C4—72no—
508C22×C4—142no—
509C22×C4—142no—
510C22×C4—142no—
511C22×C4—142no—
512C22×C4—142no—
513C22×C4—142no—
514C22×C4—142no—
515C22×C4—142no—
516C22×C4—142no—
517C22×C4—142no—
518C22×C4—142no—
519C22×C4—142no—
520C22×C4—142no—
521C22×C4—142no—
522C22×C4—142no—
523C22×C4—142no—
524C22×C4—142no—
525C22×C4—142no—
526C22×C4#115714yes—
527C22×C4D4×D714yes—
528C22×C4Q8×D714yes—
529C22×C4C23×D712yes—
530C22×C4C23×D712yes—
531C22×C4C23×D712yes—
532C22×C4C23×D712yes—
533C22×C4C23×D712yes—
534C22×C4C23×D712yes—
535C22×C4C23×D712yes—
536C4⋊C4—28no—
537C4⋊C4—28no—
538C4⋊C4—716no—
539C4⋊C4—716no—
540C4⋊C4—148no—
541C4⋊C4—148no—
542C4⋊C4—148no—
543C4⋊C4—148no—
544C4⋊C4—148no—
545C4⋊C4—148no—
546C4⋊C4—148no—
547C4⋊C4—148no—
548C4⋊C4—148no—
549C4⋊C4—148no—
550C4⋊C4—148no—
551C42—28no—
552C42—148no—
553C42—148no—
554C42—148no—
555C42—148no—
556C2×C7#246218yescomplemented
557C2×C7C2×#52511yescharacteristic
558C2×C7C2×#53311yescharacteristic
559C2×C7C2×#54111yescharacteristic
560C2×C7C2×#54711yescharacteristic
561C2×C7C2×D4×Q811yescharacteristic
562C2×C7C2×#55211yescharacteristic
563C2×C7C2×#55711yescharacteristic
564C23C2×#115712yes—
565C23C2×D4×D712yes—
566C23C2×Q8×D712yes—
567C23D7×#4112yes—
568C23D7×#4112yes—
569C23#655412yes—
570C23#655412yes—
571C23C24×D711yescharacteristic
572Q8—1432no—
573C2×C4—28no—
574C2×C4—28no—
575C2×C4—28no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—44no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—74no—
599C2×C4—74no—
600C2×C4—74no—
601C2×C4—74no—
602C2×C4—74no—
603C2×C4—74no—
604C2×C4—148no—
605C2×C4—148no—
606C2×C4—148no—
607C2×C4—148no—
608C2×C4—148no—
609C2×C4—148no—
610C2×C4—142no—
611C2×C4—142no—
612C2×C4—142no—
613C2×C4—142no—
614C2×C4—142no—
615C2×C4—142no—
616C2×C4—142no—
617C2×C4—142no—
618C2×C4—142no—
619C2×C4—142no—
620C2×C4—142no—
621C2×C4—142no—
622C2×C4—142no—
623C2×C4—142no—
624C2×C4—142no—
625C2×C4—142no—
626C2×C4—142no—
627C2×C4—142no—
628C2×C4—284no—
629C2×C4—284no—
630C2×C4C2×#115714yes—
631C2×C4C2×D4×D714yes—
632C2×C4C2×Q8×D714yes—
633C7C2×#246211yescharacteristic, complemented, Sylow
634C22#9022014yes—
635C22#9023814yes—
636C22#9025814yes—
637C22#9032314yes—
638C22#9034614yes—
639C22#9037914yes—
640C22#9039214yes—
641C22C22×#115711yescharacteristic
642C22C22×D4×D711yescharacteristic
643C22C22×Q8×D711yescharacteristic
644C22C2×D7×#4111yescharacteristic
645C22C2×D7×#4111yescharacteristic
646C22C2×#655411yescharacteristic
647C22C2×#655411yescharacteristic
648C4—24no—
649C4—24no—
650C4—24no—
651C4—42no—
652C4—42no—
653C4—42no—
654C4—42no—
655C4—144no—
656C4—144no—
657C4—144no—
658C4—144no—
659C4—144no—
660C4—144no—
661C4—282no—
662C4—282no—
663C2#1173243818yesdirect product factor
664C2C2×#9022011yescharacteristic
665C2C2×#9023811yescharacteristic
666C2C2×#9025811yescharacteristic
667C2C2×#9032311yescharacteristic
668C2C2×#9034611yescharacteristic
669C2C2×#9037911yescharacteristic
670C2C2×#9039211yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#387C2
socle, prime radicalC24×C7C24
hypercenterC2×#387D7
hypocenterC7C2×#2462
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
8. #11732438C2direct (N × H)
110. C2×Dic7⋊C4Q8semidirect
241. Dic7⋊C4C2×Q8semidirect
556. C2×C7#2462semidirect
633. C7C2×#2462semidirect
663. C2#11732438direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64502
C22×#64332
C2×C7×#3872
C2×#897512
C2×#897442
C2×C4×Dic7⋊C42
#117324382
C2×#894292
C2×#894282
C2×#894272
C2×#894252
C2×#894242
C2×#24627