Finite Group Databasebeta

← C2×#11728084 #13355772

Subgroups — C2×#11728084 #13355772

Order 1792.

1878 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90496C211yesmaximal, characteristic
2C2×#90436C211yesmaximal, characteristic, complemented
3C2×C7×#418C211yesmaximal, characteristic, complemented
4C2×#89987C211yesmaximal, characteristic, complemented
5C2×#89778C211yesmaximal, characteristic, complemented
6C2×#89352C211yesmaximal, characteristic, complemented
7C2×#89326C211yesmaximal, characteristic, complemented
8#11728084C218yesmaximal, direct product factor
9C23×C7×D4C2211yescharacteristic
10C22×#1157C2211yescharacteristic
11C22×C7×M16C2211yescharacteristic
12C2×C7×#117C2211yescharacteristic
13C2×#6516—22no—
14#90496—22no—
15#90496—22no—
16#90496C414yescomplemented
17#90496C2214yes—
18C2×#6503C412yescomplemented
19C2×#6501—22no—
20C2×#6499C412yescomplemented
21C2×#6489C2211yescharacteristic
22C2×#6489C2211yescharacteristic
23C22×#1136C2211yescharacteristic
24#90436—22no—
25#90436—22no—
26#90436—22no—
27#90436C2214yescomplemented
28C2×#6470—22no—
29C2×D7×M16—22no—
30C2×#6464—22no—
31C7×#418—22no—
32C7×#418C2214yescomplemented
33C2×C7×#102—22no—
34#89987—22no—
35#89987C2214yescomplemented
36C2×#6406—22no—
37#89778—22no—
38#89778C2214yescomplemented
39C2×#6380—22no—
40#89352C2214yescomplemented
41#89326C2214yescomplemented
42C2×#1910—71nomaximal, Sylow
43C25×C7—21no—
44C22×C7×D4—21no—
45C22×C7×D4—21no—
46C22×C7×D4—21no—
47C22×C7×D4—21no—
48C22×C7×D4—21no—
49C22×C7×D4—21no—
50C22×C7×D4—21no—
51C22×C7×D4—21no—
52C22×C7×D4—21no—
53C22×C7×D4—21no—
54C22×C7×D4—21no—
55C22×C7×D4C2×C412yes—
56C22×C7×D4C2×C412yes—
57C22×C7×D4C2312yes—
58C23×C4×C7C2311yescharacteristic
59C22×C22⋊D7—24no—
60C22×C22⋊D7D412yes—
61C2×#1157—21no—
62C2×#1157—21no—
63C2×#1157—21no—
64C2×#1157—21no—
65C2×#1157—21no—
66C2×#1157—21no—
67C2×#1157—21no—
68C2×#1157—21no—
69C2×#1157C2×C412yes—
70C2×#1157D412yes—
71C2×#1157D412yes—
72C2×#1157C2312yes—
73C22×D28C2×C411yescharacteristic
74C22×C4×D7D412yes—
75C22×Dic14C2×C411yescharacteristic
76C2×C7×M16—21no—
77C2×C7×M16—21no—
78C2×C7×M16—21no—
79C2×C7×M16—21no—
80C2×C7×M16D412yescomplemented
81C2×C7×M16C2312yes—
82C22×C7×C8D412yescomplemented
83C7×#117—21no—
84C7×#117—21no—
85C7×#117—21no—
86C7×#117C2312yes—
87C2×C7×C4⋊C4—21no—
88C2×C7×C22⋊C4—21no—
89C2×C42×C7—21no—
90#6516—28no—
91#6516—28no—
92C2×C22⋊Dic7—21no—
93C2×C22⋊Dic7—24no—
94C2×C22⋊Dic7—21no—
95#6503—24no—
96#6503C2×C418yescomplemented
97#6501—28no—
98#6501—28no—
99#6499—24no—
100#6499C2×C418yescomplemented
101#6489—21no—
102#6489—21no—
103#6489—21no—
104#6489—21no—
105#6489—21no—
106#6489C2×C412yes—
107#6489C2312yes—
108#6489C2312yes—
109C2×C4⋊Dic7—21no—
110C2×C4⋊Dic7—21no—
111C2×C4×Dic7—21no—
112C2×C4×Dic7C2×C412yes—
113C2×#1136—21no—
114C2×#1136—21no—
115C2×#1136—21no—
116C2×#1136—21no—
117C2×#1136D412yescomplemented
118C2×#1136C2312yes—
119C22×C7⋊C8D412yescomplemented
120#6470—28no—
121#6470—28no—
122D7×M16—28no—
123D7×M16—28no—
124#6464—28no—
125#6464—28no—
126C2×#1131—24no—
127C2×C8×D7—24no—
128C7×#102—28no—
129#6406—28no—
130#6380—28no—
131C2×#568—71no—
132C2×#535—71no—
133C2×#418—71no—
134C2×#418D711yescharacteristic, complemented
135C2×#410—71no—
136#1910—78no—
137C2×H(3,ℤ/4)—71no—
138C2×H(3,ℤ/4)—71no—
139C24×C7—22no—
140C24×C7—22no—
141C24×C7—22no—
142C24×C7—41no—
143C24×C7—41no—
144C24×C7—41no—
145C24×C7—41no—
146C24×C7—84no—
147C24×C7C2×D411yescharacteristic
148C23×D7C22⋊C412yes—
149C2×C7×D4—22no—
150C2×C7×D4—22no—
151C2×C7×D4—22no—
152C2×C7×D4—22no—
153C2×C7×D4—22no—
154C2×C7×D4—22no—
155C2×C7×D4—22no—
156C2×C7×D4—22no—
157C2×C7×D4—22no—
158C2×C7×D4—22no—
159C2×C7×D4—22no—
160C2×C7×D4—22no—
161C2×C7×D4—22no—
162C2×C7×D4—22no—
163C2×C7×D4—22no—
164C2×C7×D4—41no—
165C2×C7×D4—41no—
166C2×C7×D4—41no—
167C2×C7×D4—41no—
168C2×C7×D4—41no—
169C2×C7×D4—41no—
170C2×C7×D4—41no—
171C2×C7×D4—41no—
172C2×C7×D4—41no—
173C2×C7×D4—41no—
174C2×C7×D4—41no—
175C2×C7×D4—41no—
176C2×C7×D4C22×C414yes—
177C22×C4×C7—41no—
178C22×C4×C7C22×C411yescharacteristic
179C22×C4×C7C22×C411yescharacteristic
180C22×C4×C7C2×D411yescharacteristic
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2×D411yescharacteristic
183C22×C4×C7C2×D411yescharacteristic
184C22×C4×C7C2×D411yescharacteristic
185C22×C4×C7C2×D411yescharacteristic
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7#4111yescharacteristic
188C22×C4×C7#4111yescharacteristic
189C22×C4×C7#4111yescharacteristic
190C22×C4×C7#4111yescharacteristic
191C22×C4×C7C2411yescharacteristic
192C2×C22⋊D7—22no—
193C2×C22⋊D7—22no—
194C2×C22⋊D7—22no—
195C2×C22⋊D7—22no—
196C2×C22⋊D7—216no—
197C2×C22⋊D7—88no—
198C2×C22⋊D7C22⋊C414yes—
199C2×C22⋊D7C2×D414yes—
200C22×Dic7—22no—
201C22×Dic7—41no—
202C22×Dic7C22⋊C412yes—
203#1157—22no—
204#1157—22no—
205#1157—22no—
206#1157—22no—
207#1157—22no—
208#1157—22no—
209#1157—22no—
210#1157—22no—
211#1157—22no—
212#1157—22no—
213#1157—22no—
214#1157—22no—
215#1157—22no—
216#1157—22no—
217#1157—22no—
218#1157—22no—
219C2×D28—21no—
220C2×D28—21no—
221C2×D28—21no—
222C2×D28—21no—
223C2×D28C22⋊C412yes—
224C2×D28C22×C412yes—
225C2×C4×D7—22no—
226C2×C4×D7—22no—
227C2×C4×D7—22no—
228C2×C4×D7—22no—
229C2×C4×D7C22⋊C414yes—
230C2×C4×D7C2×D414yes—
231C2×Dic14—21no—
232C2×Dic14—21no—
233C2×Dic14—21no—
234C2×Dic14—21no—
235C2×Dic14C22⋊C412yes—
236C2×Dic14C22×C412yes—
237C7×M16—22no—
238C7×M16—22no—
239C7×M16—22no—
240C7×M16—22no—
241C2×C7×C8—22no—
242C2×C7×C8—22no—
243C2×C7×C8C2×D414yescomplemented
244C7×C4⋊C4—22no—
245C7×C4⋊C4—41no—
246C7×C22⋊C4—22no—
247C7×C22⋊C4—41no—
248C42×C7—22no—
249C42×C7—41no—
250C22⋊Dic7—22no—
251C22⋊Dic7—22no—
252C22⋊Dic7—216no—
253C22⋊Dic7—22no—
254C22⋊Dic7—41no—
255C4⋊Dic7—22no—
256C4⋊Dic7—22no—
257C4⋊Dic7—22no—
258C4⋊Dic7—41no—
259C4×Dic7—22no—
260C4×Dic7—22no—
261C4×Dic7—41no—
262C4×Dic7C22×C414yes—
263#1136—22no—
264#1136—22no—
265#1136—22no—
266#1136—22no—
267C2×C7⋊C8—22no—
268C2×C7⋊C8—22no—
269C2×C7⋊C8C2×D414yescomplemented
270#1131—216no—
271C8×D7—216no—
272C22×#41—71no—
273C23×D4C2×D711yescharacteristic
274#568—74no—
275#568—142no—
276#568—142no—
277#568—142no—
278C2×#131—142no—
279C2×#131—142no—
280C22×M16—71no—
281C22×M16—142no—
282C22×M16C2×D711yescharacteristic
283#535—74no—
284#535—74no—
285#535—142no—
286#535—142no—
287C2×#127—72no—
288C2×#124—72no—
289C2×#121—142no—
290C2×#120—142no—
291C2×#117—71no—
292C2×#117—71no—
293C2×#117C2×D711yescharacteristic
294#418—22no—
295#418—74no—
296#418—142no—
297#418C2×D714yescomplemented
298C2×#102—22no—
299C2×#102—142no—
300#410—74no—
301#410—142no—
302C2×#99—142no—
303H(3,ℤ/4)—74no—
304H(3,ℤ/4)—74no—
305C23×C7—24no—
306C23×C7—42no—
307C23×C7—48no—
308C23×C7—42no—
309C23×C7—42no—
310C23×C7—42no—
311C23×C7—42no—
312C23×C7—42no—
313C23×C7—42no—
314C23×C7—84no—
315C23×C7—84no—
316C23×C7—84no—
317C23×C7—84no—
318C23×C7—84no—
319C23×C7—84no—
320C23×C7C2×C22⋊C411yescharacteristic
321C23×C7C2×C22⋊C411yescharacteristic
322C23×C7#12111yescharacteristic
323C23×C7#12111yescharacteristic
324C23×C7#12111yescharacteristic
325C23×C7#12111yescharacteristic
326C23×C7C22×D411yescharacteristic
327C22×D7—22no—
328C22×D7—22no—
329C22×D7—44no—
330C22×D7C2×C22⋊C414yes—
331C7×D4—24no—
332C7×D4—24no—
333C7×D4—42no—
334C7×D4—42no—
335C7×D4—42no—
336C7×D4—42no—
337C7×D4—42no—
338C7×D4—42no—
339C2×C4×C7—42no—
340C2×C4×C7—82no—
341C2×C4×C7C2×C22⋊C411yescharacteristic
342C2×C4×C7C2×C22⋊C411yescharacteristic
343C2×C4×C7C4×D411yescharacteristic
344C2×C4×C7C4×D411yescharacteristic
345C2×C4×C7C4×D411yescharacteristic
346C2×C4×C7C4×D411yescharacteristic
347C2×C4×C7C4×D411yescharacteristic
348C2×C4×C7C4×D411yescharacteristic
349C2×C4×C7C4×D411yescharacteristic
350C2×C4×C7C4×D411yescharacteristic
351C2×C4×C7#12011yescharacteristic
352C2×C4×C7#12011yescharacteristic
353C2×C4×C7#12011yescharacteristic
354C2×C4×C7#12011yescharacteristic
355C2×C4×C7#12111yescharacteristic
356C2×C4×C7#12111yescharacteristic
357C2×C4×C7#12111yescharacteristic
358C2×C4×C7#12111yescharacteristic
359C2×C4×C7#12311yescharacteristic
360C2×C4×C7#12311yescharacteristic
361C2×C4×C7#12311yescharacteristic
362C2×C4×C7#12311yescharacteristic
363C2×C4×C7C23×C411yescharacteristic
364C2×C4×C7C22×D411yescharacteristic
365C2×C4×C7C22×D411yescharacteristic
366C2×C4×C7C22×D411yescharacteristic
367C2×C4×C7C2×#4111yescharacteristic
368C2×C4×C7C2×#4111yescharacteristic
369C22⋊D7—24no—
370C22⋊D7—24no—
371C22⋊D7—24no—
372C22⋊D7—24no—
373C22⋊D7—816no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—24no—
377C2×Dic7—44no—
378C2×Dic7—42no—
379C2×Dic7—82no—
380C2×Dic7C2×C22⋊C414yes—
381D28—22no—
382D28—22no—
383D28—22no—
384D28—22no—
385C4×D7—24no—
386C4×D7—24no—
387C4×D7—24no—
388C4×D7—24no—
389Dic14—22no—
390Dic14—22no—
391Dic14—22no—
392Dic14—22no—
393C7×C8—24no—
394C7⋊C8—24no—
395C25—21no—
396C2×#41—72no—
397C2×#41—72no—
398C2×#41—72no—
399C2×#41—72no—
400C2×#41—141no—
401C2×#41—141no—
402C2×#41—141no—
403C2×#41—141no—
404C2×#41—141no—
405C2×#41—141no—
406C2×#41—141no—
407C2×#41—141no—
408C22×Q8—71no—
409C22×D4—21no—
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—21no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4—21no—
419C22×D4—21no—
420C22×D4—72no—
421C22×D4—71no—
422C22×D4—144no—
423C22×D4C4×D712yes—
424C22×D4C4×D712yes—
425C22×D4C22×D712yes—
426C23×C4—72no—
427C23×C4C22×D711yescharacteristic
428#131—148no—
429#131—148no—
430#131—148no—
431#131—148no—
432C2×M16—21no—
433C2×M16—21no—
434C2×M16—21no—
435C2×M16—21no—
436C2×M16—72no—
437C2×M16—72no—
438C2×M16—144no—
439C2×M16—148no—
440C2×M16—148no—
441C2×M16—141no—
442C2×M16—141no—
443C2×M16—141no—
444C2×M16—141no—
445C2×M16C22⋊D712yescomplemented
446C2×M16C22×D712yes—
447C22×C8—72no—
448C22×C8—144no—
449C22×C8C22⋊D712yescomplemented
450#127—78no—
451#127—144no—
452#124—78no—
453#124—144no—
454#121—148no—
455#121—148no—
456#120—148no—
457#120—148no—
458#117—21no—
459#117—21no—
460#117—21no—
461#117—72no—
462#117—72no—
463#117—72no—
464#117—141no—
465#117—141no—
466#117—141no—
467#117—141no—
468#117—141no—
469#117C22×D712yes—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4—141no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—144no—
475C2×C22⋊C4—141no—
476C2×C22⋊C4—141no—
477C2×C42—21no—
478C2×C42—72no—
479C2×C42—141no—
480#102—28no—
481#102—148no—
482#99—148no—
483C22×C7—22no—
484C22×C7—22no—
485C22×C7—22no—
486C22×C7—41no—
487C22×C7—41no—
488C22×C7—41no—
489C22×C7—41no—
490C22×C7—48no—
491C22×C7—44no—
492C22×C7—84no—
493C22×C7—84no—
494C22×C7—84no—
495C22×C7—84no—
496C22×C7—84no—
497C22×C7—84no—
498C22×C7#38611yescharacteristic
499C22×C7#38611yescharacteristic
500C22×C7#38611yescharacteristic
501C22×C7#38611yescharacteristic
502C22×C7C22×C22⋊C411yescharacteristic
503C22×C7C2×#12111yescharacteristic
504C22×C7C2×#12111yescharacteristic
505C2×D7—24no—
506C2×D7—44no—
507C2×D7—44no—
508C2×D7—82no—
509C4×C7—82no—
510C4×C7#38611yescharacteristic
511C4×C7#38611yescharacteristic
512C4×C7#38611yescharacteristic
513C4×C7#38611yescharacteristic
514C4×C7C2×C4×D411yescharacteristic
515C4×C7C2×C4×D411yescharacteristic
516C4×C7C2×#12011yescharacteristic
517C4×C7C2×#12311yescharacteristic
518Dic7—24no—
519Dic7—44no—
520Dic7—82no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—41no—
525C24—41no—
526C24—41no—
527C24—41no—
528C24—72no—
529C24—84no—
530C24D4×D711yescharacteristic
531#41—142no—
532#41—142no—
533#41—142no—
534#41—142no—
535#41—142no—
536#41—142no—
537#41—142no—
538#41—142no—
539#41—142no—
540#41—142no—
541#41—142no—
542#41—142no—
543#41—142no—
544#41—142no—
545#41—142no—
546#41—142no—
547C2×Q8—72no—
548C2×Q8—72no—
549C2×Q8—141no—
550C2×Q8—141no—
551C2×Q8—141no—
552C2×Q8—141no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—74no—
581C2×D4—74no—
582C2×D4—72no—
583C2×D4—72no—
584C2×D4—142no—
585C2×D4—142no—
586C2×D4—142no—
587C2×D4—142no—
588C2×D4—1416no—
589C2×D4—141no—
590C2×D4—141no—
591C2×D4—141no—
592C2×D4—141no—
593C2×D4—568no—
594C2×D4C2×C4×D714yes—
595C22×C4—41no—
596C22×C4—72no—
597C22×C4—74no—
598C22×C4—74no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—281no—
605C22×C4C2×C4×D711yescharacteristic
606C22×C4C2×C4×D711yescharacteristic
607C22×C4#115711yescharacteristic
608C22×C4#115711yescharacteristic
609C22×C4D4×D711yescharacteristic
610C22×C4D4×D711yescharacteristic
611C22×C4D4×D711yescharacteristic
612C22×C4D4×D711yescharacteristic
613C22×C4D4×D711yescharacteristic
614C22×C4#115911yescharacteristic
615C22×C4#115911yescharacteristic
616C22×C4C2×C22⋊D711yescharacteristic
617C22×C4C2×C22⋊D711yescharacteristic
618C22×C4C23×D711yescharacteristic
619M16—22no—
620M16—22no—
621M16—22no—
622M16—22no—
623M16—1416no—
624M16—142no—
625M16—142no—
626M16—142no—
627M16—142no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—74no—
631C2×C8—1416no—
632C2×C8—142no—
633C2×C8—142no—
634C2×C8C2×C22⋊D714yescomplemented
635C4⋊C4—22no—
636C4⋊C4—41no—
637C4⋊C4—142no—
638C4⋊C4—142no—
639C4⋊C4—142no—
640C4⋊C4—281no—
641C22⋊C4—22no—
642C22⋊C4—41no—
643C22⋊C4—1416no—
644C22⋊C4—142no—
645C22⋊C4—142no—
646C22⋊C4—142no—
647C22⋊C4—281no—
648C42—22no—
649C42—41no—
650C42—74no—
651C42—142no—
652C42—142no—
653C42—281no—
654C2×C7—21no—
655C2×C7—21no—
656C2×C7—21no—
657C2×C7—21no—
658C2×C7—21no—
659C2×C7—21no—
660C2×C7—84no—
661C2×C7#191012yescomplemented
662C2×C7C2×#38611yescharacteristic
663D7—44no—
664C23—24no—
665C23—42no—
666C23—48no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—74no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—142no—
681C23—142no—
682C23—284no—
683C23D7×C22⋊C411yescharacteristic
684C23D7×C22⋊C411yescharacteristic
685C23#644711yescharacteristic
686C23#644711yescharacteristic
687C23#650111yescharacteristic
688C23#650111yescharacteristic
689C23C2×D4×D711yescharacteristic
690Q8—142no—
691Q8—142no—
692Q8—142no—
693Q8—142no—
694D4—24no—
695D4—24no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—144no—
703D4—144no—
704D4—144no—
705D4—144no—
706D4—142no—
707D4—142no—
708D4—142no—
709D4—142no—
710D4—5616no—
711C2×C4—42no—
712C2×C4—74no—
713C2×C4—82no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—144no—
717C2×C4—144no—
718C2×C4—144no—
719C2×C4—144no—
720C2×C4—144no—
721C2×C4—284no—
722C2×C4—282no—
723C2×C4—562no—
724C2×C4D7×C22⋊C411yescharacteristic
725C2×C4D7×C22⋊C411yescharacteristic
726C2×C4(C22⋊D7)⋊C411yescharacteristic
727C2×C4(C22⋊D7)⋊C411yescharacteristic
728C2×C4(C22⋊D7)⋊C411yescharacteristic
729C2×C4(C22⋊D7)⋊C411yescharacteristic
730C2×C4#644611yescharacteristic
731C2×C4#644611yescharacteristic
732C2×C4#644611yescharacteristic
733C2×C4#644611yescharacteristic
734C2×C4#644711yescharacteristic
735C2×C4#644711yescharacteristic
736C2×C4C4×C22⋊D711yescharacteristic
737C2×C4C4×C22⋊D711yescharacteristic
738C2×C4C4×C22⋊D711yescharacteristic
739C2×C4C4×C22⋊D711yescharacteristic
740C2×C4#650011yescharacteristic
741C2×C4#650011yescharacteristic
742C2×C4#650011yescharacteristic
743C2×C4#650011yescharacteristic
744C2×C4#650111yescharacteristic
745C2×C4#650111yescharacteristic
746C2×C4C22×C4×D711yescharacteristic
747C2×C4C2×#115711yescharacteristic
748C2×C4C2×D4×D711yescharacteristic
749C2×C4C2×D4×D711yescharacteristic
750C2×C4C2×#115911yescharacteristic
751C2×C4C22×C22⋊D711yescharacteristic
752C8—24no—
753C8—144no—
754C7C2×#191011yescharacteristic, complemented, Sylow
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—48no—
763C22—44no—
764C22—84no—
765C22—84no—
766C22—84no—
767C22—84no—
768C22—84no—
769C22—84no—
770C22—144no—
771C22—284no—
772C22—284no—
773C22—562no—
774C22#8972811yescharacteristic
775C22#8972811yescharacteristic
776C22#8972811yescharacteristic
777C22#8972811yescharacteristic
778C22C2×D7×C22⋊C411yescharacteristic
779C22C2×#644711yescharacteristic
780C22C2×#650111yescharacteristic
781C4—82no—
782C4—144no—
783C4—284no—
784C4—562no—
785C4#8972811yescharacteristic
786C4#8972811yescharacteristic
787C4#8972811yescharacteristic
788C4#8972811yescharacteristic
789C4C2×(C22⋊D7)⋊C411yescharacteristic
790C4C2×#644611yescharacteristic
791C4C2×C4×C22⋊D711yescharacteristic
792C4C2×#650011yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—84no—
800C2—284no—
801C2#1172808412yesdirect product factor
802C2C2×#8972811yescharacteristic
subgroupG/H
centerC22#89728
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#418C2
socleC22×C7#386
prime radicalC2×#90496C2
cosocleC22×C4×C7C24
hypercenterC2×#418D7
hypocenterC7C2×#1910
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#90436C2semidirect
3. C2×C7×#418C2semidirect
4. C2×#89987C2semidirect
5. C2×#89778C2semidirect
6. C2×#89352C2semidirect
7. C2×#89326C2semidirect
8. #11728084C2direct (N × H)
16. #90496C4semidirect
18. C2×#6503C4semidirect
20. C2×#6499C4semidirect
27. #90436C22semidirect
32. C7×#418C22semidirect
35. #89987C22semidirect
38. #89778C22semidirect
40. #89352C22semidirect
41. #89326C22semidirect
80. C2×C7×M16D4semidirect
82. C22×C7×C8D4semidirect
96. #6503C2×C4semidirect
100. #6499C2×C4semidirect
117. C2×#1136D4semidirect
119. C22×C7⋊C8D4semidirect
134. C2×#418D7semidirect
243. C2×C7×C8C2×D4semidirect
269. C2×C7⋊C8C2×D4semidirect
297. #418C2×D7semidirect
445. C2×M16C22⋊D7semidirect
449. C22×C8C22⋊D7semidirect
634. C2×C8C2×C22⋊D7semidirect
661. C2×C7#1910semidirect
754. C7C2×#1910semidirect
801. C2#11728084direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904962
C2×#904362
C2×C7×#4182
C2×#899872
C2×#897782
C2×#893522
C2×#893262
#117280842
C2×#19107