Finite Group Databasebeta

← C7×#11023 #13188239

Subgroups — C7×#11023 #13188239

Order 1792.

1606 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×SD16C211yesmaximal, characteristic
2C22×C7×#103C211yesmaximal, characteristic, complemented
3C22×C7×#102C211yesmaximal, characteristic
4C2×C7×#391C211yesmaximal, characteristic, complemented
5C2×C7×#390C211yesmaximal, characteristic
6C2×C7×#340C211yesmaximal, characteristic, complemented
7C2×C7×#336C211yesmaximal, characteristic, complemented
8C23×C7×Q8C2211yescharacteristic
9C23×C7×D4C2211yescharacteristic
10C22×C7×SD16—22no—
11C22×C7×SD16—22no—
12C22×C7×SD16—22no—
13C22×C7×SD16—22no—
14C22×C7×SD16—22no—
15C22×C7×SD16—22no—
16C22×C7×SD16C414yescomplemented
17C23×C7×C8C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4—22no—
22C22×C42×C7C2211yescharacteristic
23C2×C7×#103—22no—
24C2×C7×#103—22no—
25C2×C7×#103—22no—
26C2×C7×#102—22no—
27C2×C7×#102—22no—
28C2×C7×#102—22no—
29C7×#391—22no—
30C7×#391—22no—
31C7×#390—22no—
32C7×#390—22no—
33C2×C7×#95—22no—
34C7×#340—22no—
35C7×#336—22no—
36#11023C711yesmaximal, characteristic, direct product factor, Sylow
37C25×C7—21no—
38C22×C7×Q8—21no—
39C22×C7×Q8—21no—
40C22×C7×Q8—21no—
41C22×C7×Q8—21no—
42C22×C7×Q8—21no—
43C22×C7×Q8—21no—
44C22×C7×Q8—21no—
45C22×C7×Q8—21no—
46C22×C7×Q8—21no—
47C22×C7×Q8—21no—
48C22×C7×Q8—21no—
49C22×C7×Q8C2×C412yes—
50C22×C7×Q8D412yes—
51C22×C7×Q8D412yes—
52C22×C7×D4—21no—
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×D4C2×C412yes—
64C22×C7×D4D412yes—
65C22×C7×D4D412yes—
66C23×C4×C7—21no—
67C23×C4×C7—21no—
68C23×C4×C7—21no—
69C23×C4×C7D412yes—
70C23×C4×C7C2311yescharacteristic
71C2×C7×SD16—28no—
72C2×C7×SD16—28no—
73C2×C7×SD16—28no—
74C2×C7×SD16—28no—
75C2×C7×SD16—28no—
76C2×C7×SD16—28no—
77C2×C7×SD16—28no—
78C22×C7×C8—21no—
79C22×C7×C8—21no—
80C22×C7×C8—21no—
81C22×C7×C8—21no—
82C22×C7×C8—21no—
83C22×C7×C8—21no—
84C22×C7×C8—21no—
85C22×C7×C8—21no—
86C22×C7×C8—21no—
87C22×C7×C8—21no—
88C22×C7×C8C2×C412yes—
89C22×C7×C8D412yes—
90C22×C7×C8D412yes—
91C22×C7×C8D412yes—
92C2×C7×C4⋊C4—21no—
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4—21no—
95C2×C7×C4⋊C4—21no—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4D412yes—
103C2×C7×C4⋊C4D412yes—
104C2×C7×C22⋊C4—28no—
105C2×C7×C22⋊C4—44no—
106C2×C7×C22⋊C4—44no—
107C2×C42×C7—21no—
108C2×C42×C7—21no—
109C2×C42×C7—21no—
110C2×C42×C7—21no—
111C2×C42×C7—21no—
112C2×C42×C7—21no—
113C7×#103—28no—
114C7×#102—28no—
115C7×#95—28no—
116C23×SD16C2×C711yescharacteristic
117C22×#103C2×C711yescharacteristic, complemented
118C22×#102C2×C711yescharacteristic
119C2×#391C2×C711yescharacteristic, complemented
120C2×#390C2×C711yescharacteristic
121C2×#340C2×C711yescharacteristic, complemented
122C2×#336C2×C711yescharacteristic, complemented
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—41no—
127C24×C7—41no—
128C24×C7—41no—
129C24×C7—41no—
130C24×C7—42no—
131C24×C7—42no—
132C24×C7—42no—
133C24×C7—42no—
134C24×C7C2×D411yescharacteristic
135C2×C7×Q8—22no—
136C2×C7×Q8—22no—
137C2×C7×Q8—22no—
138C2×C7×Q8—22no—
139C2×C7×Q8—22no—
140C2×C7×Q8—22no—
141C2×C7×Q8—22no—
142C2×C7×Q8—22no—
143C2×C7×Q8—22no—
144C2×C7×Q8—22no—
145C2×C7×Q8—22no—
146C2×C7×Q8—22no—
147C2×C7×Q8—22no—
148C2×C7×Q8—22no—
149C2×C7×Q8—22no—
150C2×C7×Q8—41no—
151C2×C7×Q8—41no—
152C2×C7×Q8—41no—
153C2×C7×Q8—41no—
154C2×C7×Q8—41no—
155C2×C7×Q8—41no—
156C2×C7×Q8—41no—
157C2×C7×Q8—41no—
158C2×C7×Q8—41no—
159C2×C7×Q8—41no—
160C2×C7×Q8—41no—
161C2×C7×Q8—41no—
162C2×C7×Q8C22⋊C414yescomplemented
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—22no—
170C2×C7×D4—22no—
171C2×C7×D4—22no—
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—41no—
179C2×C7×D4—41no—
180C2×C7×D4—41no—
181C2×C7×D4—41no—
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×D4C22⋊C414yes—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—41no—
203C22×C4×C7—41no—
204C22×C4×C7—41no—
205C22×C4×C7—41no—
206C22×C4×C7—41no—
207C22×C4×C7—41no—
208C22×C4×C7—41no—
209C22×C4×C7—41no—
210C22×C4×C7—42no—
211C22×C4×C7—42no—
212C22×C4×C7—42no—
213C22×C4×C7—42no—
214C22×C4×C7SD1614yescomplemented
215C22×C4×C7C22×C411yescharacteristic
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×C7C2×D411yescharacteristic
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7#4111yescharacteristic
226C22×C4×C7#4111yescharacteristic
227C22×C4×C7#4111yescharacteristic
228C22×C4×C7#4111yescharacteristic
229C7×SD16—232no—
230C2×C7×C8—22no—
231C2×C7×C8—22no—
232C2×C7×C8—22no—
233C2×C7×C8—22no—
234C2×C7×C8—22no—
235C2×C7×C8—22no—
236C2×C7×C8—22no—
237C2×C7×C8—22no—
238C2×C7×C8—22no—
239C2×C7×C8—41no—
240C2×C7×C8—41no—
241C2×C7×C8—41no—
242C2×C7×C8—41no—
243C2×C7×C8C22⋊C414yescomplemented
244C7×C4⋊C4—22no—
245C7×C4⋊C4—22no—
246C7×C4⋊C4—22no—
247C7×C4⋊C4—22no—
248C7×C4⋊C4—41no—
249C7×C4⋊C4—41no—
250C7×C4⋊C4—41no—
251C7×C4⋊C4—41no—
252C7×C22⋊C4—416no—
253C42×C7—41no—
254C42×C7—41no—
255C42×C7—41no—
256C42×C7—41no—
257C23×Q8C22×C711yescharacteristic
258C23×D4C22×C711yescharacteristic
259C22×SD16—22no—
260C22×SD16—22no—
261C22×SD16—22no—
262C22×SD16—22no—
263C22×SD16—22no—
264C22×SD16—22no—
265C22×SD16C4×C714yescomplemented
266C23×C8C22×C711yescharacteristic
267C23×C8C22×C711yescharacteristic
268C22×C4⋊C4C22×C711yescharacteristic
269C22×C4⋊C4C22×C711yescharacteristic
270C22×C22⋊C4—22no—
271C22×C42C22×C711yescharacteristic
272C2×#103—22no—
273C2×#103—22no—
274C2×#103—22no—
275C2×#102—22no—
276C2×#102—22no—
277C2×#102—22no—
278#391—22no—
279#391—22no—
280#390—22no—
281#390—22no—
282C2×#95—22no—
283#340—22no—
284#336—22no—
285C23×C7—24no—
286C23×C7—42no—
287C23×C7—42no—
288C23×C7—42no—
289C23×C7—42no—
290C23×C7—42no—
291C23×C7—42no—
292C23×C7—44no—
293C23×C7—44no—
294C23×C7—44no—
295C23×C7—44no—
296C23×C7—44no—
297C23×C7—44no—
298C23×C7—82no—
299C23×C7—82no—
300C23×C7—82no—
301C23×C7—82no—
302C23×C7—82no—
303C23×C7—82no—
304C23×C7—81no—
305C23×C7—81no—
306C23×C7—81no—
307C23×C7—81no—
308C23×C7C4×D411yescharacteristic
309C23×C7#12011yescharacteristic
310C23×C7#12011yescharacteristic
311C23×C7#12111yescharacteristic
312C23×C7#12111yescharacteristic
313C23×C7#12111yescharacteristic
314C23×C7#12711yescharacteristic
315C23×C7C2×SD1612yes—
316C23×C7#13512yes—
317C23×C7AGL(1,ℤ/8)12yes—
318C23×C7#13712yes—
319C7×Q8—24no—
320C7×Q8—24no—
321C7×Q8—42no—
322C7×Q8—42no—
323C7×Q8—42no—
324C7×Q8—42no—
325C7×Q8—42no—
326C7×Q8—42no—
327C7×D4—24no—
328C7×D4—24no—
329C7×D4—42no—
330C7×D4—42no—
331C7×D4—42no—
332C7×D4—42no—
333C7×D4—42no—
334C7×D4—42no—
335C2×C4×C7—24no—
336C2×C4×C7—24no—
337C2×C4×C7—24no—
338C2×C4×C7—24no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—42no—
342C2×C4×C7—42no—
343C2×C4×C7—42no—
344C2×C4×C7—42no—
345C2×C4×C7—42no—
346C2×C4×C7—42no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7—42no—
350C2×C4×C7—42no—
351C2×C4×C7—44no—
352C2×C4×C7—44no—
353C2×C4×C7—82no—
354C2×C4×C7—82no—
355C2×C4×C7—81no—
356C2×C4×C7—81no—
357C2×C4×C7—81no—
358C2×C4×C7—81no—
359C2×C4×C7C2×C22⋊C411yescharacteristic
360C2×C4×C7C2×C22⋊C411yescharacteristic
361C2×C4×C7C2×C22⋊C411yescharacteristic
362C2×C4×C7C4×D411yescharacteristic
363C2×C4×C7C4×D411yescharacteristic
364C2×C4×C7C4×D411yescharacteristic
365C2×C4×C7#12011yescharacteristic
366C2×C4×C7#12011yescharacteristic
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#12111yescharacteristic
378C2×C4×C7#12111yescharacteristic
379C2×C4×C7#12111yescharacteristic
380C2×C4×C7#12311yescharacteristic
381C2×C4×C7#12311yescharacteristic
382C2×C4×C7#12311yescharacteristic
383C2×C4×C7#12311yescharacteristic
384C2×C4×C7#12411yescharacteristic
385C2×C4×C7#12411yescharacteristic
386C2×C4×C7#12711yescharacteristic
387C7×C8—24no—
388C7×C8—42no—
389C25—21no—
390C22×Q8—21no—
391C22×Q8—21no—
392C22×Q8—21no—
393C22×Q8—21no—
394C22×Q8—21no—
395C22×Q8—21no—
396C22×Q8—21no—
397C22×Q8—21no—
398C22×Q8—21no—
399C22×Q8—21no—
400C22×Q8—21no—
401C22×Q8C2×C4×C712yes—
402C22×Q8C7×D412yes—
403C22×Q8C7×D412yes—
404C22×D4—21no—
405C22×D4—21no—
406C22×D4—21no—
407C22×D4—21no—
408C22×D4—21no—
409C22×D4—21no—
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—21no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4C2×C4×C712yes—
416C22×D4C7×D412yes—
417C22×D4C7×D412yes—
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—21no—
421C23×C4C7×D412yes—
422C23×C4C23×C711yescharacteristic
423C2×SD16—28no—
424C2×SD16—28no—
425C2×SD16—28no—
426C2×SD16—28no—
427C2×SD16—28no—
428C2×SD16—28no—
429C2×SD16—28no—
430C22×C8—21no—
431C22×C8—21no—
432C22×C8—21no—
433C22×C8—21no—
434C22×C8—21no—
435C22×C8—21no—
436C22×C8—21no—
437C22×C8—21no—
438C22×C8—21no—
439C22×C8—21no—
440C22×C8C2×C4×C712yes—
441C22×C8C7×D412yes—
442C22×C8C7×D412yes—
443C22×C8C7×D412yes—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4C7×D412yes—
455C2×C4⋊C4C7×D412yes—
456C2×C22⋊C4—28no—
457C2×C22⋊C4—44no—
458C2×C22⋊C4—44no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465#103—28no—
466#102—28no—
467#95—28no—
468C22×C7—48no—
469C22×C7—44no—
470C22×C7—84no—
471C22×C7—84no—
472C22×C7—82no—
473C22×C7—82no—
474C22×C7—84no—
475C22×C7—82no—
476C22×C7—82no—
477C22×C7—82no—
478C22×C7—82no—
479C22×C7#38611yescharacteristic
480C22×C7#38611yescharacteristic
481C22×C7#39011yescharacteristic
482C22×C7#39211yescharacteristic
483C22×C7#39211yescharacteristic
484C22×C7#39211yescharacteristic
485C22×C7#39411yescharacteristic
486C22×C7C4×SD1612yes—
487C22×C7#44012yes—
488C22×C7#44812yes—
489C22×C7#44912yes—
490C22×C7#45012yes—
491C22×C7#45212yes—
492C22×C7#46012yes—
493C22×C7#46112yes—
494C22×C7#46312yes—
495C22×C7#46412yes—
496C22×C7#46512yes—
497C22×C7#46812yes—
498C22×C7#49211yescharacteristic
499C22×C7#49511yescharacteristic
500C22×C7#49611yescharacteristic
501C22×C7#49711yescharacteristic
502C4×C7—44no—
503C4×C7—44no—
504C4×C7—82no—
505C4×C7—82no—
506C4×C7#37911yescharacteristic
507C4×C7#38611yescharacteristic
508C4×C7#38611yescharacteristic
509C4×C7#39011yescharacteristic
510C4×C7#39211yescharacteristic
511C4×C7#39411yescharacteristic
512C4×C7#39411yescharacteristic
513C4×C7#39411yescharacteristic
514C24—22no—
515C24—22no—
516C24—22no—
517C24—41no—
518C24—41no—
519C24—41no—
520C24—41no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24—42no—
525C24C2×C7×D411yescharacteristic
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8C7×C22⋊C414yescomplemented
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—22no—
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—41no—
581C2×D4C7×C22⋊C414yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4C7×SD1614yescomplemented
606C22×C4C22×C4×C711yescharacteristic
607C22×C4C2×C7×D411yescharacteristic
608C22×C4C2×C7×D411yescharacteristic
609C22×C4C2×C7×D411yescharacteristic
610C22×C4C2×C7×D411yescharacteristic
611C22×C4C2×C7×D411yescharacteristic
612C22×C4C2×C7×D411yescharacteristic
613C22×C4C2×C7×D411yescharacteristic
614C22×C4C2×C7×D411yescharacteristic
615C22×C4C2×C7×D411yescharacteristic
616C22×C4C7×#4111yescharacteristic
617C22×C4C7×#4111yescharacteristic
618C22×C4C7×#4111yescharacteristic
619C22×C4C7×#4111yescharacteristic
620SD16—232no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8C7×C22⋊C414yescomplemented
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C22⋊C4—416no—
644C42—41no—
645C42—41no—
646C42—41no—
647C42—41no—
648C2×C7—84no—
649C2×C7#143811yescharacteristic
650C2×C7#187712yes—
651C2×C7#188012yes—
652C2×C7#196811yescharacteristic
653C2×C7#197311yescharacteristic
654C2×C7#200012yes—
655C2×C7#201211yescharacteristic
656C2×C7#201311yescharacteristic
657C2×C7#201411yescharacteristic
658C2×C7#201511yescharacteristic
659C2×C7#205512yes—
660C23—24no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—82no—
674C23—81no—
675C23—81no—
676C23—81no—
677C23—81no—
678C23—82no—
679C23—82no—
680C23—82no—
681C23—82no—
682C23—82no—
683C23C4×C7×D411yescharacteristic
684C23C7×#12011yescharacteristic
685C23C7×#12011yescharacteristic
686C23C7×#12111yescharacteristic
687C23C7×#12111yescharacteristic
688C23C7×#12111yescharacteristic
689C23C7×#12711yescharacteristic
690C23C2×C7×SD1612yes—
691C23C7×#13512yes—
692C23C7×AGL(1,ℤ/8)12yes—
693C23C7×#13712yes—
694Q8—24no—
695Q8—24no—
696Q8—42no—
697Q8—42no—
698Q8—42no—
699Q8—42no—
700Q8—42no—
701Q8—42no—
702D4—24no—
703D4—24no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4C2×C7×C22⋊C411yescharacteristic
735C2×C4C2×C7×C22⋊C411yescharacteristic
736C2×C4C2×C7×C22⋊C411yescharacteristic
737C2×C4C4×C7×D411yescharacteristic
738C2×C4C4×C7×D411yescharacteristic
739C2×C4C4×C7×D411yescharacteristic
740C2×C4C7×#12011yescharacteristic
741C2×C4C7×#12011yescharacteristic
742C2×C4C7×#12011yescharacteristic
743C2×C4C7×#12011yescharacteristic
744C2×C4C7×#12011yescharacteristic
745C2×C4C7×#12011yescharacteristic
746C2×C4C7×#12111yescharacteristic
747C2×C4C7×#12111yescharacteristic
748C2×C4C7×#12111yescharacteristic
749C2×C4C7×#12111yescharacteristic
750C2×C4C7×#12111yescharacteristic
751C2×C4C7×#12111yescharacteristic
752C2×C4C7×#12111yescharacteristic
753C2×C4C7×#12111yescharacteristic
754C2×C4C7×#12111yescharacteristic
755C2×C4C7×#12311yescharacteristic
756C2×C4C7×#12311yescharacteristic
757C2×C4C7×#12311yescharacteristic
758C2×C4C7×#12311yescharacteristic
759C2×C4C7×#12411yescharacteristic
760C2×C4C7×#12411yescharacteristic
761C2×C4C7×#12711yescharacteristic
762C8—24no—
763C8—42no—
764C7#1102311yescharacteristic, direct product factor, Sylow
765C22—48no—
766C22—44no—
767C22—82no—
768C22—82no—
769C22—84no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—84no—
775C22—84no—
776C22C7×#38611yescharacteristic
777C22C7×#38611yescharacteristic
778C22C7×#39011yescharacteristic
779C22C7×#39211yescharacteristic
780C22C7×#39211yescharacteristic
781C22C7×#39211yescharacteristic
782C22C7×#39411yescharacteristic
783C22C4×C7×SD1612yes—
784C22C7×#44012yes—
785C22C7×#44812yes—
786C22C7×#44912yes—
787C22C7×#45012yes—
788C22C7×#45212yes—
789C22C7×#46012yes—
790C22C7×#46112yes—
791C22C7×#46312yes—
792C22C7×#46412yes—
793C22C7×#46512yes—
794C22C7×#46812yes—
795C22C7×#49211yescharacteristic
796C22C7×#49511yescharacteristic
797C22C7×#49611yescharacteristic
798C22C7×#49711yescharacteristic
799C4—44no—
800C4—44no—
801C4—82no—
802C4—82no—
803C4C7×#37911yescharacteristic
804C4C7×#38611yescharacteristic
805C4C7×#38611yescharacteristic
806C4C7×#39011yescharacteristic
807C4C7×#39211yescharacteristic
808C4C7×#39411yescharacteristic
809C4C7×#39411yescharacteristic
810C4C7×#39411yescharacteristic
811C2—84no—
812C2C7×#143811yescharacteristic
813C2C7×#187712yes—
814C2C7×#188012yes—
815C2C7×#196811yescharacteristic
816C2C7×#197311yescharacteristic
817C2C7×#200012yes—
818C2C7×#201211yescharacteristic
819C2C7×#201311yescharacteristic
820C2C7×#201411yescharacteristic
821C2C7×#201511yescharacteristic
822C2C7×#205512yes—
subgroupG/H
center, socleC24×C7C2×D4
commutatorC22×C4C22×C4×C7
Frattini, cosocleC23×C4C23×C7
prime radicalC23×C7×D4C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C7 ◁ C22×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C7×#103C2semidirect
4. C2×C7×#391C2semidirect
6. C2×C7×#340C2semidirect
7. C2×C7×#336C2semidirect
16. C22×C7×SD16C4semidirect
36. #11023C7direct (N × H)
117. C22×#103C2×C7semidirect
119. C2×#391C2×C7semidirect
121. C2×#340C2×C7semidirect
122. C2×#336C2×C7semidirect
162. C2×C7×Q8C22⋊C4semidirect
214. C22×C4×C7SD16semidirect
243. C2×C7×C8C22⋊C4semidirect
265. C22×SD16C4×C7semidirect
553. C2×Q8C7×C22⋊C4semidirect
605. C22×C4C7×SD16semidirect
634. C2×C8C7×C22⋊C4semidirect
764. C7#11023direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×SD162
C22×C7×#1032
C22×C7×#1022
C2×C7×#3912
C2×C7×#3902
C2×C7×#3402
C2×C7×#3362
#110237