Finite Group Databasebeta

← C2×#11739817 #13523313

Subgroups — C2×#11739817 #13523313

Order 1792.

3070 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
1C22×C4×C7×D4C211yesmaximal, characteristic
2C22×#6489C211yesmaximal, characteristic, complemented
3C2×#89994C212yesmaximal
4C2×#89984C211yesmaximal, characteristic, complemented
5C2×#89984C211yesmaximal, characteristic, complemented
6C2×#89984C211yesmaximal, characteristic, complemented
7#11739817C2116yesmaximal, direct product factor
8C2×#89750C212yesmaximal, complemented
9C2×#89724C212yesmaximal, complemented
10C2×#89716C212yesmaximal, complemented
11C2×#89700C211yesmaximal, characteristic, complemented
12C2×#89700C211yesmaximal, characteristic, complemented
13C23×C7×D4C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C24×C4×C7C2211yescharacteristic
16C2×C4×C7×D4—28no—
17C2×C4×C7×D4C2218yes—
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×C22⋊Dic7C2212yes—
23C22×C22⋊Dic7C2212yes—
24C22×C22⋊Dic7C2212yes—
25C22×C22⋊Dic7C2212yes—
26C2×#6489—28no—
27C2×#6489C2218yescomplemented
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×Dic7⋊C4C2212yes—
33C22×Dic7⋊C4C2212yes—
34C22×C4×Dic7C2212yes—
35#89994C22116yes—
36#89984C2218yescomplemented
37#89984C2218yescomplemented
38#89984C2218yescomplemented
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41C2×C7⋊#95C2212yes—
42C2×C7⋊#95C2212yes—
43C2×C7⋊#95C2212yes—
44#89750C22116yescomplemented
45#89724C22116yescomplemented
46#89716C22116yescomplemented
47#89700C2218yescomplemented
48#89700C2218yescomplemented
49C2×#2485—71nomaximal, Sylow
50C25×C7C2311yescharacteristic
51C25×C7C2311yescharacteristic
52C22×C7×D4—24no—
53C22×C7×D4—24no—
54C22×C7×D4—24no—
55C22×C7×D4C2314yes—
56C23×C4×C7—24no—
57C23×C4×C7—24no—
58C23×C4×C7—24no—
59C23×C4×C7—24no—
60C23×C4×C7—24no—
61C23×C4×C7D418yes—
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2314yes—
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2314yes—
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×Dic7C2312yes—
70C23×Dic7C2312yes—
71C23×Dic7C2312yes—
72C23×Dic7C2312yes—
73C4×C7×D4—232no—
74C2×C7×C4⋊C4—24no—
75C2×C7×C4⋊C4C2314yes—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4C2314yes—
79C2×C7×C22⋊C4C2314yes—
80C2×C42×C7—24no—
81C2×C42×C7C2314yes—
82C2×C22⋊Dic7—28no—
83C2×C22⋊Dic7—28no—
84C2×C22⋊Dic7—44no—
85C2×C22⋊Dic7—44no—
86C2×C22⋊Dic7C2318yes—
87C2×C22⋊Dic7C2318yes—
88C2×C22⋊Dic7C2318yes—
89C2×C22⋊Dic7C2318yes—
90#6489—232no—
91C2×C4⋊Dic7—24no—
92C2×C4⋊Dic7—24no—
93C2×C4⋊Dic7—24no—
94C2×C4⋊Dic7—24no—
95C2×C4⋊Dic7C2314yes—
96C2×C4⋊Dic7C2314yes—
97C2×C4⋊Dic7C2314yes—
98C2×C4⋊Dic7C2314yes—
99C2×Dic7⋊C4—28no—
100C2×Dic7⋊C4—44no—
101C2×Dic7⋊C4C2318yes—
102C2×Dic7⋊C4C2318yes—
103C2×C4×Dic7—28no—
104C2×C4×Dic7C2318yes—
105C7⋊#95C2318yes—
106C7⋊#95C2318yes—
107C7⋊#95C2318yes—
108C7⋊#95C2318yes—
109C7⋊#95C2318yes—
110C22×C4×D4D711yescharacteristic
111C22×#117—71no—
112#2485—716no—
113C2×#397—72no—
114C2×#394—72no—
115C2×#389—71no—
116C2×#389—71no—
117C2×#388—72no—
118C2×#387—72no—
119C2×#380—71no—
120C2×#380—71no—
121C2×#380—71no—
122C24×C7—22no—
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—22no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—22no—
134C24×C7C2×D414yes—
135C24×C7#4114yes—
136C24×C7C2412yes—
137C24×C7C2412yes—
138C24×C7C2411yescharacteristic
139C2×C7×D4—232no—
140C2×C7×D4—28no—
141C2×C7×D4—28no—
142C2×C7×D4—28no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—232no—
148C22×C4×C7—28no—
149C22×C4×C7—28no—
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—28no—
157C22×C4×C7—28no—
158C22×C4×C7—28no—
159C22×C4×C7—416no—
160C22×C4×C7C2×D414yes—
161C22×C4×C7C2×D4116yes—
162C22×C4×C7C2×D414yes—
163C22×C4×C7#4114yes—
164C22×C4×C7#4114yes—
165C22×C4×C7#4114yes—
166C22×C4×C7C2412yes—
167C22×C4×C7C2412yes—
168C22×C4×C7C2412yes—
169C22×C4×C7C2412yes—
170C22×C4×C7C2412yes—
171C22×Dic7—24no—
172C22×Dic7—24no—
173C22×Dic7—24no—
174C22×Dic7—24no—
175C22×Dic7—24no—
176C22×Dic7—24no—
177C22×Dic7—24no—
178C22×Dic7—24no—
179C22×Dic7—24no—
180C22×Dic7—24no—
181C22×Dic7—24no—
182C22×Dic7—24no—
183C22×Dic7C2414yes—
184C22×Dic7C2414yes—
185C22×Dic7C2414yes—
186C22×Dic7C2414yes—
187C7×C4⋊C4—28no—
188C7×C22⋊C4—28no—
189C7×C22⋊C4—28no—
190C42×C7—28no—
191C22⋊Dic7—216no—
192C22⋊Dic7—216no—
193C22⋊Dic7—48no—
194C22⋊Dic7—48no—
195C4⋊Dic7—28no—
196C4⋊Dic7—28no—
197C4⋊Dic7—28no—
198C4⋊Dic7—28no—
199Dic7⋊C4—216no—
200Dic7⋊C4—48no—
201C4×Dic7—216no—
202C23×D4C2×D711yescharacteristic
203C24×C4C2×D711yescharacteristic
204C24×C4C2×D711yescharacteristic
205C2×C4×D4—28no—
206C2×C4×D4C2×D718yes—
207C2×#117—78no—
208C2×#117—148no—
209C22×C4⋊C4—72no—
210C22×C4⋊C4—71no—
211C22×C4⋊C4—71no—
212C22×C4⋊C4—71no—
213C22×C4⋊C4—71no—
214C22×C4⋊C4—72no—
215C22×C4⋊C4C2×D711yescharacteristic
216C22×C22⋊C4—72no—
217C22×C22⋊C4—72no—
218C22×C22⋊C4—72no—
219C22×C22⋊C4—72no—
220C22×C22⋊C4C2×D711yescharacteristic
221C22×C22⋊C4C2×D711yescharacteristic
222C22×C42—72no—
223C22×C42C2×D711yescharacteristic
224#397—716no—
225#394—716no—
226#389—78no—
227#389—78no—
228#388—716no—
229#387—716no—
230#380—78no—
231#380—78no—
232#380—78no—
233C2×#95—72no—
234C2×#95—72no—
235C2×#95—72no—
236C2×#95—72no—
237C2×#95—72no—
238C23×C7—28no—
239C23×C7—28no—
240C23×C7—28no—
241C23×C7—28no—
242C23×C7—28no—
243C23×C7—28no—
244C23×C7—22no—
245C23×C7—22no—
246C23×C7—22no—
247C23×C7—22no—
248C23×C7—22no—
249C23×C7—22no—
250C23×C7—22no—
251C23×C7—22no—
252C23×C7—22no—
253C23×C7—22no—
254C23×C7—22no—
255C23×C7—22no—
256C23×C7—44no—
257C23×C7—44no—
258C23×C7—44no—
259C23×C7—44no—
260C23×C7—44no—
261C23×C7—44no—
262C23×C7—44no—
263C23×C7—44no—
264C23×C7C22×D414yes—
265C23×C7C22×D412yes—
266C23×C7C2×#4114yes—
267C23×C7C2×#4112yes—
268C23×C7C2×#4112yes—
269C23×C7C2×#4112yes—
270C23×C7C2×#4112yes—
271C23×C7H(5,𝔽2)12yes—
272C23×C72−1+412yes—
273C23×C7C2511yescharacteristic
274C7×D4—232no—
275C2×C4×C7—28no—
276C2×C4×C7—28no—
277C2×C4×C7—22no—
278C2×C4×C7—22no—
279C2×C4×C7—22no—
280C2×C4×C7—22no—
281C2×C4×C7—232no—
282C2×C4×C7—22no—
283C2×C4×C7—22no—
284C2×C4×C7—22no—
285C2×C4×C7—22no—
286C2×C4×C7—22no—
287C2×C4×C7—22no—
288C2×C4×C7—44no—
289C2×C4×C7—44no—
290C2×C4×C7—416no—
291C2×C4×C7#123116yes—
292C2×C4×C7C22×D414yes—
293C2×C4×C7C22×D414yes—
294C2×C4×C7C2×#4114yes—
295C2×C4×C7C2×#4114yes—
296C2×C4×C7C2×#4114yes—
297C2×Dic7—24no—
298C2×Dic7—24no—
299C2×Dic7—24no—
300C2×Dic7—24no—
301C2×Dic7—24no—
302C2×Dic7—24no—
303C2×Dic7—24no—
304C2×Dic7—24no—
305C2×Dic7—24no—
306C2×Dic7—24no—
307C2×Dic7—24no—
308C2×Dic7—24no—
309C2×Dic7—48no—
310C2×Dic7—48no—
311C2×Dic7—48no—
312C2×Dic7—48no—
313C25C22×D711yescharacteristic
314C25C22×D711yescharacteristic
315C22×D4—24no—
316C22×D4—24no—
317C22×D4—24no—
318C22×D4C22×D714yes—
319C23×C4—24no—
320C23×C4—24no—
321C23×C4—24no—
322C23×C4—24no—
323C23×C4—24no—
324C23×C4—72no—
325C23×C4—72no—
326C23×C4—72no—
327C23×C4—72no—
328C23×C4C22⋊D718yes—
329C23×C4C22×D714yes—
330C23×C4C22×D711yescharacteristic
331C23×C4C22×D711yescharacteristic
332C23×C4C22×D711yescharacteristic
333C23×C4C22×D714yes—
334C23×C4C22×D711yescharacteristic
335C23×C4C22×D711yescharacteristic
336C4×D4—232no—
337#117—1432no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—74no—
340C2×C4⋊C4—74no—
341C2×C4⋊C4—78no—
342C2×C4⋊C4—74no—
343C2×C4⋊C4—74no—
344C2×C4⋊C4—78no—
345C2×C4⋊C4—148no—
346C2×C4⋊C4—144no—
347C2×C4⋊C4—144no—
348C2×C4⋊C4—144no—
349C2×C4⋊C4—144no—
350C2×C4⋊C4—284no—
351C2×C4⋊C4C22×D714yes—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—78no—
355C2×C22⋊C4—78no—
356C2×C22⋊C4—78no—
357C2×C22⋊C4—78no—
358C2×C22⋊C4—148no—
359C2×C22⋊C4—148no—
360C2×C22⋊C4—284no—
361C2×C22⋊C4—284no—
362C2×C22⋊C4C22×D714yes—
363C2×C22⋊C4C22×D714yes—
364C2×C42—24no—
365C2×C42—78no—
366C2×C42—148no—
367C2×C42C22×D714yes—
368#95—78no—
369#95—78no—
370#95—78no—
371#95—78no—
372#95—78no—
373C22×C7—24no—
374C22×C7—24no—
375C22×C7—24no—
376C22×C7—24no—
377C22×C7—24no—
378C22×C7—24no—
379C22×C7—42no—
380C22×C7—42no—
381C22×C7—42no—
382C22×C7—42no—
383C22×C7—42no—
384C22×C7—42no—
385C22×C7—42no—
386C22×C7—42no—
387C22×C7—416no—
388C22×C7—416no—
389C22×C7C2×#12314yes—
390C22×C7#52514yes—
391C22×C7#53714yes—
392C22×C7#55214yes—
393C22×C7#55314yes—
394C22×C7#55514yes—
395C22×C7#55614yes—
396C22×C7C23×D411yescharacteristic
397C22×C7C22×#4111yescharacteristic
398C22×C7C22×#4111yescharacteristic
399C22×C7C22×#4111yescharacteristic
400C22×C7C22×#4111yescharacteristic
401C22×C7C2×H(5,𝔽2)11yescharacteristic
402C22×C7C2×2−1+411yescharacteristic
403C4×C7—24no—
404C4×C7—24no—
405C4×C7—42no—
406C4×C7—42no—
407C4×C7C2×#12318yes—
408Dic7—44no—
409Dic7—44no—
410Dic7—44no—
411Dic7—44no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24#115714yes—
425C24C2×C22⋊D714yes—
426C24C23×D712yes—
427C24C23×D712yes—
428C24C23×D711yescharacteristic
429C2×D4—232no—
430C2×D4—28no—
431C2×D4—28no—
432C2×D4—28no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—232no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—416no—
450C22×C4—74no—
451C22×C4—74no—
452C22×C4—74no—
453C22×C4—74no—
454C22×C4—144no—
455C22×C4—144no—
456C22×C4—144no—
457C22×C4—144no—
458C22×C4—144no—
459C22×C4—144no—
460C22×C4—144no—
461C22×C4—144no—
462C22×C4—144no—
463C22×C4—144no—
464C22×C4—144no—
465C22×C4—144no—
466C22×C4#115714yes—
467C22×C4#115914yes—
468C22×C4#115914yes—
469C22×C4C2×C22⋊D714yes—
470C22×C4C2×C22⋊D7116yes—
471C22×C4C2×C22⋊D714yes—
472C22×C4C23×D712yes—
473C22×C4C23×D712yes—
474C22×C4C23×D712yes—
475C22×C4C23×D712yes—
476C22×C4C23×D712yes—
477C4⋊C4—28no—
478C4⋊C4—1416no—
479C4⋊C4—148no—
480C4⋊C4—148no—
481C4⋊C4—148no—
482C4⋊C4—148no—
483C4⋊C4—288no—
484C22⋊C4—28no—
485C22⋊C4—28no—
486C22⋊C4—1416no—
487C22⋊C4—1416no—
488C22⋊C4—288no—
489C22⋊C4—288no—
490C42—28no—
491C42—1416no—
492C2×C7—44no—
493C2×C7—44no—
494C2×C7#248518yescomplemented
495C2×C7C22×#12311yescharacteristic
496C2×C7C2×#52511yescharacteristic
497C2×C7C2×#53711yescharacteristic
498C2×C7C2×#55211yescharacteristic
499C2×C7C2×#55311yescharacteristic
500C2×C7C2×#55511yescharacteristic
501C2×C7C2×#55611yescharacteristic
502C23—28no—
503C23—28no—
504C23—28no—
505C23—28no—
506C23—28no—
507C23—28no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—44no—
521C23—44no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—44no—
527C23—44no—
528C23C2×#115714yes—
529C23C2×#115712yes—
530C23C2×#115712yes—
531C23C2×#115912yes—
532C23C2×#115912yes—
533C23#655312yes—
534C23#655412yes—
535C23C22×C22⋊D714yes—
536C23C22×C22⋊D712yes—
537C23C24×D711yescharacteristic
538D4—232no—
539C2×C4—28no—
540C2×C4—28no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—232no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—416no—
555C2×C4—144no—
556C2×C4—144no—
557C2×C4—144no—
558C2×C4—144no—
559C2×C4—144no—
560C2×C4—144no—
561C2×C4—144no—
562C2×C4—144no—
563C2×C4—144no—
564C2×C4—144no—
565C2×C4—144no—
566C2×C4—144no—
567C2×C4—288no—
568C2×C4—288no—
569C2×C4—288no—
570C2×C4—288no—
571C2×C4#6498116yes—
572C2×C4C2×#115714yes—
573C2×C4C2×#115914yes—
574C2×C4C2×#115914yes—
575C2×C4C22×C22⋊D714yes—
576C2×C4C22×C22⋊D714yes—
577C7C2×#248511yescharacteristic, complemented, Sylow
578C22—24no—
579C22—24no—
580C22—24no—
581C22—24no—
582C22—24no—
583C22—24no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—416no—
593C22—416no—
594C22#9023214yes—
595C22#9023314yes—
596C22#9025414yes—
597C22#9025614yes—
598C22#9048214yes—
599C22C2×#649814yes—
600C22#9052414yes—
601C22C22×#115711yescharacteristic
602C22C22×#115711yescharacteristic
603C22C22×#115911yescharacteristic
604C22C22×#115911yescharacteristic
605C22C2×#655311yescharacteristic
606C22C2×#655411yescharacteristic
607C22C23×C22⋊D711yescharacteristic
608C4—24no—
609C4—24no—
610C4—42no—
611C4—42no—
612C4—284no—
613C4—284no—
614C4—284no—
615C4—284no—
616C4C2×#649818yes—
617C2—44no—
618C2—44no—
619C2#1173981718yesdirect product factor
620C2C2×#9023211yescharacteristic
621C2C2×#9025611yescharacteristic
622C2C2×#9025411yescharacteristic
623C2C2×#9023311yescharacteristic
624C2C2×#9048211yescharacteristic
625C2C22×#649811yescharacteristic
626C2C2×#9052411yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C4×C7×D4C2
socleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC22×C4×D4D7
hypocenterC7C2×#2485
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×#6489C2semidirect
4. C2×#89984C2semidirect
5. C2×#89984C2semidirect
6. C2×#89984C2semidirect
7. #11739817C2direct (N × H)
8. C2×#89750C2semidirect
9. C2×#89724C2semidirect
10. C2×#89716C2semidirect
11. C2×#89700C2semidirect
12. C2×#89700C2semidirect
27. C2×#6489C22semidirect
36. #89984C22semidirect
37. #89984C22semidirect
38. #89984C22semidirect
44. #89750C22semidirect
45. #89724C22semidirect
46. #89716C22semidirect
47. #89700C22semidirect
48. #89700C22semidirect
494. C2×C7#2485semidirect
577. C7C2×#2485semidirect
619. C2#11739817direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C22×#64892
C2×#899942
C2×#899842
#117398172
C2×#897502
C2×#897242
C2×#897162
C2×#897002
C2×#24857