Finite Group Databasebeta

← #13260439

Subgroups — #13260439

Order 1792.

1630 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#535C211yesmaximal, characteristic
2C22×#6411C211yesmaximal, characteristic, complemented
3C2×#90004C211yesmaximal, characteristic, complemented
4C2×#89993C211yesmaximal, characteristic, complemented
5C22×#6407C211yesmaximal, characteristic, complemented
6#11729335C211yesmaximal, characteristic, complemented
7C2×#89327C211yesmaximal, characteristic, complemented
8C22×C7×#41C2211yescharacteristic
9C23×C7×D4C2211yescharacteristic
10C7×#535—22no—
11C7×#535—22no—
12C7×#535—22no—
13C7×#535C414yescomplemented
14C2×C7×#127—21no—
15C2×C7×#124—21no—
16C2×C7×#121—22no—
17C2×C7×#120—22no—
18C2×C7×#117C2211yescharacteristic
19C22×C22⋊Dic7—22no—
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4×Dic7C2211yescharacteristic
22C22×#1136C2211yescharacteristic
23C22×#1136C2211yescharacteristic
24C2×#6411—22no—
25C2×#6411—22no—
26C2×#6411—22no—
27#90004—22no—
28#90004—22no—
29C2×#6409—21no—
30#89993—22no—
31#89993—22no—
32C2×#6407—22no—
33C2×#6407—22no—
34C2×#6407—22no—
35C2×#6406—21no—
36#89327—22no—
37#89324—22no—
38#10997—71nomaximal, Sylow
39C25×C7D412yes—
40C2×C7×#41—21no—
41C2×C7×#41—21no—
42C2×C7×#41—21no—
43C2×C7×#41—21no—
44C2×C7×#41—21no—
45C2×C7×#41—21no—
46C2×C7×#41—21no—
47C2×C7×#41—21no—
48C2×C7×#41—21no—
49C2×C7×#41—21no—
50C2×C7×#41C2×C412yes—
51C2×C7×#41D412yes—
52C22×C7×Q8D411yescharacteristic
53C22×C7×D4—21no—
54C22×C7×D4—24no—
55C22×C7×D4—21no—
56C22×C7×D4—21no—
57C22×C7×D4—21no—
58C22×C7×D4—21no—
59C22×C7×D4—21no—
60C22×C7×D4—21no—
61C22×C7×D4—21no—
62C22×C7×D4—21no—
63C22×C7×D4—21no—
64C22×C7×D4—21no—
65C22×C7×D4—21no—
66C22×C7×D4—21no—
67C22×C7×D4C2×C412yes—
68C22×C7×D4D412yes—
69C22×C7×D4D411yescharacteristic
70C23×C4×C7—21no—
71C23×C4×C7C2311yescharacteristic
72C23×Dic7—21no—
73C23×Dic7—21no—
74C7×#127—24no—
75C7×#127—24no—
76C7×#124—24no—
77C7×#124—24no—
78C7×#121—28no—
79C7×#121—28no—
80C7×#120—28no—
81C7×#120—28no—
82C7×#117—21no—
83C7×#117—21no—
84C7×#117C2×C412yes—
85C7×#117D412yes—
86C2×C7×C4⋊C4D412yes—
87C2×C7×C22⋊C4—24no—
88C2×C7×C22⋊C4—21no—
89C2×C42×C7—21no—
90C2×C22⋊Dic7—28no—
91C2×C22⋊Dic7—48no—
92C2×C4⋊Dic7—21no—
93C2×C4⋊Dic7—21no—
94C2×C4⋊Dic7—21no—
95C2×C4⋊Dic7—21no—
96C2×C4⋊Dic7—21no—
97C2×C4⋊Dic7D412yescomplemented
98C2×C4×Dic7—21no—
99C2×C4×Dic7—21no—
100C2×C4×Dic7—21no—
101C2×C4×Dic7—21no—
102C2×C4×Dic7—21no—
103C2×C4×Dic7D412yescomplemented
104C2×#1136—21no—
105C2×#1136—21no—
106C2×#1136—21no—
107C2×#1136—21no—
108C2×#1136—21no—
109C2×#1136—21no—
110C2×#1136—21no—
111C2×#1136—21no—
112C2×#1136—21no—
113C2×#1136—21no—
114C2×#1136D412yescomplemented
115C2×#1136D412yescomplemented
116C22×C7⋊C8—21no—
117C22×C7⋊C8—21no—
118#6411—28no—
119#6409—24no—
120#6407—28no—
121#6406—24no—
122C2×#535D711yescharacteristic
123C22×#104—71no—
124C2×#417—71no—
125C22×#100—71no—
126C2×#390—71no—
127#1736—71no—
128C2×#339—71no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—21no—
132C24×C7—22no—
133C24×C7—22no—
134C24×C7—22no—
135C24×C7—22no—
136C24×C7—44no—
137C24×C7—44no—
138C24×C7C22⋊C414yes—
139C24×C7C2×D411yescharacteristic
140C7×#41—22no—
141C7×#41—22no—
142C7×#41—22no—
143C7×#41—22no—
144C7×#41—22no—
145C7×#41—22no—
146C7×#41—22no—
147C7×#41—22no—
148C7×#41—41no—
149C7×#41—41no—
150C7×#41—41no—
151C7×#41—41no—
152C7×#41—41no—
153C7×#41—41no—
154C7×#41—41no—
155C7×#41—41no—
156C2×C7×Q8—21no—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8C22⋊C412yescomplemented
162C2×C7×D4—22no—
163C2×C7×D4—22no—
164C2×C7×D4—216no—
165C2×C7×D4—22no—
166C2×C7×D4—22no—
167C2×C7×D4—22no—
168C2×C7×D4—22no—
169C2×C7×D4—22no—
170C2×C7×D4—22no—
171C2×C7×D4—21no—
172C2×C7×D4—22no—
173C2×C7×D4—22no—
174C2×C7×D4—22no—
175C2×C7×D4—21no—
176C2×C7×D4—21no—
177C2×C7×D4—21no—
178C2×C7×D4—22no—
179C2×C7×D4—22no—
180C2×C7×D4—21no—
181C2×C7×D4—22no—
182C2×C7×D4—41no—
183C2×C7×D4—41no—
184C2×C7×D4—41no—
185C2×C7×D4—41no—
186C2×C7×D4—41no—
187C2×C7×D4—41no—
188C2×C7×D4—41no—
189C2×C7×D4—41no—
190C2×C7×D4—41no—
191C2×C7×D4—41no—
192C2×C7×D4—41no—
193C2×C7×D4—41no—
194C2×C7×D4—41no—
195C2×C7×D4—41no—
196C2×C7×D4—41no—
197C2×C7×D4—41no—
198C2×C7×D4—41no—
199C2×C7×D4—41no—
200C2×C7×D4—41no—
201C2×C7×D4—41no—
202C2×C7×D4—84no—
203C2×C7×D4—84no—
204C2×C7×D4C22⋊C412yescomplemented
205C22×C4×C7—22no—
206C22×C4×C7—21no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—41no—
210C22×C4×C7—41no—
211C22×C4×C7—41no—
212C22×C4×C7—41no—
213C22×C4×C7C22×C411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7#4111yescharacteristic
224C22×C4×C7#4111yescharacteristic
225C22×C4×C7#4111yescharacteristic
226C22×C4×C7#4111yescharacteristic
227C22×Dic7—24no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—42no—
231C22×Dic7—41no—
232C22×Dic7—41no—
233C22×Dic7—44no—
234C22×Dic7—41no—
235C22×Dic7—41no—
236C7×C4⋊C4—22no—
237C7×C4⋊C4C22⋊C414yescomplemented
238C7×C22⋊C4—216no—
239C7×C22⋊C4—22no—
240C7×C22⋊C4—22no—
241C42×C7—22no—
242C42×C7—22no—
243C22⋊Dic7—416no—
244C4⋊Dic7—22no—
245C4⋊Dic7—22no—
246C4⋊Dic7—41no—
247C4⋊Dic7—41no—
248C4×Dic7—22no—
249C4×Dic7—22no—
250C4×Dic7—41no—
251C4×Dic7—41no—
252#1136—22no—
253#1136—22no—
254#1136—22no—
255#1136—22no—
256#1136—41no—
257#1136—41no—
258#1136—41no—
259#1136—41no—
260C2×C7⋊C8—22no—
261C2×C7⋊C8—22no—
262C2×C7⋊C8—41no—
263C2×C7⋊C8—41no—
264C2×C7⋊C8—41no—
265C2×C7⋊C8—41no—
266C22×#41C2×D711yescharacteristic
267C23×D4C2×D711yescharacteristic
268C22×M16—71no—
269C22×M16—71no—
270#535—22no—
271#535—22no—
272#535—22no—
273#535Dic714yescomplemented
274C2×#127—21no—
275C2×#124—21no—
276C2×#121—22no—
277C2×#120—22no—
278C2×#117C2×D711yescharacteristic
279C22×C4⋊C4—71no—
280C22×C22⋊C4—142no—
281C22×C42—71no—
282C2×#104—142no—
283C2×#104—142no—
284C2×#104—142no—
285#417—142no—
286#417—142no—
287C2×#103—141no—
288C2×#102—141no—
289C2×#100—142no—
290C2×#100—142no—
291C2×#100—142no—
292#390—142no—
293#390—142no—
294#340—142no—
295#339—142no—
296C23×C7—22no—
297C23×C7—22no—
298C23×C7—24no—
299C23×C7—22no—
300C23×C7—24no—
301C23×C7—24no—
302C23×C7—48no—
303C23×C7—44no—
304C23×C7—44no—
305C23×C7—48no—
306C23×C7—41no—
307C23×C7—42no—
308C23×C7—42no—
309C23×C7—41no—
310C23×C7—42no—
311C23×C7—42no—
312C23×C7—42no—
313C23×C7—44no—
314C23×C7—42no—
315C23×C7—44no—
316C23×C7—84no—
317C23×C7—82no—
318C23×C7—82no—
319C23×C7—84no—
320C23×C7C2×C22⋊C411yescharacteristic
321C23×C7#12011yescharacteristic
322C23×C7#12011yescharacteristic
323C23×C7#12011yescharacteristic
324C23×C7#12111yescharacteristic
325C23×C7#12111yescharacteristic
326C23×C7#12311yescharacteristic
327C7×Q8—22no—
328C7×Q8—22no—
329C7×Q8—41no—
330C7×Q8—41no—
331C7×D4—22no—
332C7×D4—22no—
333C7×D4—42no—
334C7×D4—42no—
335C7×D4—42no—
336C7×D4—42no—
337C7×D4—42no—
338C7×D4—42no—
339C7×D4—42no—
340C7×D4—42no—
341C7×D4—42no—
342C7×D4—42no—
343C7×D4—41no—
344C7×D4—42no—
345C7×D4—42no—
346C7×D4—41no—
347C7×D4—816no—
348C2×C4×C7—24no—
349C2×C4×C7—22no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—42no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7—42no—
358C2×C4×C7C2×C22⋊C411yescharacteristic
359C2×C4×C7C2×C22⋊C411yescharacteristic
360C2×C4×C7C4×D411yescharacteristic
361C2×C4×C7C4×D411yescharacteristic
362C2×C4×C7C4×D411yescharacteristic
363C2×C4×C7C4×D411yescharacteristic
364C2×C4×C7#12011yescharacteristic
365C2×C4×C7#12011yescharacteristic
366C2×C4×C7#12011yescharacteristic
367C2×C4×C7#12011yescharacteristic
368C2×C4×C7#12011yescharacteristic
369C2×C4×C7#12111yescharacteristic
370C2×C4×C7#12111yescharacteristic
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#12111yescharacteristic
378C2×C4×C7#12111yescharacteristic
379C2×C4×C7#12311yescharacteristic
380C2×C4×C7#12311yescharacteristic
381C2×C4×C7#12311yescharacteristic
382C2×C4×C7#12411yescharacteristic
383C2×C4×C7#12411yescharacteristic
384C2×C4×C7#12711yescharacteristic
385C2×C4×C7#12711yescharacteristic
386C2×Dic7—24no—
387C2×Dic7—44no—
388C2×Dic7—42no—
389C2×Dic7—44no—
390C2×Dic7—42no—
391C2×Dic7—44no—
392C2×Dic7—42no—
393C2×Dic7—82no—
394C2×Dic7—82no—
395C7⋊C8—42no—
396C7⋊C8—42no—
397C25C22⋊D712yes—
398C2×#41—21no—
399C2×#41—21no—
400C2×#41—21no—
401C2×#41—21no—
402C2×#41—21no—
403C2×#41—21no—
404C2×#41—21no—
405C2×#41—21no—
406C2×#41—21no—
407C2×#41—21no—
408C2×#41C2×Dic712yes—
409C2×#41C22⋊D712yes—
410C22×Q8C22⋊D711yescharacteristic
411C22×D4—21no—
412C22×D4—24no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4—21no—
419C22×D4—21no—
420C22×D4—21no—
421C22×D4—21no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4C2×Dic712yes—
426C22×D4C22⋊D712yes—
427C22×D4C22⋊D711yescharacteristic
428C23×C4—21no—
429C23×C4—141no—
430C23×C4—141no—
431C23×C4C22×D711yescharacteristic
432C2×M16—72no—
433C2×M16—72no—
434C2×M16—141no—
435C2×M16—141no—
436C2×M16—141no—
437C2×M16—141no—
438C2×M16—141no—
439C2×M16—141no—
440C2×M16—141no—
441C2×M16—141no—
442C2×M16—141no—
443C2×M16—141no—
444C22×C8—141no—
445C22×C8—141no—
446#127—24no—
447#127—24no—
448#124—24no—
449#124—24no—
450#121—28no—
451#121—28no—
452#120—28no—
453#120—28no—
454#117—21no—
455#117—21no—
456#117C2×Dic712yes—
457#117C22⋊D712yes—
458C2×C4⋊C4—72no—
459C2×C4⋊C4—141no—
460C2×C4⋊C4—141no—
461C2×C4⋊C4—141no—
462C2×C4⋊C4—141no—
463C2×C4⋊C4—141no—
464C2×C4⋊C4C22⋊D712yes—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—148no—
468C2×C22⋊C4—288no—
469C2×C42—21no—
470C2×C42—72no—
471C2×C42—141no—
472C2×C42—141no—
473C2×C42—141no—
474C2×C42—141no—
475C2×C42—141no—
476#104—148no—
477#103—144no—
478#102—144no—
479#100—148no—
480C22×C7—22no—
481C22×C7—22no—
482C22×C7—21no—
483C22×C7—21no—
484C22×C7—21no—
485C22×C7—21no—
486C22×C7—22no—
487C22×C7—22no—
488C22×C7—48no—
489C22×C7—44no—
490C22×C7—48no—
491C22×C7—42no—
492C22×C7—44no—
493C22×C7—84no—
494C22×C7—84no—
495C22×C7—84no—
496C22×C7—81no—
497C22×C7—82no—
498C22×C7—81no—
499C22×C7—82no—
500C22×C7—82no—
501C22×C7—84no—
502C22×C7#37911yescharacteristic
503C22×C7#38611yescharacteristic
504C22×C7#38611yescharacteristic
505C22×C7#39211yescharacteristic
506C22×C7#39211yescharacteristic
507C22×C7#39411yescharacteristic
508C22×C7#39411yescharacteristic
509C22×C7#45312yes—
510C22×C7#45512yes—
511C4×C7—44no—
512C4×C7—42no—
513C4×C7#38611yescharacteristic
514C4×C7#38611yescharacteristic
515C4×C7#39011yescharacteristic
516C4×C7#39011yescharacteristic
517C4×C7#39211yescharacteristic
518C4×C7#39211yescharacteristic
519C4×C7#39411yescharacteristic
520C4×C7#39411yescharacteristic
521Dic7—44no—
522Dic7—82no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—21no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—44no—
531C24—44no—
532C24C22⋊Dic714yes—
533C24C2×C22⋊D711yescharacteristic
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8C22⋊Dic712yescomplemented
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—216no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—84no—
597C2×D4—84no—
598C2×D4C22⋊Dic712yescomplemented
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—144no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—282no—
611C22×C4—281no—
612C22×C4—281no—
613C22×C4—284no—
614C22×C4—281no—
615C22×C4—281no—
616C22×C4D4×D711yescharacteristic
617C22×C4D4×D711yescharacteristic
618C22×C4D4×D711yescharacteristic
619C22×C4D4×D711yescharacteristic
620C22×C4#115911yescharacteristic
621C22×C4#115911yescharacteristic
622C22×C4#115911yescharacteristic
623C22×C4#115911yescharacteristic
624C22×C4C22×Dic711yescharacteristic
625C22×C4C2×C22⋊D711yescharacteristic
626C22×C4C2×C22⋊D711yescharacteristic
627C22×C4C2×C22⋊D711yescharacteristic
628C22×C4C2×C22⋊D711yescharacteristic
629C22×C4C2×C22⋊D711yescharacteristic
630M16—142no—
631M16—142no—
632M16—142no—
633M16—142no—
634M16—281no—
635M16—281no—
636M16—281no—
637M16—281no—
638C2×C8—142no—
639C2×C8—142no—
640C2×C8—281no—
641C2×C8—281no—
642C2×C8—281no—
643C2×C8—281no—
644C4⋊C4—22no—
645C4⋊C4—142no—
646C4⋊C4—142no—
647C4⋊C4—281no—
648C4⋊C4—281no—
649C4⋊C4C22⋊Dic714yescomplemented
650C22⋊C4—216no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—2816no—
654C42—22no—
655C42—22no—
656C42—142no—
657C42—142no—
658C42—281no—
659C42—281no—
660C2×C7—21no—
661C2×C7—21no—
662C2×C7—21no—
663C2×C7—21no—
664C2×C7—84no—
665C2×C7—82no—
666C2×C7#143811yescharacteristic
667C2×C7#179212yes—
668C2×C7#200211yescharacteristic
669C2×C7#200411yescharacteristic
670C2×C7#203712yes—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—22no—
676C23—24no—
677C23—48no—
678C23—44no—
679C23—48no—
680C23—44no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—44no—
689C23—42no—
690C23—44no—
691C23—84no—
692C23—84no—
693C23—82no—
694C23—82no—
695C23#649811yescharacteristic
696C23#650011yescharacteristic
697C23#650211yescharacteristic
698C23#650211yescharacteristic
699C23C2×C22⋊Dic711yescharacteristic
700C23#651611yescharacteristic
701C23#651611yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706D4—22no—
707D4—22no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—42no—
721D4—41no—
722D4—816no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—144no—
734C2×C4—284no—
735C2×C4—282no—
736C2×C4—284no—
737C2×C4—282no—
738C2×C4—284no—
739C2×C4—282no—
740C2×C4—562no—
741C2×C4—562no—
742C2×C4D4×Dic711yescharacteristic
743C2×C4D4×Dic711yescharacteristic
744C2×C4D4×Dic711yescharacteristic
745C2×C4D4×Dic711yescharacteristic
746C2×C4#649811yescharacteristic
747C2×C4#649811yescharacteristic
748C2×C4#649811yescharacteristic
749C2×C4#649911yescharacteristic
750C2×C4#649911yescharacteristic
751C2×C4#650011yescharacteristic
752C2×C4#650011yescharacteristic
753C2×C4#650011yescharacteristic
754C2×C4#650111yescharacteristic
755C2×C4#650111yescharacteristic
756C2×C4#650111yescharacteristic
757C2×C4#650111yescharacteristic
758C2×C4#650211yescharacteristic
759C2×C4#650211yescharacteristic
760C2×C4#650211yescharacteristic
761C2×C4#650211yescharacteristic
762C2×C4#650211yescharacteristic
763C2×C4#650211yescharacteristic
764C2×C4#650311yescharacteristic
765C2×C4#650311yescharacteristic
766C2×C4C2×C22⋊Dic711yescharacteristic
767C2×C4C2×C22⋊Dic711yescharacteristic
768C2×C4#651611yescharacteristic
769C2×C4#651611yescharacteristic
770C8—282no—
771C8—282no—
772C7#1099711yescharacteristic, complemented, Sylow
773C22—22no—
774C22—22no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—22no—
780C22—22no—
781C22—48no—
782C22—42no—
783C22—44no—
784C22—44no—
785C22—48no—
786C22—84no—
787C22—84no—
788C22—84no—
789C22—84no—
790C22—82no—
791C22—82no—
792C22—81no—
793C22—82no—
794C22—81no—
795C22#8999211yescharacteristic
796C22#8999211yescharacteristic
797C22#8999411yescharacteristic
798C22#8999411yescharacteristic
799C22#8999511yescharacteristic
800C22#8999511yescharacteristic
801C22#9001312yes—
802C22#9001412yes—
803C22#9001911yescharacteristic
804C4—42no—
805C4—44no—
806C4—284no—
807C4—562no—
808C4#8999211yescharacteristic
809C4#8999211yescharacteristic
810C4#8999311yescharacteristic
811C4#8999311yescharacteristic
812C4#8999411yescharacteristic
813C4#8999411yescharacteristic
814C4#8999511yescharacteristic
815C4#8999511yescharacteristic
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—84no—
821C2—82no—
822C2#1172960612yes—
823C2#1172961011yescharacteristic
824C2#1172961111yescharacteristic
825C2#1172988511yescharacteristic
826C2#1172989412yes—
subgroupG/H
centerC23#6516
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
Fitting, prime radicalC2×C7×#535C2
socleC23×C7#120
cosocleC23×C4×C7C23
hypercenterC2×#535D7
hypocenterC7#10997
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
2. C22×#6411C2semidirect
3. C2×#90004C2semidirect
4. C2×#89993C2semidirect
5. C22×#6407C2semidirect
6. #11729335C2semidirect
7. C2×#89327C2semidirect
13. C7×#535C4semidirect
97. C2×C4⋊Dic7D4semidirect
103. C2×C4×Dic7D4semidirect
114. C2×#1136D4semidirect
115. C2×#1136D4semidirect
161. C2×C7×Q8C22⋊C4semidirect
204. C2×C7×D4C22⋊C4semidirect
237. C7×C4⋊C4C22⋊C4semidirect
273. #535Dic7semidirect
555. C2×Q8C22⋊Dic7semidirect
598. C2×D4C22⋊Dic7semidirect
649. C4⋊C4C22⋊Dic7semidirect
772. C7#10997semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5352
C22×#64112
C2×#900042
C2×#899932
C22×#64072
#117293352
C2×#893272
#109977