Finite Group Databasebeta

← #13369396

Subgroups — #13369396

Order 1792.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#546C211yesmaximal, characteristic
2C2×#90004C211yesmaximal, characteristic, complemented
3C2×#89987C211yesmaximal, characteristic, complemented
4#11739780C211yesmaximal, characteristic, complemented
5C2×#89784C211yesmaximal, characteristic, complemented
6#11729889C211yesmaximal, characteristic, complemented
7#11729882C211yesmaximal, characteristic, complemented
8#11729479C211yesmaximal, characteristic, complemented
9#11729475C211yesmaximal, characteristic, complemented
10#11729451C211yesmaximal, characteristic, complemented
11#11729447C211yesmaximal, characteristic, complemented
12#11729436C211yesmaximal, characteristic, complemented
13#11729431C211yesmaximal, characteristic, complemented
14C4×#6406C211yesmaximal, characteristic, complemented
15#11729359C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C23×C7×D4C2211yescharacteristic
18C7×#546—24no—
19C7×#546C418yescomplemented
20C2×C7×#124C2211yescharacteristic
21C2×C7×#123—21no—
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×C7×#121—21no—
24C2×C7×#121C2211yescharacteristic
25C2×C7×#120—21no—
26C2×C4×C7×D4C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C22×C7×C22⋊C4—21no—
29C2×#6489C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic, complemented
31C22×#1136C2211yescharacteristic
32C22×#1136C2211yescharacteristic, complemented
33#90004—24no—
34C2×#6409C2211yescharacteristic, complemented
35C2×#6409C2211yescharacteristic, complemented
36C2×#6409C2211yescharacteristic, complemented
37C2×#6409C2211yescharacteristic, complemented
38#89992—21no—
39#89987—24no—
40C2×#6406C2211yescharacteristic
41C2×#6406C2211yescharacteristic
42C2×#6406C2211yescharacteristic
43C2×#6406C2211yescharacteristic
44C2×#6406C2211yescharacteristic
45C2×#6406C2211yescharacteristic
46C2×#6406C2211yescharacteristic
47C2×#6406C2211yescharacteristic
48#89984C2211yescharacteristic
49#89984C2211yescharacteristic, complemented
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51C2×C22⋊(C7⋊C8)C2211yescharacteristic, complemented
52#89784—24no—
53#89753—21no—
54#89723—21no—
55C22⋊C4×Dic7—21no—
56#89708C2211yescharacteristic, complemented
57C4×C4⋊Dic7C2211yescharacteristic, complemented
58C2×C4⋊(C7⋊C8)C2211yescharacteristic, complemented
59C2×C4×C7⋊C8C2211yescharacteristic, complemented
60#89324C2211yescharacteristic, complemented
61#89324C2211yescharacteristic, complemented
62#89324C2211yescharacteristic, complemented
63#89324C2211yescharacteristic, complemented
64#22427—71nomaximal, Sylow
65C25×C7—21no—
66C2×C7×#41—22no—
67C2×C7×#41—22no—
68C2×C7×#41—22no—
69C2×C7×#41—41no—
70C2×C7×#41—41no—
71C2×C7×#41C2×C414yes—
72C22×C7×Q8C2311yescharacteristic
73C22×C7×D4—22no—
74C22×C7×D4—22no—
75C22×C7×D4—21no—
76C22×C7×D4—21no—
77C22×C7×D4—21no—
78C22×C7×D4—22no—
79C22×C7×D4—41no—
80C22×C7×D4—41no—
81C22×C7×D4C2×C414yescomplemented
82C22×C7×D4D411yescharacteristic
83C22×C7×D4C2311yescharacteristic
84C22×C7×D4C2311yescharacteristic
85C23×C4×C7—21no—
86C23×C4×C7—21no—
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C23×Dic7—21no—
90C7×#124—22no—
91C7×#124C2×C414yescomplemented
92C7×#123—28no—
93C7×C22⋊Q8—22no—
94C7×C22⋊Q8C2×C414yescomplemented
95C7×#121—22no—
96C7×#121—28no—
97C7×#121C2×C414yes—
98C7×#120—28no—
99C4×C7×D4—22no—
100C4×C7×D4C2×C414yes—
101C4×C7×D4C2×C414yescomplemented
102C4×C7×D4D414yes—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4D411yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
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—28no—
112C2×C7×C22⋊C4D411yescharacteristic
113C2×C7×C22⋊C4D411yescharacteristic
114C2×C42×C7C2311yescharacteristic
115C2×C22⋊Dic7—21no—
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118#6489—22no—
119#6489—41no—
120C2×C4⋊Dic7—22no—
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7—41no—
123C2×C4⋊Dic7C2311yescharacteristic
124C2×C4⋊Dic7C2311yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4×Dic7—21no—
128C2×C4×Dic7—21no—
129C2×#1136—22no—
130C2×#1136—22no—
131C2×#1136—22no—
132C2×#1136—22no—
133C2×#1136—41no—
134C2×#1136—41no—
135C22×C7⋊C8C2311yescharacteristic
136C22×C7⋊C8C2311yescharacteristic
137C22×C7⋊C8C2311yescharacteristic
138C22×C7⋊C8C2311yescharacteristic
139#6409—22no—
140#6409—22no—
141#6409—41no—
142#6409—41no—
143#6406—22no—
144#6406—22no—
145#6406—22no—
146#6406—22no—
147#6406—22no—
148#6406—41no—
149#6406—41no—
150#6406D414yescomplemented
151C7⋊#95—21no—
152C7⋊#95—21no—
153C7⋊#95—21no—
154C7⋊#95—21no—
155C7⋊#95—21no—
156C22⋊(C7⋊C8)—22no—
157C22⋊(C7⋊C8)—22no—
158C4⋊(C7⋊C8)—22no—
159C4×C7⋊C8—22no—
160C2×#546D711yescharacteristic
161C2×#436—71no—
162C2×#417—71no—
163C2×#418—71no—
164#2352—71no—
165#1983—71no—
166#1958—71no—
167#1895—71no—
168#1894—71no—
169#1874—71no—
170#1873—71no—
171#1804—71no—
172#1788—71no—
173#1786—71no—
174C4×#102—71no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7—24no—
178C24×C7—42no—
179C24×C7—42no—
180C24×C7—42no—
181C24×C7—42no—
182C24×C7—81no—
183C24×C7—81no—
184C24×C7C2×D411yescharacteristic
185C24×C7C2×D411yescharacteristic
186C7×#41—28no—
187C7×#41—44no—
188C7×#41—44no—
189C7×#41—44no—
190C2×C7×Q8—21no—
191C2×C7×Q8—21no—
192C2×C7×Q8—21no—
193C2×C7×Q8—21no—
194C2×C7×Q8—21no—
195C2×C7×Q8C22×C412yes—
196C2×C7×D4—28no—
197C2×C7×D4—24no—
198C2×C7×D4—24no—
199C2×C7×D4—24no—
200C2×C7×D4—21no—
201C2×C7×D4—21no—
202C2×C7×D4—21no—
203C2×C7×D4—21no—
204C2×C7×D4—21no—
205C2×C7×D4—21no—
206C2×C7×D4—21no—
207C2×C7×D4—21no—
208C2×C7×D4—44no—
209C2×C7×D4—44no—
210C2×C7×D4—44no—
211C2×C7×D4—41no—
212C2×C7×D4—41no—
213C2×C7×D4—42no—
214C2×C7×D4—42no—
215C2×C7×D4—42no—
216C2×C7×D4—42no—
217C2×C7×D4—81no—
218C2×C7×D4—81no—
219C2×C7×D4C22⋊C414yes—
220C2×C7×D4C22×C412yes—
221C2×C7×D4C22×C412yes—
222C2×C7×D4C2×D412yes—
223C2×C7×D4#4112yes—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—24no—
235C22×C4×C7—24no—
236C22×C4×C7—42no—
237C22×C4×C7—42no—
238C22×C4×C7—81no—
239C22×C4×C7—81no—
240C22×C4×C7C22×C412yes—
241C22×C4×C7C22×C412yes—
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D412yes—
247C22×C4×C7C2×D412yes—
248C22×C4×C7C2411yescharacteristic
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—42no—
254C22×Dic7—42no—
255C22×Dic7—81no—
256C7×C4⋊C4—24no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4C22⋊C414yes—
259C7×C4⋊C4C22×C412yes—
260C7×C22⋊C4—24no—
261C7×C22⋊C4—24no—
262C7×C22⋊C4—24no—
263C7×C22⋊C4—24no—
264C7×C22⋊C4—24no—
265C7×C22⋊C4C22⋊C414yes—
266C7×C22⋊C4C22⋊C414yes—
267C42×C7C22×C412yes—
268C42×C7C2×D412yes—
269C22⋊Dic7—42no—
270C22⋊Dic7—42no—
271C22⋊Dic7—81no—
272C4⋊Dic7—21no—
273C4⋊Dic7—21no—
274C4⋊Dic7—21no—
275C4⋊Dic7—21no—
276C4⋊Dic7—21no—
277C4⋊Dic7—21no—
278C4⋊Dic7—21no—
279C4⋊Dic7—42no—
280C4⋊Dic7C2×D412yes—
281C4×Dic7—42no—
282C4×Dic7—81no—
283#1136—44no—
284#1136—44no—
285C2×C7⋊C8—21no—
286C2×C7⋊C8—21no—
287C2×C7⋊C8—21no—
288C2×C7⋊C8—21no—
289C2×C7⋊C8—21no—
290C2×C7⋊C8—21no—
291C2×C7⋊C8—21no—
292C2×C7⋊C8—21no—
293C2×C7⋊C8—21no—
294C2×C7⋊C8—21no—
295C2×C7⋊C8—21no—
296C2×C7⋊C8C2×D412yes—
297C22×#41C2×D711yescharacteristic
298C23×D4C2×D711yescharacteristic
299C22×M16—71no—
300C22×M16—71no—
301#546—24no—
302#546Dic718yescomplemented
303C2×#124C2×D711yescharacteristic
304C2×#123—21no—
305C2×C22⋊Q8C2×D711yescharacteristic
306C2×#121—21no—
307C2×#121C2×D711yescharacteristic
308C2×#120—21no—
309C2×C4×D4C2×D711yescharacteristic
310C2×C4×D4C2×D711yescharacteristic
311C2×#117—71no—
312C22×C4⋊C4—71no—
313C22×C22⋊C4—21no—
314#436—144no—
315C2×C4⋊C8—71no—
316#418—144no—
317#417—144no—
318C2×#103—71no—
319C2×#103—71no—
320C2×#103—71no—
321C2×#103—71no—
322C2×#102—71no—
323C2×#102—71no—
324C2×#102—71no—
325C2×#102—71no—
326C2×#102—71no—
327C2×#102—71no—
328C2×#102—71no—
329C2×#102—71no—
330C2×C22⋊C8—71no—
331C2×C22⋊C8—71no—
332C2×C4×C8—71no—
333#388—141no—
334#387—141no—
335#386—141no—
336#382—71no—
337#380—71no—
338#380—71no—
339C4×C4⋊C4—71no—
340C4×C22⋊C4—141no—
341#340—71no—
342#340—71no—
343#340—71no—
344#340—71no—
345C23×C7—22no—
346C23×C7—21no—
347C23×C7—21no—
348C23×C7—22no—
349C23×C7—21no—
350C23×C7—21no—
351C23×C7—22no—
352C23×C7—21no—
353C23×C7—21no—
354C23×C7—21no—
355C23×C7—21no—
356C23×C7—21no—
357C23×C7—21no—
358C23×C7—21no—
359C23×C7—21no—
360C23×C7—22no—
361C23×C7—48no—
362C23×C7—48no—
363C23×C7—41no—
364C23×C7—41no—
365C23×C7—41no—
366C23×C7—41no—
367C23×C7—41no—
368C23×C7—41no—
369C23×C7—41no—
370C23×C7—41no—
371C23×C7—41no—
372C23×C7—41no—
373C23×C7—84no—
374C23×C7—84no—
375C23×C7—84no—
376C23×C7—84no—
377C23×C7—84no—
378C23×C7C2×C22⋊C412yes—
379C23×C7C2×C22⋊C412yes—
380C23×C7C22×D411yescharacteristic
381C7×Q8—22no—
382C7×Q8—22no—
383C7×Q8—41no—
384C7×Q8—41no—
385C7×D4—22no—
386C7×D4—22no—
387C7×D4—22no—
388C7×D4—22no—
389C7×D4—22no—
390C7×D4—44no—
391C7×D4—48no—
392C7×D4—48no—
393C7×D4—41no—
394C7×D4—41no—
395C7×D4—84no—
396C7×D4C4×D414yes—
397C2×C4×C7—21no—
398C2×C4×C7—21no—
399C2×C4×C7—21no—
400C2×C4×C7—21no—
401C2×C4×C7—21no—
402C2×C4×C7—21no—
403C2×C4×C7—21no—
404C2×C4×C7—21no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—48no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—84no—
421C2×C4×C7C2×C22⋊C412yes—
422C2×C4×C7C2×C22⋊C412yes—
423C2×C4×C7C2×C22⋊C412yes—
424C2×C4×C7C2×C22⋊C412yes—
425C2×C4×C7C23×C411yescharacteristic
426C2×C4×C7C22×D411yescharacteristic
427C2×C4×C7C22×D411yescharacteristic
428C2×C4×C7C2×#4111yescharacteristic
429C2×C4×C7H(5,𝔽2)11yescharacteristic
430C2×C4×C7H(5,𝔽2)11yescharacteristic
431C2×Dic7—22no—
432C2×Dic7—41no—
433C2×Dic7—41no—
434C2×Dic7—41no—
435C2×Dic7—41no—
436C2×Dic7—41no—
437C2×Dic7—41no—
438C2×Dic7—41no—
439C2×Dic7—41no—
440C2×Dic7—41no—
441C2×Dic7—41no—
442C2×Dic7—41no—
443C2×Dic7—84no—
444C7⋊C8—22no—
445C7⋊C8—41no—
446C7⋊C8—41no—
447C7⋊C8—41no—
448C25—21no—
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—41no—
453C2×#41—41no—
454C2×#41C2×Dic714yes—
455C22×Q8C22×D711yescharacteristic
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—22no—
462C22×D4—41no—
463C22×D4—41no—
464C22×D4C2×Dic714yescomplemented
465C22×D4C22⋊D711yescharacteristic
466C22×D4C22×D711yescharacteristic
467C22×D4C22×D711yescharacteristic
468C23×C4—21no—
469C23×C4—21no—
470C23×C4—141no—
471C23×C4C22×D711yescharacteristic
472C23×C4C22×D711yescharacteristic
473C2×M16—142no—
474C2×M16—142no—
475C2×M16—142no—
476C2×M16—142no—
477C2×M16—281no—
478C2×M16—281no—
479C22×C8—71no—
480C22×C8—71no—
481C22×C8—71no—
482C22×C8—71no—
483#124—22no—
484#124C2×Dic714yescomplemented
485#123—28no—
486C22⋊Q8—22no—
487C22⋊Q8C2×Dic714yescomplemented
488#121—22no—
489#121—28no—
490#121C2×Dic714yes—
491#120—28no—
492C4×D4—22no—
493C4×D4C2×Dic714yes—
494C4×D4C2×Dic714yescomplemented
495C4×D4C22⋊D714yes—
496#117—142no—
497#117—281no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—71no—
500C2×C4⋊C4—71no—
501C2×C4⋊C4—71no—
502C2×C4⋊C4—71no—
503C2×C4⋊C4—142no—
504C2×C4⋊C4—141no—
505C2×C4⋊C4—281no—
506C2×C4⋊C4C22⋊D711yescharacteristic
507C2×C4⋊C4C22×D711yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—28no—
514C2×C22⋊C4—141no—
515C2×C22⋊C4—141no—
516C2×C22⋊C4—141no—
517C2×C22⋊C4C22⋊D711yescharacteristic
518C2×C22⋊C4C22⋊D711yescharacteristic
519C2×C42—141no—
520C2×C42—141no—
521C2×C42C22×D711yescharacteristic
522C4⋊C8—142no—
523#103—142no—
524#103—142no—
525#103—281no—
526#103—281no—
527#102—74no—
528#102—142no—
529#102—142no—
530#102—142no—
531#102—142no—
532#102—142no—
533#102—281no—
534#102—281no—
535C22⋊C8—142no—
536C22⋊C8—142no—
537C4×C8—142no—
538#95—141no—
539#95—141no—
540#95—141no—
541#95—141no—
542#95—141no—
543C22×C7—22no—
544C22×C7—22no—
545C22×C7—24no—
546C22×C7—22no—
547C22×C7—22no—
548C22×C7—22no—
549C22×C7—22no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—41no—
553C22×C7—41no—
554C22×C7—42no—
555C22×C7—41no—
556C22×C7—41no—
557C22×C7—42no—
558C22×C7—41no—
559C22×C7—41no—
560C22×C7—42no—
561C22×C7—41no—
562C22×C7—41no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—816no—
568C22×C7—81no—
569C22×C7—81no—
570C22×C7—81no—
571C22×C7—81no—
572C22×C7C22×C22⋊C411yescharacteristic
573C22×C7D4211yescharacteristic
574C22×C7#54611yescharacteristic
575C22×C7#57511yescharacteristic
576C22×C7#57511yescharacteristic
577C22×C7#57611yescharacteristic
578C22×C7#57711yescharacteristic
579C4×C7—22no—
580C4×C7—22no—
581C4×C7—22no—
582C4×C7—22no—
583C4×C7—42no—
584C4×C7—42no—
585C4×C7C2×C4×D411yescharacteristic
586C4×C7#51811yescharacteristic
587C4×C7D4211yescharacteristic
588C4×C7#54611yescharacteristic
589Dic7—42no—
590Dic7—81no—
591Dic7—81no—
592Dic7—81no—
593C24—21no—
594C24—21no—
595C24—24no—
596C24—42no—
597C24—42no—
598C24—42no—
599C24—42no—
600C24—81no—
601C24—81no—
602C24C2×C22⋊D711yescharacteristic
603C24C2×C22⋊D711yescharacteristic
604#41—28no—
605#41—44no—
606#41—44no—
607#41—44no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8C22×Dic712yes—
614C2×D4—28no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—81no—
636C2×D4—81no—
637C2×D4C22⋊Dic714yes—
638C2×D4D4×D712yes—
639C2×D4#115912yes—
640C2×D4C22×Dic712yes—
641C2×D4C22×Dic712yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—24no—
653C22×C4—24no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—81no—
657C22×C4—81no—
658C22×C4—141no—
659C22×C4—141no—
660C22×C4—141no—
661C22×C4—141no—
662C22×C4—282no—
663C22×C4—282no—
664C22×C4—561no—
665C22×C4C22×Dic712yes—
666C22×C4C22×Dic712yes—
667C22×C4C2×C22⋊D711yescharacteristic
668C22×C4C2×C22⋊D711yescharacteristic
669C22×C4C2×C22⋊D711yescharacteristic
670C22×C4C2×C22⋊D711yescharacteristic
671C22×C4C2×C22⋊D712yes—
672C22×C4C2×C22⋊D712yes—
673C22×C4C23×D711yescharacteristic
674M16—284no—
675M16—284no—
676C2×C8—72no—
677C2×C8—141no—
678C2×C8—141no—
679C2×C8—141no—
680C2×C8—141no—
681C2×C8—141no—
682C2×C8—141no—
683C2×C8—141no—
684C2×C8—141no—
685C2×C8—141no—
686C2×C8—141no—
687C2×C8—141no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—72no—
691C4⋊C4—141no—
692C4⋊C4—141no—
693C4⋊C4—141no—
694C4⋊C4—141no—
695C4⋊C4—141no—
696C4⋊C4—141no—
697C4⋊C4—141no—
698C4⋊C4—282no—
699C4⋊C4C22⋊Dic714yes—
700C4⋊C4C22×Dic712yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—282no—
707C22⋊C4—282no—
708C22⋊C4—561no—
709C22⋊C4C22⋊Dic714yes—
710C22⋊C4C22⋊Dic714yes—
711C42—282no—
712C42—561no—
713C42C22×Dic712yes—
714C42C2×C22⋊D712yes—
715C2×C7—42no—
716C2×C7—42no—
717C2×C7—44no—
718C2×C7—82no—
719C2×C7D4×C22⋊C411yescharacteristic
720C2×C7#289611yescharacteristic
721C2×C7#289711yescharacteristic
722C2×C7#327311yescharacteristic
723C2×C7#327511yescharacteristic
724C2×C7#332211yescharacteristic
725C2×C7#332311yescharacteristic
726C23—21no—
727C23—21no—
728C23—22no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊Dic712yes—
760C23C2×C22⋊Dic712yes—
761C23C22×C22⋊D711yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4D4×Dic714yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—48no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—84no—
802C2×C4—142no—
803C2×C4—281no—
804C2×C4—281no—
805C2×C4—281no—
806C2×C4—281no—
807C2×C4—281no—
808C2×C4—281no—
809C2×C4—281no—
810C2×C4—281no—
811C2×C4—281no—
812C2×C4—281no—
813C2×C4—281no—
814C2×C4—564no—
815C2×C4C2×C22⋊Dic712yes—
816C2×C4C2×C22⋊Dic712yes—
817C2×C4C2×C22⋊Dic712yes—
818C2×C4C2×C22⋊Dic712yes—
819C2×C4C2×D4×D711yescharacteristic
820C2×C4C2×#115911yescharacteristic
821C2×C4#654811yescharacteristic
822C2×C4#654811yescharacteristic
823C2×C4C23×Dic711yescharacteristic
824C2×C4C22×C22⋊D711yescharacteristic
825C8—142no—
826C8—281no—
827C8—281no—
828C8—281no—
829C7#2242711yescharacteristic, complemented, Sylow
830C22—22no—
831C22—22no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22D4×C22⋊D711yescharacteristic
860C22#9049711yescharacteristic
861C22#9051311yescharacteristic
862C22#9051311yescharacteristic
863C22#9052611yescharacteristic
864C22#9052711yescharacteristic
865C22C22×C22⋊Dic711yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—282no—
873C4—561no—
874C4—561no—
875C4—561no—
876C4C2×D4×Dic711yescharacteristic
877C4#9048911yescharacteristic
878C4D4×C22⋊D711yescharacteristic
879C4#9049711yescharacteristic
880C2—42no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2#1174094511yescharacteristic
885C2#1174094611yescharacteristic
886C2#1174094911yescharacteristic
887C2#1174095311yescharacteristic
888C2D4×C22⋊Dic711yescharacteristic
889C2#1174151711yescharacteristic
890C2#1174154411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#546C2
socleC23×C7C22×D4
cosocleC22×C4×C7C24
hypercenterC2×#546D7
hypocenterC7#22427
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
2. C2×#90004C2semidirect
3. C2×#89987C2semidirect
4. #11739780C2semidirect
5. C2×#89784C2semidirect
6. #11729889C2semidirect
7. #11729882C2semidirect
8. #11729479C2semidirect
9. #11729475C2semidirect
10. #11729451C2semidirect
11. #11729447C2semidirect
12. #11729436C2semidirect
13. #11729431C2semidirect
14. C4×#6406C2semidirect
15. #11729359C2semidirect
19. C7×#546C4semidirect
30. C22×C4⋊Dic7C22semidirect
32. C22×#1136C22semidirect
34. C2×#6409C22semidirect
35. C2×#6409C22semidirect
36. C2×#6409C22semidirect
37. C2×#6409C22semidirect
49. #89984C22semidirect
51. C2×C22⋊(C7⋊C8)C22semidirect
56. #89708C22semidirect
57. C4×C4⋊Dic7C22semidirect
58. C2×C4⋊(C7⋊C8)C22semidirect
59. C2×C4×C7⋊C8C22semidirect
60. #89324C22semidirect
61. #89324C22semidirect
62. #89324C22semidirect
63. #89324C22semidirect
81. C22×C7×D4C2×C4semidirect
91. C7×#124C2×C4semidirect
94. C7×C22⋊Q8C2×C4semidirect
101. C4×C7×D4C2×C4semidirect
150. #6406D4semidirect
302. #546Dic7semidirect
464. C22×D4C2×Dic7semidirect
484. #124C2×Dic7semidirect
487. C22⋊Q8C2×Dic7semidirect
494. C4×D4C2×Dic7semidirect
829. C7#22427semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5462
C2×#900042
C2×#899872
#117397802
C2×#897842
#117298892
#117298822
#117294792
#117294752
#117294512
#117294472
#117294362
#117294312
C4×#64062
#117293592
#224277