Finite Group Databasebeta

← C2×#11733995 #13524067

Subgroups — C2×#11733995 #13524067

Order 1792.

2182 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#391C211yesmaximal, characteristic
2C2×#90001C211yesmaximal, characteristic
3C2×#90002C211yesmaximal, characteristic
4C2×#89751C211yesmaximal, characteristic
5C2×#89744C211yesmaximal, characteristic
6C2×#89705C211yesmaximal, characteristic
7C2×C4×C4⋊Dic7C211yesmaximal, characteristic
8#11733995C2116yesmaximal, direct product factor
9C2×#89429C211yesmaximal, characteristic
10C2×#89428C211yesmaximal, characteristic
11C2×#89418C211yesmaximal, characteristic
12C2×#89419C211yesmaximal, characteristic
13C2×#89425C211yesmaximal, characteristic
14C2×#89425C211yesmaximal, characteristic
15C2×#89424C211yesmaximal, characteristic
16C2×#89421C211yesmaximal, characteristic
17C23×C7×Q8C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
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×C4×Dic7C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C22×C4×Dic7C2211yescharacteristic
36C7×#391C2218yes—
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
41#90002C2218yes—
42#90001C2218yes—
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
55#89751C2218yes—
56#89744C2218yes—
57C4×C4⋊Dic7C2218yes—
58#89705C2218yes—
59#89429C2218yes—
60#89428C2218yes—
61#89425C2218yes—
62#89425C2218yes—
63#89424C2218yes—
64#89421C2218yes—
65#89419C2218yes—
66#89418C2218yes—
67C2×#2586—71nomaximal, Sylow
68C22×C7×Q8—24no—
69C22×C7×Q8—24no—
70C22×C7×Q8—42no—
71C22×C7×Q8C2314yes—
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C22×Dic14—24no—
88C22×Dic14—42no—
89C22×Dic14—42no—
90C22×Dic14C2314yes—
91C2×C7×C4⋊C4—42no—
92C2×C7×C4⋊C4C2314yes—
93C2×C42×C7—24no—
94C2×C42×C7C2314yes—
95C2×C4⋊Dic7—24no—
96C2×C4⋊Dic7—42no—
97C2×C4⋊Dic7Q818yescomplemented
98C2×C4⋊Dic7C2314yes—
99C2×C4⋊Dic7C2314yes—
100C2×C4⋊Dic7C2314yes—
101C2×Dic7⋊C4—24no—
102C2×Dic7⋊C4—24no—
103C2×Dic7⋊C4—24no—
104C2×Dic7⋊C4—42no—
105C2×Dic7⋊C4—42no—
106C2×Dic7⋊C4—42no—
107C2×Dic7⋊C4—42no—
108C2×Dic7⋊C4Q818yescomplemented
109C2×Dic7⋊C4C2314yes—
110C2×Dic7⋊C4C2314yes—
111C2×Dic7⋊C4C2314yes—
112C2×Dic7⋊C4C2314yes—
113C2×Dic7⋊C4C2314yes—
114C2×Dic7⋊C4C2314yes—
115C2×Dic7⋊C4C2314yes—
116C2×Dic7⋊C4C2314yes—
117C2×C4×Dic7—24no—
118C2×C4×Dic7—42no—
119C2×C4×Dic7—42no—
120C2×C4×Dic7—42no—
121C2×C4×Dic7C2314yes—
122C2×C4×Dic7C2314yes—
123C2×C4×Dic7C2314yes—
124C2×C4×Dic7C2314yes—
125C7×#95C2314yes—
126C7×#95C2314yes—
127C7×#95C2314yes—
128C7×#95C2314yes—
129C7⋊#95C2314yes—
130C7⋊#95C2314yes—
131C7⋊#95C2314yes—
132C7⋊#95C2314yes—
133C7⋊#95C2314yes—
134C7⋊#95C2314yes—
135C7⋊#95C2314yes—
136C7⋊#95C2314yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141#2586—716no—
142C2×#398—71no—
143C2×#395—71no—
144C2×#395—71no—
145C2×#395—71no—
146C2×#391—71no—
147C2×#391—71no—
148C2×#391D711yescharacteristic
149C2×#389—71no—
150C2×#389—71no—
151C2×#387—71no—
152C2×#387—71no—
153C2×#387—71no—
154C2×#387—71no—
155C2×C4×C4⋊C4—71no—
156C2×C4×C4⋊C4—71no—
157C24×C7C2411yescharacteristic
158C2×C7×Q8—28no—
159C2×C7×Q8—28no—
160C2×C7×Q8—44no—
161C2×C7×Q8—416no—
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×C7C2×Q814yes—
180C22×C4×C7C2×Q814yes—
181C22×C4×C7#4114yes—
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×Dic7—22no—
209C22×Dic7C2×Q814yes—
210C22×Dic7C2×Q814yes—
211C22×Dic7C2×Q814yes—
212C22×Dic7C2×Q814yes—
213C22×Dic7#4114yes—
214C22×Dic7C2412yes—
215C22×Dic7C2412yes—
216C22×Dic7C2412yes—
217C22×Dic7C2412yes—
218C22×Dic7C2412yes—
219C22×Dic7C2412yes—
220C22×Dic7C2412yes—
221C22×Dic7C2412yes—
222C2×Dic14—28no—
223C2×Dic14—44no—
224C2×Dic14—44no—
225C2×Dic14—416no—
226C7×C4⋊C4—44no—
227C42×C7—28no—
228C4⋊Dic7—28no—
229C4⋊Dic7—44no—
230C4⋊Dic7C2×Q8116yescomplemented
231Dic7⋊C4—28no—
232Dic7⋊C4—28no—
233Dic7⋊C4—28no—
234Dic7⋊C4—44no—
235Dic7⋊C4—44no—
236Dic7⋊C4—44no—
237Dic7⋊C4—44no—
238Dic7⋊C4C2×Q8116yescomplemented
239C4×Dic7—28no—
240C4×Dic7—44no—
241C4×Dic7—44no—
242C4×Dic7—44no—
243C23×Q8—71no—
244C23×Q8C2×D711yescharacteristic
245C22×C4⋊C4—71no—
246C22×C4⋊C4—71no—
247C22×C4⋊C4—71no—
248C22×C4⋊C4—71no—
249C22×C4⋊C4—71no—
250C22×C4⋊C4—71no—
251C22×C4⋊C4—71no—
252C22×C4⋊C4—71no—
253C22×C4⋊C4—71no—
254C22×C4⋊C4—71no—
255C22×C4⋊C4—71no—
256C22×C4⋊C4C2×D711yescharacteristic
257C22×C42—71no—
258C22×C42—71no—
259C22×C42—71no—
260C22×C42—71no—
261C22×C42C2×D711yescharacteristic
262#398—78no—
263#395—78no—
264#395—78no—
265#395—78no—
266#391—78no—
267#391—78no—
268#391C2×D718yes—
269#389—78no—
270#389—78no—
271#387—78no—
272#387—78no—
273#387—78no—
274#387—78no—
275C4×C4⋊C4—78no—
276C4×C4⋊C4—78no—
277C2×#95—71no—
278C2×#95—71no—
279C2×#95—71no—
280C2×#95—71no—
281C2×#95—71no—
282C2×#95—71no—
283C2×#95—71no—
284C2×#95—71no—
285C2×#95—71no—
286C2×#95—71no—
287C2×#95—71no—
288C2×#95—71no—
289C2×#95C2×D711yescharacteristic
290C2×#95C2×D711yescharacteristic
291C2×#95C2×D711yescharacteristic
292C2×#95C2×D711yescharacteristic
293C23×C7C22×Q812yes—
294C23×C7C22×Q812yes—
295C23×C7C2×#4112yes—
296C23×C7C2×#4112yes—
297C23×C7C2×#4112yes—
298C23×C7H(5,𝔽2)12yes—
299C23×C7H(5,𝔽2)12yes—
300C23×C7C2511yescharacteristic
301C7×Q8—416no—
302C2×C4×C7—28no—
303C2×C4×C7—28no—
304C2×C4×C7—28no—
305C2×C4×C7—28no—
306C2×C4×C7—22no—
307C2×C4×C7—22no—
308C2×C4×C7—22no—
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—44no—
324C2×C4×C7—44no—
325C2×C4×C7—44no—
326C2×C4×C7C22×Q814yes—
327C2×C4×C7C22×Q814yes—
328C2×C4×C7C2×#4114yes—
329C2×C4×C7C2×#4114yes—
330C2×Dic7—28no—
331C2×Dic7—28no—
332C2×Dic7—28no—
333C2×Dic7—28no—
334C2×Dic7—28no—
335C2×Dic7—22no—
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—22no—
339C2×Dic7—22no—
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—44no—
355C2×Dic7—44no—
356C2×Dic7—44no—
357C2×Dic7C22×Q814yes—
358C2×Dic7C22×Q814yes—
359C2×Dic7C22×Q814yes—
360C2×Dic7C22×Q814yes—
361C2×Dic7C2×#4114yes—
362Dic14—416no—
363C22×Q8—24no—
364C22×Q8—24no—
365C22×Q8—42no—
366C22×Q8—74no—
367C22×Q8—144no—
368C22×Q8—282no—
369C22×Q8—282no—
370C22×Q8C22×D714yes—
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
386C2×C4⋊C4—42no—
387C2×C4⋊C4—78no—
388C2×C4⋊C4—78no—
389C2×C4⋊C4—74no—
390C2×C4⋊C4—74no—
391C2×C4⋊C4—74no—
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—144no—
401C2×C4⋊C4—144no—
402C2×C4⋊C4—144no—
403C2×C4⋊C4—144no—
404C2×C4⋊C4—282no—
405C2×C4⋊C4—282no—
406C2×C4⋊C4—282no—
407C2×C4⋊C4—282no—
408C2×C4⋊C4—282no—
409C2×C4⋊C4C22×D714yes—
410C2×C42—24no—
411C2×C42—74no—
412C2×C42—74no—
413C2×C42—74no—
414C2×C42—74no—
415C2×C42—144no—
416C2×C42—282no—
417C2×C42—282no—
418C2×C42—282no—
419C2×C42C22×D714yes—
420#95—74no—
421#95—74no—
422#95—74no—
423#95—74no—
424#95—74no—
425#95—74no—
426#95—74no—
427#95—74no—
428#95—74no—
429#95—74no—
430#95—74no—
431#95—74no—
432#95C22×D714yes—
433#95C22×D714yes—
434#95C22×D714yes—
435#95C22×D714yes—
436C22×C7#53314yes—
437C22×C7#53314yes—
438C22×C7#53814yes—
439C22×C7#55114yes—
440C22×C7#55414yes—
441C22×C7#55414yes—
442C22×C7Q8214yes—
443C22×C7C23×Q811yescharacteristic
444C22×C7C23×Q811yescharacteristic
445C22×C7C22×#4111yescharacteristic
446C22×C7C22×#4111yescharacteristic
447C22×C7C22×#4111yescharacteristic
448C22×C7C2×H(5,𝔽2)11yescharacteristic
449C22×C7C2×H(5,𝔽2)11yescharacteristic
450C4×C7—24no—
451C4×C7—24no—
452C4×C7—24no—
453C4×C7—24no—
454C4×C7—42no—
455C4×C7—42no—
456C4×C7—42no—
457Dic7—24no—
458Dic7—24no—
459Dic7—24no—
460Dic7—24no—
461Dic7—24no—
462Dic7—42no—
463Dic7—42no—
464Dic7—42no—
465C24C23×D711yescharacteristic
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8—44no—
469C2×Q8—416no—
470C2×Q8—148no—
471C2×Q8—284no—
472C2×Q8—284no—
473C2×Q8—2816no—
474C22×C4—22no—
475C22×C4—22no—
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—74no—
492C22×C4—74no—
493C22×C4—74no—
494C22×C4—74no—
495C22×C4—74no—
496C22×C4—72no—
497C22×C4—72no—
498C22×C4—72no—
499C22×C4—72no—
500C22×C4—72no—
501C22×C4—72no—
502C22×C4—72no—
503C22×C4—72no—
504C22×C4—142no—
505C22×C4—142no—
506C22×C4—142no—
507C22×C4—142no—
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#115714yes—
524C22×C4#115914yes—
525C22×C4Q8×D714yes—
526C22×C4Q8×D714yes—
527C22×C4C23×D712yes—
528C22×C4C23×D712yes—
529C22×C4C23×D712yes—
530C22×C4C23×D712yes—
531C22×C4C23×D712yes—
532C22×C4C23×D712yes—
533C22×C4C23×D712yes—
534C4⋊C4—44no—
535C4⋊C4—716no—
536C4⋊C4—716no—
537C4⋊C4—148no—
538C4⋊C4—148no—
539C4⋊C4—148no—
540C4⋊C4—148no—
541C4⋊C4—284no—
542C4⋊C4—284no—
543C4⋊C4—284no—
544C4⋊C4—284no—
545C4⋊C4—284no—
546C42—28no—
547C42—148no—
548C42—284no—
549C42—284no—
550C42—284no—
551C2×C7#258618yescomplemented
552C2×C7C2×#53311yescharacteristic
553C2×C7C2×#53311yescharacteristic
554C2×C7C2×#53811yescharacteristic
555C2×C7C2×#55111yescharacteristic
556C2×C7C2×#55411yescharacteristic
557C2×C7C2×#55411yescharacteristic
558C2×C7C2×Q8211yescharacteristic
559C23C2×#115712yes—
560C23C2×#115912yes—
561C23#654812yes—
562C23C2×Q8×D712yes—
563C23C2×Q8×D712yes—
564C23D7×#4112yes—
565C23#655312yes—
566C23C24×D711yescharacteristic
567Q8—416no—
568Q8—2816no—
569C2×C4—28no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
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—44no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—74no—
594C2×C4—74no—
595C2×C4—74no—
596C2×C4—74no—
597C2×C4—74no—
598C2×C4—148no—
599C2×C4—148no—
600C2×C4—148no—
601C2×C4—148no—
602C2×C4—148no—
603C2×C4—142no—
604C2×C4—142no—
605C2×C4—142no—
606C2×C4—142no—
607C2×C4—142no—
608C2×C4—142no—
609C2×C4—142no—
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—284no—
623C2×C4—284no—
624C2×C4—284no—
625C2×C4C2×#115714yes—
626C2×C4C2×#115914yes—
627C2×C4C2×Q8×D714yes—
628C2×C4C2×Q8×D714yes—
629C7C2×#258611yescharacteristic, complemented, Sylow
630C22#9018614yes—
631C22#9026914yes—
632C22#9027014yes—
633C22#9031314yes—
634C22#9032614yes—
635C22#9036914yes—
636C22#9041314yes—
637C22C22×#115711yescharacteristic
638C22C22×#115911yescharacteristic
639C22C2×#654811yescharacteristic
640C22C22×Q8×D711yescharacteristic
641C22C22×Q8×D711yescharacteristic
642C22C2×D7×#4111yescharacteristic
643C22C2×#655311yescharacteristic
644C4—24no—
645C4—24no—
646C4—24no—
647C4—24no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—144no—
652C4—144no—
653C4—144no—
654C4—144no—
655C4—144no—
656C4—282no—
657C4—282no—
658C4—282no—
659C2#1173399518yesdirect product factor
660C2C2×#9018611yescharacteristic
661C2C2×#9026911yescharacteristic
662C2C2×#9027011yescharacteristic
663C2C2×#9031311yescharacteristic
664C2C2×#9032611yescharacteristic
665C2C2×#9036911yescharacteristic
666C2C2×#9041311yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#391C2
socle, prime radicalC24×C7C24
hypercenterC2×#391D7
hypocenterC7C2×#2586
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
8. #11733995C2direct (N × H)
97. C2×C4⋊Dic7Q8semidirect
108. C2×Dic7⋊C4Q8semidirect
230. C4⋊Dic7C2×Q8semidirect
238. Dic7⋊C4C2×Q8semidirect
551. C2×C7#2586semidirect
629. C7C2×#2586semidirect
659. C2#11733995direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3912
C2×#900012
C2×#900022
C2×#897512
C2×#897442
C2×#897052
C2×C4×C4⋊Dic72
#117339952
C2×#894292
C2×#894282
C2×#894182
C2×#894192
C2×#894252
C2×#894242
C2×#894212
C2×#25867