Finite Group Databasebeta

← C2×#11729774 #13355270

Subgroups — C2×#11729774 #13355270

Order 1792.

1682 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#568C211yesmaximal, characteristic, complemented
2C2×#90513C211yesmaximal, characteristic
3C2×#90005C211yesmaximal, characteristic, complemented
4C2×#89911C211yesmaximal, characteristic, complemented
5C2×#89901C211yesmaximal, characteristic, complemented
6#11729774C218yesmaximal, direct product factor
7C2×#89353C211yesmaximal, characteristic, complemented
8C2×#89351C211yesmaximal, characteristic, complemented
9C22×C7×#41C2211yescharacteristic
10C22×#1157C2211yescharacteristic
11C7×#568—22no—
12C7×#568—22no—
13C7×#568—22no—
14C7×#568C2214yescomplemented
15C2×C7×#131—22no—
16C2×C7×#131—22no—
17C22×C7×M16—22no—
18C22×C7×M16C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C2×#6514C412yescomplemented
21#90513—22no—
22#90513—22no—
23#90513C414yescomplemented
24#90513C2214yes—
25C2×#6513—22no—
26C2×#6512C412yescomplemented
27C2×#6505—21no—
28C2×#6495—21no—
29C2×#6489C2211yescharacteristic
30C22×#1136C2211yescharacteristic
31C23×C7⋊C8C2211yescharacteristic
32#90005—22no—
33#90005C2214yescomplemented
34C2×#6409—21no—
35C2×#6406—21no—
36#89911—22no—
37#89911C2214yescomplemented
38C2×#6399—22no—
39#89901—22no—
40#89901C2214yescomplemented
41C2×(C2×D7)⋊C8—22no—
42#89353C2214yescomplemented
43#89351C2214yescomplemented
44C2×#1881—71nomaximal, Sylow
45C2×C7×#41—21no—
46C2×C7×#41—21no—
47C2×C7×#41—21no—
48C2×C7×#41—21no—
49C2×C7×#41—21no—
50C2×C7×#41—21no—
51C2×C7×#41C2×C412yes—
52C2×C7×#41C2×C412yes—
53C2×C7×#41D412yes—
54C2×C7×#41D412yes—
55C2×C7×#41D412yes—
56C2×C7×#41C2312yes—
57C22×C7×Q8D411yescharacteristic
58C22×C7×D4—21no—
59C22×C7×D4D411yescharacteristic
60C23×C4×C7—21no—
61C23×C4×C7C2311yescharacteristic
62C22×C22⋊D7—21no—
63C2×#1157—21no—
64C2×#1157—21no—
65C2×#1157—21no—
66C2×#1157—21no—
67C2×#1157—21no—
68C2×#1157—21no—
69C2×#1157—21no—
70C2×#1157—21no—
71C2×#1157—21no—
72C2×#1157—21no—
73C2×#1157C2×C412yes—
74C2×#1157C2312yes—
75C22×D28C2×C411yescharacteristic
76C22×C4×D7—21no—
77C22×Dic14C2×C411yescharacteristic
78C7×#131—28no—
79C7×#131—28no—
80C7×#131—28no—
81C7×#131—28no—
82C2×C7×M16—24no—
83C2×C7×M16—28no—
84C2×C7×M16—21no—
85C2×C7×M16—21no—
86C2×C7×M16—21no—
87C2×C7×M16—21no—
88C2×C7×M16—21no—
89C2×C7×M16—21no—
90C2×C7×M16—21no—
91C2×C7×M16—28no—
92C2×C7×M16D412yes—
93C2×C7×M16D412yes—
94C2×C7×M16D412yes—
95C2×C7×M16C2312yes—
96C2×C7×M16C2312yes—
97C22×C7×C8—24no—
98C22×C7×C8—21no—
99C22×C7×C8D412yes—
100C2×C22⋊Dic7—21no—
101#6514—24no—
102#6514C2×C418yescomplemented
103#6513—28no—
104#6513—28no—
105#6512—24no—
106#6512C2×C418yescomplemented
107C2×#1144—22no—
108#6505—24no—
109#6505—24no—
110C2×#1143—22no—
111C2×#1142—22no—
112#6495—24no—
113#6495—24no—
114C2×#1141—22no—
115#6489—21no—
116#6489—21no—
117#6489—21no—
118#6489C2312yes—
119C2×C4⋊Dic7—21no—
120C2×C4×Dic7—21no—
121C2×#1136—21no—
122C2×#1136—21no—
123C2×#1136—21no—
124C2×#1136C2×C412yes—
125C2×#1136C2×C412yes—
126C2×#1136C2312yes—
127C22×C7⋊C8—21no—
128C22×C7⋊C8—21no—
129C22×C7⋊C8—21no—
130C22×C7⋊C8—21no—
131C22×C7⋊C8—21no—
132C22×C7⋊C8—21no—
133C22×C7⋊C8—21no—
134C22×C7⋊C8C2312yes—
135#6409—24no—
136#6406—24no—
137#6399—28no—
138(C2×D7)⋊C8—28no—
139C2×#575—71no—
140C2×#568D711yescharacteristic, complemented
141C2×#421—71no—
142C2×#416—71no—
143C2×#408—71no—
144#1881—78no—
145C2×#344—71no—
146C2×#341—71no—
147C24×C7—21no—
148C24×C7#4111yescharacteristic
149C23×D7—21no—
150C7×#41—22no—
151C7×#41—22no—
152C7×#41—22no—
153C7×#41—22no—
154C7×#41—22no—
155C7×#41—22no—
156C7×#41—22no—
157C7×#41—22no—
158C7×#41—22no—
159C7×#41—22no—
160C7×#41—22no—
161C7×#41—22no—
162C7×#41C22⋊C414yes—
163C7×#41C22⋊C414yes—
164C7×#41C22×C414yes—
165C7×#41C2×D414yes—
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8C22⋊C412yes—
170C2×C7×Q8C22⋊C412yes—
171C2×C7×Q8C2×D412yes—
172C2×C7×D4—22no—
173C2×C7×D4—22no—
174C2×C7×D4—22no—
175C2×C7×D4—22no—
176C2×C7×D4—22no—
177C2×C7×D4—22no—
178C2×C7×D4—21no—
179C2×C7×D4—21no—
180C2×C7×D4—21no—
181C2×C7×D4C22⋊C412yes—
182C2×C7×D4C22⋊C412yes—
183C2×C7×D4C2×D412yes—
184C22×C4×C7—21no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7C22×C411yescharacteristic
192C22×C4×C7C22×C411yescharacteristic
193C22×C4×C7C2×D411yescharacteristic
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7C2×D411yescharacteristic
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7#4111yescharacteristic
202C22×C4×C7#4111yescharacteristic
203C22×C4×C7#4111yescharacteristic
204C22×C4×C7C2411yescharacteristic
205C2×C22⋊D7—22no—
206C2×C22⋊D7—22no—
207C2×C22⋊D7—41no—
208C2×C22⋊D7—41no—
209C2×C22⋊D7—41no—
210C2×C22⋊D7—41no—
211C22×Dic7—21no—
212C22×Dic7—41no—
213#1157—22no—
214#1157—22no—
215#1157—22no—
216#1157—22no—
217#1157—22no—
218#1157—22no—
219#1157—22no—
220#1157—22no—
221#1157—41no—
222#1157—41no—
223#1157—41no—
224#1157—41no—
225#1157—41no—
226#1157—41no—
227#1157—41no—
228#1157—41no—
229C2×D28—21no—
230C2×D28—21no—
231C2×D28—21no—
232C2×D28—21no—
233C2×D28—21no—
234C2×D28C22×C412yes—
235C2×C4×D7—22no—
236C2×C4×D7—22no—
237C2×C4×D7—41no—
238C2×C4×D7—41no—
239C2×C4×D7—41no—
240C2×C4×D7—41no—
241C2×Dic14—21no—
242C2×Dic14—21no—
243C2×Dic14—21no—
244C2×Dic14—21no—
245C2×Dic14—21no—
246C2×Dic14C22×C412yes—
247C7×M16—216no—
248C7×M16—22no—
249C7×M16—22no—
250C7×M16—22no—
251C7×M16—22no—
252C7×M16—22no—
253C7×M16—22no—
254C7×M16—22no—
255C7×M16C2×D414yes—
256C2×C7×C8—216no—
257C2×C7×C8—22no—
258C2×C7×C8—22no—
259C2×C7×C8—22no—
260C2×C7×C8—22no—
261C2×C7×C8—22no—
262C2×C7×C8C2×D414yes—
263C22⋊Dic7—22no—
264C22⋊Dic7—41no—
265#1144—28no—
266#1143—28no—
267#1142—28no—
268#1141—28no—
269C4⋊Dic7—22no—
270C4⋊Dic7—41no—
271C4×Dic7—22no—
272C4×Dic7—41no—
273#1136—22no—
274#1136—22no—
275#1136—22no—
276#1136C22×C414yes—
277C2×C7⋊C8—22no—
278C2×C7⋊C8—22no—
279C2×C7⋊C8—22no—
280C2×C7⋊C8—22no—
281C2×C7⋊C8—22no—
282C2×C7⋊C8—22no—
283C2×C7⋊C8—41no—
284C2×C7⋊C8—41no—
285C2×C7⋊C8—41no—
286C2×C7⋊C8—41no—
287C22×#41—71no—
288C22×#41C2×D711yescharacteristic
289#575—74no—
290#575—74no—
291#575—142no—
292#575—142no—
293C2×#137—72no—
294C2×#137—141no—
295C2×AGL(1,ℤ/8)—72no—
296C2×AGL(1,ℤ/8)—141no—
297C2×#135—142no—
298#568—22no—
299#568—22no—
300#568—22no—
301#568C2×D714yescomplemented
302C2×#131—22no—
303C2×#131—22no—
304C22×M16—22no—
305C22×M16—71no—
306C22×M16C2×D711yescharacteristic
307C22×M16C2×D711yescharacteristic
308C23×C8—71no—
309C2×#117—71no—
310#421—74no—
311#421—142no—
312C2×#104—142no—
313#416—74no—
314#416—142no—
315C2×#103—141no—
316C2×#102—141no—
317#408—74no—
318#408—142no—
319C2×C22⋊C8—142no—
320#344—74no—
321#341—74no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—42no—
326C23×C7—82no—
327C23×C7C4×D411yescharacteristic
328C23×C7C4×D411yescharacteristic
329C23×C7#12111yescharacteristic
330C23×C7#12111yescharacteristic
331C23×C7#12311yescharacteristic
332C23×C7#12311yescharacteristic
333C23×C7C2×#4111yescharacteristic
334C22×D7—22no—
335C22×D7—44no—
336C22×D7—41no—
337C22×D7—41no—
338C7×Q8—22no—
339C7×Q8—22no—
340C7×Q8—22no—
341C7×Q8C2×C22⋊C414yes—
342C7×D4—24no—
343C7×D4—24no—
344C7×D4—24no—
345C7×D4—24no—
346C7×D4—22no—
347C7×D4—22no—
348C7×D4—22no—
349C7×D4C2×C22⋊C414yes—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—24no—
354C2×C4×C7—24no—
355C2×C4×C7—24no—
356C2×C4×C7—24no—
357C2×C4×C7C2×C22⋊C411yescharacteristic
358C2×C4×C7C2×C22⋊C411yescharacteristic
359C2×C4×C7C2×C22⋊C411yescharacteristic
360C2×C4×C7C2×C22⋊C411yescharacteristic
361C2×C4×C7C4×D411yescharacteristic
362C2×C4×C7C4×D411yescharacteristic
363C2×C4×C7C4×D411yescharacteristic
364C2×C4×C7C4×D411yescharacteristic
365C2×C4×C7C4×D411yescharacteristic
366C2×C4×C7C4×D411yescharacteristic
367C2×C4×C7#12011yescharacteristic
368C2×C4×C7#12011yescharacteristic
369C2×C4×C7#12011yescharacteristic
370C2×C4×C7#12011yescharacteristic
371C2×C4×C7#12111yescharacteristic
372C2×C4×C7#12111yescharacteristic
373C2×C4×C7#12111yescharacteristic
374C2×C4×C7#12111yescharacteristic
375C2×C4×C7#12111yescharacteristic
376C2×C4×C7#12111yescharacteristic
377C2×C4×C7#12311yescharacteristic
378C2×C4×C7#12311yescharacteristic
379C2×C4×C7C23×C411yescharacteristic
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C22×D411yescharacteristic
383C2×C4×C7C22×D411yescharacteristic
384C2×C4×C7C2×#4111yescharacteristic
385C22⋊D7—42no—
386C22⋊D7—42no—
387C22⋊D7—42no—
388C22⋊D7—42no—
389C2×Dic7—22no—
390C2×Dic7—41no—
391C2×Dic7—41no—
392C2×Dic7—42no—
393C2×Dic7—82no—
394D28—22no—
395D28—22no—
396D28—41no—
397D28—41no—
398C4×D7—42no—
399C4×D7—42no—
400C4×D7—42no—
401C4×D7—42no—
402Dic14—22no—
403Dic14—22no—
404Dic14—41no—
405Dic14—41no—
406C7×C8—24no—
407C7×C8—24no—
408C7⋊C8—24no—
409C7⋊C8—42no—
410C2×#41—21no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—72no—
417C2×#41—72no—
418C2×#41—141no—
419C2×#41—141no—
420C2×#41—141no—
421C2×#41—141no—
422C2×#41—141no—
423C2×#41—141no—
424C2×#41—141no—
425C2×#41—141no—
426C2×#41—141no—
427C2×#41—141no—
428C2×#41C4×D712yes—
429C2×#41C4×D712yes—
430C2×#41D2812yes—
431C2×#41C22⋊D712yes—
432C2×#41C22⋊D712yes—
433C2×#41C22×D712yes—
434C22×Q8—71no—
435C22×Q8D2811yescharacteristic
436C22×D4—21no—
437C22×D4—71no—
438C22×D4—141no—
439C22×D4D2811yescharacteristic
440C23×C4—21no—
441C23×C4—141no—
442C23×C4C22×D711yescharacteristic
443#137—78no—
444#137—144no—
445#137—144no—
446#137—144no—
447AGL(1,ℤ/8)—78no—
448AGL(1,ℤ/8)—144no—
449AGL(1,ℤ/8)—144no—
450AGL(1,ℤ/8)—144no—
451#135—148no—
452#135—148no—
453C2×Q16—142no—
454C2×SD16—142no—
455C2×SD16—142no—
456C2×D8—142no—
457#131—28no—
458#131—28no—
459#131—28no—
460#131—28no—
461C2×M16—24no—
462C2×M16—28no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—28no—
471C2×M16—72no—
472C2×M16—72no—
473C2×M16—72no—
474C2×M16—141no—
475C2×M16—141no—
476C2×M16—141no—
477C2×M16C22⋊D712yes—
478C2×M16C22⋊D712yes—
479C2×M16C22⋊D712yes—
480C2×M16C22×D712yes—
481C2×M16C22×D712yes—
482C22×C8—24no—
483C22×C8—21no—
484C22×C8—72no—
485C22×C8—141no—
486C22×C8—141no—
487C22×C8—141no—
488C22×C8—141no—
489C22×C8—141no—
490C22×C8—141no—
491C22×C8—141no—
492C22×C8C22⋊D712yes—
493#117—72no—
494#117—141no—
495#117—141no—
496#117—141no—
497C2×C4⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C42—141no—
500#104—148no—
501#103—144no—
502#102—144no—
503C22⋊C8—148no—
504C22×C7—22no—
505C22×C7—22no—
506C22×C7—22no—
507C22×C7—24no—
508C22×C7—41no—
509C22×C7—41no—
510C22×C7—41no—
511C22×C7—41no—
512C22×C7—44no—
513C22×C7—82no—
514C22×C7—82no—
515C22×C7#38611yescharacteristic
516C22×C7#38611yescharacteristic
517C22×C7#38611yescharacteristic
518C22×C7#38611yescharacteristic
519C22×C7C2×C4×D411yescharacteristic
520C22×C7C2×#12111yescharacteristic
521C22×C7C2×#12311yescharacteristic
522C2×D7—44no—
523C2×D7—42no—
524C2×D7—82no—
525C2×D7—82no—
526C4×C7—24no—
527C4×C7#38611yescharacteristic
528C4×C7#38611yescharacteristic
529C4×C7#38611yescharacteristic
530C4×C7#38611yescharacteristic
531C4×C7C22×C22⋊C411yescharacteristic
532C4×C7C2×C4×D411yescharacteristic
533C4×C7C2×#12011yescharacteristic
534C4×C7C2×#12111yescharacteristic
535Dic7—42no—
536Dic7—82no—
537C24—21no—
538C24—141no—
539C24#115711yescharacteristic
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—142no—
553#41—142no—
554#41—142no—
555#41—142no—
556#41—142no—
557#41—142no—
558#41—142no—
559#41—142no—
560#41—281no—
561#41—281no—
562#41—281no—
563#41—281no—
564#41—281no—
565#41—281no—
566#41—281no—
567#41—281no—
568#41(C2×D7)⋊C414yes—
569#41(C2×D7)⋊C414yes—
570#41C2×C4×D714yes—
571#41C2×C22⋊D714yes—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—72no—
576C2×Q8—141no—
577C2×Q8—141no—
578C2×Q8—141no—
579C2×Q8—141no—
580C2×Q8—141no—
581C2×Q8(C2×D7)⋊C412yes—
582C2×Q8(C2×D7)⋊C412yes—
583C2×Q8C2×D2812yes—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—72no—
594C2×D4—142no—
595C2×D4—142no—
596C2×D4—141no—
597C2×D4—141no—
598C2×D4—141no—
599C2×D4—141no—
600C2×D4—141no—
601C2×D4—281no—
602C2×D4—281no—
603C2×D4—281no—
604C2×D4—281no—
605C2×D4(C2×D7)⋊C412yes—
606C2×D4(C2×D7)⋊C412yes—
607C2×D4C2×D2812yes—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—141no—
616C22×C4—142no—
617C22×C4—142no—
618C22×C4—281no—
619C22×C4—281no—
620C22×C4—281no—
621C22×C4—281no—
622C22×C4—281no—
623C22×C4C2×C4×D711yescharacteristic
624C22×C4C2×C4×D711yescharacteristic
625C22×C4C2×D2811yescharacteristic
626C22×C4C2×D2811yescharacteristic
627C22×C4#115711yescharacteristic
628C22×C4#115711yescharacteristic
629C22×C4#115711yescharacteristic
630C22×C4C2×C22⋊D711yescharacteristic
631C22×C4C2×C22⋊D711yescharacteristic
632C22×C4C2×C22⋊D711yescharacteristic
633C22×C4C2×C22⋊D711yescharacteristic
634C22×C4C2×C22⋊D711yescharacteristic
635C22×C4C2×C22⋊D711yescharacteristic
636C22×C4C23×D711yescharacteristic
637Q16—148no—
638SD16—148no—
639SD16—148no—
640D8—148no—
641M16—216no—
642M16—22no—
643M16—22no—
644M16—22no—
645M16—22no—
646M16—22no—
647M16—22no—
648M16—22no—
649M16—74no—
650M16—142no—
651M16—142no—
652M16—142no—
653M16C2×C22⋊D714yes—
654C2×C8—216no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—142no—
661C2×C8—142no—
662C2×C8—142no—
663C2×C8—142no—
664C2×C8—142no—
665C2×C8—142no—
666C2×C8—281no—
667C2×C8—281no—
668C2×C8—281no—
669C2×C8—281no—
670C2×C8C2×C22⋊D714yes—
671C4⋊C4—142no—
672C4⋊C4—281no—
673C22⋊C4—142no—
674C22⋊C4—281no—
675C42—142no—
676C42—281no—
677C2×C7—21no—
678C2×C7—21no—
679C2×C7—21no—
680C2×C7—21no—
681C2×C7—21no—
682C2×C7—21no—
683C2×C7—44no—
684C2×C7#188112yescomplemented
685C2×C7C2×#38611yescharacteristic
686D7—82no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—82no—
692C23—142no—
693C23—284no—
694C23—281no—
695C23—281no—
696C23C4×C22⋊D711yescharacteristic
697C23C4×C22⋊D711yescharacteristic
698C23#649211yescharacteristic
699C23#649211yescharacteristic
700C23#649311yescharacteristic
701C23#649311yescharacteristic
702C23C2×#115711yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—22no—
706Q8—142no—
707Q8—142no—
708Q8—281no—
709Q8—281no—
710Q8C2×(C2×D7)⋊C414yes—
711D4—24no—
712D4—24no—
713D4—24no—
714D4—24no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—142no—
719D4—142no—
720D4—282no—
721D4—282no—
722D4—282no—
723D4—282no—
724D4—281no—
725D4—281no—
726D4C2×(C2×D7)⋊C414yes—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—142no—
735C2×C4—281no—
736C2×C4—281no—
737C2×C4—282no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4—282no—
741C2×C4—282no—
742C2×C4—562no—
743C2×C4C2×(C2×D7)⋊C411yescharacteristic
744C2×C4C2×(C2×D7)⋊C411yescharacteristic
745C2×C4C2×(C2×D7)⋊C411yescharacteristic
746C2×C4C2×(C2×D7)⋊C411yescharacteristic
747C2×C4C4×C22⋊D711yescharacteristic
748C2×C4C4×C22⋊D711yescharacteristic
749C2×C4C4×C22⋊D711yescharacteristic
750C2×C4C4×C22⋊D711yescharacteristic
751C2×C4C4×C22⋊D711yescharacteristic
752C2×C4C4×C22⋊D711yescharacteristic
753C2×C4#649211yescharacteristic
754C2×C4#649211yescharacteristic
755C2×C4#649311yescharacteristic
756C2×C4#649311yescharacteristic
757C2×C4#649311yescharacteristic
758C2×C4#649311yescharacteristic
759C2×C4#649311yescharacteristic
760C2×C4#649311yescharacteristic
761C2×C4#651611yescharacteristic
762C2×C4#651611yescharacteristic
763C2×C4#651611yescharacteristic
764C2×C4#651611yescharacteristic
765C2×C4C22×C4×D711yescharacteristic
766C2×C4C22×D2811yescharacteristic
767C2×C4C2×#115711yescharacteristic
768C2×C4C22×C22⋊D711yescharacteristic
769C2×C4C22×C22⋊D711yescharacteristic
770C2×C4C22×C22⋊D711yescharacteristic
771C8—24no—
772C8—24no—
773C8—144no—
774C8—282no—
775C7C2×#188111yescharacteristic, complemented, Sylow
776C22—22no—
777C22—22no—
778C22—22no—
779C22—24no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—44no—
785C22—82no—
786C22—82no—
787C22—284no—
788C22—282no—
789C22—562no—
790C22—562no—
791C22#8998511yescharacteristic
792C22#8998511yescharacteristic
793C22#8998511yescharacteristic
794C22#8998511yescharacteristic
795C22C2×C4×C22⋊D711yescharacteristic
796C22C2×#649211yescharacteristic
797C22C2×#649311yescharacteristic
798C4—24no—
799C4—282no—
800C4—562no—
801C4#8998511yescharacteristic
802C4#8998511yescharacteristic
803C4#8998511yescharacteristic
804C4#8998511yescharacteristic
805C4C22×(C2×D7)⋊C411yescharacteristic
806C4C2×C4×C22⋊D711yescharacteristic
807C4C2×#649311yescharacteristic
808C4C2×#651611yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—44no—
816C2—562no—
817C2#1172977412yesdirect product factor
818C2C2×#8998511yescharacteristic
subgroupG/H
centerC2×C4#6516
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#568C2
socleC22×C7#386
prime radicalC2×#90513C2
cosocleC22×C4×C7C24
hypercenterC2×#568D7
hypocenterC7C2×#1881
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
1. C2×C7×#568C2semidirect
3. C2×#90005C2semidirect
4. C2×#89911C2semidirect
5. C2×#89901C2semidirect
6. #11729774C2direct (N × H)
7. C2×#89353C2semidirect
8. C2×#89351C2semidirect
14. C7×#568C22semidirect
20. C2×#6514C4semidirect
23. #90513C4semidirect
26. C2×#6512C4semidirect
33. #90005C22semidirect
37. #89911C22semidirect
40. #89901C22semidirect
42. #89353C22semidirect
43. #89351C22semidirect
102. #6514C2×C4semidirect
106. #6512C2×C4semidirect
140. C2×#568D7semidirect
301. #568C2×D7semidirect
684. C2×C7#1881semidirect
775. C7C2×#1881semidirect
817. C2#11729774direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5682
C2×#905132
C2×#900052
C2×#899112
C2×#899012
#117297742
C2×#893532
C2×#893512
C2×#18817