Finite Group Databasebeta

← #13320960

Subgroups — #13320960

Order 1792.

1574 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
1C2×C7×#525C211yesmaximal, characteristic
2C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
3C2×#89979C211yesmaximal, characteristic, complemented
4#11729462C214yesmaximal, complemented
5#11729461C214yesmaximal, complemented
6#11729442C212yesmaximal, complemented
7#11729427C212yesmaximal, complemented
8C22×C7×#41C411yescharacteristic, complemented
9C24×C4×C7C2211yescharacteristic
10C7×#525—21no—
11C7×#525—21no—
12C7×#525—21no—
13C7×#525—21no—
14C7×#525C412yescomplemented
15C7×#525C412yescomplemented
16C7×#525C2212yes—
17C7×#525C2212yes—
18C2×C7×#123—21no—
19C2×C7×C22⋊Q8C411yescharacteristic, complemented
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×C7×#121C411yescharacteristic, complemented
22C2×C7×#121C2211yescharacteristic
23C2×C7×#120—21no—
24C2×C4×C7×D4—21no—
25C2×C4×C7×D4—21no—
26C2×C7×#117C411yescharacteristic, complemented
27C22×C22⋊Dic7—21no—
28C22×C4×Dic7—21no—
29C22×#1136—21no—
30C4×C22⋊Dic7—21no—
31C4×C22⋊Dic7—21no—
32C4×C22⋊Dic7C2212yes—
33C4×C22⋊Dic7C2212yescomplemented
34C2×C7⋊#95C2212yescomplemented
35#89979—21no—
36#89979—21no—
37#89979C2212yes—
38#89979C2212yescomplemented
39C2×C22⋊(C7⋊C8)—21no—
40C2×C22⋊(C7⋊C8)C2212yescomplemented
41#89333C2218yescomplemented
42#89332C2218yescomplemented
43#17542—71nomaximal, Sylow
44C25×C7D411yescharacteristic
45C2×C7×#41—21no—
46C2×C7×#41—21no—
47C2×C7×#41—44no—
48C2×C7×#41C2×C412yes—
49C2×C7×#41C2×C412yescomplemented
50C22×C7×Q8C2×C411yescharacteristic, complemented
51C22×C7×D4—21no—
52C22×C7×D4—21no—
53C22×C7×D4—21no—
54C22×C7×D4C2×C411yescharacteristic, complemented
55C23×C4×C7—21no—
56C23×C4×C7—44no—
57C23×C4×C7C2×C411yescharacteristic
58C23×C4×C7C2×C411yescharacteristic
59C23×C4×C7C2×C411yescharacteristic
60C23×C4×C7C2×C411yescharacteristic
61C23×C4×C7D411yescharacteristic
62C23×C4×C7D411yescharacteristic
63C23×C4×C7D411yescharacteristic
64C23×C4×C7D411yescharacteristic
65C23×C4×C7D411yescharacteristic
66C23×C4×C7D411yescharacteristic
67C23×C4×C7D411yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×Dic7—22no—
72C7×#123—22no—
73C7×#123—22no—
74C7×#123—22no—
75C7×#123—22no—
76C7×C22⋊Q8—21no—
77C7×C22⋊Q8—21no—
78C7×C22⋊Q8—21no—
79C7×C22⋊Q8—21no—
80C7×C22⋊Q8C2×C412yes—
81C7×C22⋊Q8C2×C412yescomplemented
82C7×C22⋊Q8C2×C412yescomplemented
83C7×C22⋊Q8C2312yes—
84C7×#121—21no—
85C7×#121—21no—
86C7×#121—21no—
87C7×#121—21no—
88C7×#121C2×C412yes—
89C7×#121C2×C412yescomplemented
90C7×#121C2×C412yescomplemented
91C7×#121C2312yes—
92C7×#120—22no—
93C7×#120—22no—
94C7×#120—22no—
95C7×#120—22no—
96C4×C7×D4—22no—
97C4×C7×D4—22no—
98C4×C7×D4—22no—
99C4×C7×D4—22no—
100C4×C7×D4—22no—
101C4×C7×D4—22no—
102C4×C7×D4—22no—
103C4×C7×D4—22no—
104C7×#117—21no—
105C7×#117—21no—
106C7×#117C2×C412yes—
107C7×#117C2×C412yescomplemented
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
111C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C42×C7—21no—
118C2×C22⋊Dic7—28no—
119C2×C22⋊Dic7—22no—
120C2×C22⋊Dic7—22no—
121C2×C4×Dic7—22no—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—44no—
124C2×#1136—22no—
125C2×#1136—22no—
126C2×#1136—44no—
127C22×C7⋊C8—22no—
128C7⋊#95—22no—
129C7⋊#95C2314yes—
130C22⋊(C7⋊C8)—22no—
131C22⋊(C7⋊C8)—22no—
132C22⋊(C7⋊C8)—22no—
133C22⋊(C7⋊C8)C2314yes—
134C2×#525D711yescharacteristic
135C2×#407—71no—
136C2×C4×C22⋊C4—71no—
137#1508—72no—
138#1507—72no—
139#1504—74no—
140#1501—74no—
141C24×C7—24no—
142C24×C7—21no—
143C24×C7—42no—
144C24×C7—42no—
145C24×C7C22⋊C411yescharacteristic
146C24×C7C22⋊C411yescharacteristic
147C24×C7C22⋊C411yescharacteristic
148C24×C7C22⋊C411yescharacteristic
149C24×C7C2×D411yescharacteristic
150C24×C7C2×D411yescharacteristic
151C24×C7C2×D411yescharacteristic
152C7×#41—44no—
153C7×#41—44no—
154C7×#41—44no—
155C7×#41—44no—
156C2×C7×Q8—21no—
157C2×C7×Q8—42no—
158C2×C7×Q8C22×C412yes—
159C2×C7×D4—22no—
160C2×C7×D4—22no—
161C2×C7×D4—22no—
162C2×C7×D4—22no—
163C2×C7×D4—22no—
164C2×C7×D4—22no—
165C2×C7×D4—21no—
166C2×C7×D4—42no—
167C2×C7×D4—44no—
168C2×C7×D4—44no—
169C2×C7×D4—44no—
170C2×C7×D4C22×C412yes—
171C22×C4×C7—24no—
172C22×C4×C7—24no—
173C22×C4×C7—24no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—42no—
180C22×C4×C7—42no—
181C22×C4×C7—42no—
182C22×C4×C7—42no—
183C22×C4×C7—42no—
184C22×C4×C7—42no—
185C22×C4×C7—42no—
186C22×C4×C7—42no—
187C22×C4×C7—42no—
188C22×C4×C7—42no—
189C22×C4×C7—42no—
190C22×C4×C7—44no—
191C22×C4×C7C22⋊C411yescharacteristic
192C22×C4×C7C22⋊C411yescharacteristic
193C22×C4×C7C22⋊C411yescharacteristic
194C22×C4×C7C22⋊C411yescharacteristic
195C22×C4×C7C22⋊C411yescharacteristic
196C22×C4×C7C22⋊C411yescharacteristic
197C22×C4×C7C22⋊C411yescharacteristic
198C22×C4×C7C22⋊C411yescharacteristic
199C22×C4×C7C22⋊C411yescharacteristic
200C22×C4×C7C22⋊C411yescharacteristic
201C22×C4×C7C22⋊C411yescharacteristic
202C22×C4×C7C22⋊C411yescharacteristic
203C22×C4×C7C22×C411yescharacteristic
204C22×C4×C7C22×C411yescharacteristic
205C22×C4×C7C22×C411yescharacteristic
206C22×C4×C7C22×C411yescharacteristic
207C22×C4×C7C22×C411yescharacteristic
208C22×C4×C7C22×C411yescharacteristic
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2411yescharacteristic
219C22×Dic7—28no—
220C22×Dic7—24no—
221C22×Dic7—44no—
222C22×Dic7—44no—
223C7×C4⋊C4—22no—
224C7×C4⋊C4—22no—
225C7×C4⋊C4—22no—
226C7×C4⋊C4—21no—
227C7×C4⋊C4—21no—
228C7×C4⋊C4—22no—
229C7×C4⋊C4C22×C412yes—
230C7×C4⋊C4C22×C412yes—
231C7×C22⋊C4—22no—
232C7×C22⋊C4—22no—
233C7×C22⋊C4—22no—
234C7×C22⋊C4—22no—
235C7×C22⋊C4—22no—
236C7×C22⋊C4—22no—
237C7×C22⋊C4—22no—
238C7×C22⋊C4—22no—
239C7×C22⋊C4—22no—
240C7×C22⋊C4—22no—
241C42×C7—22no—
242C42×C7—22no—
243C22⋊Dic7—28no—
244C22⋊Dic7—28no—
245C4×Dic7—44no—
246C4×Dic7—44no—
247#1136—44no—
248#1136—44no—
249C2×C7⋊C8—24no—
250C2×C7⋊C8—44no—
251C22×#41Dic711yescharacteristic, complemented
252C24×C4C2×D711yescharacteristic
253C22×M16—141no—
254#525—21no—
255#525—21no—
256#525—21no—
257#525—21no—
258#525Dic712yescomplemented
259#525Dic712yescomplemented
260#525C2×D712yes—
261#525C2×D712yes—
262C2×#123—21no—
263C2×C22⋊Q8Dic711yescharacteristic, complemented
264C2×C22⋊Q8C2×D711yescharacteristic
265C2×#121Dic711yescharacteristic, complemented
266C2×#121C2×D711yescharacteristic
267C2×#120—21no—
268C2×C4×D4—21no—
269C2×C4×D4—21no—
270C2×#117Dic711yescharacteristic, complemented
271C22×C22⋊C4—141no—
272C22×C42—141no—
273#407—72no—
274#407—72no—
275#407—141no—
276#407—141no—
277C2×C22⋊C8—72no—
278C2×C22⋊C8—141no—
279C4×C22⋊C4—72no—
280C4×C22⋊C4—72no—
281C4×C22⋊C4—141no—
282C4×C22⋊C4—141no—
283C2×#95—72no—
284#328—78no—
285#327—78no—
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—22no—
296C23×C7—22no—
297C23×C7—22no—
298C23×C7—22no—
299C23×C7—41no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7—416no—
308C23×C7—42no—
309C23×C7—42no—
310C23×C7—42no—
311C23×C7#10414yes—
312C23×C7C2×C22⋊C411yescharacteristic
313C23×C7C2×C22⋊C411yescharacteristic
314C23×C7C2×C22⋊C411yescharacteristic
315C23×C7C2×C22⋊C411yescharacteristic
316C23×C7C2×C22⋊C411yescharacteristic
317C23×C7C2×C22⋊C411yescharacteristic
318C23×C7C22×D411yescharacteristic
319C7×Q8—42no—
320C7×Q8—42no—
321C7×D4—42no—
322C7×D4—44no—
323C7×D4—44no—
324C7×D4—44no—
325C7×D4—44no—
326C7×D4—44no—
327C7×D4—44no—
328C7×D4—42no—
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—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—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—44no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—44no—
364C2×C4×C7#9914yes—
365C2×C4×C7C2×C22⋊C411yescharacteristic
366C2×C4×C7C2×C22⋊C411yescharacteristic
367C2×C4×C7C2×C22⋊C411yescharacteristic
368C2×C4×C7C2×C22⋊C411yescharacteristic
369C2×C4×C7C2×C22⋊C411yescharacteristic
370C2×C4×C7C2×C22⋊C411yescharacteristic
371C2×C4×C7C23×C411yescharacteristic
372C2×C4×C7C22×D411yescharacteristic
373C2×Dic7—28no—
374C2×Dic7—44no—
375C2×Dic7—416no—
376C2×Dic7—44no—
377C7⋊C8—44no—
378C25C22⋊D711yescharacteristic
379C2×#41—21no—
380C2×#41—21no—
381C2×#41—44no—
382C2×#41C2×Dic712yes—
383C2×#41C2×Dic712yescomplemented
384C22×Q8C2×Dic711yescharacteristic, complemented
385C22×D4—21no—
386C22×D4—21no—
387C22×D4—21no—
388C22×D4C2×Dic711yescharacteristic, complemented
389C23×C4—21no—
390C23×C4—44no—
391C23×C4—142no—
392C23×C4C2×Dic711yescharacteristic
393C23×C4C2×Dic711yescharacteristic
394C23×C4C2×Dic711yescharacteristic
395C23×C4C2×Dic711yescharacteristic
396C23×C4C22⋊D711yescharacteristic
397C23×C4C22⋊D711yescharacteristic
398C23×C4C22⋊D711yescharacteristic
399C23×C4C22⋊D711yescharacteristic
400C23×C4C22⋊D711yescharacteristic
401C23×C4C22⋊D711yescharacteristic
402C23×C4C22⋊D711yescharacteristic
403C23×C4C22×D711yescharacteristic
404C23×C4C22×D711yescharacteristic
405C23×C4C22×D711yescharacteristic
406C2×M16—142no—
407C2×M16—142no—
408C2×M16—284no—
409C22×C8—142no—
410#123—22no—
411#123—22no—
412#123—22no—
413#123—22no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8C2×Dic712yes—
419C22⋊Q8C2×Dic712yescomplemented
420C22⋊Q8C2×Dic712yescomplemented
421C22⋊Q8C22×D712yes—
422#121—21no—
423#121—21no—
424#121—21no—
425#121—21no—
426#121C2×Dic712yes—
427#121C2×Dic712yescomplemented
428#121C2×Dic712yescomplemented
429#121C22×D712yes—
430#120—22no—
431#120—22no—
432#120—22no—
433#120—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442#117—21no—
443#117—21no—
444#117C2×Dic712yes—
445#117C2×Dic712yescomplemented
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4C2×Dic711yescharacteristic, complemented
449C2×C4⋊C4C2×Dic711yescharacteristic, complemented
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—148no—
456C2×C22⋊C4—142no—
457C2×C22⋊C4—142no—
458C2×C42—21no—
459C2×C42—142no—
460C2×C42—142no—
461C2×C42—284no—
462C22⋊C8—74no—
463C22⋊C8—142no—
464C22⋊C8—142no—
465C22⋊C8—142no—
466#95—74no—
467#95—142no—
468C22×C7—28no—
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—21no—
484C22×C7—21no—
485C22×C7—44no—
486C22×C7—44no—
487C22×C7—44no—
488C22×C7—44no—
489C22×C7—44no—
490C22×C7—44no—
491C22×C7—42no—
492C22×C7—42no—
493C22×C7—42no—
494C22×C7—84no—
495C22×C7C2×#9912yes—
496C22×C7C2×#10412yes—
497C22×C7C2×#10412yes—
498C22×C7C2×#10412yes—
499C22×C7C22×C22⋊C411yescharacteristic
500C22×C7#57512yes—
501C4×C7—21no—
502C4×C7—21no—
503C4×C7—21no—
504C4×C7—21no—
505C4×C7—21no—
506C4×C7—21no—
507C4×C7—42no—
508C4×C7—42no—
509C4×C7—42no—
510C4×C7C2×#9912yes—
511C4×C7C2×#9912yes—
512Dic7—48no—
513C24—24no—
514C24—21no—
515C24—42no—
516C24—42no—
517C24C22⋊Dic711yescharacteristic
518C24C22⋊Dic711yescharacteristic
519C24C22⋊Dic711yescharacteristic
520C24C22⋊Dic711yescharacteristic
521C24C2×C22⋊D711yescharacteristic
522C24C2×C22⋊D711yescharacteristic
523C24C2×C22⋊D711yescharacteristic
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—21no—
529C2×Q8—42no—
530C2×Q8C22×Dic712yes—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—21no—
538C2×D4—42no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4C22×Dic712yes—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—44no—
563C22×C4—148no—
564C22×C4—144no—
565C22×C4—284no—
566C22×C4—284no—
567C22×C4C22⋊Dic711yescharacteristic
568C22×C4C22⋊Dic711yescharacteristic
569C22×C4C22⋊Dic711yescharacteristic
570C22×C4C22⋊Dic711yescharacteristic
571C22×C4C22⋊Dic711yescharacteristic
572C22×C4C22⋊Dic711yescharacteristic
573C22×C4C22⋊Dic711yescharacteristic
574C22×C4C22⋊Dic711yescharacteristic
575C22×C4C22⋊Dic711yescharacteristic
576C22×C4C22⋊Dic711yescharacteristic
577C22×C4C22⋊Dic711yescharacteristic
578C22×C4C22⋊Dic711yescharacteristic
579C22×C4C22×Dic711yescharacteristic
580C22×C4C22×Dic711yescharacteristic
581C22×C4C22×Dic711yescharacteristic
582C22×C4C22×Dic711yescharacteristic
583C22×C4C22×Dic711yescharacteristic
584C22×C4C22×Dic711yescharacteristic
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×C4C2×C22⋊D711yescharacteristic
592C22×C4C2×C22⋊D711yescharacteristic
593C22×C4C2×C22⋊D711yescharacteristic
594C22×C4C23×D711yescharacteristic
595M16—284no—
596M16—284no—
597C2×C8—144no—
598C2×C8—284no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4C22×Dic712yes—
606C4⋊C4C22×Dic712yes—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—148no—
618C22⋊C4—148no—
619C42—22no—
620C42—22no—
621C42—284no—
622C42—284no—
623C2×C7—22no—
624C2×C7—22no—
625C2×C7—22no—
626C2×C7—22no—
627C2×C7—22no—
628C2×C7—41no—
629C2×C7—41no—
630C2×C7—82no—
631C2×C7C22×#9911yescharacteristic
632C2×C7#289611yescharacteristic
633C2×C7C22×#10411yescharacteristic
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—416no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23#641114yes—
660C23C2×C22⋊Dic711yescharacteristic
661C23C2×C22⋊Dic711yescharacteristic
662C23C2×C22⋊Dic711yescharacteristic
663C23C2×C22⋊Dic711yescharacteristic
664C23C2×C22⋊Dic711yescharacteristic
665C23C2×C22⋊Dic711yescharacteristic
666C23C22×C22⋊D711yescharacteristic
667Q8—42no—
668Q8—42no—
669D4—42no—
670D4—44no—
671D4—44no—
672D4—44no—
673D4—44no—
674D4—44no—
675D4—44no—
676D4—42no—
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—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
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—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—148no—
713C2×C4—284no—
714C2×C4—2816no—
715C2×C4—284no—
716C2×C4#640814yes—
717C2×C4C2×C22⋊Dic711yescharacteristic
718C2×C4C2×C22⋊Dic711yescharacteristic
719C2×C4C2×C22⋊Dic711yescharacteristic
720C2×C4C2×C22⋊Dic711yescharacteristic
721C2×C4C2×C22⋊Dic711yescharacteristic
722C2×C4C2×C22⋊Dic711yescharacteristic
723C2×C4C23×Dic711yescharacteristic
724C2×C4C22×C22⋊D711yescharacteristic
725C8—284no—
726C7#1754211yescharacteristic, complemented, Sylow
727C22—28no—
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—21no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—84no—
754C22C2×#640812yes—
755C22C2×#641112yes—
756C22C2×#641112yes—
757C22C2×#641112yes—
758C22#9051312yes—
759C22C22×C22⋊Dic711yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—288no—
770C4C2×#640812yes—
771C4C2×#640812yes—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—41no—
778C2—41no—
779C2—82no—
780C2C22×#640811yescharacteristic
781C2#1174151711yescharacteristic
782C2C22×#641111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#525C2
socleC22×C7C22×C22⋊C4
cosocleC22×C4×C7C24
hypercenterC2×#525D7
hypocenterC7#17542
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Dic7C2semidirect
3. C2×#89979C2semidirect
4. #11729462C2semidirect
5. #11729461C2semidirect
6. #11729442C2semidirect
7. #11729427C2semidirect
8. C22×C7×#41C4semidirect
14. C7×#525C4semidirect
15. C7×#525C4semidirect
19. C2×C7×C22⋊Q8C4semidirect
21. C2×C7×#121C4semidirect
26. C2×C7×#117C4semidirect
33. C4×C22⋊Dic7C22semidirect
34. C2×C7⋊#95C22semidirect
38. #89979C22semidirect
40. C2×C22⋊(C7⋊C8)C22semidirect
41. #89333C22semidirect
42. #89332C22semidirect
49. C2×C7×#41C2×C4semidirect
50. C22×C7×Q8C2×C4semidirect
54. C22×C7×D4C2×C4semidirect
81. C7×C22⋊Q8C2×C4semidirect
82. C7×C22⋊Q8C2×C4semidirect
89. C7×#121C2×C4semidirect
90. C7×#121C2×C4semidirect
107. C7×#117C2×C4semidirect
110. C2×C7×C4⋊C4C2×C4semidirect
111. C2×C7×C4⋊C4C2×C4semidirect
251. C22×#41Dic7semidirect
258. #525Dic7semidirect
259. #525Dic7semidirect
263. C2×C22⋊Q8Dic7semidirect
265. C2×#121Dic7semidirect
270. C2×#117Dic7semidirect
383. C2×#41C2×Dic7semidirect
384. C22×Q8C2×Dic7semidirect
388. C22×D4C2×Dic7semidirect
419. C22⋊Q8C2×Dic7semidirect
420. C22⋊Q8C2×Dic7semidirect
427. #121C2×Dic7semidirect
428. #121C2×Dic7semidirect
445. #117C2×Dic7semidirect
448. C2×C4⋊C4C2×Dic7semidirect
449. C2×C4⋊C4C2×Dic7semidirect
726. C7#17542semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5252
C2×C4×C22⋊Dic72
C2×#899792
#117294622
#117294612
#117294422
#117294272
#175427