Finite Group Databasebeta

← C2×#11733552 #13520439

Subgroups — C2×#11733552 #13520439

Order 1792.

1766 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C211yesmaximal, characteristic
2C2×#89754C211yesmaximal, characteristic
3C2×#89758C211yesmaximal, characteristic
4C2×#89755C211yesmaximal, characteristic
5C2×#89752C211yesmaximal, characteristic
6C2×#89750C211yesmaximal, characteristic
7C2×#89750C211yesmaximal, characteristic
8C2×#89753C211yesmaximal, characteristic
9C2×#89753C211yesmaximal, characteristic
10C2×#89705C211yesmaximal, characteristic
11C2×C4×Dic7⋊C4C211yesmaximal, characteristic
12#11733552C2116yesmaximal, direct product factor
13C2×C7⋊#401C211yesmaximal, characteristic
14C2×#89432C211yesmaximal, characteristic
15C2×#89430C211yesmaximal, characteristic
16C2×#89429C211yesmaximal, characteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
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×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C7×#389C2218yes—
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7⋊#95C2211yescharacteristic
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2211yescharacteristic
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
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
53#89758C2218yes—
54#89755C2218yes—
55#89754C2218yes—
56#89753C2218yes—
57#89753C2218yes—
58#89752C2218yes—
59#89750C2218yes—
60#89750C2218yes—
61#89705C2218yes—
62C4×Dic7⋊C4C2218yes—
63C7⋊#401C2218yes—
64#89432C2218yes—
65#89430C2218yes—
66#89429C2218yes—
67C2×#2655—71nomaximal, Sylow
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C2×C7×C4⋊C4—24no—
84C2×C7×C4⋊C4—24no—
85C2×C7×C4⋊C4—24no—
86C2×C7×C4⋊C4—42no—
87C2×C7×C4⋊C4C2314yes—
88C2×C7×C4⋊C4C2314yes—
89C2×C7×C4⋊C4C2314yes—
90C2×C7×C4⋊C4C2314yes—
91C2×C42×C7—42no—
92C2×C42×C7C2314yes—
93C2×C4⋊Dic7—42no—
94C2×C4⋊Dic7—42no—
95C2×C4⋊Dic7C2314yes—
96C2×C4⋊Dic7C2314yes—
97C2×Dic7⋊C4—24no—
98C2×Dic7⋊C4—24no—
99C2×Dic7⋊C4—24no—
100C2×Dic7⋊C4—24no—
101C2×Dic7⋊C4—24no—
102C2×Dic7⋊C4—42no—
103C2×Dic7⋊C4C2314yes—
104C2×Dic7⋊C4C2314yes—
105C2×Dic7⋊C4C2314yes—
106C2×Dic7⋊C4C2314yes—
107C2×Dic7⋊C4C2314yes—
108C2×Dic7⋊C4C2314yes—
109C2×C4×Dic7—24no—
110C2×C4×Dic7—42no—
111C2×C4×Dic7C2314yes—
112C2×C4×Dic7C2314yes—
113C7×#95C2314yes—
114C7×#95C2314yes—
115C7⋊#95C2314yes—
116C7⋊#95C2314yes—
117C7⋊#95C2314yes—
118C7⋊#95C2314yes—
119C7⋊#95C2314yes—
120C7⋊#95C2314yes—
121C7⋊#95C2314yes—
122C7⋊#95C2314yes—
123C7⋊#95C2314yes—
124C7⋊#95C2314yes—
125C7⋊#95C2314yes—
126C7⋊#95C2314yes—
127C7⋊#95C2314yes—
128C7⋊#95C2314yes—
129C7⋊#95C2314yes—
130C7⋊#95C2314yes—
131C7⋊#95C2314yes—
132C7⋊#95C2314yes—
133#2655—716no—
134C2×#401—71no—
135C2×#400—71no—
136C2×#400—71no—
137C2×#400—71no—
138C2×#400—71no—
139C2×#398—71no—
140C2×#398—71no—
141C2×#398—71no—
142C2×#389D711yescharacteristic
143C2×#387—71no—
144C2×#387—71no—
145C2×#387—71no—
146C2×#387—71no—
147C2×#387—71no—
148C2×C4×C4⋊C4—71no—
149C24×C7C2411yescharacteristic
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
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#4114yes—
170C22×C4×C7#4114yes—
171C22×C4×C7C2412yes—
172C22×C4×C7C2412yes—
173C22×C4×C7C2412yes—
174C22×C4×C7C2412yes—
175C22×C4×C7C2412yes—
176C22×C4×C7C2412yes—
177C22×C4×C7C2412yes—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—22no—
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#4114yes—
202C22×Dic7C2412yes—
203C22×Dic7C2412yes—
204C22×Dic7C2412yes—
205C22×Dic7C2412yes—
206C22×Dic7C2412yes—
207C22×Dic7C2412yes—
208C22×Dic7C2412yes—
209C22×Dic7C2412yes—
210C7×C4⋊C4—28no—
211C7×C4⋊C4—28no—
212C7×C4⋊C4—28no—
213C7×C4⋊C4—44no—
214C42×C7—44no—
215C4⋊Dic7—44no—
216C4⋊Dic7—44no—
217Dic7⋊C4—28no—
218Dic7⋊C4—28no—
219Dic7⋊C4—28no—
220Dic7⋊C4—28no—
221Dic7⋊C4—28no—
222Dic7⋊C4—44no—
223C4×Dic7—28no—
224C4×Dic7—44no—
225C22×C4⋊C4—71no—
226C22×C4⋊C4—71no—
227C22×C4⋊C4—71no—
228C22×C4⋊C4—71no—
229C22×C4⋊C4—71no—
230C22×C4⋊C4—71no—
231C22×C4⋊C4—71no—
232C22×C4⋊C4—71no—
233C22×C4⋊C4C2×D711yescharacteristic
234C22×C4⋊C4C2×D711yescharacteristic
235C22×C4⋊C4C2×D711yescharacteristic
236C22×C4⋊C4C2×D711yescharacteristic
237C22×C42—71no—
238C22×C42—71no—
239C22×C42C2×D711yescharacteristic
240#401—78no—
241#400—78no—
242#400—78no—
243#400—78no—
244#400—78no—
245#398—78no—
246#398—78no—
247#398—78no—
248#389C2×D718yes—
249#387—78no—
250#387—78no—
251#387—78no—
252#387—78no—
253#387—78no—
254C4×C4⋊C4—78no—
255C2×#95—71no—
256C2×#95—71no—
257C2×#95—71no—
258C2×#95—71no—
259C2×#95—71no—
260C2×#95—71no—
261C2×#95—71no—
262C2×#95—71no—
263C2×#95—71no—
264C2×#95—71no—
265C2×#95—71no—
266C2×#95—71no—
267C2×#95—71no—
268C2×#95—71no—
269C2×#95—71no—
270C2×#95—71no—
271C2×#95—71no—
272C2×#95—71no—
273C2×#95C2×D711yescharacteristic
274C2×#95C2×D711yescharacteristic
275C23×C7C2×#4112yes—
276C23×C7C2×#4112yes—
277C23×C7C2×#4112yes—
278C23×C7H(5,𝔽2)12yes—
279C23×C72−1+412yes—
280C23×C72−1+412yes—
281C23×C72−1+412yes—
282C23×C7C2511yescharacteristic
283C2×C4×C7—28no—
284C2×C4×C7—28no—
285C2×C4×C7—22no—
286C2×C4×C7—22no—
287C2×C4×C7—22no—
288C2×C4×C7—22no—
289C2×C4×C7—22no—
290C2×C4×C7—22no—
291C2×C4×C7—22no—
292C2×C4×C7—22no—
293C2×C4×C7—22no—
294C2×C4×C7—22no—
295C2×C4×C7—22no—
296C2×C4×C7—22no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—22no—
300C2×C4×C7—22no—
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—44no—
305C2×C4×C7—44no—
306C2×C4×C7—44no—
307C2×C4×C7—44no—
308C2×C4×C7—44no—
309C2×C4×C7C2×#4114yes—
310C2×C4×C7C2×#4114yes—
311C2×Dic7—28no—
312C2×Dic7—22no—
313C2×Dic7—22no—
314C2×Dic7—22no—
315C2×Dic7—22no—
316C2×Dic7—22no—
317C2×Dic7—22no—
318C2×Dic7—22no—
319C2×Dic7—22no—
320C2×Dic7—22no—
321C2×Dic7—22no—
322C2×Dic7—22no—
323C2×Dic7—22no—
324C2×Dic7—22no—
325C2×Dic7—22no—
326C2×Dic7—22no—
327C2×Dic7—22no—
328C2×Dic7—22no—
329C2×Dic7—22no—
330C2×Dic7—22no—
331C2×Dic7—22no—
332C2×Dic7—22no—
333C2×Dic7—22no—
334C2×Dic7—22no—
335C2×Dic7—44no—
336C2×Dic7—44no—
337C2×Dic7—44no—
338C2×Dic7—44no—
339C2×Dic7—44no—
340C2×Dic7—44no—
341C2×Dic7—44no—
342C2×Dic7C2×#4114yes—
343C23×C4—71no—
344C23×C4—71no—
345C23×C4—71no—
346C23×C4—71no—
347C23×C4—71no—
348C23×C4—71no—
349C23×C4—71no—
350C23×C4—71no—
351C23×C4C22×D711yescharacteristic
352C23×C4C22×D711yescharacteristic
353C23×C4C22×D711yescharacteristic
354C23×C4C22×D711yescharacteristic
355C23×C4C22×D711yescharacteristic
356C23×C4C22×D711yescharacteristic
357C23×C4C22×D711yescharacteristic
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—74no—
363C2×C4⋊C4—74no—
364C2×C4⋊C4—74no—
365C2×C4⋊C4—74no—
366C2×C4⋊C4—74no—
367C2×C4⋊C4—74no—
368C2×C4⋊C4—74no—
369C2×C4⋊C4—74no—
370C2×C4⋊C4—144no—
371C2×C4⋊C4—144no—
372C2×C4⋊C4—144no—
373C2×C4⋊C4—144no—
374C2×C4⋊C4—144no—
375C2×C4⋊C4—282no—
376C2×C4⋊C4—282no—
377C2×C4⋊C4—282no—
378C2×C4⋊C4C22×D714yes—
379C2×C4⋊C4C22×D714yes—
380C2×C4⋊C4C22×D714yes—
381C2×C4⋊C4C22×D714yes—
382C2×C42—42no—
383C2×C42—74no—
384C2×C42—74no—
385C2×C42—144no—
386C2×C42—282no—
387C2×C42C22×D714yes—
388#95—74no—
389#95—74no—
390#95—74no—
391#95—74no—
392#95—74no—
393#95—74no—
394#95—74no—
395#95—74no—
396#95—74no—
397#95—74no—
398#95—74no—
399#95—74no—
400#95—74no—
401#95—74no—
402#95—74no—
403#95—74no—
404#95—74no—
405#95—74no—
406#95C22×D714yes—
407#95C22×D714yes—
408C22×C7#52914yes—
409C22×C7#53914yes—
410C22×C7#53914yes—
411C22×C7#54114yes—
412C22×C7#54114yes—
413C22×C7#54114yes—
414C22×C7#54214yes—
415C22×C7C22×#4111yescharacteristic
416C22×C7C22×#4111yescharacteristic
417C22×C7C22×#4111yescharacteristic
418C22×C7C2×H(5,𝔽2)11yescharacteristic
419C22×C7C2×2−1+411yescharacteristic
420C22×C7C2×2−1+411yescharacteristic
421C22×C7C2×2−1+411yescharacteristic
422C4×C7—24no—
423C4×C7—24no—
424C4×C7—42no—
425C4×C7—42no—
426C4×C7—42no—
427C4×C7—42no—
428C4×C7—42no—
429Dic7—24no—
430Dic7—42no—
431Dic7—42no—
432Dic7—42no—
433Dic7—42no—
434Dic7—42no—
435Dic7—42no—
436Dic7—42no—
437C24C23×D711yescharacteristic
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—74no—
458C22×C4—72no—
459C22×C4—72no—
460C22×C4—72no—
461C22×C4—72no—
462C22×C4—72no—
463C22×C4—72no—
464C22×C4—72no—
465C22×C4—72no—
466C22×C4—142no—
467C22×C4—142no—
468C22×C4—142no—
469C22×C4—142no—
470C22×C4—142no—
471C22×C4—142no—
472C22×C4—142no—
473C22×C4—142no—
474C22×C4—142no—
475C22×C4—142no—
476C22×C4—142no—
477C22×C4—142no—
478C22×C4—142no—
479C22×C4—142no—
480C22×C4—142no—
481C22×C4—142no—
482C22×C4—142no—
483C22×C4—142no—
484C22×C4—142no—
485C22×C4—142no—
486C22×C4—142no—
487C22×C4—142no—
488C22×C4—142no—
489C22×C4#115714yes—
490C22×C4#115914yes—
491C22×C4C23×D712yes—
492C22×C4C23×D712yes—
493C22×C4C23×D712yes—
494C22×C4C23×D712yes—
495C22×C4C23×D712yes—
496C22×C4C23×D712yes—
497C22×C4C23×D712yes—
498C4⋊C4—28no—
499C4⋊C4—28no—
500C4⋊C4—28no—
501C4⋊C4—44no—
502C4⋊C4—148no—
503C4⋊C4—148no—
504C4⋊C4—148no—
505C4⋊C4—148no—
506C4⋊C4—148no—
507C4⋊C4—284no—
508C4⋊C4—284no—
509C4⋊C4—284no—
510C42—44no—
511C42—148no—
512C42—284no—
513C2×C7#265518yescomplemented
514C2×C7C2×#52911yescharacteristic
515C2×C7C2×#53911yescharacteristic
516C2×C7C2×#53911yescharacteristic
517C2×C7C2×#54111yescharacteristic
518C2×C7C2×#54111yescharacteristic
519C2×C7C2×#54111yescharacteristic
520C2×C7C2×#54211yescharacteristic
521C23C2×#115712yes—
522C23C2×#115912yes—
523C23#654812yes—
524C23#655112yes—
525C23#655112yes—
526C23D7×#4112yes—
527C23#655412yes—
528C23C24×D711yescharacteristic
529C2×C4—28no—
530C2×C4—28no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—74no—
556C2×C4—148no—
557C2×C4—142no—
558C2×C4—142no—
559C2×C4—142no—
560C2×C4—142no—
561C2×C4—142no—
562C2×C4—142no—
563C2×C4—142no—
564C2×C4—142no—
565C2×C4—142no—
566C2×C4—142no—
567C2×C4—142no—
568C2×C4—142no—
569C2×C4—142no—
570C2×C4—142no—
571C2×C4—142no—
572C2×C4—142no—
573C2×C4—142no—
574C2×C4—142no—
575C2×C4—142no—
576C2×C4—142no—
577C2×C4—142no—
578C2×C4—142no—
579C2×C4—142no—
580C2×C4—284no—
581C2×C4—284no—
582C2×C4—284no—
583C2×C4—284no—
584C2×C4—284no—
585C2×C4—284no—
586C2×C4—284no—
587C2×C4C2×#115714yes—
588C2×C4C2×#115914yes—
589C7C2×#265511yescharacteristic, complemented, Sylow
590C22#9020614yes—
591C22#9024814yes—
592C22#9027414yes—
593C22#9029314yes—
594C22#9033114yes—
595C22#9038714yes—
596C22#9042214yes—
597C22C22×#115711yescharacteristic
598C22C22×#115911yescharacteristic
599C22C2×#654811yescharacteristic
600C22C2×#655111yescharacteristic
601C22C2×#655111yescharacteristic
602C22C2×D7×#4111yescharacteristic
603C22C2×#655411yescharacteristic
604C4—24no—
605C4—24no—
606C4—42no—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—144no—
612C4—282no—
613C4—282no—
614C4—282no—
615C4—282no—
616C4—282no—
617C4—282no—
618C4—282no—
619C2#1173355218yesdirect product factor
620C2C2×#9020611yescharacteristic
621C2C2×#9024811yescharacteristic
622C2C2×#9027411yescharacteristic
623C2C2×#9029311yescharacteristic
624C2C2×#9033111yescharacteristic
625C2C2×#9038711yescharacteristic
626C2C2×#9042211yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#389C2
socle, prime radicalC24×C7C24
hypercenterC2×#389D7
hypocenterC7C2×#2655
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
12. #11733552C2direct (N × H)
513. C2×C7#2655semidirect
589. C7C2×#2655semidirect
619. C2#11733552direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×#897542
C2×#897582
C2×#897552
C2×#897522
C2×#897502
C2×#897532
C2×#897052
C2×C4×Dic7⋊C42
#117335522
C2×C7⋊#4012
C2×#894322
C2×#894302
C2×#894292
C2×#26557