Finite Group Databasebeta

← C7×#11020 #13188236

Subgroups — C7×#11020 #13188236

Order 1792.

1406 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×C7×#417C211yesmaximal, characteristic, complemented
3C22×C7×#102C211yesmaximal, characteristic, complemented
4C22×C7×#100C211yesmaximal, characteristic, complemented
5C2×C7×#408C211yesmaximal, characteristic, complemented
6C2×C7×#343C211yesmaximal, characteristic, complemented
7C2×C7×#341C211yesmaximal, characteristic, complemented
8C22×C7×#41C2211yescharacteristic
9C23×C7×D4C2211yescharacteristic
10C2×C7×AGL(1,ℤ/8)—22no—
11C2×C7×AGL(1,ℤ/8)—22no—
12C2×C7×AGL(1,ℤ/8)—22no—
13C2×C7×AGL(1,ℤ/8)—22no—
14C2×C7×AGL(1,ℤ/8)—22no—
15C2×C7×AGL(1,ℤ/8)C414yescomplemented
16C22×C7×SD16—21no—
17C22×C7×D8—21no—
18C22×C7×M16C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C22×C7×M16C2211yescharacteristic
21C23×C7×C8C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C7×#417—22no—
24C7×#417—22no—
25C2×C7×#103—21no—
26C2×C7×#102—22no—
27C2×C7×#102—21no—
28C2×C7×#102—22no—
29C2×C7×#102—22no—
30C2×C7×#100—22no—
31C2×C7×#100—22no—
32C2×C7×#100—22no—
33C7×#408—22no—
34C7×#408—22no—
35C2×C7×C22⋊C8—22no—
36C7×#343—22no—
37C7×#341—22no—
38#11020C711yesmaximal, characteristic, direct product factor, Sylow
39C25×C7—21no—
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—21no—
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×D4C2×C412yes—
66C22×C7×D4D412yes—
67C22×C7×D4D412yes—
68C22×C7×D4D411yescharacteristic
69C23×C4×C7—21no—
70C23×C4×C7—21no—
71C23×C4×C7C2311yescharacteristic
72C7×AGL(1,ℤ/8)—28no—
73C7×AGL(1,ℤ/8)—28no—
74C7×AGL(1,ℤ/8)—28no—
75C7×AGL(1,ℤ/8)—28no—
76C2×C7×SD16—24no—
77C2×C7×SD16—24no—
78C2×C7×SD16—24no—
79C2×C7×D8—24no—
80C2×C7×D8—24no—
81C2×C7×D8—24no—
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×M16—21no—
89C2×C7×M16—21no—
90C2×C7×M16—21no—
91C2×C7×M16—21no—
92C2×C7×M16—21no—
93C2×C7×M16—21no—
94C2×C7×M16—21no—
95C2×C7×M16C2×C412yes—
96C2×C7×M16D412yes—
97C2×C7×M16D412yes—
98C2×C7×M16D412yes—
99C2×C7×M16D412yes—
100C22×C7×C8—21no—
101C22×C7×C8—21no—
102C22×C7×C8—21no—
103C22×C7×C8—21no—
104C22×C7×C8—21no—
105C22×C7×C8—21no—
106C22×C7×C8—21no—
107C22×C7×C8—21no—
108C22×C7×C8—21no—
109C22×C7×C8D412yes—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4—21no—
115C2×C7×C4⋊C4D412yes—
116C7×#103—24no—
117C7×#102—28no—
118C7×#102—24no—
119C7×#100—28no—
120C7×C22⋊C8—28no—
121C22×AGL(1,ℤ/8)C2×C711yescharacteristic
122C2×#417C2×C711yescharacteristic, complemented
123C22×#102C2×C711yescharacteristic, complemented
124C22×#100C2×C711yescharacteristic, complemented
125C2×#408C2×C711yescharacteristic, complemented
126C2×#343C2×C711yescharacteristic, complemented
127C2×#341C2×C711yescharacteristic, complemented
128C24×C7—21no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—41no—
133C24×C7—41no—
134C24×C7—41no—
135C24×C7—41no—
136C24×C7—82no—
137C24×C7—82no—
138C24×C7#4111yescharacteristic
139C7×#41—22no—
140C7×#41—22no—
141C7×#41—22no—
142C7×#41—22no—
143C7×#41—22no—
144C7×#41—22no—
145C7×#41—22no—
146C7×#41—22no—
147C7×#41—41no—
148C7×#41—41no—
149C7×#41—41no—
150C7×#41—41no—
151C7×#41—41no—
152C7×#41—41no—
153C7×#41—41no—
154C7×#41—41no—
155C2×C7×Q8—21no—
156C2×C7×Q8—21no—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8C22⋊C412yes—
161C2×C7×D4—22no—
162C2×C7×D4—22no—
163C2×C7×D4—22no—
164C2×C7×D4—22no—
165C2×C7×D4—22no—
166C2×C7×D4—22no—
167C2×C7×D4—22no—
168C2×C7×D4—22no—
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
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—22no—
179C2×C7×D4—22no—
180C2×C7×D4—21no—
181C2×C7×D4—22no—
182C2×C7×D4—21no—
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×D4C22⋊C412yes—
200C2×C7×D4C22⋊C414yes—
201C22×C4×C7—21no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—41no—
206C22×C4×C7—41no—
207C22×C4×C7—41no—
208C22×C4×C7—41no—
209C22×C4×C7—41no—
210C22×C4×C7—41no—
211C22×C4×C7—82no—
212C22×C4×C7C22×C411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
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
226C7×SD16—216no—
227C7×D8—216no—
228C7×M16—22no—
229C7×M16—22no—
230C7×M16—22no—
231C7×M16—22no—
232C7×M16—22no—
233C7×M16—22no—
234C7×M16—22no—
235C7×M16—41no—
236C7×M16—41no—
237C7×M16—41no—
238C7×M16—41no—
239C7×M16C22⋊C414yes—
240C2×C7×C8—22no—
241C2×C7×C8—22no—
242C2×C7×C8—22no—
243C2×C7×C8—22no—
244C2×C7×C8—22no—
245C2×C7×C8—22no—
246C2×C7×C8—22no—
247C2×C7×C8—22no—
248C2×C7×C8—41no—
249C2×C7×C8—41no—
250C2×C7×C8—41no—
251C2×C7×C8—41no—
252C2×C7×C8—41no—
253C2×C7×C8—41no—
254C2×C7×C8—41no—
255C2×C7×C8—41no—
256C7×C4⋊C4—22no—
257C7×C4⋊C4—22no—
258C7×C4⋊C4—41no—
259C7×C4⋊C4—41no—
260C22×#41C22×C711yescharacteristic
261C23×D4C22×C711yescharacteristic
262C2×AGL(1,ℤ/8)—22no—
263C2×AGL(1,ℤ/8)—22no—
264C2×AGL(1,ℤ/8)—22no—
265C2×AGL(1,ℤ/8)—22no—
266C2×AGL(1,ℤ/8)—22no—
267C2×AGL(1,ℤ/8)C4×C714yescomplemented
268C22×SD16—21no—
269C22×D8—21no—
270C22×M16C22×C711yescharacteristic
271C22×M16C22×C711yescharacteristic
272C22×M16C22×C711yescharacteristic
273C23×C8C22×C711yescharacteristic
274C22×C4⋊C4C22×C711yescharacteristic
275#417—22no—
276#417—22no—
277C2×#103—21no—
278C2×#102—22no—
279C2×#102—21no—
280C2×#102—22no—
281C2×#102—22no—
282C2×#100—22no—
283C2×#100—22no—
284C2×#100—22no—
285#408—22no—
286#408—22no—
287C2×C22⋊C8—22no—
288#343—22no—
289#341—22no—
290C23×C7—22no—
291C23×C7—22no—
292C23×C7—22no—
293C23×C7—24no—
294C23×C7—42no—
295C23×C7—42no—
296C23×C7—41no—
297C23×C7—42no—
298C23×C7—41no—
299C23×C7—42no—
300C23×C7—42no—
301C23×C7—42no—
302C23×C7—42no—
303C23×C7—42no—
304C23×C7—84no—
305C23×C7—84no—
306C23×C7—82no—
307C23×C7—82no—
308C23×C7—84no—
309C23×C7—84no—
310C23×C7—82no—
311C23×C7—82no—
312C23×C7—82no—
313C23×C7—82no—
314C23×C7C4×D411yescharacteristic
315C23×C7#12111yescharacteristic
316C23×C7#12111yescharacteristic
317C23×C7#12111yescharacteristic
318C23×C7#12311yescharacteristic
319C23×C7#12311yescharacteristic
320C23×C7#12411yescharacteristic
321C7×Q8—22no—
322C7×Q8—22no—
323C7×Q8—41no—
324C7×Q8—41no—
325C7×D4—22no—
326C7×D4—24no—
327C7×D4—24no—
328C7×D4—22no—
329C7×D4—42no—
330C7×D4—42no—
331C7×D4—42no—
332C7×D4—42no—
333C7×D4—42no—
334C7×D4—42no—
335C7×D4—42no—
336C7×D4—42no—
337C7×D4—42no—
338C7×D4—41no—
339C7×D4—42no—
340C7×D4—41no—
341C2×C4×C7—22no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—42no—
345C2×C4×C7—42no—
346C2×C4×C7—42no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7—82no—
350C2×C4×C7—82no—
351C2×C4×C7—82no—
352C2×C4×C7C2×C22⋊C411yescharacteristic
353C2×C4×C7C2×C22⋊C411yescharacteristic
354C2×C4×C7C2×C22⋊C411yescharacteristic
355C2×C4×C7C4×D411yescharacteristic
356C2×C4×C7C4×D411yescharacteristic
357C2×C4×C7C4×D411yescharacteristic
358C2×C4×C7#12011yescharacteristic
359C2×C4×C7#12011yescharacteristic
360C2×C4×C7#12011yescharacteristic
361C2×C4×C7#12011yescharacteristic
362C2×C4×C7#12011yescharacteristic
363C2×C4×C7#12011yescharacteristic
364C2×C4×C7#12011yescharacteristic
365C2×C4×C7#12011yescharacteristic
366C2×C4×C7#12111yescharacteristic
367C2×C4×C7#12111yescharacteristic
368C2×C4×C7#12111yescharacteristic
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#12311yescharacteristic
376C2×C4×C7#12311yescharacteristic
377C2×C4×C7#12411yescharacteristic
378C2×C4×C7#12711yescharacteristic
379C2×C4×C7#12711yescharacteristic
380C7×C8—24no—
381C7×C8—42no—
382C7×C8—42no—
383C7×C8—42no—
384C25—21no—
385C2×#41—21no—
386C2×#41—21no—
387C2×#41—21no—
388C2×#41—21no—
389C2×#41—21no—
390C2×#41—21no—
391C2×#41—21no—
392C2×#41—21no—
393C2×#41—21no—
394C2×#41—21no—
395C2×#41C2×C4×C712yes—
396C2×#41C7×D412yes—
397C22×Q8C7×D411yescharacteristic
398C22×D4—21no—
399C22×D4—21no—
400C22×D4—21no—
401C22×D4—21no—
402C22×D4—21no—
403C22×D4—21no—
404C22×D4—21no—
405C22×D4—21no—
406C22×D4—21no—
407C22×D4—21no—
408C22×D4—21no—
409C22×D4—21no—
410C22×D4C2×C4×C712yes—
411C22×D4C7×D411yescharacteristic
412C22×D4C7×D412yes—
413C22×D4C7×D412yes—
414C23×C4—21no—
415C23×C4—21no—
416C23×C4C23×C711yescharacteristic
417AGL(1,ℤ/8)—28no—
418AGL(1,ℤ/8)—28no—
419AGL(1,ℤ/8)—28no—
420AGL(1,ℤ/8)—28no—
421C2×SD16—24no—
422C2×SD16—24no—
423C2×SD16—24no—
424C2×D8—24no—
425C2×D8—24no—
426C2×D8—24no—
427C2×M16—21no—
428C2×M16—21no—
429C2×M16—21no—
430C2×M16—21no—
431C2×M16—21no—
432C2×M16—21no—
433C2×M16—21no—
434C2×M16—21no—
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—21no—
440C2×M16C2×C4×C712yes—
441C2×M16C7×D412yes—
442C2×M16C7×D412yes—
443C2×M16C7×D412yes—
444C2×M16C7×D412yes—
445C22×C8—21no—
446C22×C8—21no—
447C22×C8—21no—
448C22×C8—21no—
449C22×C8—21no—
450C22×C8—21no—
451C22×C8—21no—
452C22×C8—21no—
453C22×C8—21no—
454C22×C8C7×D412yes—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4C7×D412yes—
461#103—24no—
462#102—28no—
463#102—24no—
464#100—28no—
465C22⋊C8—28no—
466C22×C7—22no—
467C22×C7—22no—
468C22×C7—22no—
469C22×C7—22no—
470C22×C7—21no—
471C22×C7—21no—
472C22×C7—21no—
473C22×C7—21no—
474C22×C7—44no—
475C22×C7—42no—
476C22×C7—44no—
477C22×C7—84no—
478C22×C7—84no—
479C22×C7—84no—
480C22×C7—84no—
481C22×C7—82no—
482C22×C7—84no—
483C22×C7—84no—
484C22×C7—81no—
485C22×C7—82no—
486C22×C7—81no—
487C22×C7—82no—
488C22×C7#38611yescharacteristic
489C22×C7#38611yescharacteristic
490C22×C7#39011yescharacteristic
491C22×C7#39211yescharacteristic
492C22×C7#39411yescharacteristic
493C22×C7#39411yescharacteristic
494C22×C7#39411yescharacteristic
495C22×C7#47112yes—
496C22×C7#47212yes—
497C4×C7—42no—
498C4×C7—82no—
499C4×C7#37911yescharacteristic
500C4×C7#38611yescharacteristic
501C4×C7#38611yescharacteristic
502C4×C7#39011yescharacteristic
503C4×C7#39211yescharacteristic
504C4×C7#39211yescharacteristic
505C4×C7#39211yescharacteristic
506C4×C7#39411yescharacteristic
507C24—21no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—41no—
512C24—41no—
513C24—41no—
514C24—41no—
515C24—82no—
516C24—82no—
517C24C7×#4111yescharacteristic
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—22no—
525#41—22no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—41no—
532#41—41no—
533#41—41no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8C7×C22⋊C412yes—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
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×D4C7×C22⋊C412yes—
579C2×D4C7×C22⋊C414yes—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—82no—
591C22×C4C22×C4×C711yescharacteristic
592C22×C4C2×C7×D411yescharacteristic
593C22×C4C2×C7×D411yescharacteristic
594C22×C4C2×C7×D411yescharacteristic
595C22×C4C2×C7×D411yescharacteristic
596C22×C4C2×C7×D411yescharacteristic
597C22×C4C2×C7×D411yescharacteristic
598C22×C4C2×C7×D411yescharacteristic
599C22×C4C2×C7×D411yescharacteristic
600C22×C4C2×C7×D411yescharacteristic
601C22×C4C2×C7×D411yescharacteristic
602C22×C4C7×#4111yescharacteristic
603C22×C4C7×#4111yescharacteristic
604C22×C4C7×#4111yescharacteristic
605SD16—216no—
606D8—216no—
607M16—22no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—22no—
612M16—22no—
613M16—22no—
614M16—41no—
615M16—41no—
616M16—41no—
617M16—41no—
618M16C7×C22⋊C414yes—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C2×C7—21no—
640C2×C7—21no—
641C2×C7—21no—
642C2×C7—21no—
643C2×C7—82no—
644C2×C7—84no—
645C2×C7#143811yescharacteristic
646C2×C7#190712yes—
647C2×C7#201811yescharacteristic
648C2×C7#201911yescharacteristic
649C2×C7#205112yes—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—41no—
659C23—42no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—82no—
665C23—82no—
666C23—84no—
667C23—84no—
668C23—82no—
669C23—82no—
670C23—84no—
671C23—84no—
672C23—82no—
673C23—82no—
674C23C4×C7×D411yescharacteristic
675C23C7×#12111yescharacteristic
676C23C7×#12111yescharacteristic
677C23C7×#12111yescharacteristic
678C23C7×#12311yescharacteristic
679C23C7×#12311yescharacteristic
680C23C7×#12411yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—41no—
684Q8—41no—
685D4—22no—
686D4—24no—
687D4—24no—
688D4—22no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—41no—
699D4—42no—
700D4—41no—
701C2×C4—22no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4C2×C7×C22⋊C411yescharacteristic
713C2×C4C2×C7×C22⋊C411yescharacteristic
714C2×C4C2×C7×C22⋊C411yescharacteristic
715C2×C4C4×C7×D411yescharacteristic
716C2×C4C4×C7×D411yescharacteristic
717C2×C4C4×C7×D411yescharacteristic
718C2×C4C7×#12011yescharacteristic
719C2×C4C7×#12011yescharacteristic
720C2×C4C7×#12011yescharacteristic
721C2×C4C7×#12011yescharacteristic
722C2×C4C7×#12011yescharacteristic
723C2×C4C7×#12011yescharacteristic
724C2×C4C7×#12011yescharacteristic
725C2×C4C7×#12011yescharacteristic
726C2×C4C7×#12111yescharacteristic
727C2×C4C7×#12111yescharacteristic
728C2×C4C7×#12111yescharacteristic
729C2×C4C7×#12111yescharacteristic
730C2×C4C7×#12111yescharacteristic
731C2×C4C7×#12111yescharacteristic
732C2×C4C7×#12111yescharacteristic
733C2×C4C7×#12111yescharacteristic
734C2×C4C7×#12111yescharacteristic
735C2×C4C7×#12311yescharacteristic
736C2×C4C7×#12311yescharacteristic
737C2×C4C7×#12411yescharacteristic
738C2×C4C7×#12711yescharacteristic
739C2×C4C7×#12711yescharacteristic
740C8—24no—
741C8—42no—
742C8—42no—
743C8—42no—
744C7#1102011yescharacteristic, direct product factor, Sylow
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—44no—
756C22—84no—
757C22—84no—
758C22—84no—
759C22—84no—
760C22—81no—
761C22—82no—
762C22—81no—
763C22—82no—
764C22—82no—
765C22—84no—
766C22—84no—
767C22C7×#38611yescharacteristic
768C22C7×#38611yescharacteristic
769C22C7×#39011yescharacteristic
770C22C7×#39211yescharacteristic
771C22C7×#39411yescharacteristic
772C22C7×#39411yescharacteristic
773C22C7×#39411yescharacteristic
774C22C7×#47112yes—
775C22C7×#47212yes—
776C4—42no—
777C4—82no—
778C4C7×#37911yescharacteristic
779C4C7×#38611yescharacteristic
780C4C7×#38611yescharacteristic
781C4C7×#39011yescharacteristic
782C4C7×#39211yescharacteristic
783C4C7×#39211yescharacteristic
784C4C7×#39211yescharacteristic
785C4C7×#39411yescharacteristic
786C2—21no—
787C2—21no—
788C2—21no—
789C2—21no—
790C2—82no—
791C2—84no—
792C2C7×#143811yescharacteristic
793C2C7×#190712yes—
794C2C7×#201811yescharacteristic
795C2C7×#201911yescharacteristic
796C2C7×#205112yes—
subgroupG/H
center, socleC23×C7#121
commutatorC22×C4C22×C4×C7
Frattini, cosocleC23×C4C23×C7
prime radicalC22×C7×AGL(1,ℤ/8)C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#417C2semidirect
3. C22×C7×#102C2semidirect
4. C22×C7×#100C2semidirect
5. C2×C7×#408C2semidirect
6. C2×C7×#343C2semidirect
7. C2×C7×#341C2semidirect
15. C2×C7×AGL(1,ℤ/8)C4semidirect
38. #11020C7direct (N × H)
122. C2×#417C2×C7semidirect
123. C22×#102C2×C7semidirect
124. C22×#100C2×C7semidirect
125. C2×#408C2×C7semidirect
126. C2×#343C2×C7semidirect
127. C2×#341C2×C7semidirect
267. C2×AGL(1,ℤ/8)C4×C7semidirect
744. C7#11020direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×AGL(1,ℤ/8)2
C2×C7×#4172
C22×C7×#1022
C22×C7×#1002
C2×C7×#4082
C2×C7×#3432
C2×C7×#3412
#110207