Finite Group Databasebeta

← C2×#11740106 #13523243

Subgroups — C2×#11740106 #13523243

Order 1792.

3158 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#121C211yesmaximal, characteristic
2C22×#6453C211yesmaximal, characteristic, complemented
3C2×#89994C212yesmaximal, complemented
4C2×#89993C211yesmaximal, characteristic, complemented
5C2×#89993C211yesmaximal, characteristic, complemented
6C2×#89993C212yesmaximal, complemented
7C2×#89984C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
9#11740106C2116yesmaximal, direct product factor
10C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
11C2×#89725C212yesmaximal, complemented
12C2×#89717C212yesmaximal, complemented
13C23×C7×D4C2211yescharacteristic
14C23×C7×D4C2212yes—
15C24×C4×C7C2211yescharacteristic
16C2×C7×#121—28no—
17C2×C7×#121C2218yes—
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2212yes—
20C22×C22⋊Dic7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2212yes—
23C22×C22⋊Dic7C2212yes—
24C22×C22⋊Dic7C2212yes—
25C22×C22⋊Dic7C2212yes—
26C22×C22⋊Dic7C2212yes—
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2212yes—
30C22×Dic7⋊C4C2212yes—
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C22×C4×Dic7C2212yes—
34C2×#6453—28no—
35C2×#6453C2218yescomplemented
36#89994C22116yescomplemented
37#89993C2218yescomplemented
38#89993C2218yescomplemented
39#89993C22116yescomplemented
40#89984C2218yescomplemented
41C4×C22⋊Dic7C2218yescomplemented
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2212yes—
45C2×C7⋊#95C2212yes—
46C4⋊C4×Dic7C2218yescomplemented
47#89725C22116yescomplemented
48#89717C22116yescomplemented
49C2×#2490—71nomaximal, Sylow
50C25×C7C2312yes—
51C25×C7C2311yescharacteristic
52C22×C7×D4—28no—
53C22×C7×D4—28no—
54C22×C7×D4—24no—
55C22×C7×D4—24no—
56C22×C7×D4—24no—
57C22×C7×D4—44no—
58C22×C7×D4C2314yes—
59C22×C7×D4C2318yes—
60C23×C4×C7—24no—
61C23×C4×C7—24no—
62C23×C4×C7—24no—
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2314yes—
65C23×C4×C7C2312yes—
66C23×C4×C7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2312yes—
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2312yes—
72C23×Dic7C2311yescharacteristic
73C7×#121—232no—
74C2×C7×C4⋊C4D418yes—
75C2×C7×C4⋊C4C2314yes—
76C2×C7×C22⋊C4—28no—
77C2×C7×C22⋊C4C2318yes—
78C2×C22⋊Dic7—24no—
79C2×C22⋊Dic7—24no—
80C2×C22⋊Dic7—28no—
81C2×C22⋊Dic7—44no—
82C2×C22⋊Dic7—44no—
83C2×C22⋊Dic7—44no—
84C2×C22⋊Dic7—44no—
85C2×C22⋊Dic7C2318yes—
86C2×C22⋊Dic7C2314yes—
87C2×C22⋊Dic7C2314yes—
88C2×C22⋊Dic7C2318yes—
89C2×C22⋊Dic7C2318yes—
90C2×C22⋊Dic7C2318yes—
91C2×C22⋊Dic7C2318yes—
92C2×C4⋊Dic7—28no—
93C2×C4⋊Dic7—24no—
94C2×C4⋊Dic7—24no—
95C2×C4⋊Dic7C2318yes—
96C2×C4⋊Dic7C2314yes—
97C2×C4⋊Dic7C2314yes—
98C2×Dic7⋊C4—28no—
99C2×Dic7⋊C4C2318yes—
100C2×C4×Dic7—24no—
101C2×C4×Dic7—24no—
102C2×C4×Dic7—44no—
103C2×C4×Dic7C2314yes—
104C2×C4×Dic7C2314yes—
105C2×C4×Dic7C2318yes—
106#6453—232no—
107C7⋊#95C2314yes—
108C7⋊#95C2318yes—
109C7⋊#95C2314yes—
110C7⋊#95C2318yes—
111C22×#125—71no—
112C22×#121D711yescharacteristic
113#2490—716no—
114C2×#397—72no—
115C2×#394—72no—
116C2×#390—72no—
117C2×#390—71no—
118C2×#390—71no—
119C2×#388—72no—
120C2×#380—71no—
121C2×C4×C4⋊C4—71no—
122C2×C4×C22⋊C4—71no—
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—22no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—24no—
130C24×C7—24no—
131C24×C7—24no—
132C24×C7—24no—
133C24×C7—24no—
134C24×C7—24no—
135C24×C7—24no—
136C24×C7#4114yes—
137C24×C7C2414yes—
138C24×C7C2412yes—
139C24×C7C2411yescharacteristic
140C2×C7×D4—216no—
141C2×C7×D4—216no—
142C2×C7×D4—28no—
143C2×C7×D4—28no—
144C2×C7×D4—28no—
145C2×C7×D4—48no—
146C2×C7×D4—432no—
147C2×C7×D4—416no—
148C22×C4×C7—24no—
149C22×C4×C7—24no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—28no—
154C22×C4×C7—28no—
155C22×C4×C7—28no—
156C22×C4×C7—416no—
157C22×C4×C7C2×D418yes—
158C22×C4×C7C2×D414yes—
159C22×C4×C7#4114yes—
160C22×C4×C7#4114yes—
161C22×C4×C7C2412yes—
162C22×C4×C7C2414yes—
163C22×C4×C7C2412yes—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—24no—
169C22×Dic7—22no—
170C22×Dic7—24no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—24no—
174C22×Dic7—22no—
175C22×Dic7—24no—
176C22×Dic7—24no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—24no—
180C22×Dic7—22no—
181C22×Dic7#4114yes—
182C22×Dic7C2412yes—
183C22×Dic7C2414yes—
184C22×Dic7C2412yes—
185C22×Dic7C2412yes—
186C22×Dic7C2414yes—
187C22×Dic7C2412yes—
188C7×C4⋊C4C2×D4116yes—
189C7×C22⋊C4—216no—
190C22⋊Dic7—28no—
191C22⋊Dic7—28no—
192C22⋊Dic7—216no—
193C22⋊Dic7—48no—
194C22⋊Dic7—48no—
195C22⋊Dic7—48no—
196C22⋊Dic7—48no—
197C4⋊Dic7—216no—
198C4⋊Dic7—28no—
199C4⋊Dic7—28no—
200Dic7⋊C4—216no—
201C4×Dic7—28no—
202C4×Dic7—28no—
203C4×Dic7—48no—
204C23×D4C2×D711yescharacteristic
205C23×D4C2×D712yes—
206C24×C4C2×D711yescharacteristic
207C2×#125—78no—
208C2×#125—148no—
209C2×#121—28no—
210C2×#121C2×D718yes—
211C22×C4⋊C4—72no—
212C22×C4⋊C4—72no—
213C22×C4⋊C4—71no—
214C22×C4⋊C4—71no—
215C22×C4⋊C4C2×D711yescharacteristic
216C22×C22⋊C4—71no—
217C22×C22⋊C4—71no—
218C22×C22⋊C4—72no—
219C22×C22⋊C4—72no—
220C22×C22⋊C4—72no—
221C22×C22⋊C4—72no—
222C22×C22⋊C4—72no—
223C22×C22⋊C4C2×D712yes—
224C22×C42—71no—
225C22×C42—71no—
226C22×C42—72no—
227#397—716no—
228#394—716no—
229#390—78no—
230#390—78no—
231#390—716no—
232#388—716no—
233#380—78no—
234C4×C4⋊C4—78no—
235C4×C22⋊C4—78no—
236C2×#95—72no—
237C2×#95—71no—
238C2×#95—72no—
239C2×#95—71no—
240C23×C7—28no—
241C23×C7—28no—
242C23×C7—28no—
243C23×C7—22no—
244C23×C7—22no—
245C23×C7—22no—
246C23×C7—22no—
247C23×C7—22no—
248C23×C7—22no—
249C23×C7—24no—
250C23×C7—24no—
251C23×C7—24no—
252C23×C7—24no—
253C23×C7—24no—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—44no—
257C23×C7—44no—
258C23×C7—44no—
259C23×C7—44no—
260C23×C7—48no—
261C23×C7—48no—
262C23×C7—48no—
263C23×C7—48no—
264C23×C7—48no—
265C23×C7—48no—
266C23×C7—48no—
267C23×C7C22×D412yes—
268C23×C7C2×#4114yes—
269C23×C7C2×#4112yes—
270C23×C7C2×#4112yes—
271C23×C7C2×#4112yes—
272C23×C7C2×#4112yes—
273C23×C7H(5,𝔽2)12yes—
274C23×C7H(5,𝔽2)12yes—
275C23×C7C2511yescharacteristic
276C7×D4—432no—
277C7×D4—416no—
278C2×C4×C7—216no—
279C2×C4×C7—24no—
280C2×C4×C7—24no—
281C2×C4×C7—22no—
282C2×C4×C7—22no—
283C2×C4×C7—22no—
284C2×C4×C7—44no—
285C2×C4×C7—416no—
286C2×C4×C7#124116yes—
287C2×C4×C7C22×D418yes—
288C2×C4×C7C22×D414yes—
289C2×C4×C7C2×#4114yes—
290C2×C4×C7C2×#4114yes—
291C2×Dic7—28no—
292C2×Dic7—22no—
293C2×Dic7—22no—
294C2×Dic7—22no—
295C2×Dic7—22no—
296C2×Dic7—24no—
297C2×Dic7—22no—
298C2×Dic7—24no—
299C2×Dic7—22no—
300C2×Dic7—22no—
301C2×Dic7—22no—
302C2×Dic7—24no—
303C2×Dic7—24no—
304C2×Dic7—22no—
305C2×Dic7—24no—
306C2×Dic7—22no—
307C2×Dic7—24no—
308C2×Dic7—22no—
309C2×Dic7—48no—
310C2×Dic7—44no—
311C2×Dic7—44no—
312C2×Dic7—48no—
313C2×Dic7—44no—
314C2×Dic7C2×#4114yes—
315C25C22×D712yes—
316C25C22×D711yescharacteristic
317C22×D4—28no—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—28no—
321C22×D4—24no—
322C22×D4—44no—
323C22×D4C22×D714yes—
324C22×D4C22×D718yes—
325C23×C4—24no—
326C23×C4—24no—
327C23×C4—24no—
328C23×C4—71no—
329C23×C4—72no—
330C23×C4—71no—
331C23×C4—71no—
332C23×C4—72no—
333C23×C4—71no—
334C23×C4C22×D714yes—
335C23×C4C22×D711yescharacteristic
336C23×C4C22×D712yes—
337C23×C4C22×D711yescharacteristic
338#125—1432no—
339#121—232no—
340C2×C4⋊C4—78no—
341C2×C4⋊C4—74no—
342C2×C4⋊C4—78no—
343C2×C4⋊C4—74no—
344C2×C4⋊C4—144no—
345C2×C4⋊C4—148no—
346C2×C4⋊C4—148no—
347C2×C4⋊C4—144no—
348C2×C4⋊C4C22⋊D718yes—
349C2×C4⋊C4C22×D714yes—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—74no—
352C2×C22⋊C4—74no—
353C2×C22⋊C4—78no—
354C2×C22⋊C4—78no—
355C2×C22⋊C4—78no—
356C2×C22⋊C4—78no—
357C2×C22⋊C4—78no—
358C2×C22⋊C4—144no—
359C2×C22⋊C4—148no—
360C2×C22⋊C4—144no—
361C2×C22⋊C4—284no—
362C2×C22⋊C4—284no—
363C2×C22⋊C4—284no—
364C2×C22⋊C4—284no—
365C2×C22⋊C4C22×D718yes—
366C2×C42—74no—
367C2×C42—74no—
368C2×C42—78no—
369C2×C42—144no—
370C2×C42—144no—
371C2×C42—284no—
372#95—74no—
373#95—74no—
374#95—78no—
375#95—78no—
376C22×C7—24no—
377C22×C7—24no—
378C22×C7—24no—
379C22×C7—42no—
380C22×C7—42no—
381C22×C7—42no—
382C22×C7—42no—
383C22×C7—416no—
384C22×C7—44no—
385C22×C7—44no—
386C22×C7—44no—
387C22×C7—44no—
388C22×C7—44no—
389C22×C7—44no—
390C22×C7—44no—
391C22×C7—816no—
392C22×C7C2×#12414yes—
393C22×C7#52914yes—
394C22×C7#54014yes—
395C22×C7#54614yes—
396C22×C7#55014yes—
397C22×C7#55314yes—
398C22×C7#55314yes—
399C22×C7C23×D411yescharacteristic
400C22×C7C22×#4111yescharacteristic
401C22×C7C22×#4111yescharacteristic
402C22×C7C22×#4111yescharacteristic
403C22×C7C22×#4111yescharacteristic
404C22×C7C2×H(5,𝔽2)11yescharacteristic
405C22×C7C2×H(5,𝔽2)11yescharacteristic
406C4×C7—28no—
407C4×C7—42no—
408C4×C7C2×#12418yes—
409Dic7—24no—
410Dic7—44no—
411Dic7—42no—
412Dic7—42no—
413Dic7—44no—
414Dic7—42no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—24no—
422C24—24no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24—24no—
427C24—24no—
428C24#115914yes—
429C24C23×D714yes—
430C24C23×D712yes—
431C24C23×D711yescharacteristic
432C2×D4—216no—
433C2×D4—28no—
434C2×D4—28no—
435C2×D4—216no—
436C2×D4—28no—
437C2×D4—48no—
438C2×D4—432no—
439C2×D4—416no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—416no—
449C22×C4—74no—
450C22×C4—72no—
451C22×C4—72no—
452C22×C4—74no—
453C22×C4—72no—
454C22×C4—72no—
455C22×C4—74no—
456C22×C4—142no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—142no—
461C22×C4—144no—
462C22×C4—144no—
463C22×C4—142no—
464C22×C4—144no—
465C22×C4—142no—
466C22×C4—144no—
467C22×C4—142no—
468C22×C4—142no—
469C22×C4—144no—
470C22×C4—142no—
471C22×C4—142no—
472C22×C4—144no—
473C22×C4#115914yes—
474C22×C4#115914yes—
475C22×C4C2×C22⋊D718yes—
476C22×C4C2×C22⋊D714yes—
477C22×C4C23×D712yes—
478C22×C4C23×D714yes—
479C22×C4C23×D712yes—
480C4⋊C4—148no—
481C4⋊C4—1416no—
482C4⋊C4—1416no—
483C4⋊C4—148no—
484C4⋊C4C2×C22⋊D7116yes—
485C22⋊C4—216no—
486C22⋊C4—148no—
487C22⋊C4—1416no—
488C22⋊C4—148no—
489C22⋊C4—288no—
490C22⋊C4—288no—
491C22⋊C4—288no—
492C22⋊C4—288no—
493C42—148no—
494C42—148no—
495C42—288no—
496C2×C7—44no—
497C2×C7—84no—
498C2×C7#249018yescomplemented
499C2×C7C22×#12411yescharacteristic
500C2×C7C2×#52911yescharacteristic
501C2×C7C2×#54011yescharacteristic
502C2×C7C2×#54611yescharacteristic
503C2×C7C2×#55011yescharacteristic
504C2×C7C2×#55311yescharacteristic
505C2×C7C2×#55311yescharacteristic
506C23—28no—
507C23—28no—
508C23—28no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—48no—
527C23—48no—
528C23—48no—
529C23—48no—
530C23—48no—
531C23—48no—
532C23—48no—
533C23C2×#115914yes—
534C23C2×#115912yes—
535C23C2×#115912yes—
536C23C2×#115912yes—
537C23#654812yes—
538C23D7×#4112yes—
539C23#655312yes—
540C23C22×C22⋊D712yes—
541C23C24×D711yescharacteristic
542D4—432no—
543D4—416no—
544C2×C4—216no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—44no—
551C2×C4—416no—
552C2×C4—74no—
553C2×C4—148no—
554C2×C4—142no—
555C2×C4—142no—
556C2×C4—142no—
557C2×C4—142no—
558C2×C4—142no—
559C2×C4—144no—
560C2×C4—144no—
561C2×C4—142no—
562C2×C4—142no—
563C2×C4—144no—
564C2×C4—144no—
565C2×C4—142no—
566C2×C4—142no—
567C2×C4—144no—
568C2×C4—142no—
569C2×C4—142no—
570C2×C4—144no—
571C2×C4—284no—
572C2×C4—284no—
573C2×C4—288no—
574C2×C4—284no—
575C2×C4—288no—
576C2×C4#6499116yes—
577C2×C4C2×#115914yes—
578C2×C4C2×#115914yes—
579C2×C4C22×C22⋊D718yes—
580C2×C4C22×C22⋊D714yes—
581C7C2×#249011yescharacteristic, complemented, Sylow
582C22—24no—
583C22—24no—
584C22—24no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—416no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—816no—
598C22#9029114yes—
599C22#9030514yes—
600C22#9030914yes—
601C22#9031014yes—
602C22C2×#649914yes—
603C22#9049714yes—
604C22#9052514yes—
605C22C22×#115911yescharacteristic
606C22C22×#115911yescharacteristic
607C22C22×#115911yescharacteristic
608C22C2×#654811yescharacteristic
609C22C2×D7×#4111yescharacteristic
610C22C2×#655311yescharacteristic
611C22C23×C22⋊D711yescharacteristic
612C4—28no—
613C4—42no—
614C4—144no—
615C4—284no—
616C4—282no—
617C4—282no—
618C4—282no—
619C4—284no—
620C4C2×#649918yes—
621C2—44no—
622C2—84no—
623C2#1174010618yesdirect product factor
624C2C2×#9029111yescharacteristic
625C2C2×#9031011yescharacteristic
626C2C2×#9030911yescharacteristic
627C2C2×#9030511yescharacteristic
628C2C22×#649911yescharacteristic
629C2C2×#9049711yescharacteristic
630C2C2×#9052511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
Fitting, prime radicalC22×C7×#121C2
socleC24×C7C24
hypercenterC22×#121D7
hypocenterC7C2×#2490
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
2. C22×#6453C2semidirect
3. C2×#89994C2semidirect
4. C2×#89993C2semidirect
5. C2×#89993C2semidirect
6. C2×#89993C2semidirect
7. C2×#89984C2semidirect
8. C2×C4×C22⋊Dic7C2semidirect
9. #11740106C2direct (N × H)
10. C2×C4⋊C4×Dic7C2semidirect
11. C2×#89725C2semidirect
12. C2×#89717C2semidirect
35. C2×#6453C22semidirect
36. #89994C22semidirect
37. #89993C22semidirect
38. #89993C22semidirect
39. #89993C22semidirect
40. #89984C22semidirect
41. C4×C22⋊Dic7C22semidirect
46. C4⋊C4×Dic7C22semidirect
47. #89725C22semidirect
48. #89717C22semidirect
498. C2×C7#2490semidirect
581. C7C2×#2490semidirect
623. C2#11740106direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1212
C22×#64532
C2×#899942
C2×#899932
C2×#899842
C2×C4×C22⋊Dic72
#117401062
C2×C4⋊C4×Dic72
C2×#897252
C2×#897172
C2×#24907