Finite Group Databasebeta

← #13319671

Subgroups — #13319671

Order 1792.

1738 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D7C211yesmaximal, characteristic
2C2×C7×#407C211yesmaximal, characteristic, complemented
3C2×#89979C211yesmaximal, characteristic, complemented
4#11727725C212yesmaximal, complemented
5#11727722C214yesmaximal, complemented
6#11727721C212yesmaximal, complemented
7#11727673C214yesmaximal, complemented
8C24×C4×C7C2211yescharacteristic
9C23×C22⋊D7C411yescharacteristic
10C23×C4×D7C411yescharacteristic
11C22×C7×M16—21no—
12C22×C22⋊Dic7C411yescharacteristic
13C2×C4×C22⋊D7—21no—
14C2×C4×C22⋊D7—21no—
15C2×C4×C22⋊D7—21no—
16C2×C4×C22⋊D7—21no—
17C2×C4×C22⋊D7—21no—
18C2×C4×C22⋊D7—21no—
19C2×C4×C22⋊D7—21no—
20C2×C4×C22⋊D7—21no—
21C2×C4×C22⋊D7C412yes—
22C2×C4×C22⋊D7C412yes—
23C2×C4×C22⋊D7C2212yes—
24C2×C4×C22⋊D7C2212yes—
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×C4×Dic7C411yescharacteristic
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#17362—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—28no—
66C22×C22⋊D7C2×C412yes—
67C22×C22⋊D7C2×C412yes—
68C23×Dic7C2×C411yescharacteristic
69C23×Dic7C2×C411yescharacteristic
70C23×Dic7C2×C411yescharacteristic
71C22×C4×D7—21no—
72C22×C4×D7—21no—
73C22×C4×D7—21no—
74C22×C4×D7—21no—
75C22×C4×D7—44no—
76C22×C4×D7C2×C412yes—
77C22×C4×D7C2×C412yes—
78C2×C7×M16—22no—
79C2×C7×M16—22no—
80C2×C7×M16—44no—
81C22×C7×C8—22no—
82C2×C22⋊Dic7—21no—
83C2×C22⋊Dic7—21no—
84C2×C22⋊Dic7—21no—
85C2×C22⋊Dic7—21no—
86C2×C22⋊Dic7C2×C412yes—
87C2×C22⋊Dic7C2×C412yes—
88C4×C22⋊D7—22no—
89C4×C22⋊D7—22no—
90C4×C22⋊D7—22no—
91C4×C22⋊D7—22no—
92C4×C22⋊D7—22no—
93C4×C22⋊D7—22no—
94C4×C22⋊D7—22no—
95C4×C22⋊D7—22no—
96C4×C22⋊D7—22no—
97C4×C22⋊D7—22no—
98C4×C22⋊D7—22no—
99C4×C22⋊D7—22no—
100C4×C22⋊D7—22no—
101C4×C22⋊D7—22no—
102C4×C22⋊D7—22no—
103C4×C22⋊D7—22no—
104C2×(C2×D7)⋊C4—21no—
105C2×(C2×D7)⋊C4—21no—
106C2×(C2×D7)⋊C4—21no—
107C2×(C2×D7)⋊C4—21no—
108C2×(C2×D7)⋊C4C2×C412yes—
109C2×(C2×D7)⋊C4C2312yes—
110C2×Dic7⋊C4—21no—
111C2×Dic7⋊C4—21no—
112C2×Dic7⋊C4—21no—
113C2×Dic7⋊C4—21no—
114C2×Dic7⋊C4C2×C412yes—
115C2×Dic7⋊C4C2312yes—
116C2×C4×Dic7—21no—
117C2×C4×Dic7—21no—
118C2×C4×Dic7—21no—
119C2×C4×Dic7—21no—
120C2×C4×Dic7C2×C412yes—
121C2×C4×Dic7C2×C412yes—
122C2×#1136—22no—
123C2×#1136—22no—
124C2×#1136—44no—
125C22×C7⋊C8—22no—
126C7×C22⋊C8—22no—
127C7×C22⋊C8—22no—
128C7×C22⋊C8—22no—
129C7×C22⋊C8C2314yes—
130C22⋊(C7⋊C8)—22no—
131C22⋊(C7⋊C8)—22no—
132C22⋊(C7⋊C8)—22no—
133C22⋊(C7⋊C8)C2314yes—
134C22×C4×D4—71no—
135C2×#407—71no—
136C2×#407D711yescharacteristic, complemented
137#1465—74no—
138#1463—72no—
139#1462—72no—
140#1459—74no—
141C24×C7—24no—
142C24×C7—42no—
143C24×C7—42no—
144C24×C7C22⋊C411yescharacteristic
145C24×C7C22⋊C411yescharacteristic
146C24×C7C22⋊C411yescharacteristic
147C24×C7C22⋊C411yescharacteristic
148C24×C7C22×C411yescharacteristic
149C24×C7C22×C411yescharacteristic
150C24×C7C22×C411yescharacteristic
151C23×D7—21no—
152C23×D7—21no—
153C23×D7—24no—
154C23×D7—42no—
155C23×D7—42no—
156C23×D7C22×C412yes—
157C22×C4×C7—24no—
158C22×C4×C7—24no—
159C22×C4×C7—24no—
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×C7—42no—
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×C7C22×C411yescharacteristic
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×C7C2×D411yescharacteristic
198C22×C4×C7C2411yescharacteristic
199C2×C22⋊D7—28no—
200C2×C22⋊D7—28no—
201C2×C22⋊D7—28no—
202C2×C22⋊D7—28no—
203C2×C22⋊D7—22no—
204C2×C22⋊D7—22no—
205C2×C22⋊D7—22no—
206C2×C22⋊D7—22no—
207C2×C22⋊D7—24no—
208C2×C22⋊D7—24no—
209C2×C22⋊D7—24no—
210C2×C22⋊D7M1618yescomplemented
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—24no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—42no—
219C22×Dic7—42no—
220C22×Dic7C22×C412yes—
221C22×Dic7C22×C412yes—
222C22×Dic7C22×C412yes—
223C2×C4×D7—22no—
224C2×C4×D7—22no—
225C2×C4×D7—22no—
226C2×C4×D7—22no—
227C2×C4×D7—44no—
228C2×C4×D7—44no—
229C2×C4×D7—44no—
230C2×C4×D7—44no—
231C2×C4×D7—44no—
232C2×C4×D7—44no—
233C7×M16—44no—
234C7×M16—44no—
235C2×C7×C8—24no—
236C2×C7×C8—44no—
237C22⋊Dic7—22no—
238C22⋊Dic7—22no—
239C22⋊Dic7—22no—
240C22⋊Dic7—22no—
241(C2×D7)⋊C4—22no—
242(C2×D7)⋊C4—22no—
243(C2×D7)⋊C4—22no—
244(C2×D7)⋊C4—22no—
245Dic7⋊C4—22no—
246Dic7⋊C4—22no—
247Dic7⋊C4—22no—
248Dic7⋊C4—22no—
249C4×Dic7—22no—
250C4×Dic7—22no—
251C4×Dic7—22no—
252C4×Dic7—22no—
253#1136—44no—
254#1136—44no—
255C2×C7⋊C8—24no—
256C2×C7⋊C8—44no—
257C23×D4—71no—
258C24×C4—71no—
259C24×C4C2×D711yescharacteristic
260C22×M16—21no—
261C22×M16—141no—
262C2×C4×D4—72no—
263C2×C4×D4—72no—
264C2×C4×D4—72no—
265C2×C4×D4—72no—
266C2×C4×D4—141no—
267C2×C4×D4—141no—
268C2×C4×D4—141no—
269C2×C4×D4—141no—
270C2×C4×D4—141no—
271C2×C4×D4—141no—
272C2×C4×D4—141no—
273C2×C4×D4—141no—
274C22×C4⋊C4—71no—
275C22×C22⋊C4—71no—
276C22×C22⋊C4—71no—
277C22×C42—71no—
278#407—21no—
279#407—21no—
280#407—72no—
281#407—72no—
282#407—141no—
283#407—141no—
284#407C2×D712yes—
285#407C2×D712yescomplemented
286C2×C22⋊C8—21no—
287C2×C22⋊C8—72no—
288C2×C22⋊C8—141no—
289C2×C22⋊C8C2×D712yescomplemented
290#324—78no—
291#323—78no—
292C23×C7—22no—
293C23×C7—22no—
294C23×C7—22no—
295C23×C7—22no—
296C23×C7—22no—
297C23×C7—22no—
298C23×C7—22no—
299C23×C7—22no—
300C23×C7—22no—
301C23×C7—22no—
302C23×C7—22no—
303C23×C7—22no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7—41no—
308C23×C7—41no—
309C23×C7—41no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7—416no—
313C23×C7C2×C22⋊C411yescharacteristic
314C23×C7C2×C22⋊C411yescharacteristic
315C23×C7C2×C22⋊C411yescharacteristic
316C23×C7C2×C22⋊C411yescharacteristic
317C23×C7C2×C22⋊C411yescharacteristic
318C23×C7C2×C22⋊C411yescharacteristic
319C23×C7C2×M1614yes—
320C23×C7C23×C411yescharacteristic
321C22×D7—24no—
322C22×D7—24no—
323C22×D7—22no—
324C22×D7—22no—
325C22×D7—42no—
326C22×D7—416no—
327C22×D7—42no—
328C22×D7—42no—
329C22×D7—42no—
330C22×D7—42no—
331C22×D7—42no—
332C22×D7C2×M1614yescomplemented
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
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#9914yes—
361C2×C4×C7C2×C22⋊C411yescharacteristic
362C2×C4×C7C2×C22⋊C411yescharacteristic
363C2×C4×C7C2×C22⋊C411yescharacteristic
364C2×C4×C7C2×C22⋊C411yescharacteristic
365C2×C4×C7C2×C22⋊C411yescharacteristic
366C2×C4×C7C2×C22⋊C411yescharacteristic
367C2×C4×C7C22×D411yescharacteristic
368C2×C4×C7C22×D411yescharacteristic
369C22⋊D7—28no—
370C22⋊D7—28no—
371C22⋊D7—28no—
372C22⋊D7—28no—
373C2×Dic7—24no—
374C2×Dic7—24no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—42no—
380C2×Dic7—42no—
381C2×Dic7—42no—
382C2×Dic7—42no—
383C2×Dic7—42no—
384C2×Dic7—42no—
385C2×Dic7C2×M1614yescomplemented
386C4×D7—44no—
387C4×D7—44no—
388C4×D7—44no—
389C4×D7—44no—
390C7×C8—44no—
391C7⋊C8—44no—
392C25—71no—
393C25C4×D711yescharacteristic
394C22×D4—72no—
395C22×D4—72no—
396C22×D4—148no—
397C22×D4—141no—
398C22×D4—141no—
399C22×D4—141no—
400C22×D4—141no—
401C23×C4—44no—
402C23×C4—71no—
403C23×C4—71no—
404C23×C4—71no—
405C23×C4—72no—
406C23×C4—72no—
407C23×C4—141no—
408C23×C4—141no—
409C23×C4—141no—
410C23×C4—141no—
411C23×C4—284no—
412C23×C4C4×D711yescharacteristic
413C23×C4C4×D711yescharacteristic
414C23×C4C4×D711yescharacteristic
415C23×C4D2811yescharacteristic
416C23×C4D2811yescharacteristic
417C23×C4D2811yescharacteristic
418C23×C4D2811yescharacteristic
419C23×C4C22⋊D711yescharacteristic
420C23×C4C22⋊D711yescharacteristic
421C23×C4C22⋊D711yescharacteristic
422C23×C4C22⋊D711yescharacteristic
423C23×C4C22×D711yescharacteristic
424C23×C4C22×D711yescharacteristic
425C23×C4C22×D711yescharacteristic
426C2×M16—22no—
427C2×M16—22no—
428C2×M16—44no—
429C2×M16—142no—
430C2×M16—142no—
431C2×M16—284no—
432C22×C8—22no—
433C22×C8—142no—
434C4×D4—142no—
435C4×D4—142no—
436C4×D4—142no—
437C4×D4—142no—
438C4×D4—142no—
439C4×D4—142no—
440C4×D4—142no—
441C4×D4—142no—
442C4×D4—142no—
443C4×D4—142no—
444C4×D4—142no—
445C4×D4—142no—
446C4×D4—142no—
447C4×D4—142no—
448C4×D4—142no—
449C4×D4—142no—
450C2×C4⋊C4—72no—
451C2×C4⋊C4—72no—
452C2×C4⋊C4—141no—
453C2×C4⋊C4—141no—
454C2×C4⋊C4—141no—
455C2×C4⋊C4—141no—
456C2×C22⋊C4—72no—
457C2×C22⋊C4—72no—
458C2×C22⋊C4—72no—
459C2×C22⋊C4—72no—
460C2×C22⋊C4—141no—
461C2×C22⋊C4—141no—
462C2×C22⋊C4—141no—
463C2×C22⋊C4—141no—
464C2×C22⋊C4—141no—
465C2×C22⋊C4—141no—
466C2×C22⋊C4—141no—
467C2×C22⋊C4—141no—
468C2×C42—72no—
469C2×C42—72no—
470C2×C42—141no—
471C2×C42—141no—
472C2×C42—141no—
473C2×C42—141no—
474C22⋊C8—22no—
475C22⋊C8—22no—
476C22⋊C8—22no—
477C22⋊C8—74no—
478C22⋊C8—142no—
479C22⋊C8—142no—
480C22⋊C8—142no—
481C22⋊C8C22×D714yes—
482C22×C7—28no—
483C22×C7—21no—
484C22×C7—21no—
485C22×C7—21no—
486C22×C7—21no—
487C22×C7—21no—
488C22×C7—21no—
489C22×C7—21no—
490C22×C7—21no—
491C22×C7—21no—
492C22×C7—21no—
493C22×C7—21no—
494C22×C7—21no—
495C22×C7—21no—
496C22×C7—21no—
497C22×C7—21no—
498C22×C7—21no—
499C22×C7—44no—
500C22×C7—44no—
501C22×C7—44no—
502C22×C7—44no—
503C22×C7—44no—
504C22×C7—44no—
505C22×C7#40712yes—
506C22×C7#40712yes—
507C22×C7C2×#9912yes—
508C22×C7#41312yes—
509C22×C7C22×C22⋊C411yescharacteristic
510C22×C7C22×M1612yes—
511C2×D7—24no—
512C2×D7—44no—
513C2×D7—48no—
514C2×D7—48no—
515C2×D7—42no—
516C2×D7—42no—
517C2×D7—44no—
518C4×C7—21no—
519C4×C7—21no—
520C4×C7—21no—
521C4×C7—21no—
522C4×C7—21no—
523C4×C7—21no—
524C4×C7C2×#9912yes—
525C4×C7C2×#9912yes—
526Dic7—24no—
527Dic7—42no—
528Dic7—42no—
529C24—24no—
530C24—42no—
531C24—42no—
532C24—72no—
533C24—144no—
534C24—141no—
535C24—141no—
536C24—282no—
537C24—282no—
538C24(C2×D7)⋊C411yescharacteristic
539C24(C2×D7)⋊C411yescharacteristic
540C24(C2×D7)⋊C411yescharacteristic
541C24(C2×D7)⋊C411yescharacteristic
542C24C2×C4×D711yescharacteristic
543C24C2×C4×D711yescharacteristic
544C24C2×C4×D711yescharacteristic
545C2×D4—78no—
546C2×D4—144no—
547C2×D4—144no—
548C2×D4—148no—
549C2×D4—148no—
550C2×D4—148no—
551C2×D4—148no—
552C2×D4—144no—
553C2×D4—142no—
554C2×D4—142no—
555C2×D4—142no—
556C2×D4—142no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—72no—
572C22×C4—72no—
573C22×C4—72no—
574C22×C4—144no—
575C22×C4—141no—
576C22×C4—141no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—142no—
584C22×C4—142no—
585C22×C4—284no—
586C22×C4—284no—
587C22×C4—284no—
588C22×C4—284no—
589C22×C4—284no—
590C22×C4—284no—
591C22×C4—282no—
592C22×C4—282no—
593C22×C4(C2×D7)⋊C411yescharacteristic
594C22×C4(C2×D7)⋊C411yescharacteristic
595C22×C4(C2×D7)⋊C411yescharacteristic
596C22×C4(C2×D7)⋊C411yescharacteristic
597C22×C4(C2×D7)⋊C411yescharacteristic
598C22×C4(C2×D7)⋊C411yescharacteristic
599C22×C4(C2×D7)⋊C411yescharacteristic
600C22×C4(C2×D7)⋊C411yescharacteristic
601C22×C4(C2×D7)⋊C411yescharacteristic
602C22×C4(C2×D7)⋊C411yescharacteristic
603C22×C4(C2×D7)⋊C411yescharacteristic
604C22×C4(C2×D7)⋊C411yescharacteristic
605C22×C4C2×C4×D711yescharacteristic
606C22×C4C2×C4×D711yescharacteristic
607C22×C4C2×C4×D711yescharacteristic
608C22×C4C2×D2811yescharacteristic
609C22×C4C2×D2811yescharacteristic
610C22×C4C2×D2811yescharacteristic
611C22×C4C2×D2811yescharacteristic
612C22×C4C2×D2811yescharacteristic
613C22×C4C2×D2811yescharacteristic
614C22×C4C2×C22⋊D711yescharacteristic
615C22×C4C2×C22⋊D711yescharacteristic
616C22×C4C2×C22⋊D711yescharacteristic
617C22×C4C2×C22⋊D711yescharacteristic
618C22×C4C2×C22⋊D711yescharacteristic
619C22×C4C2×C22⋊D711yescharacteristic
620C22×C4C23×D711yescharacteristic
621M16—44no—
622M16—44no—
623M16—284no—
624M16—284no—
625C2×C8—24no—
626C2×C8—44no—
627C2×C8—144no—
628C2×C8—284no—
629C4⋊C4—142no—
630C4⋊C4—142no—
631C4⋊C4—142no—
632C4⋊C4—142no—
633C22⋊C4—142no—
634C22⋊C4—142no—
635C22⋊C4—142no—
636C22⋊C4—142no—
637C22⋊C4—142no—
638C22⋊C4—142no—
639C22⋊C4—142no—
640C22⋊C4—142no—
641C42—142no—
642C42—142no—
643C42—142no—
644C42—142no—
645C2×C7—22no—
646C2×C7—22no—
647C2×C7—22no—
648C2×C7—22no—
649C2×C7—22no—
650C2×C7—41no—
651C2×C7—41no—
652C2×C7C2×#40711yescharacteristic
653C2×C7C22×#9911yescharacteristic
654C2×C7C2×#41311yescharacteristic
655D7—44no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—416no—
677C23—74no—
678C23—144no—
679C23—144no—
680C23—142no—
681C23—142no—
682C23—282no—
683C23—282no—
684C23—282no—
685C23—2816no—
686C23—282no—
687C23—282no—
688C23—282no—
689C23D7×M1614yes—
690C23C2×(C2×D7)⋊C411yescharacteristic
691C23C2×(C2×D7)⋊C411yescharacteristic
692C23C2×(C2×D7)⋊C411yescharacteristic
693C23C2×(C2×D7)⋊C411yescharacteristic
694C23C2×(C2×D7)⋊C411yescharacteristic
695C23C2×(C2×D7)⋊C411yescharacteristic
696C23C22×C4×D711yescharacteristic
697D4—148no—
698D4—148no—
699D4—148no—
700D4—148no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—74no—
729C2×C4—144no—
730C2×C4—144no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—284no—
736C2×C4—284no—
737C2×C4—282no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4—282no—
741C2×C4—284no—
742C2×C4—284no—
743C2×C4—282no—
744C2×C4—282no—
745C2×C4#638014yes—
746C2×C4C2×(C2×D7)⋊C411yescharacteristic
747C2×C4C2×(C2×D7)⋊C411yescharacteristic
748C2×C4C2×(C2×D7)⋊C411yescharacteristic
749C2×C4C2×(C2×D7)⋊C411yescharacteristic
750C2×C4C2×(C2×D7)⋊C411yescharacteristic
751C2×C4C2×(C2×D7)⋊C411yescharacteristic
752C2×C4C22×D2811yescharacteristic
753C2×C4C22×C22⋊D711yescharacteristic
754C8—44no—
755C8—284no—
756C7#1736211yescharacteristic, complemented, Sylow
757C22—28no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—144no—
781C22—284no—
782C22—288no—
783C22—284no—
784C22—288no—
785C22—282no—
786C22—282no—
787C22C2×#638012yes—
788C22#8989812yes—
789C22#8989812yes—
790C22#8990412yes—
791C22C2×D7×M1612yes—
792C22C22×(C2×D7)⋊C411yescharacteristic
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—144no—
800C4—282no—
801C4—282no—
802C4C2×#638012yes—
803C4C2×#638012yes—
804C2—22no—
805C2—22no—
806C2—22no—
807C2—22no—
808C2—22no—
809C2—41no—
810C2—41no—
811C2—284no—
812C2C22×#638011yescharacteristic
813C2C2×#8989811yescharacteristic
814C2C2×#8990411yescharacteristic
subgroupG/H
centerC2×C4C2×(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#17362
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ 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. #11727722C2semidirect
6. #11727721C2semidirect
7. #11727673C2semidirect
32. C7×#407C22semidirect
34. C2×C7×C22⋊C8C22semidirect
38. #89979C22semidirect
40. C2×C22⋊(C7⋊C8)C22semidirect
41. #89264C22semidirect
42. #89263C22semidirect
136. C2×#407D7semidirect
210. C2×C22⋊D7M16semidirect
285. #407C2×D7semidirect
289. C2×C22⋊C8C2×D7semidirect
332. C22×D7C2×M16semidirect
385. C2×Dic7C2×M16semidirect
756. C7#17362semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D72
C2×C7×#4072
C2×#899792
#117277252
#117277222
#117277212
#117276732
#173627