Finite Group Databasebeta

← C7×#24519 #13201735

Subgroups — C7×#24519 #13201735

Order 1792.

986 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#449C211yesmaximal, characteristic
2C2×C7×#433C211yesmaximal, characteristic, complemented
3C7×#2624C211yesmaximal, characteristic, complemented
4C7×#2311C211yesmaximal, characteristic, complemented
5C7×#2066C211yesmaximal, characteristic, complemented
6C7×#2065C211yesmaximal, characteristic, complemented
7C7×#2055C211yesmaximal, characteristic, complemented
8C7×#2054C211yesmaximal, characteristic, complemented
9C7×#1972C211yesmaximal, characteristic, complemented
10C7×#1968C211yesmaximal, characteristic, complemented
11C7×#1935C211yesmaximal, characteristic, complemented
12C7×#1934C211yesmaximal, characteristic, complemented
13C7×#1874C211yesmaximal, characteristic, complemented
14C7×#1853C211yesmaximal, characteristic, complemented
15C7×#1788C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×SD16C2211yescharacteristic
18C22×C7×D8C2211yescharacteristic
19C2×C7×#121C2211yescharacteristic
20C2×C7×#117C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C7×#449—24no—
23C7×#433—24no—
24C2×C7×#106C2211yescharacteristic
25C2×C7×#106C2211yescharacteristic
26C2×C7×C4⋊C8C2211yescharacteristic
27C2×C7×C4⋊C8C2211yescharacteristic
28C2×C7×#103C2211yescharacteristic
29C2×C7×#103C2211yescharacteristic
30C2×C7×#103C2211yescharacteristic
31C2×C7×#102C2211yescharacteristic
32C2×C7×#102C2211yescharacteristic
33C2×C7×#102C2211yescharacteristic
34C2×C7×#102C2211yescharacteristic
35C2×C7×#102C2211yescharacteristic
36C2×C7×C22⋊C8C2211yescharacteristic
37C2×C7×C22⋊C8C2211yescharacteristic
38C2×C7×#97C2211yescharacteristic
39C2×C4×C7×C8C2211yescharacteristic
40C7×#399—21no—
41C7×#397—21no—
42C7×#394—21no—
43C7×#394—21no—
44C7×#391C2211yescharacteristic
45C7×#391C2211yescharacteristic
46C7×#390C2211yescharacteristic
47C7×#390C2211yescharacteristic
48C7×#390C2211yescharacteristic
49C7×#390C2211yescharacteristic
50C7×#389C2211yescharacteristic
51C7×#389C2211yescharacteristic
52C7×#386—21no—
53C7×#386—21no—
54C7×#380—21no—
55C7×#380—21no—
56C7×#380C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#340C2211yescharacteristic
60C7×#340C2211yescharacteristic
61#24519C711yesmaximal, characteristic, direct product factor, Sylow
62C2×C7×#41—22no—
63C2×C7×#41—22no—
64C2×C7×#41—22no—
65C2×C7×#41—22no—
66C2×C7×#41—41no—
67C2×C7×#41—41no—
68C22×C7×Q8C2311yescharacteristic
69C22×C7×D4—21no—
70C22×C7×D4—21no—
71C22×C7×D4C2311yescharacteristic
72C22×C7×D4C2311yescharacteristic
73C23×C4×C7—21no—
74C23×C4×C7—21no—
75C23×C4×C7C2311yescharacteristic
76C2×C7×SD16—22no—
77C2×C7×SD16—22no—
78C2×C7×SD16—41no—
79C2×C7×D8—22no—
80C2×C7×D8—22no—
81C2×C7×D8—41no—
82C22×C7×C8C2311yescharacteristic
83C22×C7×C8C2311yescharacteristic
84C22×C7×C8C2311yescharacteristic
85C22×C7×C8C2311yescharacteristic
86C7×#121—22no—
87C7×#121—22no—
88C7×#117—22no—
89C7×#117—22no—
90C2×C7×C4⋊C4—21no—
91C2×C7×C4⋊C4—21no—
92C2×C7×C4⋊C4—21no—
93C2×C7×C4⋊C4—41no—
94C2×C7×C4⋊C4—41no—
95C2×C7×C4⋊C4D411yescharacteristic
96C2×C7×C4⋊C4D411yescharacteristic
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C22⋊C4—21no—
103C2×C7×C22⋊C4—21no—
104C2×C7×C22⋊C4—21no—
105C2×C7×C22⋊C4—21no—
106C2×C7×C22⋊C4—21no—
107C2×C7×C22⋊C4—21no—
108C2×C7×C22⋊C4—21no—
109C2×C7×C22⋊C4—21no—
110C2×C7×C22⋊C4—21no—
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4D411yescharacteristic
113C2×C7×C22⋊C4D411yescharacteristic
114C2×C42×C7C2311yescharacteristic
115C2×C42×C7C2311yescharacteristic
116C7×#106—41no—
117C7×#106—41no—
118C7×C4⋊C8—22no—
119C7×C4⋊C8—22no—
120C7×#103—22no—
121C7×#103—22no—
122C7×#103—41no—
123C7×#102—22no—
124C7×#102—22no—
125C7×#102—41no—
126C7×#102—41no—
127C7×#102—41no—
128C7×C22⋊C8—22no—
129C7×C22⋊C8D414yes—
130C7×#97—22no—
131C4×C7×C8—22no—
132C7×#95—21no—
133C7×#95—21no—
134C7×#95—21no—
135C7×#95—21no—
136C7×#95—21no—
137C7×#95—21no—
138C7×#95—21no—
139C2×#449C2×C711yescharacteristic
140C2×#433C2×C711yescharacteristic, complemented
141#2624C2×C711yescharacteristic, complemented
142#2311C2×C711yescharacteristic, complemented
143#2066C2×C711yescharacteristic, complemented
144#2065C2×C711yescharacteristic, complemented
145#2055C2×C711yescharacteristic, complemented
146#2054C2×C711yescharacteristic, complemented
147#1972C2×C711yescharacteristic, complemented
148#1968C2×C711yescharacteristic, complemented
149#1935C2×C711yescharacteristic, complemented
150#1934C2×C711yescharacteristic, complemented
151#1874C2×C711yescharacteristic, complemented
152#1853C2×C711yescharacteristic, complemented
153#1788C2×C711yescharacteristic, complemented
154C24×C7—21no—
155C24×C7—21no—
156C24×C7C2×D411yescharacteristic
157C7×#41—44no—
158C7×#41—44no—
159C7×#41—44no—
160C7×#41—44no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8#4112yes—
167C2×C7×D4—24no—
168C2×C7×D4—21no—
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—21no—
175C2×C7×D4—21no—
176C2×C7×D4—21no—
177C2×C7×D4—21no—
178C2×C7×D4—21no—
179C2×C7×D4—42no—
180C2×C7×D4—42no—
181C2×C7×D4—42no—
182C2×C7×D4—81no—
183C2×C7×D4—81no—
184C2×C7×D4#4112yes—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—24no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—42no—
197C22×C4×C7—42no—
198C22×C4×C7—42no—
199C22×C4×C7—81no—
200C22×C4×C7—81no—
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7C2×D411yescharacteristic
203C22×C4×C7C2×D411yescharacteristic
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D412yes—
207C22×C4×C7#4112yes—
208C22×C4×C7C2411yescharacteristic
209C7×SD16—44no—
210C7×D8—44no—
211C2×C7×C8—21no—
212C2×C7×C8—21no—
213C2×C7×C8—21no—
214C2×C7×C8—21no—
215C2×C7×C8—21no—
216C2×C7×C8—21no—
217C2×C7×C8—21no—
218C2×C7×C8—21no—
219C2×C7×C8—21no—
220C2×C7×C8—21no—
221C2×C7×C8C2×D412yes—
222C2×C7×C8C2×D412yes—
223C7×C4⋊C4—22no—
224C7×C4⋊C4—22no—
225C7×C4⋊C4—21no—
226C7×C4⋊C4—21no—
227C7×C4⋊C4—21no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—21no—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—21no—
233C7×C4⋊C4—21no—
234C7×C4⋊C4—21no—
235C7×C4⋊C4—42no—
236C7×C4⋊C4—81no—
237C7×C4⋊C4—81no—
238C7×C22⋊C4—22no—
239C7×C22⋊C4—22no—
240C7×C22⋊C4—42no—
241C7×C22⋊C4—81no—
242C7×C22⋊C4—81no—
243C7×C22⋊C4—81no—
244C7×C22⋊C4—81no—
245C7×C22⋊C4—81no—
246C7×C22⋊C4—81no—
247C7×C22⋊C4—81no—
248C7×C22⋊C4—81no—
249C7×C22⋊C4—81no—
250C42×C7—21no—
251C42×C7—21no—
252C42×C7—21no—
253C42×C7—21no—
254C22×#41C22×C711yescharacteristic
255C22×SD16C22×C711yescharacteristic
256C22×D8C22×C711yescharacteristic
257C2×#121C22×C711yescharacteristic
258C2×#117C22×C711yescharacteristic
259C22×C4⋊C4C22×C711yescharacteristic
260#449—24no—
261#433—24no—
262C2×#106C22×C711yescharacteristic
263C2×#106C22×C711yescharacteristic
264C2×C4⋊C8C22×C711yescharacteristic
265C2×C4⋊C8C22×C711yescharacteristic
266C2×#103C22×C711yescharacteristic
267C2×#103C22×C711yescharacteristic
268C2×#103C22×C711yescharacteristic
269C2×#102C22×C711yescharacteristic
270C2×#102C22×C711yescharacteristic
271C2×#102C22×C711yescharacteristic
272C2×#102C22×C711yescharacteristic
273C2×#102C22×C711yescharacteristic
274C2×C22⋊C8C22×C711yescharacteristic
275C2×C22⋊C8C22×C711yescharacteristic
276C2×#97C22×C711yescharacteristic
277C2×C4×C8C22×C711yescharacteristic
278#399—21no—
279#397—21no—
280#394—21no—
281#394—21no—
282#391C22×C711yescharacteristic
283#391C22×C711yescharacteristic
284#390C22×C711yescharacteristic
285#390C22×C711yescharacteristic
286#390C22×C711yescharacteristic
287#390C22×C711yescharacteristic
288#389C22×C711yescharacteristic
289#389C22×C711yescharacteristic
290#386—21no—
291#386—21no—
292#380—21no—
293#380—21no—
294#380C22×C711yescharacteristic
295#340C22×C711yescharacteristic
296#340C22×C711yescharacteristic
297#340C22×C711yescharacteristic
298#340C22×C711yescharacteristic
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—22no—
306C23×C7—41no—
307C23×C7—41no—
308C23×C7—41no—
309C23×C7—41no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7#12112yes—
320C23×C7C22×D411yescharacteristic
321C7×Q8—22no—
322C7×Q8—22no—
323C7×Q8—41no—
324C7×Q8—41no—
325C7×D4—22no—
326C7×D4—22no—
327C7×D4—48no—
328C7×D4—41no—
329C7×D4—41no—
330C7×D4—41no—
331C7×D4—41no—
332C7×D4—41no—
333C7×D4—41no—
334C7×D4—84no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—22no—
346C2×C4×C7—21no—
347C2×C4×C7—21no—
348C2×C4×C7—21no—
349C2×C4×C7—21no—
350C2×C4×C7—21no—
351C2×C4×C7—21no—
352C2×C4×C7—21no—
353C2×C4×C7—21no—
354C2×C4×C7—48no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7—41no—
371C2×C4×C7—41no—
372C2×C4×C7—84no—
373C2×C4×C7#12112yes—
374C2×C4×C7C22×D411yescharacteristic
375C2×C4×C7C2×#4111yescharacteristic
376C2×C4×C7C2×#4111yescharacteristic
377C2×C4×C7C2×#4111yescharacteristic
378C2×C4×C7H(5,𝔽2)11yescharacteristic
379C2×C4×C7H(5,𝔽2)11yescharacteristic
380C7×C8—22no—
381C7×C8—22no—
382C7×C8—41no—
383C7×C8—41no—
384C2×#41—22no—
385C2×#41—22no—
386C2×#41—22no—
387C2×#41—22no—
388C2×#41—41no—
389C2×#41—41no—
390C22×Q8C23×C711yescharacteristic
391C22×D4—21no—
392C22×D4—21no—
393C22×D4C23×C711yescharacteristic
394C22×D4C23×C711yescharacteristic
395C23×C4—21no—
396C23×C4—21no—
397C23×C4C23×C711yescharacteristic
398C2×SD16—22no—
399C2×SD16—22no—
400C2×SD16—41no—
401C2×D8—22no—
402C2×D8—22no—
403C2×D8—41no—
404C22×C8C23×C711yescharacteristic
405C22×C8C23×C711yescharacteristic
406C22×C8C23×C711yescharacteristic
407C22×C8C23×C711yescharacteristic
408#121—22no—
409#121—22no—
410#117—22no—
411#117—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—41no—
417C2×C4⋊C4C7×D411yescharacteristic
418C2×C4⋊C4C7×D411yescharacteristic
419C2×C4⋊C4C23×C711yescharacteristic
420C2×C4⋊C4C23×C711yescharacteristic
421C2×C4⋊C4C23×C711yescharacteristic
422C2×C4⋊C4C23×C711yescharacteristic
423C2×C4⋊C4C23×C711yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4C7×D411yescharacteristic
435C2×C22⋊C4C7×D411yescharacteristic
436C2×C42C23×C711yescharacteristic
437C2×C42C23×C711yescharacteristic
438#106—41no—
439#106—41no—
440C4⋊C8—22no—
441C4⋊C8—22no—
442#103—22no—
443#103—22no—
444#103—41no—
445#102—22no—
446#102—22no—
447#102—41no—
448#102—41no—
449#102—41no—
450C22⋊C8—22no—
451C22⋊C8C7×D414yes—
452#97—22no—
453C4×C8—22no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461C22×C7—22no—
462C22×C7—22no—
463C22×C7—22no—
464C22×C7—41no—
465C22×C7—41no—
466C22×C7—41no—
467C22×C7—41no—
468C22×C7—42no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7—81no—
472C22×C7—81no—
473C22×C7—81no—
474C22×C7—81no—
475C22×C7—81no—
476C22×C7—81no—
477C22×C7—81no—
478C22×C7—81no—
479C22×C7—81no—
480C22×C7—81no—
481C22×C7—81no—
482C22×C7C2×#12111yescharacteristic
483C22×C7#52511yescharacteristic
484C22×C7#53511yescharacteristic
485C22×C7#57611yescharacteristic
486C22×C7#57711yescharacteristic
487C22×C7#57711yescharacteristic
488C22×C7#57711yescharacteristic
489C4×C7—22no—
490C4×C7—42no—
491C4×C7—41no—
492C4×C7—41no—
493C4×C7—41no—
494C4×C7—41no—
495C4×C7—81no—
496C4×C7—81no—
497C4×C7—81no—
498C4×C7—81no—
499C4×C7—81no—
500C4×C7#54611yescharacteristic
501C4×C7#54611yescharacteristic
502C4×C7#55111yescharacteristic
503C4×C7#55111yescharacteristic
504C24—21no—
505C24—21no—
506C24C2×C7×D411yescharacteristic
507#41—44no—
508#41—44no—
509#41—44no—
510#41—44no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8C7×#4112yes—
517C2×D4—24no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4C7×#4112yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—24no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4C2×C7×D411yescharacteristic
552C22×C4C2×C7×D411yescharacteristic
553C22×C4C2×C7×D411yescharacteristic
554C22×C4C2×C7×D411yescharacteristic
555C22×C4C2×C7×D411yescharacteristic
556C22×C4C2×C7×D412yes—
557C22×C4C7×#4112yes—
558C22×C4C24×C711yescharacteristic
559SD16—44no—
560D8—44no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8C2×C7×D412yes—
572C2×C8C2×C7×D412yes—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—42no—
586C4⋊C4—81no—
587C4⋊C4—81no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C22⋊C4—81no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—81no—
599C22⋊C4—81no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—21no—
604C2×C7—42no—
605C2×C7—82no—
606C2×C7—161no—
607C2×C7#241111yescharacteristic
608C2×C7#306011yescharacteristic
609C2×C7#306211yescharacteristic
610C2×C7#311911yescharacteristic
611C2×C7#312511yescharacteristic
612C2×C7#322111yescharacteristic
613C2×C7#322411yescharacteristic
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—22no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23C7×#12112yes—
635C23C22×C7×D411yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—41no—
639Q8—41no—
640D4—22no—
641D4—22no—
642D4—48no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—84no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—48no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—84no—
688C2×C4C7×#12112yes—
689C2×C4C22×C7×D411yescharacteristic
690C2×C4C2×C7×#4111yescharacteristic
691C2×C4C2×C7×#4111yescharacteristic
692C2×C4C2×C7×#4111yescharacteristic
693C2×C4C7×H(5,𝔽2)11yescharacteristic
694C2×C4C7×H(5,𝔽2)11yescharacteristic
695C8—22no—
696C8—22no—
697C8—41no—
698C8—41no—
699C7#2451911yescharacteristic, direct product factor, Sylow
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22C2×C7×#12111yescharacteristic
722C22C7×#52511yescharacteristic
723C22C7×#53511yescharacteristic
724C22C7×#57611yescharacteristic
725C22C7×#57711yescharacteristic
726C22C7×#57711yescharacteristic
727C22C7×#57711yescharacteristic
728C4—22no—
729C4—42no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—81no—
735C4—81no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4C7×#54611yescharacteristic
740C4C7×#54611yescharacteristic
741C4C7×#55111yescharacteristic
742C4C7×#55111yescharacteristic
743C2—42no—
744C2—82no—
745C2—161no—
746C2C7×#241111yescharacteristic
747C2C7×#306011yescharacteristic
748C2C7×#306211yescharacteristic
749C2C7×#311911yescharacteristic
750C2C7×#312511yescharacteristic
751C2C7×#322111yescharacteristic
752C2C7×#322411yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#433C2semidirect
3. C7×#2624C2semidirect
4. C7×#2311C2semidirect
5. C7×#2066C2semidirect
6. C7×#2065C2semidirect
7. C7×#2055C2semidirect
8. C7×#2054C2semidirect
9. C7×#1972C2semidirect
10. C7×#1968C2semidirect
11. C7×#1935C2semidirect
12. C7×#1934C2semidirect
13. C7×#1874C2semidirect
14. C7×#1853C2semidirect
15. C7×#1788C2semidirect
61. #24519C7direct (N × H)
140. C2×#433C2×C7semidirect
141. #2624C2×C7semidirect
142. #2311C2×C7semidirect
143. #2066C2×C7semidirect
144. #2065C2×C7semidirect
145. #2055C2×C7semidirect
146. #2054C2×C7semidirect
147. #1972C2×C7semidirect
148. #1968C2×C7semidirect
149. #1935C2×C7semidirect
150. #1934C2×C7semidirect
151. #1874C2×C7semidirect
152. #1853C2×C7semidirect
153. #1788C2×C7semidirect
699. C7#24519direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4492
C2×C7×#4332
C7×#26242
C7×#23112
C7×#20662
C7×#20652
C7×#20552
C7×#20542
C7×#19722
C7×#19682
C7×#19352
C7×#19342
C7×#18742
C7×#18532
C7×#17882
#245197