Finite Group Databasebeta

← #13355673

Subgroups — #13355673

Order 1792.

1664 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90513C211yesmaximal, characteristic
2C2×#90436C211yesmaximal, characteristic, complemented
3C2×C7×#413C211yesmaximal, characteristic, complemented
4#11741517C211yesmaximal, characteristic, complemented
5C2×#89911C211yesmaximal, characteristic, complemented
6C2×#89354C211yesmaximal, characteristic, complemented
7C2×C7⋊#338C211yesmaximal, characteristic, complemented
8#11727876C214yesmaximal, complemented
9#11727841C214yesmaximal, complemented
10C22×C7×#41C2211yescharacteristic
11C22×#1157C2211yescharacteristic
12C22×C7×M16C2211yescharacteristic
13C22×C7×M16C2211yescharacteristic
14C2×#6514C412yescomplemented
15#90513—22no—
16#90513—22no—
17#90513—22no—
18#90513—22no—
19C2×#6513C414yescomplemented
20C2×#6512C412yescomplemented
21C2×#6505C2212yes—
22C2×#6495C2212yes—
23C2×#6489C2211yescharacteristic
24C22×#1136C2211yescharacteristic
25C22×#1136C2211yescharacteristic
26#90436—22no—
27#90436—22no—
28#90436—22no—
29#90436C2214yes—
30C2×#6470—22no—
31C2×D7×M16—22no—
32C2×#6464—22no—
33C7×#413—22no—
34C7×#413—22no—
35C2×C7×#101C2212yescomplemented
36C2×C7×#100C2212yescomplemented
37#90005—22no—
38#90004—22no—
39#89997C2212yescomplemented
40#89987C2212yescomplemented
41#89911—22no—
42#89911C2214yes—
43C2×#6399—22no—
44C7⋊#338C2214yescomplemented
45#89354C2214yescomplemented
46#20995—71nomaximal, Sylow
47C2×C7×#41—21no—
48C2×C7×#41—21no—
49C2×C7×#41—21no—
50C2×C7×#41—21no—
51C2×C7×#41—21no—
52C2×C7×#41—21no—
53C2×C7×#41—21no—
54C2×C7×#41—21no—
55C2×C7×#41—21no—
56C2×C7×#41—21no—
57C2×C7×#41C2×C412yes—
58C2×C7×#41C2×C412yes—
59C22×C7×Q8C2311yescharacteristic
60C22×C7×D4—21no—
61C22×C7×D4C2311yescharacteristic
62C23×C4×C7—21no—
63C23×C4×C7C2311yescharacteristic
64C22×C22⋊D7—21no—
65C2×#1157—21no—
66C2×#1157—21no—
67C2×#1157—21no—
68C2×#1157—21no—
69C2×#1157—21no—
70C2×#1157—21no—
71C2×#1157C2×C412yes—
72C2×#1157D412yes—
73C2×#1157D412yes—
74C2×#1157D412yes—
75C2×#1157D412yes—
76C2×#1157C2312yes—
77C22×D28C2×C411yescharacteristic
78C22×C4×D7—21no—
79C22×Dic14C2×C411yescharacteristic
80C2×C7×M16—21no—
81C2×C7×M16—21no—
82C2×C7×M16—21no—
83C2×C7×M16—21no—
84C2×C7×M16—21no—
85C2×C7×M16—21no—
86C2×C7×M16—21no—
87C2×C7×M16—21no—
88C2×C7×M16D412yes—
89C2×C7×M16D412yes—
90C2×C7×M16C2312yes—
91C2×C7×M16C2312yes—
92C22×C7×C8—21no—
93C22×C7×C8—21no—
94C2×C22⋊Dic7—21no—
95#6514—24no—
96#6514—24no—
97#6513—28no—
98#6513—28no—
99#6512—24no—
100#6512—24no—
101C2×#1144C2×C414yescomplemented
102#6505—24no—
103#6505—24no—
104C2×#1143C2×C414yescomplemented
105C2×#1142C2×C414yescomplemented
106#6495—24no—
107#6495—24no—
108C2×#1141C2×C414yescomplemented
109#6489—21no—
110#6489—21no—
111#6489—21no—
112#6489C2312yes—
113C2×C4⋊Dic7—21no—
114C2×C4×Dic7—21no—
115C2×#1136—21no—
116C2×#1136—21no—
117C2×#1136—21no—
118C2×#1136—21no—
119C2×#1136—21no—
120C2×#1136—21no—
121C2×#1136—21no—
122C2×#1136—21no—
123C2×#1136C2×C412yes—
124C2×#1136D412yes—
125C2×#1136C2312yes—
126C2×#1136C2312yes—
127C22×C7⋊C8C2×C412yes—
128C22×C7⋊C8D412yes—
129#6470—28no—
130#6470—28no—
131D7×M16—28no—
132D7×M16—28no—
133#6464—28no—
134#6464—28no—
135C2×#1131—24no—
136C2×C8×D7—24no—
137C7×#101—24no—
138C7×#100—24no—
139#6409—24no—
140#6406—24no—
141#6399—28no—
142C2×#575—71no—
143C2×#568—71no—
144C2×#421—71no—
145#2896—71no—
146C2×#413D711yescharacteristic, complemented
147#1903—74no—
148#1902—74no—
149C2×#344—71no—
150C2×#338—71no—
151C24×C7—21no—
152C24×C7#4111yescharacteristic
153C23×D7—21no—
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×#41—41no—
163C7×#41—41no—
164C7×#41—41no—
165C7×#41—41no—
166C7×#41—41no—
167C7×#41—41no—
168C7×#41—41no—
169C7×#41—41no—
170C2×C7×Q8—21no—
171C2×C7×Q8—21no—
172C2×C7×Q8—21no—
173C2×C7×Q8—21no—
174C2×C7×Q8—21no—
175C2×C7×Q8C22×C412yes—
176C2×C7×D4—22no—
177C2×C7×D4—22no—
178C2×C7×D4—21no—
179C2×C7×D4—21no—
180C2×C7×D4—21no—
181C2×C7×D4—21no—
182C2×C7×D4—21no—
183C2×C7×D4—41no—
184C2×C7×D4—41no—
185C2×C7×D4—41no—
186C2×C7×D4—41no—
187C2×C7×D4C22×C412yes—
188C22×C4×C7—21no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—41no—
192C22×C4×C7—41no—
193C22×C4×C7—41no—
194C22×C4×C7—41no—
195C22×C4×C7C22×C411yescharacteristic
196C22×C4×C7C22×C411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7C2×D411yescharacteristic
203C22×C4×C7C2×D411yescharacteristic
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7#4111yescharacteristic
206C22×C4×C7#4111yescharacteristic
207C22×C4×C7#4111yescharacteristic
208C22×C4×C7C2411yescharacteristic
209C2×C22⋊D7—22no—
210C2×C22⋊D7—22no—
211C2×C22⋊D7—22no—
212C2×C22⋊D7—22no—
213C2×C22⋊D7—22no—
214C2×C22⋊D7—22no—
215C22×Dic7—21no—
216C22×Dic7—41no—
217#1157—22no—
218#1157—22no—
219#1157—22no—
220#1157—22no—
221#1157—22no—
222#1157—22no—
223#1157—22no—
224#1157—22no—
225#1157—22no—
226#1157—22no—
227#1157—22no—
228#1157—22no—
229#1157C22⋊C414yes—
230#1157C22⋊C414yes—
231#1157C2×D414yes—
232#1157C2×D414yes—
233C2×D28—21no—
234C2×D28—21no—
235C2×D28—21no—
236C2×D28C22⋊C412yes—
237C2×D28C22⋊C412yes—
238C2×D28C22×C412yes—
239C2×C4×D7—22no—
240C2×C4×D7—22no—
241C2×C4×D7—22no—
242C2×C4×D7—22no—
243C2×C4×D7—22no—
244C2×C4×D7—22no—
245C2×Dic14—21no—
246C2×Dic14—21no—
247C2×Dic14—21no—
248C2×Dic14C22⋊C412yes—
249C2×Dic14C22⋊C412yes—
250C2×Dic14C22×C412yes—
251C7×M16—22no—
252C7×M16—22no—
253C7×M16—22no—
254C7×M16—22no—
255C7×M16—22no—
256C7×M16—41no—
257C7×M16—41no—
258C7×M16C2×D414yes—
259C2×C7×C8—22no—
260C2×C7×C8—22no—
261C2×C7×C8—22no—
262C2×C7×C8—22no—
263C2×C7×C8—41no—
264C2×C7×C8—41no—
265C22⋊Dic7—22no—
266C22⋊Dic7—41no—
267#1144—28no—
268#1143—28no—
269#1142—28no—
270#1141—28no—
271C4⋊Dic7—22no—
272C4⋊Dic7—41no—
273C4×Dic7—22no—
274C4×Dic7—41no—
275#1136—22no—
276#1136—22no—
277#1136—22no—
278#1136—22no—
279#1136—22no—
280#1136—22no—
281#1136—22no—
282#1136—22no—
283C2×C7⋊C8—22no—
284C2×C7⋊C8—22no—
285C2×C7⋊C8—22no—
286C2×C7⋊C8—22no—
287C2×C7⋊C8C22×C414yes—
288C2×C7⋊C8C2×D414yes—
289#1131—216no—
290C8×D7—216no—
291C22×#41—71no—
292C22×#41C2×D711yescharacteristic
293#575—142no—
294#575—142no—
295#575—142no—
296#575—142no—
297C2×#137—72no—
298C2×#137—72no—
299C2×AGL(1,ℤ/8)—72no—
300C2×AGL(1,ℤ/8)—72no—
301C2×#135—74no—
302#568—74no—
303#568—142no—
304#568—142no—
305#568—142no—
306C2×#131—142no—
307C2×#131—142no—
308C22×M16—71no—
309C22×M16—71no—
310C22×M16—142no—
311C22×M16C2×D711yescharacteristic
312C22×M16C2×D711yescharacteristic
313C2×#117—71no—
314#421—74no—
315#421—142no—
316C2×#104—142no—
317#419—72no—
318#418—72no—
319#417—142no—
320#416—142no—
321#413—22no—
322#413—22no—
323C2×#101C2×D712yescomplemented
324C2×#100C2×D712yescomplemented
325#344—74no—
326#338—74no—
327C23×C7—22no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—81no—
331C23×C7—82no—
332C23×C7C4×D411yescharacteristic
333C23×C7C4×D411yescharacteristic
334C23×C7#12111yescharacteristic
335C23×C7#12111yescharacteristic
336C23×C7#12311yescharacteristic
337C23×C7#12311yescharacteristic
338C23×C7C2×#4111yescharacteristic
339C22×D7—22no—
340C22×D7—22no—
341C22×D7—22no—
342C22×D7—82no—
343C7×Q8—22no—
344C7×Q8—22no—
345C7×Q8—41no—
346C7×Q8—41no—
347C7×D4—22no—
348C7×D4—22no—
349C7×D4—42no—
350C7×D4—42no—
351C7×D4—42no—
352C7×D4—42no—
353C7×D4—41no—
354C7×D4—41no—
355C2×C4×C7—22no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—42no—
359C2×C4×C7—42no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7C2×C22⋊C411yescharacteristic
363C2×C4×C7C2×C22⋊C411yescharacteristic
364C2×C4×C7C2×C22⋊C411yescharacteristic
365C2×C4×C7C2×C22⋊C411yescharacteristic
366C2×C4×C7C4×D411yescharacteristic
367C2×C4×C7C4×D411yescharacteristic
368C2×C4×C7C4×D411yescharacteristic
369C2×C4×C7C4×D411yescharacteristic
370C2×C4×C7C4×D411yescharacteristic
371C2×C4×C7C4×D411yescharacteristic
372C2×C4×C7#12011yescharacteristic
373C2×C4×C7#12011yescharacteristic
374C2×C4×C7#12011yescharacteristic
375C2×C4×C7#12011yescharacteristic
376C2×C4×C7#12111yescharacteristic
377C2×C4×C7#12111yescharacteristic
378C2×C4×C7#12111yescharacteristic
379C2×C4×C7#12111yescharacteristic
380C2×C4×C7#12111yescharacteristic
381C2×C4×C7#12111yescharacteristic
382C2×C4×C7#12311yescharacteristic
383C2×C4×C7#12311yescharacteristic
384C2×C4×C7C23×C411yescharacteristic
385C2×C4×C7C22×D411yescharacteristic
386C2×C4×C7C22×D411yescharacteristic
387C2×C4×C7C22×D411yescharacteristic
388C2×C4×C7C22×D411yescharacteristic
389C2×C4×C7C2×#4111yescharacteristic
390C22⋊D7—24no—
391C22⋊D7—24no—
392C22⋊D7—24no—
393C22⋊D7—24no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—42no—
398C2×Dic7—82no—
399D28—22no—
400D28—22no—
401D28—22no—
402D28C2×C22⋊C414yes—
403C4×D7—24no—
404C4×D7—24no—
405C4×D7—24no—
406C4×D7—24no—
407Dic14—22no—
408Dic14—22no—
409Dic14—22no—
410Dic14C2×C22⋊C414yes—
411C7×C8—24no—
412C7×C8—42no—
413C7⋊C8—24no—
414C7⋊C8—24no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—72no—
426C2×#41—72no—
427C2×#41—72no—
428C2×#41—72no—
429C2×#41—72no—
430C2×#41—72no—
431C2×#41—141no—
432C2×#41—141no—
433C2×#41—141no—
434C2×#41—141no—
435C2×#41—141no—
436C2×#41—141no—
437C2×#41C4×D712yes—
438C2×#41C4×D712yes—
439C22×Q8—71no—
440C22×Q8C22×D711yescharacteristic
441C22×D4—21no—
442C22×D4—71no—
443C22×D4—141no—
444C22×D4C22×D711yescharacteristic
445C23×C4—21no—
446C23×C4—141no—
447C23×C4C22×D711yescharacteristic
448#137—144no—
449#137—144no—
450#137—144no—
451#137—144no—
452AGL(1,ℤ/8)—144no—
453AGL(1,ℤ/8)—144no—
454AGL(1,ℤ/8)—144no—
455AGL(1,ℤ/8)—144no—
456#135—148no—
457#135—148no—
458C2×Q16—74no—
459C2×SD16—74no—
460C2×SD16—74no—
461C2×D8—74no—
462#131—148no—
463#131—148no—
464#131—148no—
465#131—148no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—72no—
475C2×M16—72no—
476C2×M16—72no—
477C2×M16—72no—
478C2×M16—144no—
479C2×M16—148no—
480C2×M16—141no—
481C2×M16—141no—
482C2×M16—141no—
483C2×M16—141no—
484C2×M16—141no—
485C2×M16—141no—
486C2×M16—141no—
487C2×M16—141no—
488C2×M16—148no—
489C2×M16C22⋊D712yes—
490C2×M16C22⋊D712yes—
491C2×M16C22×D712yes—
492C2×M16C22×D712yes—
493C22×C8—21no—
494C22×C8—21no—
495C22×C8—72no—
496C22×C8—72no—
497C22×C8—144no—
498#117—72no—
499#117—141no—
500#117—141no—
501#117—141no—
502C2×C4⋊C4—141no—
503C2×C22⋊C4—141no—
504C2×C42—141no—
505#104—148no—
506#103—144no—
507#102—144no—
508#101—24no—
509#100—24no—
510C22×C7—41no—
511C22×C7—41no—
512C22×C7—41no—
513C22×C7—41no—
514C22×C7—41no—
515C22×C7—41no—
516C22×C7—41no—
517C22×C7—42no—
518C22×C7—82no—
519C22×C7—82no—
520C22×C7—82no—
521C22×C7#38611yescharacteristic
522C22×C7#38611yescharacteristic
523C22×C7#38611yescharacteristic
524C22×C7#38611yescharacteristic
525C22×C7C2×C4×D411yescharacteristic
526C22×C7C2×#12111yescharacteristic
527C22×C7C2×#12311yescharacteristic
528C2×D7—24no—
529C2×D7—44no—
530C2×D7—82no—
531C2×D7—82no—
532C4×C7—42no—
533C4×C7#38611yescharacteristic
534C4×C7#38611yescharacteristic
535C4×C7#38611yescharacteristic
536C4×C7#38611yescharacteristic
537C4×C7C22×C22⋊C411yescharacteristic
538C4×C7C2×C4×D411yescharacteristic
539C4×C7C2×#12011yescharacteristic
540C4×C7C2×#12111yescharacteristic
541Dic7—24no—
542Dic7—82no—
543C24—21no—
544C24—141no—
545C24#115711yescharacteristic
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—74no—
563#41—74no—
564#41—74no—
565#41—74no—
566#41—142no—
567#41—142no—
568#41—142no—
569#41—142no—
570#41—142no—
571#41—142no—
572#41—142no—
573#41—142no—
574#41—142no—
575#41—142no—
576#41—142no—
577#41—142no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—72no—
584C2×Q8—72no—
585C2×Q8—72no—
586C2×Q8—141no—
587C2×Q8—141no—
588C2×Q8—141no—
589C2×Q8C2×C4×D712yes—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—72no—
602C2×D4—72no—
603C2×D4—72no—
604C2×D4—142no—
605C2×D4—142no—
606C2×D4—142no—
607C2×D4—142no—
608C2×D4—142no—
609C2×D4—142no—
610C2×D4—141no—
611C2×D4—141no—
612C2×D4—141no—
613C2×D4C2×C4×D712yes—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—141no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—142no—
625C22×C4—142no—
626C22×C4—142no—
627C22×C4—142no—
628C22×C4—281no—
629C22×C4C2×C4×D711yescharacteristic
630C22×C4C2×C4×D711yescharacteristic
631C22×C4#115711yescharacteristic
632C22×C4D4×D711yescharacteristic
633C22×C4D4×D711yescharacteristic
634C22×C4D4×D711yescharacteristic
635C22×C4D4×D711yescharacteristic
636C22×C4D4×D711yescharacteristic
637C22×C4D4×D711yescharacteristic
638C22×C4#115911yescharacteristic
639C22×C4#115911yescharacteristic
640C22×C4C2×C22⋊D711yescharacteristic
641C22×C4C2×C22⋊D711yescharacteristic
642C22×C4C23×D711yescharacteristic
643Q16—148no—
644SD16—148no—
645SD16—148no—
646D8—148no—
647M16—22no—
648M16—22no—
649M16—22no—
650M16—22no—
651M16—22no—
652M16—41no—
653M16—41no—
654M16—1416no—
655M16—142no—
656M16—142no—
657M16—142no—
658M16—142no—
659M16—142no—
660M16—142no—
661M16—142no—
662M16—142no—
663M16C2×C22⋊D714yes—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8—41no—
669C2×C8—41no—
670C2×C8—74no—
671C2×C8—74no—
672C2×C8—1416no—
673C2×C8—142no—
674C2×C8—142no—
675C2×C8—142no—
676C2×C8—142no—
677C4⋊C4—142no—
678C4⋊C4—281no—
679C22⋊C4—142no—
680C22⋊C4—281no—
681C42—142no—
682C42—281no—
683C2×C7—21no—
684C2×C7—21no—
685C2×C7—21no—
686C2×C7—21no—
687C2×C7—21no—
688C2×C7—21no—
689C2×C7—21no—
690C2×C7—82no—
691C2×C7C2×#38611yescharacteristic
692D7—44no—
693C23—22no—
694C23—41no—
695C23—41no—
696C23—81no—
697C23—82no—
698C23—142no—
699C23—142no—
700C23—142no—
701C23—562no—
702C23#644611yescharacteristic
703C23#644611yescharacteristic
704C23#644711yescharacteristic
705C23#644711yescharacteristic
706C23C4×C22⋊D711yescharacteristic
707C23C4×C22⋊D711yescharacteristic
708C23C2×#115711yescharacteristic
709Q8—22no—
710Q8—22no—
711Q8—41no—
712Q8—41no—
713Q8—74no—
714Q8—142no—
715Q8—142no—
716Q8—142no—
717D4—22no—
718D4—22no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—41no—
724D4—41no—
725D4—74no—
726D4—144no—
727D4—144no—
728D4—144no—
729D4—144no—
730D4—142no—
731D4—142no—
732D4—142no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—144no—
744C2×C4—144no—
745C2×C4—144no—
746C2×C4—144no—
747C2×C4—282no—
748C2×C4—562no—
749C2×C4D7×C22⋊C411yescharacteristic
750C2×C4D7×C22⋊C411yescharacteristic
751C2×C4D7×C22⋊C411yescharacteristic
752C2×C4D7×C22⋊C411yescharacteristic
753C2×C4(C22⋊D7)⋊C411yescharacteristic
754C2×C4(C22⋊D7)⋊C411yescharacteristic
755C2×C4(C22⋊D7)⋊C411yescharacteristic
756C2×C4(C22⋊D7)⋊C411yescharacteristic
757C2×C4#644611yescharacteristic
758C2×C4#644611yescharacteristic
759C2×C4#644711yescharacteristic
760C2×C4#644711yescharacteristic
761C2×C4C4×C22⋊D711yescharacteristic
762C2×C4C4×C22⋊D711yescharacteristic
763C2×C4#650011yescharacteristic
764C2×C4#650011yescharacteristic
765C2×C4#650011yescharacteristic
766C2×C4#650011yescharacteristic
767C2×C4#650111yescharacteristic
768C2×C4#650111yescharacteristic
769C2×C4#650111yescharacteristic
770C2×C4#650111yescharacteristic
771C2×C4C22×C4×D711yescharacteristic
772C2×C4C2×D4×D711yescharacteristic
773C2×C4C2×D4×D711yescharacteristic
774C2×C4C2×D4×D711yescharacteristic
775C2×C4C2×#115911yescharacteristic
776C2×C4C22×C22⋊D711yescharacteristic
777C8—24no—
778C8—42no—
779C8—144no—
780C8—144no—
781C7#2099511yescharacteristic, complemented, Sylow
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—42no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—144no—
794C22—284no—
795C22—562no—
796C22—562no—
797C22#8972811yescharacteristic
798C22#8972811yescharacteristic
799C22#8972811yescharacteristic
800C22#8972811yescharacteristic
801C22C2×#644611yescharacteristic
802C22C2×#644711yescharacteristic
803C22C2×C4×C22⋊D711yescharacteristic
804C4—42no—
805C4—144no—
806C4—562no—
807C4#8972811yescharacteristic
808C4#8972811yescharacteristic
809C4#8972811yescharacteristic
810C4#8972811yescharacteristic
811C4C2×D7×C22⋊C411yescharacteristic
812C4C2×(C22⋊D7)⋊C411yescharacteristic
813C4C2×#650011yescharacteristic
814C4C2×#650111yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—82no—
823C2—284no—
824C2C2×#8972811yescharacteristic
subgroupG/H
centerC4#89728
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#413C2
socleC2×C7C2×#386
prime radicalC2×#90513C2
cosocleC22×C4×C7C24
hypercenterC2×#413D7
hypocenterC7#20995
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#90436C2semidirect
3. C2×C7×#413C2semidirect
4. #11741517C2semidirect
5. C2×#89911C2semidirect
6. C2×#89354C2semidirect
7. C2×C7⋊#338C2semidirect
8. #11727876C2semidirect
9. #11727841C2semidirect
14. C2×#6514C4semidirect
19. C2×#6513C4semidirect
20. C2×#6512C4semidirect
35. C2×C7×#101C22semidirect
36. C2×C7×#100C22semidirect
39. #89997C22semidirect
40. #89987C22semidirect
44. C7⋊#338C22semidirect
45. #89354C22semidirect
101. C2×#1144C2×C4semidirect
104. C2×#1143C2×C4semidirect
105. C2×#1142C2×C4semidirect
108. C2×#1141C2×C4semidirect
146. C2×#413D7semidirect
323. C2×#101C2×D7semidirect
324. C2×#100C2×D7semidirect
781. C7#20995semidirect

Maximal subgroups

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

subgroupindex
C2×#905132
C2×#904362
C2×C7×#4132
#117415172
C2×#899112
C2×#893542
C2×C7⋊#3382
#117278762
#117278412
#209957