Finite Group Databasebeta

← #13370171

Subgroups — #13370171

Order 1792.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90270C211yesmaximal, characteristic
2C2×#89608C211yesmaximal, characteristic
3#11731674C211yesmaximal, characteristic
4C7×#1805C211yesmaximal, characteristic, complemented
5#11729385C211yesmaximal, characteristic, complemented
6#11728214C211yesmaximal, characteristic, complemented
7#11728025C211yesmaximal, characteristic, complemented
8#11728024C211yesmaximal, characteristic, complemented
9#11728023C211yesmaximal, characteristic, complemented
10#11728022C211yesmaximal, characteristic, complemented
11#11727309C211yesmaximal, characteristic, complemented
12#11726626C211yesmaximal, characteristic, complemented
13#11726625C211yesmaximal, characteristic, complemented
14#11726621C211yesmaximal, characteristic, complemented
15D7×#340C211yesmaximal, characteristic, complemented
16C2×C4×C7×Q8C2211yescharacteristic
17C2×#6509C2211yescharacteristic
18C2×#6509C2211yescharacteristic
19C22×#1131C2211yescharacteristic
20C22×C8×D7C2211yescharacteristic
21#90270—24no—
22#90270C418yescomplemented
23C2×#6459—21no—
24C2×#6459—21no—
25C2×#6455C2211yescharacteristic
26C2×D7×C4⋊C4C2211yescharacteristic
27C2×D7×C4⋊C4C2211yescharacteristic
28C2×D7×C4⋊C4C2211yescharacteristic
29C2×C4×D28—21no—
30C2×C4×D28C2211yescharacteristic
31C2×#6433—21no—
32C2×#6432C2211yescharacteristic
33C2×C7×C4⋊C8C2211yescharacteristic
34C2×C7×#103C2211yescharacteristic
35C2×C7×#103C2211yescharacteristic
36C7×#382C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38C2×#6409C2211yescharacteristic
39C2×(C2×D7)⋊C8C2211yescharacteristic
40C2×(C2×D7)⋊C8C2211yescharacteristic
41#89759C2211yescharacteristic
42#89759C2211yescharacteristic
43C4×C4⋊Dic7C2211yescharacteristic
44C2×#6377C2211yescharacteristic
45#89608—24no—
46#89441—21no—
47#89438—21no—
48#89437—21no—
49#89426—21no—
50C7×#340C2211yescharacteristic
51C7×#340C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#22497—71nomaximal, Sylow
63C22×C7×Q8C2311yescharacteristic
64C22×D28D411yescharacteristic
65C22×C4×D7—21no—
66C22×C4×D7—21no—
67C22×C4×D7—21no—
68C22×C4×D7C2311yescharacteristic
69C22×C4×D7C2311yescharacteristic
70C22×Dic14—21no—
71C22×C7×C8C2311yescharacteristic
72C22×C7×C8C2311yescharacteristic
73C4×C7×Q8—22no—
74C4×C7×Q8C2×C414yescomplemented
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4C2311yescharacteristic
77C2×C7×C4⋊C4C2311yescharacteristic
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C42×C7—21no—
80C2×C42×C7C2311yescharacteristic
81#6509—22no—
82#6509—22no—
83#6509C2×C414yes—
84#6509C2×C414yescomplemented
85C2×(C2×D7)⋊C4—21no—
86C2×(C2×D7)⋊C4—21no—
87C2×(C2×D7)⋊C4—21no—
88C2×(C2×D7)⋊C4—21no—
89C2×(C2×D7)⋊C4—21no—
90C2×(C2×D7)⋊C4D411yescharacteristic
91C2×(C2×D7)⋊C4D411yescharacteristic
92C2×C4⋊Dic7—21no—
93C2×C4⋊Dic7D411yescharacteristic
94C2×C4⋊Dic7C2311yescharacteristic
95C2×C4⋊Dic7C2311yescharacteristic
96C2×C4⋊Dic7C2311yescharacteristic
97C2×C4⋊Dic7C2311yescharacteristic
98C2×Dic7⋊C4—21no—
99C2×Dic7⋊C4—21no—
100C2×Dic7⋊C4—21no—
101C2×Dic7⋊C4—21no—
102C2×Dic7⋊C4—21no—
103C2×C4×Dic7—21no—
104C2×C4×Dic7—21no—
105C22×C7⋊C8C2311yescharacteristic
106C22×C7⋊C8C2311yescharacteristic
107C2×#1131—22no—
108C2×#1131—22no—
109C2×#1131—41no—
110C2×C8×D7—22no—
111C2×C8×D7—22no—
112C2×C8×D7—41no—
113#6459—28no—
114#6459—28no—
115#6455—22no—
116#6455—41no—
117D7×C4⋊C4—22no—
118D7×C4⋊C4—22no—
119D7×C4⋊C4—22no—
120D7×C4⋊C4—41no—
121D7×C4⋊C4C2×C414yes—
122D7×C4⋊C4C2×C414yescomplemented
123C4×D28—28no—
124C4×D28C2×C414yes—
125C4×D28D414yes—
126#6433—28no—
127#6432—22no—
128#6432C2×C414yescomplemented
129C7×C4⋊C8—22no—
130C7×#103—41no—
131C7×#103—41no—
132C7×#95—21no—
133C7×#95—21no—
134#6409—22no—
135#6409—22no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138C7⋊#95—21no—
139(C2×D7)⋊C8—22no—
140(C2×D7)⋊C8—22no—
141#6377—22no—
142C2×#554—71no—
143C2×#435—71no—
144#2352—71no—
145#1993—71no—
146#1988—71no—
147#1894—71no—
148#1892—71no—
149#1873—71no—
150#1872—71no—
151#1824—71no—
152#1823—71no—
153#1805D711yescharacteristic, complemented
154#1763—71no—
155#1736—71no—
156C2×#340—71no—
157C23×D7C2×D411yescharacteristic
158C23×D7C2×D411yescharacteristic
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8C22×C412yes—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7C2×D411yescharacteristic
170C22×C4×C7C2×D411yescharacteristic
171C22×C4×C7C2411yescharacteristic
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C22×Dic7—21no—
176C22×Dic7C2×D411yescharacteristic
177C22×Dic7C2×D411yescharacteristic
178C2×D28—22no—
179C2×D28—22no—
180C2×D28C22⋊C414yes—
181C2×C4×D7—21no—
182C2×C4×D7—21no—
183C2×C4×D7—21no—
184C2×C4×D7—21no—
185C2×C4×D7—21no—
186C2×C4×D7—21no—
187C2×C4×D7—21no—
188C2×C4×D7—21no—
189C2×C4×D7—24no—
190C2×C4×D7—24no—
191C2×C4×D7—42no—
192C2×C4×D7—42no—
193C2×C4×D7—81no—
194C2×C4×D7—81no—
195C2×C4×D7—81no—
196C2×C4×D7—81no—
197C2×C4×D7—81no—
198C2×C4×D7C22×C412yes—
199C2×C4×D7C22×C412yes—
200C2×C4×D7C2×D412yes—
201C2×C4×D7C2×D412yes—
202C2×Dic14—24no—
203C2×Dic14—81no—
204C2×Dic14—81no—
205C2×C7×C8—21no—
206C2×C7×C8—21no—
207C2×C7×C8—21no—
208C2×C7×C8—21no—
209C2×C7×C8—21no—
210C2×C7×C8—21no—
211C7×C4⋊C4—24no—
212C7×C4⋊C4—21no—
213C7×C4⋊C4—21no—
214C7×C4⋊C4—21no—
215C7×C4⋊C4—21no—
216C7×C4⋊C4—21no—
217C7×C4⋊C4C22×C412yes—
218C42×C7—24no—
219C42×C7C22×C412yes—
220C42×C7C2×D412yes—
221(C2×D7)⋊C4—24no—
222(C2×D7)⋊C4—24no—
223(C2×D7)⋊C4—42no—
224(C2×D7)⋊C4—42no—
225(C2×D7)⋊C4—81no—
226(C2×D7)⋊C4C22⋊C414yes—
227(C2×D7)⋊C4C22⋊C414yes—
228C4⋊Dic7—24no—
229C4⋊Dic7—21no—
230C4⋊Dic7—21no—
231C4⋊Dic7—21no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7C22⋊C414yes—
235C4⋊Dic7C22×C412yes—
236C4⋊Dic7C22×C412yes—
237C4⋊Dic7#4112yes—
238Dic7⋊C4—24no—
239Dic7⋊C4—24no—
240Dic7⋊C4—24no—
241Dic7⋊C4—24no—
242Dic7⋊C4—42no—
243C4×Dic7—42no—
244C4×Dic7—81no—
245C2×C7⋊C8—21no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8#4112yes—
251#1131—44no—
252C8×D7—44no—
253C22×M16—71no—
254C23×C8—71no—
255#554—78no—
256#554—144no—
257C2×C4⋊Q8—71no—
258C2×#125—141no—
259C2×C22⋊Q8—71no—
260C2×C22⋊Q8—71no—
261C2×C22⋊Q8—141no—
262C2×C22⋊Q8—141no—
263C2×C4×Q8C2×D711yescharacteristic
264C2×C4×D4—71no—
265C2×C4×D4—141no—
266C2×#117—71no—
267C22×C4⋊C4—71no—
268C22×C4⋊C4—71no—
269C22×C4⋊C4—71no—
270#435—144no—
271C2×C4⋊C8C2×D711yescharacteristic
272C2×#103—71no—
273C2×#103—71no—
274C2×#103C2×D711yescharacteristic
275C2×#103C2×D711yescharacteristic
276C2×C22⋊C8—71no—
277C2×C22⋊C8—71no—
278C2×#97—71no—
279#388—141no—
280#387—141no—
281#386—141no—
282#382C2×D711yescharacteristic
283#380—71no—
284#380—71no—
285C4×C4⋊C4—71no—
286C4×C22⋊C4—141no—
287#340—71no—
288#340—71no—
289#340—71no—
290#340—71no—
291#340—71no—
292#340—71no—
293#340—71no—
294#340—71no—
295#340—71no—
296#340—71no—
297#340C2×D711yescharacteristic
298#340C2×D711yescharacteristic
299C23×C7C22×D411yescharacteristic
300C22×D7—21no—
301C22×D7—21no—
302C22×D7—21no—
303C22×D7—21no—
304C22×D7—21no—
305C22×D7—21no—
306C22×D7—21no—
307C22×D7—21no—
308C22×D7—21no—
309C22×D7—21no—
310C22×D7C2×C22⋊C412yes—
311C22×D7C2×C22⋊C412yes—
312C22×D7#13712yes—
313C22×D7#13712yes—
314C7×Q8—22no—
315C7×Q8—22no—
316C7×Q8—41no—
317C7×Q8—41no—
318C2×C4×C7—21no—
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7C2×C22⋊C412yes—
335C2×C4×C7C2×C22⋊C412yes—
336C2×C4×C7C23×C411yescharacteristic
337C2×C4×C7C22×D411yescharacteristic
338C2×C4×C7C2×#4111yescharacteristic
339C2×C4×C7C2×#4111yescharacteristic
340C2×C4×C7H(5,𝔽2)11yescharacteristic
341C2×C4×C72−1+411yescharacteristic
342C2×Dic7—21no—
343C2×Dic7—21no—
344C2×Dic7—21no—
345C2×Dic7—21no—
346C2×Dic7—22no—
347C2×Dic7—22no—
348C2×Dic7—22no—
349C2×Dic7—41no—
350C2×Dic7—41no—
351C2×Dic7—41no—
352C2×Dic7—41no—
353C2×Dic7—41no—
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7C2×C22⋊C412yes—
359C2×Dic7C2×C22⋊C412yes—
360D28—28no—
361C4×D7—22no—
362C4×D7—22no—
363C4×D7—22no—
364C4×D7—22no—
365C4×D7—22no—
366C4×D7—22no—
367C4×D7—22no—
368C4×D7—22no—
369C4×D7—84no—
370C4×D7—84no—
371C4×D7—84no—
372Dic14—84no—
373C7×C8—41no—
374C7×C8—41no—
375C7⋊C8—22no—
376C7⋊C8—41no—
377C22×Q8—141no—
378C22×Q8C22×D711yescharacteristic
379C22×D4—71no—
380C23×C4—71no—
381C23×C4—71no—
382C23×C4—141no—
383C23×C4—141no—
384C23×C4—141no—
385C2×M16—142no—
386C2×M16—142no—
387C2×M16—281no—
388C22×C8—71no—
389C22×C8—71no—
390C22×C8—142no—
391C22×C8—142no—
392C22×C8—281no—
393C22×C8C22×D711yescharacteristic
394C22×C8C22×D711yescharacteristic
395C4⋊Q8—74no—
396C4⋊Q8—142no—
397#125—148no—
398C22⋊Q8—74no—
399C22⋊Q8—74no—
400C22⋊Q8—148no—
401C22⋊Q8—148no—
402C22⋊Q8—142no—
403C22⋊Q8—142no—
404C4×Q8—22no—
405C4×Q8C4×D714yescomplemented
406C4×D4—74no—
407C4×D4—74no—
408C4×D4—148no—
409#117—142no—
410#117—281no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—71no—
413C2×C4⋊C4—71no—
414C2×C4⋊C4—71no—
415C2×C4⋊C4—71no—
416C2×C4⋊C4—74no—
417C2×C4⋊C4—74no—
418C2×C4⋊C4—71no—
419C2×C4⋊C4—142no—
420C2×C4⋊C4—142no—
421C2×C4⋊C4—142no—
422C2×C4⋊C4—141no—
423C2×C4⋊C4—141no—
424C2×C4⋊C4—141no—
425C2×C4⋊C4—141no—
426C2×C4⋊C4—141no—
427C2×C4⋊C4—141no—
428C2×C4⋊C4—281no—
429C2×C4⋊C4C22×D711yescharacteristic
430C2×C4⋊C4C22×D711yescharacteristic
431C2×C4⋊C4C22×D711yescharacteristic
432C2×C22⋊C4—71no—
433C2×C22⋊C4—71no—
434C2×C22⋊C4—141no—
435C2×C22⋊C4—141no—
436C2×C22⋊C4—141no—
437C2×C22⋊C4—141no—
438C2×C22⋊C4—141no—
439C2×C42—21no—
440C2×C42—141no—
441C2×C42—141no—
442C2×C42C22×D711yescharacteristic
443C4⋊C8—22no—
444#103—41no—
445#103—41no—
446#103—142no—
447#103—142no—
448C22⋊C8—142no—
449C22⋊C8—142no—
450#97—142no—
451#95—21no—
452#95—21no—
453#95—141no—
454#95—141no—
455#95—141no—
456C22×C7C22×C22⋊C411yescharacteristic
457C22×C7#54611yescharacteristic
458C22×C7#54711yescharacteristic
459C22×C7C2×#13711yescharacteristic
460C22×C7C2×#13711yescharacteristic
461C22×C7#57611yescharacteristic
462C22×C7#57711yescharacteristic
463C2×D7—22no—
464C2×D7—22no—
465C2×D7—22no—
466C2×D7—22no—
467C2×D7—22no—
468C2×D7—22no—
469C2×D7—22no—
470C2×D7—22no—
471C2×D7—22no—
472C2×D7—41no—
473C2×D7—41no—
474C2×D7—41no—
475C2×D7—41no—
476C2×D7#41914yes—
477C4×C7—22no—
478C4×C7—22no—
479C4×C7—42no—
480C4×C7—42no—
481C4×C7—81no—
482C4×C7—81no—
483C4×C7C4×#4111yescharacteristic
484C4×C7#52011yescharacteristic
485C4×C7#54611yescharacteristic
486C4×C7#54711yescharacteristic
487Dic7—22no—
488Dic7—22no—
489Dic7—42no—
490Dic7—42no—
491Dic7—42no—
492Dic7—81no—
493C24—71no—
494C24—71no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—144no—
501C2×Q8—561no—
502C2×Q8—561no—
503C2×Q8C2×C4×D712yes—
504C2×D4—74no—
505C2×D4—142no—
506C2×D4—142no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—71no—
512C22×C4—71no—
513C22×C4—72no—
514C22×C4—72no—
515C22×C4—72no—
516C22×C4—72no—
517C22×C4—144no—
518C22×C4—144no—
519C22×C4—141no—
520C22×C4—141no—
521C22×C4—141no—
522C22×C4—141no—
523C22×C4—141no—
524C22×C4—141no—
525C22×C4—141no—
526C22×C4—141no—
527C22×C4—141no—
528C22×C4—141no—
529C22×C4—141no—
530C22×C4—141no—
531C22×C4—282no—
532C22×C4—282no—
533C22×C4—561no—
534C22×C4—561no—
535C22×C4—561no—
536C22×C4—561no—
537C22×C4—561no—
538C22×C4D4×D711yescharacteristic
539C22×C4D4×D711yescharacteristic
540C22×C4C23×D711yescharacteristic
541M16—284no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—72no—
549C2×C8—141no—
550C2×C8—141no—
551C2×C8—141no—
552C2×C8—141no—
553C2×C8—141no—
554C2×C8—284no—
555C4⋊C4—24no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—74no—
562C4⋊C4—72no—
563C4⋊C4—72no—
564C4⋊C4—72no—
565C4⋊C4—144no—
566C4⋊C4—144no—
567C4⋊C4—144no—
568C4⋊C4—144no—
569C4⋊C4—144no—
570C4⋊C4—141no—
571C4⋊C4—141no—
572C4⋊C4—141no—
573C4⋊C4—141no—
574C4⋊C4—141no—
575C4⋊C4—282no—
576C4⋊C4C2×C4×D712yes—
577C22⋊C4—74no—
578C22⋊C4—74no—
579C22⋊C4—144no—
580C22⋊C4—144no—
581C22⋊C4—282no—
582C22⋊C4—282no—
583C22⋊C4—561no—
584C42—24no—
585C42—282no—
586C42—561no—
587C42C2×C4×D712yes—
588C42D4×D712yes—
589C2×C7#233911yescharacteristic
590C2×C7C2×#41911yescharacteristic
591C2×C7#289711yescharacteristic
592C2×C7#331411yescharacteristic
593C2×C7#331611yescharacteristic
594C2×C7#334411yescharacteristic
595C2×C7#334611yescharacteristic
596D7—24no—
597D7—42no—
598C23—72no—
599C23—72no—
600C23—72no—
601C23—72no—
602C23—141no—
603C23—141no—
604C23—141no—
605C23—141no—
606C23—141no—
607C23—141no—
608C23—141no—
609C23—141no—
610C23—141no—
611C23—141no—
612C23C2×D4×D711yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—41no—
616Q8—41no—
617Q8—564no—
618D4—148no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—72no—
636C2×C4—72no—
637C2×C4—141no—
638C2×C4—141no—
639C2×C4—141no—
640C2×C4—141no—
641C2×C4—142no—
642C2×C4—142no—
643C2×C4—142no—
644C2×C4—142no—
645C2×C4—142no—
646C2×C4—142no—
647C2×C4—142no—
648C2×C4—142no—
649C2×C4—142no—
650C2×C4—142no—
651C2×C4—142no—
652C2×C4—281no—
653C2×C4—281no—
654C2×C4—281no—
655C2×C4—281no—
656C2×C4—281no—
657C2×C4—281no—
658C2×C4—281no—
659C2×C4—281no—
660C2×C4—281no—
661C2×C4—564no—
662C2×C4—564no—
663C2×C4—564no—
664C2×C4D7×C22⋊C412yes—
665C2×C4D7×C22⋊C412yes—
666C2×C4C22×C4×D711yescharacteristic
667C2×C4C2×D4×D711yescharacteristic
668C2×C4#654811yescharacteristic
669C2×C4#655111yescharacteristic
670C2×C4D7×#4111yescharacteristic
671C2×C4D7×#4111yescharacteristic
672C8—41no—
673C8—41no—
674C8—142no—
675C8—281no—
676C7#2249711yescharacteristic, complemented, Sylow
677C22—74no—
678C22—142no—
679C22—142no—
680C22—142no—
681C22—142no—
682C22—142no—
683C22—142no—
684C22—142no—
685C22—142no—
686C22—142no—
687C22—281no—
688C22—281no—
689C22—281no—
690C22—281no—
691C22C2×D7×C22⋊C411yescharacteristic
692C22#9030311yescharacteristic
693C22#9032211yescharacteristic
694C22#9046011yescharacteristic
695C22#9046111yescharacteristic
696C22D7×#13711yescharacteristic
697C22D7×#13711yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—81no—
704C4—142no—
705C4—142no—
706C4—282no—
707C4—282no—
708C4—282no—
709C4—561no—
710C4#9019511yescharacteristic
711C4#9021311yescharacteristic
712C4#9030311yescharacteristic
713C4#9032211yescharacteristic
714C2—144no—
715C2—282no—
716C2#1173145311yescharacteristic
717C2#1173627611yescharacteristic
718C2D7×#41911yescharacteristic
719C2#1173806411yescharacteristic
720C2#1173806511yescharacteristic
721C2#1173870011yescharacteristic
722C2#1173870111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1805C2
socleC23×C7C22×D4
prime radicalC22×D28D4
cosocleC22×C4×C7C24
hypercenter#1805D7
hypocenterC7#22497
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
4. C7×#1805C2semidirect
5. #11729385C2semidirect
6. #11728214C2semidirect
7. #11728025C2semidirect
8. #11728024C2semidirect
9. #11728023C2semidirect
10. #11728022C2semidirect
11. #11727309C2semidirect
12. #11726626C2semidirect
13. #11726625C2semidirect
14. #11726621C2semidirect
15. D7×#340C2semidirect
22. #90270C4semidirect
74. C4×C7×Q8C2×C4semidirect
84. #6509C2×C4semidirect
122. D7×C4⋊C4C2×C4semidirect
128. #6432C2×C4semidirect
153. #1805D7semidirect
405. C4×Q8C4×D7semidirect
676. C7#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#902702
C2×#896082
#117316742
C7×#18052
#117293852
#117282142
#117280252
#117280242
#117280232
#117280222
#117273092
#117266262
#117266252
#117266212
D7×#3402
#224977