Finite Group Databasebeta

← #13319863

Subgroups — #13319863

Order 1792.

1450 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6492C211yesmaximal, characteristic
2C2×C7×#407C211yesmaximal, characteristic, complemented
3C2×#89979C211yesmaximal, characteristic, complemented
4#11727725C212yesmaximal, complemented
5#11727723C214yesmaximal, complemented
6#11727721C212yesmaximal, complemented
7#11727674C214yesmaximal, complemented
8C24×C4×C7C2211yescharacteristic
9C23×C22⋊D7C411yescharacteristic
10C22×C7×M16—21no—
11C22×C22⋊Dic7C411yescharacteristic
12C2×#6492—21no—
13C2×#6492—21no—
14C2×#6492—21no—
15C2×#6492—21no—
16C2×#6492—21no—
17C2×#6492—21no—
18C2×#6492—21no—
19C2×#6492—21no—
20C2×#6492C412yes—
21C2×#6492C412yes—
22C2×#6492C2212yes—
23C2×#6492C2212yes—
24C22×(C2×D7)⋊C4C411yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C411yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×#1136—21no—
29C7×#407—21no—
30C7×#407—21no—
31C7×#407C2212yes—
32C7×#407C2212yescomplemented
33C2×C7×C22⋊C8—21no—
34C2×C7×C22⋊C8C2212yescomplemented
35#89979—21no—
36#89979—21no—
37#89979C2212yes—
38#89979C2212yescomplemented
39C2×C22⋊(C7⋊C8)—21no—
40C2×C22⋊(C7⋊C8)C2212yescomplemented
41#89264C2218yescomplemented
42#89263C2218yescomplemented
43#17392—71nomaximal, Sylow
44C25×C7C2×C411yescharacteristic
45C24×D7C2×C411yescharacteristic
46C23×C4×C7—44no—
47C23×C4×C7C2×C411yescharacteristic
48C23×C4×C7C2×C411yescharacteristic
49C23×C4×C7C2×C411yescharacteristic
50C23×C4×C7D411yescharacteristic
51C23×C4×C7D411yescharacteristic
52C23×C4×C7D411yescharacteristic
53C23×C4×C7D411yescharacteristic
54C23×C4×C7D411yescharacteristic
55C23×C4×C7D411yescharacteristic
56C23×C4×C7D411yescharacteristic
57C23×C4×C7D411yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C22×C22⋊D7—21no—
62C22×C22⋊D7—21no—
63C22×C22⋊D7—21no—
64C22×C22⋊D7—21no—
65C22×C22⋊D7—44no—
66C22×C22⋊D7C2×C412yes—
67C22×C22⋊D7C2×C412yes—
68C23×Dic7C2×C411yescharacteristic
69C23×Dic7C2×C411yescharacteristic
70C23×Dic7C2×C411yescharacteristic
71C2×C7×M16—22no—
72C2×C7×M16—22no—
73C2×C7×M16—44no—
74C22×C7×C8—22no—
75C2×C22⋊Dic7—21no—
76C2×C22⋊Dic7—21no—
77C2×C22⋊Dic7—21no—
78C2×C22⋊Dic7—21no—
79C2×C22⋊Dic7C2×C412yes—
80C2×C22⋊Dic7C2×C412yes—
81#6492—22no—
82#6492—22no—
83#6492—22no—
84#6492—22no—
85#6492—22no—
86#6492—22no—
87#6492—22no—
88#6492—22no—
89#6492—22no—
90#6492—22no—
91#6492—22no—
92#6492—22no—
93#6492—22no—
94#6492—22no—
95#6492—22no—
96#6492—22no—
97C2×(C2×D7)⋊C4—21no—
98C2×(C2×D7)⋊C4—21no—
99C2×(C2×D7)⋊C4—21no—
100C2×(C2×D7)⋊C4—21no—
101C2×(C2×D7)⋊C4—21no—
102C2×(C2×D7)⋊C4—21no—
103C2×(C2×D7)⋊C4—21no—
104C2×(C2×D7)⋊C4—21no—
105C2×(C2×D7)⋊C4C2×C412yes—
106C2×(C2×D7)⋊C4C2×C412yes—
107C2×(C2×D7)⋊C4C2×C412yes—
108C2×(C2×D7)⋊C4C2312yes—
109C2×Dic7⋊C4—21no—
110C2×Dic7⋊C4—21no—
111C2×Dic7⋊C4—21no—
112C2×Dic7⋊C4—21no—
113C2×Dic7⋊C4—21no—
114C2×Dic7⋊C4—21no—
115C2×Dic7⋊C4—21no—
116C2×Dic7⋊C4—21no—
117C2×Dic7⋊C4C2×C412yes—
118C2×Dic7⋊C4C2×C412yes—
119C2×Dic7⋊C4C2×C412yes—
120C2×Dic7⋊C4C2312yes—
121C2×#1136—22no—
122C2×#1136—22no—
123C2×#1136—44no—
124C22×C7⋊C8—22no—
125C7×C22⋊C8—22no—
126C7×C22⋊C8—22no—
127C7×C22⋊C8—22no—
128C7×C22⋊C8C2314yes—
129C22⋊(C7⋊C8)—22no—
130C22⋊(C7⋊C8)—22no—
131C22⋊(C7⋊C8)—22no—
132C22⋊(C7⋊C8)C2314yes—
133C22×#123—71no—
134C2×#407—71no—
135C2×#407D711yescharacteristic, complemented
136#1468—74no—
137#1468—74no—
138#1463—72no—
139#1462—72no—
140C24×C7—24no—
141C24×C7—42no—
142C24×C7—42no—
143C24×C7C22⋊C411yescharacteristic
144C24×C7C22⋊C411yescharacteristic
145C24×C7C22⋊C411yescharacteristic
146C24×C7C22⋊C411yescharacteristic
147C24×C7C22×C411yescharacteristic
148C24×C7C22×C411yescharacteristic
149C24×C7C22×C411yescharacteristic
150C23×D7—21no—
151C23×D7—21no—
152C23×D7—42no—
153C23×D7—42no—
154C23×D7—42no—
155C23×D7C22×C412yes—
156C22×C4×C7—24no—
157C22×C4×C7—24no—
158C22×C4×C7—42no—
159C22×C4×C7—42no—
160C22×C4×C7—42no—
161C22×C4×C7—42no—
162C22×C4×C7—42no—
163C22×C4×C7—42no—
164C22×C4×C7—42no—
165C22×C4×C7—42no—
166C22×C4×C7—42no—
167C22×C4×C7—42no—
168C22×C4×C7—42no—
169C22×C4×C7—42no—
170C22×C4×C7C22⋊C411yescharacteristic
171C22×C4×C7C22⋊C411yescharacteristic
172C22×C4×C7C22⋊C411yescharacteristic
173C22×C4×C7C22⋊C411yescharacteristic
174C22×C4×C7C22⋊C411yescharacteristic
175C22×C4×C7C22⋊C411yescharacteristic
176C22×C4×C7C22⋊C411yescharacteristic
177C22×C4×C7C22⋊C411yescharacteristic
178C22×C4×C7C22⋊C411yescharacteristic
179C22×C4×C7C22⋊C411yescharacteristic
180C22×C4×C7C22⋊C411yescharacteristic
181C22×C4×C7C22⋊C411yescharacteristic
182C22×C4×C7C22×C411yescharacteristic
183C22×C4×C7C22×C411yescharacteristic
184C22×C4×C7C22×C411yescharacteristic
185C22×C4×C7C2×D411yescharacteristic
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7C2×D411yescharacteristic
188C22×C4×C7C2×D411yescharacteristic
189C22×C4×C7C2×D411yescharacteristic
190C22×C4×C7C2×D411yescharacteristic
191C22×C4×C7C2×D411yescharacteristic
192C22×C4×C7C2×D411yescharacteristic
193C22×C4×C7C2×D411yescharacteristic
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7C2×D411yescharacteristic
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2411yescharacteristic
198C2×C22⋊D7—22no—
199C2×C22⋊D7—22no—
200C2×C22⋊D7—22no—
201C2×C22⋊D7—22no—
202C2×C22⋊D7—44no—
203C2×C22⋊D7—44no—
204C2×C22⋊D7—44no—
205C2×C22⋊D7—44no—
206C2×C22⋊D7—44no—
207C2×C22⋊D7—44no—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—42no—
215C22×Dic7—42no—
216C22×Dic7—42no—
217C22×Dic7C22×C412yes—
218C22×Dic7C22×C412yes—
219C22×Dic7C22×C412yes—
220C7×M16—44no—
221C7×M16—44no—
222C2×C7×C8—24no—
223C2×C7×C8—44no—
224C22⋊Dic7—22no—
225C22⋊Dic7—22no—
226C22⋊Dic7—22no—
227C22⋊Dic7—22no—
228(C2×D7)⋊C4—22no—
229(C2×D7)⋊C4—22no—
230(C2×D7)⋊C4—22no—
231(C2×D7)⋊C4—22no—
232(C2×D7)⋊C4—22no—
233(C2×D7)⋊C4—22no—
234(C2×D7)⋊C4—22no—
235(C2×D7)⋊C4—22no—
236Dic7⋊C4—22no—
237Dic7⋊C4—22no—
238Dic7⋊C4—22no—
239Dic7⋊C4—22no—
240Dic7⋊C4—22no—
241Dic7⋊C4—22no—
242Dic7⋊C4—22no—
243Dic7⋊C4—22no—
244#1136—44no—
245#1136—44no—
246C2×C7⋊C8—24no—
247C2×C7⋊C8—44no—
248C23×D4—71no—
249C24×C4C2×D711yescharacteristic
250C22×M16—21no—
251C22×M16—141no—
252C2×#123—72no—
253C2×#123—72no—
254C2×#123—72no—
255C2×#123—72no—
256C2×#123—141no—
257C2×#123—141no—
258C2×#123—141no—
259C2×#123—141no—
260C2×#123—141no—
261C2×#123—141no—
262C2×#123—141no—
263C2×#123—141no—
264C22×C4⋊C4—71no—
265C22×C4⋊C4—71no—
266C22×C22⋊C4—71no—
267C22×C22⋊C4—71no—
268C22×C22⋊C4—71no—
269#407—21no—
270#407—21no—
271#407—72no—
272#407—72no—
273#407—141no—
274#407—141no—
275#407C2×D712yes—
276#407C2×D712yescomplemented
277C2×C22⋊C8—21no—
278C2×C22⋊C8—72no—
279C2×C22⋊C8—141no—
280C2×C22⋊C8C2×D712yescomplemented
281#324—78no—
282#323—78no—
283C23×C7—22no—
284C23×C7—22no—
285C23×C7—22no—
286C23×C7—22no—
287C23×C7—22no—
288C23×C7—22no—
289C23×C7—22no—
290C23×C7—22no—
291C23×C7—22no—
292C23×C7—22no—
293C23×C7—22no—
294C23×C7—22no—
295C23×C7—41no—
296C23×C7—41no—
297C23×C7—41no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—416no—
304C23×C7#9914yes—
305C23×C7C2×C22⋊C411yescharacteristic
306C23×C7C2×C22⋊C411yescharacteristic
307C23×C7C2×C22⋊C411yescharacteristic
308C23×C7C2×C22⋊C411yescharacteristic
309C23×C7C2×C22⋊C411yescharacteristic
310C23×C7C2×C22⋊C411yescharacteristic
311C23×C7C23×C411yescharacteristic
312C22×D7—22no—
313C22×D7—24no—
314C22×D7—42no—
315C22×D7—42no—
316C22×D7—42no—
317C22×D7—42no—
318C22×D7—42no—
319C22×D7—42no—
320C22×D7—42no—
321C22×D7—42no—
322C22×D7—88no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
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×C7C2×C22⋊C411yescharacteristic
352C2×C4×C7C2×C22⋊C411yescharacteristic
353C2×C4×C7C2×C22⋊C411yescharacteristic
354C2×C4×C7C2×C22⋊C411yescharacteristic
355C2×C4×C7C2×C22⋊C411yescharacteristic
356C2×C4×C7C2×C22⋊C411yescharacteristic
357C2×C4×C7C22×D411yescharacteristic
358C2×C4×C7C22×D411yescharacteristic
359C22⋊D7—44no—
360C22⋊D7—44no—
361C22⋊D7—44no—
362C22⋊D7—44no—
363C2×Dic7—22no—
364C2×Dic7—22no—
365C2×Dic7—22no—
366C2×Dic7—24no—
367C2×Dic7—42no—
368C2×Dic7—42no—
369C2×Dic7—42no—
370C2×Dic7—42no—
371C2×Dic7—42no—
372C2×Dic7—42no—
373C2×Dic7—42no—
374C2×Dic7—42no—
375C7×C8—44no—
376C7⋊C8—44no—
377C25—71no—
378C25C4×D711yescharacteristic
379C22×D4—72no—
380C22×D4—72no—
381C22×D4—141no—
382C22×D4—141no—
383C22×D4—141no—
384C22×D4—141no—
385C22×D4—284no—
386C23×C4—44no—
387C23×C4—71no—
388C23×C4—71no—
389C23×C4—71no—
390C23×C4C4×D711yescharacteristic
391C23×C4C4×D711yescharacteristic
392C23×C4C4×D711yescharacteristic
393C23×C4D2811yescharacteristic
394C23×C4D2811yescharacteristic
395C23×C4D2811yescharacteristic
396C23×C4D2811yescharacteristic
397C23×C4C22⋊D711yescharacteristic
398C23×C4C22⋊D711yescharacteristic
399C23×C4C22⋊D711yescharacteristic
400C23×C4C22⋊D711yescharacteristic
401C23×C4C22×D711yescharacteristic
402C23×C4C22×D711yescharacteristic
403C23×C4C22×D711yescharacteristic
404C2×M16—22no—
405C2×M16—22no—
406C2×M16—44no—
407C2×M16—142no—
408C2×M16—142no—
409C2×M16—284no—
410C22×C8—22no—
411C22×C8—142no—
412#123—142no—
413#123—142no—
414#123—142no—
415#123—142no—
416#123—142no—
417#123—142no—
418#123—142no—
419#123—142no—
420#123—142no—
421#123—142no—
422#123—142no—
423#123—142no—
424#123—142no—
425#123—142no—
426#123—142no—
427#123—142no—
428C2×C4⋊C4—72no—
429C2×C4⋊C4—72no—
430C2×C4⋊C4—72no—
431C2×C4⋊C4—72no—
432C2×C4⋊C4—141no—
433C2×C4⋊C4—141no—
434C2×C4⋊C4—141no—
435C2×C4⋊C4—141no—
436C2×C4⋊C4—141no—
437C2×C4⋊C4—141no—
438C2×C4⋊C4—141no—
439C2×C4⋊C4—141no—
440C2×C22⋊C4—72no—
441C2×C22⋊C4—72no—
442C2×C22⋊C4—72no—
443C2×C22⋊C4—72no—
444C2×C22⋊C4—72no—
445C2×C22⋊C4—72no—
446C2×C22⋊C4—141no—
447C2×C22⋊C4—141no—
448C2×C22⋊C4—141no—
449C2×C22⋊C4—141no—
450C2×C22⋊C4—141no—
451C2×C22⋊C4—141no—
452C2×C22⋊C4—141no—
453C2×C22⋊C4—141no—
454C2×C22⋊C4—141no—
455C2×C22⋊C4—141no—
456C2×C22⋊C4—141no—
457C2×C22⋊C4—141no—
458C22⋊C8—22no—
459C22⋊C8—22no—
460C22⋊C8—22no—
461C22⋊C8—74no—
462C22⋊C8—142no—
463C22⋊C8—142no—
464C22⋊C8—142no—
465C22⋊C8C22×D714yes—
466C22×C7—28no—
467C22×C7—21no—
468C22×C7—21no—
469C22×C7—21no—
470C22×C7—21no—
471C22×C7—21no—
472C22×C7—21no—
473C22×C7—21no—
474C22×C7—21no—
475C22×C7—21no—
476C22×C7—21no—
477C22×C7—21no—
478C22×C7—21no—
479C22×C7—21no—
480C22×C7—21no—
481C22×C7—21no—
482C22×C7—21no—
483C22×C7—44no—
484C22×C7—44no—
485C22×C7—44no—
486C22×C7—44no—
487C22×C7—44no—
488C22×C7—44no—
489C22×C7C2×#9912yes—
490C22×C7C2×#9912yes—
491C22×C7C2×#9912yes—
492C22×C7#41312yes—
493C22×C7C22×C22⋊C411yescharacteristic
494C22×C7#56812yes—
495C2×D7—42no—
496C2×D7—42no—
497C2×D7—42no—
498C2×D7—84no—
499C2×D7—84no—
500C2×D7—84no—
501C4×C7—21no—
502C4×C7—21no—
503C4×C7—21no—
504C4×C7—21no—
505C4×C7—21no—
506C4×C7—21no—
507C4×C7—21no—
508C4×C7—21no—
509Dic7—42no—
510Dic7—42no—
511Dic7—42no—
512C24—24no—
513C24—42no—
514C24—42no—
515C24—72no—
516C24—141no—
517C24—141no—
518C24—282no—
519C24—282no—
520C24—282no—
521C24(C2×D7)⋊C411yescharacteristic
522C24(C2×D7)⋊C411yescharacteristic
523C24(C2×D7)⋊C411yescharacteristic
524C24(C2×D7)⋊C411yescharacteristic
525C24C2×C4×D711yescharacteristic
526C24C2×C4×D711yescharacteristic
527C24C2×C4×D711yescharacteristic
528C2×D4—142no—
529C2×D4—142no—
530C2×D4—142no—
531C2×D4—142no—
532C2×D4—284no—
533C2×D4—284no—
534C2×D4—284no—
535C2×D4—284no—
536C2×D4—284no—
537C2×D4—284no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—72no—
553C22×C4—72no—
554C22×C4—72no—
555C22×C4—141no—
556C22×C4—141no—
557C22×C4—141no—
558C22×C4—141no—
559C22×C4—141no—
560C22×C4—141no—
561C22×C4—282no—
562C22×C4—282no—
563C22×C4—282no—
564C22×C4(C2×D7)⋊C411yescharacteristic
565C22×C4(C2×D7)⋊C411yescharacteristic
566C22×C4(C2×D7)⋊C411yescharacteristic
567C22×C4(C2×D7)⋊C411yescharacteristic
568C22×C4(C2×D7)⋊C411yescharacteristic
569C22×C4(C2×D7)⋊C411yescharacteristic
570C22×C4(C2×D7)⋊C411yescharacteristic
571C22×C4(C2×D7)⋊C411yescharacteristic
572C22×C4(C2×D7)⋊C411yescharacteristic
573C22×C4(C2×D7)⋊C411yescharacteristic
574C22×C4(C2×D7)⋊C411yescharacteristic
575C22×C4(C2×D7)⋊C411yescharacteristic
576C22×C4C2×C4×D711yescharacteristic
577C22×C4C2×C4×D711yescharacteristic
578C22×C4C2×C4×D711yescharacteristic
579C22×C4C2×D2811yescharacteristic
580C22×C4C2×D2811yescharacteristic
581C22×C4C2×D2811yescharacteristic
582C22×C4C2×D2811yescharacteristic
583C22×C4C2×D2811yescharacteristic
584C22×C4C2×D2811yescharacteristic
585C22×C4C2×C22⋊D711yescharacteristic
586C22×C4C2×C22⋊D711yescharacteristic
587C22×C4C2×C22⋊D711yescharacteristic
588C22×C4C2×C22⋊D711yescharacteristic
589C22×C4C2×C22⋊D711yescharacteristic
590C22×C4C2×C22⋊D711yescharacteristic
591C22×C4C23×D711yescharacteristic
592M16—44no—
593M16—44no—
594M16—284no—
595M16—284no—
596C2×C8—24no—
597C2×C8—44no—
598C2×C8—144no—
599C2×C8—284no—
600C4⋊C4—142no—
601C4⋊C4—142no—
602C4⋊C4—142no—
603C4⋊C4—142no—
604C4⋊C4—142no—
605C4⋊C4—142no—
606C4⋊C4—142no—
607C4⋊C4—142no—
608C22⋊C4—142no—
609C22⋊C4—142no—
610C22⋊C4—142no—
611C22⋊C4—142no—
612C22⋊C4—142no—
613C22⋊C4—142no—
614C22⋊C4—142no—
615C22⋊C4—142no—
616C22⋊C4—142no—
617C22⋊C4—142no—
618C22⋊C4—142no—
619C22⋊C4—142no—
620C2×C7—22no—
621C2×C7—22no—
622C2×C7—22no—
623C2×C7—22no—
624C2×C7—22no—
625C2×C7—41no—
626C2×C7—41no—
627C2×C7#287911yescharacteristic
628C2×C7C22×#9911yescharacteristic
629C2×C7C2×#41311yescharacteristic
630D7—82no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—416no—
652C23—142no—
653C23—144no—
654C23—282no—
655C23—282no—
656C23—282no—
657C23—282no—
658C23—282no—
659C23—282no—
660C23—282no—
661C23—282no—
662C23—568no—
663C23#638014yes—
664C23C2×(C2×D7)⋊C411yescharacteristic
665C23C2×(C2×D7)⋊C411yescharacteristic
666C23C2×(C2×D7)⋊C411yescharacteristic
667C23C2×(C2×D7)⋊C411yescharacteristic
668C23C2×(C2×D7)⋊C411yescharacteristic
669C23C2×(C2×D7)⋊C411yescharacteristic
670C23C22×C4×D711yescharacteristic
671D4—284no—
672D4—284no—
673D4—284no—
674D4—284no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—144no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—142no—
707C2×C4—282no—
708C2×C4—282no—
709C2×C4—282no—
710C2×C4—282no—
711C2×C4—282no—
712C2×C4—282no—
713C2×C4—282no—
714C2×C4—282no—
715C2×C4C2×(C2×D7)⋊C411yescharacteristic
716C2×C4C2×(C2×D7)⋊C411yescharacteristic
717C2×C4C2×(C2×D7)⋊C411yescharacteristic
718C2×C4C2×(C2×D7)⋊C411yescharacteristic
719C2×C4C2×(C2×D7)⋊C411yescharacteristic
720C2×C4C2×(C2×D7)⋊C411yescharacteristic
721C2×C4C22×D2811yescharacteristic
722C2×C4C22×C22⋊D711yescharacteristic
723C8—44no—
724C8—284no—
725C7#1739211yescharacteristic, complemented, Sylow
726C22—28no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—282no—
750C22—282no—
751C22—282no—
752C22—564no—
753C22—564no—
754C22—564no—
755C22C2×#638012yes—
756C22C2×#638012yes—
757C22C2×#638012yes—
758C22#8990412yes—
759C22#9043612yes—
760C22C22×(C2×D7)⋊C411yescharacteristic
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—21no—
768C4—21no—
769C4—282no—
770C4—282no—
771C4—282no—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—41no—
778C2—41no—
779C2—562no—
780C2C22×#638011yescharacteristic
781C2#1174120711yescharacteristic
782C2C2×#8990411yescharacteristic
subgroupG/H
centerC22C22×(C2×D7)⋊C4
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#407C2
socleC22×C7C22×C22⋊C4
prime radicalC23×C22⋊D7C4
cosocleC22×C4×C7C24
hypercenterC2×#407D7
hypocenterC7#17392
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×C7×#407C2semidirect
3. C2×#89979C2semidirect
4. #11727725C2semidirect
5. #11727723C2semidirect
6. #11727721C2semidirect
7. #11727674C2semidirect
32. C7×#407C22semidirect
34. C2×C7×C22⋊C8C22semidirect
38. #89979C22semidirect
40. C2×C22⋊(C7⋊C8)C22semidirect
41. #89264C22semidirect
42. #89263C22semidirect
135. C2×#407D7semidirect
276. #407C2×D7semidirect
280. C2×C22⋊C8C2×D7semidirect
725. C7#17392semidirect

Maximal subgroups

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

subgroupindex
C22×#64922
C2×C7×#4072
C2×#899792
#117277252
#117277232
#117277212
#117276742
#173927