Finite Group Databasebeta

← C7×#24515 #13201731

Subgroups — C7×#24515 #13201731

Order 1792.

944 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#452C211yesmaximal, characteristic
2C2×C7×#433C211yesmaximal, characteristic, complemented
3C7×#2625C211yesmaximal, characteristic, complemented
4C7×#2311C211yesmaximal, characteristic
5C7×#2068C211yesmaximal, characteristic, complemented
6C7×#2067C211yesmaximal, characteristic, complemented
7C7×#2056C211yesmaximal, characteristic, complemented
8C7×#2055C211yesmaximal, characteristic, complemented
9C7×#1973C211yesmaximal, characteristic, complemented
10C7×#1969C211yesmaximal, characteristic, complemented
11C7×#1935C211yesmaximal, characteristic, complemented
12C7×#1934C211yesmaximal, characteristic, complemented
13C7×#1872C211yesmaximal, characteristic, complemented
14C7×#1852C211yesmaximal, characteristic, complemented
15C7×#1788C211yesmaximal, characteristic
16C22×C7×#41C2211yescharacteristic
17C22×C7×Q16C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×#117C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C7×#452—24no—
23C7×#433—24no—
24C2×C7×#107C2211yescharacteristic
25C2×C7×#107C2211yescharacteristic
26C2×C7×C4⋊C8C2211yescharacteristic
27C2×C7×C4⋊C8C2211yescharacteristic
28C2×C7×#103C2211yescharacteristic
29C2×C7×#103C2211yescharacteristic
30C2×C7×#103C2211yescharacteristic
31C2×C7×#103C2211yescharacteristic
32C2×C7×#103C2211yescharacteristic
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×#400—21no—
41C7×#398—21no—
42C7×#397—21no—
43C7×#397—21no—
44C7×#391C2211yescharacteristic
45C7×#391C2211yescharacteristic
46C7×#391C2211yescharacteristic
47C7×#391C2211yescharacteristic
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#24515C711yesmaximal, 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×Q8C2311yescharacteristic
70C22×C7×D4—21no—
71C22×C7×D4C2311yescharacteristic
72C23×C4×C7—21no—
73C23×C4×C7—21no—
74C23×C4×C7C2311yescharacteristic
75C2×C7×Q16—22no—
76C2×C7×Q16—22no—
77C2×C7×Q16—41no—
78C2×C7×SD16—22no—
79C2×C7×SD16—22no—
80C2×C7×SD16—41no—
81C22×C7×C8C2311yescharacteristic
82C22×C7×C8C2311yescharacteristic
83C22×C7×C8C2311yescharacteristic
84C22×C7×C8C2311yescharacteristic
85C7×C22⋊Q8—22no—
86C7×C22⋊Q8—22no—
87C7×#117—22no—
88C7×#117—22no—
89C2×C7×C4⋊C4—21no—
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⋊C4D411yescharacteristic
109C2×C7×C22⋊C4D411yescharacteristic
110C2×C42×C7C2311yescharacteristic
111C2×C42×C7C2311yescharacteristic
112C7×#107—41no—
113C7×#107—41no—
114C7×C4⋊C8—22no—
115C7×C4⋊C8—22no—
116C7×#103—22no—
117C7×#103—22no—
118C7×#103—41no—
119C7×#103—41no—
120C7×#103—41no—
121C7×#102—22no—
122C7×#102—22no—
123C7×#102—41no—
124C7×C22⋊C8—22no—
125C7×C22⋊C8D414yes—
126C7×#97—22no—
127C4×C7×C8—22no—
128C7×#95—21no—
129C7×#95—21no—
130C7×#95—21no—
131C7×#95—21no—
132C7×#95—21no—
133C7×#95—21no—
134C7×#95—21no—
135C7×#95—21no—
136C7×#95—21no—
137C7×#95—21no—
138C7×#95—21no—
139C2×#452C2×C711yescharacteristic
140C2×#433C2×C711yescharacteristic, complemented
141#2625C2×C711yescharacteristic, complemented
142#2311C2×C711yescharacteristic
143#2068C2×C711yescharacteristic, complemented
144#2067C2×C711yescharacteristic, complemented
145#2056C2×C711yescharacteristic, complemented
146#2055C2×C711yescharacteristic, complemented
147#1973C2×C711yescharacteristic, complemented
148#1969C2×C711yescharacteristic, complemented
149#1935C2×C711yescharacteristic, complemented
150#1934C2×C711yescharacteristic, complemented
151#1872C2×C711yescharacteristic, complemented
152#1852C2×C711yescharacteristic, complemented
153#1788C2×C711yescharacteristic
154C24×C7—21no—
155C24×C7C2×D411yescharacteristic
156C7×#41—44no—
157C7×#41—44no—
158C7×#41—44no—
159C7×#41—44no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8—21no—
171C2×C7×Q8#4112yes—
172C2×C7×D4—24no—
173C2×C7×D4—21no—
174C2×C7×D4—21no—
175C2×C7×D4—21no—
176C2×C7×D4—21no—
177C2×C7×D4—21no—
178C2×C7×D4—42no—
179C2×C7×D4—42no—
180C2×C7×D4#4112yes—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—24no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—42no—
194C22×C4×C7—42no—
195C22×C4×C7—42no—
196C22×C4×C7—81no—
197C22×C4×C7—81no—
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7C2×D411yescharacteristic
203C22×C4×C7C2×D412yes—
204C22×C4×C7#4112yes—
205C22×C4×C7C2411yescharacteristic
206C7×Q16—44no—
207C7×SD16—44no—
208C2×C7×C8—21no—
209C2×C7×C8—21no—
210C2×C7×C8—21no—
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×C8C2×D412yes—
219C2×C7×C8C2×D412yes—
220C7×C4⋊C4—22no—
221C7×C4⋊C4—22no—
222C7×C4⋊C4—21no—
223C7×C4⋊C4—21no—
224C7×C4⋊C4—21no—
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—42no—
233C7×C4⋊C4—42no—
234C7×C4⋊C4—81no—
235C7×C4⋊C4—81no—
236C7×C22⋊C4—22no—
237C7×C22⋊C4—22no—
238C7×C22⋊C4—42no—
239C7×C22⋊C4—81no—
240C7×C22⋊C4—81no—
241C7×C22⋊C4—81no—
242C7×C22⋊C4—81no—
243C7×C22⋊C4—81no—
244C42×C7—21no—
245C42×C7—21no—
246C42×C7—21no—
247C42×C7—21no—
248C22×#41C22×C711yescharacteristic
249C22×Q16C22×C711yescharacteristic
250C22×SD16C22×C711yescharacteristic
251C2×C22⋊Q8C22×C711yescharacteristic
252C2×#117C22×C711yescharacteristic
253C22×C4⋊C4C22×C711yescharacteristic
254#452—24no—
255#433—24no—
256C2×#107C22×C711yescharacteristic
257C2×#107C22×C711yescharacteristic
258C2×C4⋊C8C22×C711yescharacteristic
259C2×C4⋊C8C22×C711yescharacteristic
260C2×#103C22×C711yescharacteristic
261C2×#103C22×C711yescharacteristic
262C2×#103C22×C711yescharacteristic
263C2×#103C22×C711yescharacteristic
264C2×#103C22×C711yescharacteristic
265C2×#102C22×C711yescharacteristic
266C2×#102C22×C711yescharacteristic
267C2×#102C22×C711yescharacteristic
268C2×C22⋊C8C22×C711yescharacteristic
269C2×C22⋊C8C22×C711yescharacteristic
270C2×#97C22×C711yescharacteristic
271C2×C4×C8C22×C711yescharacteristic
272#400—21no—
273#398—21no—
274#397—21no—
275#397—21no—
276#391C22×C711yescharacteristic
277#391C22×C711yescharacteristic
278#391C22×C711yescharacteristic
279#391C22×C711yescharacteristic
280#390C22×C711yescharacteristic
281#390C22×C711yescharacteristic
282#389C22×C711yescharacteristic
283#389C22×C711yescharacteristic
284#386—21no—
285#386—21no—
286#380—21no—
287#380—21no—
288#380C22×C711yescharacteristic
289#340C22×C711yescharacteristic
290#340C22×C711yescharacteristic
291#340C22×C711yescharacteristic
292#340C22×C711yescharacteristic
293C23×C7—21no—
294C23×C7—21no—
295C23×C7—21no—
296C23×C7—21no—
297C23×C7—21no—
298C23×C7—21no—
299C23×C7—22no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7#12112yes—
307C23×C7C22×D411yescharacteristic
308C7×Q8—22no—
309C7×Q8—22no—
310C7×Q8—41no—
311C7×Q8—41no—
312C7×Q8—41no—
313C7×Q8—41no—
314C7×Q8—41no—
315C7×Q8—41no—
316C7×D4—22no—
317C7×D4—22no—
318C7×D4—48no—
319C7×D4—41no—
320C7×D4—41no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—21no—
328C2×C4×C7—21no—
329C2×C4×C7—21no—
330C2×C4×C7—21no—
331C2×C4×C7—22no—
332C2×C4×C7—21no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—21no—
338C2×C4×C7—21no—
339C2×C4×C7—21no—
340C2×C4×C7—48no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
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—84no—
362C2×C4×C7#12112yes—
363C2×C4×C7C22×D411yescharacteristic
364C2×C4×C7C2×#4111yescharacteristic
365C2×C4×C7C2×#4111yescharacteristic
366C2×C4×C7C2×#4111yescharacteristic
367C2×C4×C7H(5,𝔽2)11yescharacteristic
368C2×C4×C7H(5,𝔽2)11yescharacteristic
369C7×C8—22no—
370C7×C8—22no—
371C7×C8—41no—
372C7×C8—41no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—41no—
378C2×#41—41no—
379C22×Q8C23×C711yescharacteristic
380C22×Q8C23×C711yescharacteristic
381C22×D4—21no—
382C22×D4C23×C711yescharacteristic
383C23×C4—21no—
384C23×C4—21no—
385C23×C4C23×C711yescharacteristic
386C2×Q16—22no—
387C2×Q16—22no—
388C2×Q16—41no—
389C2×SD16—22no—
390C2×SD16—22no—
391C2×SD16—41no—
392C22×C8C23×C711yescharacteristic
393C22×C8C23×C711yescharacteristic
394C22×C8C23×C711yescharacteristic
395C22×C8C23×C711yescharacteristic
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398#117—22no—
399#117—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—41no—
405C2×C4⋊C4—41no—
406C2×C4⋊C4C7×D411yescharacteristic
407C2×C4⋊C4C7×D411yescharacteristic
408C2×C4⋊C4C23×C711yescharacteristic
409C2×C4⋊C4C23×C711yescharacteristic
410C2×C4⋊C4C23×C711yescharacteristic
411C2×C4⋊C4C23×C711yescharacteristic
412C2×C4⋊C4C23×C711yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4C7×D411yescharacteristic
420C2×C22⋊C4C7×D411yescharacteristic
421C2×C42C23×C711yescharacteristic
422C2×C42C23×C711yescharacteristic
423#107—41no—
424#107—41no—
425C4⋊C8—22no—
426C4⋊C8—22no—
427#103—22no—
428#103—22no—
429#103—41no—
430#103—41no—
431#103—41no—
432#102—22no—
433#102—22no—
434#102—41no—
435C22⋊C8—22no—
436C22⋊C8C7×D414yes—
437#97—22no—
438C4×C8—22no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450C22×C7—22no—
451C22×C7—22no—
452C22×C7—22no—
453C22×C7—41no—
454C22×C7—41no—
455C22×C7—41no—
456C22×C7—41no—
457C22×C7—42no—
458C22×C7—42no—
459C22×C7—42no—
460C22×C7—81no—
461C22×C7—81no—
462C22×C7—81no—
463C22×C7—81no—
464C22×C7C2×#12111yescharacteristic
465C22×C7#52511yescharacteristic
466C22×C7#53511yescharacteristic
467C22×C7#57611yescharacteristic
468C22×C7#57711yescharacteristic
469C22×C7#57811yescharacteristic
470C22×C7#57811yescharacteristic
471C4×C7—22no—
472C4×C7—42no—
473C4×C7—41no—
474C4×C7—41no—
475C4×C7—41no—
476C4×C7—41no—
477C4×C7—81no—
478C4×C7—81no—
479C4×C7—81no—
480C4×C7—81no—
481C4×C7—81no—
482C4×C7—81no—
483C4×C7#54611yescharacteristic
484C4×C7#54611yescharacteristic
485C4×C7#55111yescharacteristic
486C4×C7#55111yescharacteristic
487C24—21no—
488C24C2×C7×D411yescharacteristic
489#41—44no—
490#41—44no—
491#41—44no—
492#41—44no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C7×#4112yes—
505C2×D4—24no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4C7×#4112yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—24no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4C2×C7×D411yescharacteristic
532C22×C4C2×C7×D411yescharacteristic
533C22×C4C2×C7×D411yescharacteristic
534C22×C4C2×C7×D411yescharacteristic
535C22×C4C2×C7×D411yescharacteristic
536C22×C4C2×C7×D412yes—
537C22×C4C7×#4112yes—
538C22×C4C24×C711yescharacteristic
539Q16—44no—
540SD16—44no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8C2×C7×D412yes—
552C2×C8C2×C7×D412yes—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—81no—
568C4⋊C4—81no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C2×C7—42no—
582C2×C7—82no—
583C2×C7#241111yescharacteristic
584C2×C7#306111yescharacteristic
585C2×C7#306311yescharacteristic
586C2×C7#312011yescharacteristic
587C2×C7#312411yescharacteristic
588C2×C7#322311yescharacteristic
589C2×C7#322411yescharacteristic
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—22no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23C7×#12112yes—
604C23C22×C7×D411yescharacteristic
605Q8—22no—
606Q8—22no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611Q8—41no—
612Q8—41no—
613D4—22no—
614D4—22no—
615D4—48no—
616D4—41no—
617D4—41no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—48no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—84no—
659C2×C4C7×#12112yes—
660C2×C4C22×C7×D411yescharacteristic
661C2×C4C2×C7×#4111yescharacteristic
662C2×C4C2×C7×#4111yescharacteristic
663C2×C4C2×C7×#4111yescharacteristic
664C2×C4C7×H(5,𝔽2)11yescharacteristic
665C2×C4C7×H(5,𝔽2)11yescharacteristic
666C8—22no—
667C8—22no—
668C8—41no—
669C8—41no—
670C7#2451511yescharacteristic, direct product factor, Sylow
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×C7×#12111yescharacteristic
686C22C7×#52511yescharacteristic
687C22C7×#53511yescharacteristic
688C22C7×#57611yescharacteristic
689C22C7×#57711yescharacteristic
690C22C7×#57811yescharacteristic
691C22C7×#57811yescharacteristic
692C4—22no—
693C4—42no—
694C4—41no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C7×#54611yescharacteristic
705C4C7×#54611yescharacteristic
706C4C7×#55111yescharacteristic
707C4C7×#55111yescharacteristic
708C2—42no—
709C2—82no—
710C2C7×#241111yescharacteristic
711C2C7×#306111yescharacteristic
712C2C7×#306311yescharacteristic
713C2C7×#312011yescharacteristic
714C2C7×#312411yescharacteristic
715C2C7×#322311yescharacteristic
716C2C7×#322411yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC22×C7×#41C22
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×#2625C2semidirect
5. C7×#2068C2semidirect
6. C7×#2067C2semidirect
7. C7×#2056C2semidirect
8. C7×#2055C2semidirect
9. C7×#1973C2semidirect
10. C7×#1969C2semidirect
11. C7×#1935C2semidirect
12. C7×#1934C2semidirect
13. C7×#1872C2semidirect
14. C7×#1852C2semidirect
61. #24515C7direct (N × H)
140. C2×#433C2×C7semidirect
141. #2625C2×C7semidirect
143. #2068C2×C7semidirect
144. #2067C2×C7semidirect
145. #2056C2×C7semidirect
146. #2055C2×C7semidirect
147. #1973C2×C7semidirect
148. #1969C2×C7semidirect
149. #1935C2×C7semidirect
150. #1934C2×C7semidirect
151. #1872C2×C7semidirect
152. #1852C2×C7semidirect
670. C7#24515direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4522
C2×C7×#4332
C7×#26252
C7×#23112
C7×#20682
C7×#20672
C7×#20562
C7×#20552
C7×#19732
C7×#19692
C7×#19352
C7×#19342
C7×#18722
C7×#18522
C7×#17882
#245157