Finite Group Databasebeta

← C4×#89724 #13275612

Subgroups — C4×#89724 #13275612

Order 1792.

1790 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
2C2×C4×C22⋊Dic7C211yesmaximal, characteristic
3C2×C4×C22⋊Dic7C211yesmaximal, characteristic
4C2×#89724C211yesmaximal, characteristic
5C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
6#11729303C211yesmaximal, characteristic
7#11729302C211yesmaximal, characteristic
8#11729301C211yesmaximal, characteristic
9C4×C7⋊#95C211yesmaximal, characteristic, complemented
10C4×C7⋊#95C211yesmaximal, characteristic, complemented
11C4×C7⋊#95C211yesmaximal, characteristic, complemented
12#11727175C211yesmaximal, characteristic, complemented
13#11727172C211yesmaximal, characteristic, complemented
14#11727171C211yesmaximal, characteristic, complemented
15#11727167C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C4×C7×C22⋊C4—24no—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C4×C22⋊Dic7—24no—
35C4×C22⋊Dic7—24no—
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2211yescharacteristic
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54#89724C418yesdirect product factor
55C4×Dic7⋊C4—24no—
56C4×#397—71nomaximal, Sylow
57C25×C7C2311yescharacteristic
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7D414yes—
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4C2×C414yes—
85C2×C42×C7—22no—
86C2×C42×C7—22no—
87C2×C42×C7—22no—
88C2×C42×C7—22no—
89C2×C42×C7—22no—
90C2×C42×C7—22no—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7—22no—
93C2×C22⋊Dic7—22no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—22no—
99C2×C22⋊Dic7—22no—
100C2×C22⋊Dic7—22no—
101C2×C22⋊Dic7C2×C414yes—
102C2×C22⋊Dic7C2×C414yes—
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—22no—
105C2×Dic7⋊C4—22no—
106C2×Dic7⋊C4—22no—
107C2×Dic7⋊C4—22no—
108C2×Dic7⋊C4C2×C414yescomplemented
109C2×C4×Dic7—22no—
110C2×C4×Dic7—22no—
111C2×C4×Dic7—22no—
112C2×C4×Dic7—22no—
113C2×C4×Dic7—22no—
114C2×C4×Dic7—22no—
115C2×C4×Dic7—22no—
116C2×C4×Dic7—22no—
117C2×C4×Dic7—22no—
118C2×C4×Dic7—22no—
119C2×C4×Dic7—22no—
120C2×C4×Dic7D414yes—
121C7×#95—22no—
122C7×#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95C2×C414yescomplemented
139C7⋊#95C2×C414yescomplemented
140C7⋊#95C2×C414yescomplemented
141C2×#397—71no—
142C2×C4×C4⋊C4—71no—
143C2×C4×C22⋊C4—71no—
144C2×C4×C22⋊C4—71no—
145C2×C4×C22⋊C4D711yescharacteristic
146#1445—71no—
147#1443—71no—
148#1443—71no—
149#1442—71no—
150#1440—71no—
151#1440—71no—
152#1439—71no—
153C4×#95—71no—
154C4×#95—71no—
155C4×#95—71no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7C22×C412yes—
169C24×C7C2×D412yes—
170C24×C7#4112yes—
171C24×C7C2411yescharacteristic
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—28no—
203C22×C4×C7—28no—
204C22×C4×C7—28no—
205C22×C4×C7—44no—
206C22×C4×C7—44no—
207C22×C4×C7—44no—
208C22×C4×C7—44no—
209C22×C4×C7C22×C412yes—
210C22×C4×C7C22×C412yes—
211C22×C4×C7C2×D412yes—
212C22×C4×C7C2×D412yes—
213C22×C4×C7C2×D412yes—
214C22×C4×C7#4112yes—
215C22×C4×C7#4112yes—
216C22×C4×C7#4112yes—
217C22×C4×C7#4112yes—
218C22×C4×C7#4112yes—
219C22×C4×C7#4112yes—
220C22×C4×C7#4112yes—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—21no—
265C22×Dic7—21no—
266C22×Dic7—21no—
267C22×Dic7C22×C412yes—
268C22×Dic7C22×C412yes—
269C22×Dic7C22×C412yes—
270C22×Dic7C22×C412yes—
271C22×Dic7C2×D412yes—
272C22×Dic7C2×D412yes—
273C22×Dic7#4112yes—
274C22×Dic7#4112yes—
275C22×Dic7#4112yes—
276C22×Dic7#4112yes—
277C7×C22⋊C4—28no—
278C7×C22⋊C4—28no—
279C42×C7—44no—
280C42×C7—44no—
281C22⋊Dic7—28no—
282C22⋊Dic7—28no—
283C22⋊Dic7—28no—
284C22⋊Dic7—28no—
285Dic7⋊C4—28no—
286Dic7⋊C4—28no—
287C4×Dic7—28no—
288C4×Dic7—44no—
289C4×Dic7—44no—
290C4×Dic7—44no—
291C24×C4C2×D711yescharacteristic
292C22×C4⋊C4—71no—
293C22×C4⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4—71no—
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4C2×D711yescharacteristic
299C22×C22⋊C4C2×D711yescharacteristic
300C22×C42—71no—
301C22×C42—71no—
302C22×C42—71no—
303C22×C42—71no—
304C22×C42C2×D711yescharacteristic
305C22×C42C2×D711yescharacteristic
306#397—78no—
307C4×C4⋊C4—144no—
308C4×C22⋊C4—24no—
309C4×C22⋊C4—144no—
310C4×C22⋊C4—144no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95—71no—
328C2×#95—71no—
329C2×#95C2×D711yescharacteristic
330C2×#95C2×D711yescharacteristic
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7—41no—
353C23×C7—41no—
354C23×C7—41no—
355C23×C7—41no—
356C23×C7—41no—
357C23×C7—41no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7—41no—
362C23×C7—41no—
363C23×C7—41no—
364C23×C7—41no—
365C23×C7C4×D414yes—
366C23×C7C23×C411yescharacteristic
367C23×C7C22×D411yescharacteristic
368C23×C7C22×D411yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7C2×#4111yescharacteristic
373C23×C7C2×#4111yescharacteristic
374C23×C7C2×#4111yescharacteristic
375C23×C7C2×#4111yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7C2×#4111yescharacteristic
378C23×C7C2×#4111yescharacteristic
379C23×C7C2×#4111yescharacteristic
380C23×C7C2×#4111yescharacteristic
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—416no—
417C2×C4×C7#12114yes—
418C2×C4×C7#12314yes—
419C2×C4×C7#12314yes—
420C2×C4×C7#12314yes—
421C2×C4×C7#12414yes—
422C2×C4×C7#12614yes—
423C2×C4×C7#12614yes—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—41no—
452C2×Dic7—41no—
453C2×Dic7—41no—
454C2×Dic7—41no—
455C2×Dic7—41no—
456C2×Dic7—41no—
457C2×Dic7—41no—
458C2×Dic7—41no—
459C2×Dic7—41no—
460C2×Dic7—41no—
461C2×Dic7—41no—
462C2×Dic7—41no—
463C2×Dic7—41no—
464C2×Dic7—41no—
465C2×Dic7—41no—
466C2×Dic7—41no—
467C2×Dic7—41no—
468C2×Dic7—41no—
469C2×Dic7—41no—
470C2×Dic7—41no—
471C2×Dic7—41no—
472C2×Dic7—41no—
473C2×Dic7—41no—
474C2×Dic7—41no—
475C2×Dic7—41no—
476C2×Dic7—41no—
477C2×Dic7—41no—
478C2×Dic7—41no—
479C2×Dic7C4×D414yes—
480C25C22×D711yescharacteristic
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—22no—
486C23×C4—22no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—71no—
493C23×C4—71no—
494C23×C4—71no—
495C23×C4C22⋊D714yes—
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500C23×C4C22×D711yescharacteristic
501C23×C4C22×D711yescharacteristic
502C2×C4⋊C4—74no—
503C2×C4⋊C4—142no—
504C2×C4⋊C4—142no—
505C2×C4⋊C4—142no—
506C2×C4⋊C4—142no—
507C2×C4⋊C4—142no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—74no—
514C2×C22⋊C4—74no—
515C2×C22⋊C4—142no—
516C2×C22⋊C4—142no—
517C2×C22⋊C4—142no—
518C2×C22⋊C4—142no—
519C2×C22⋊C4—142no—
520C2×C22⋊C4—142no—
521C2×C22⋊C4—142no—
522C2×C22⋊C4—142no—
523C2×C22⋊C4—142no—
524C2×C22⋊C4—142no—
525C2×C22⋊C4C4×D714yes—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—74no—
533C2×C42—142no—
534C2×C42—142no—
535C2×C42—142no—
536C2×C42—142no—
537C2×C42—142no—
538C2×C42—142no—
539C2×C42—142no—
540C2×C42—142no—
541C2×C42—142no—
542C2×C42—142no—
543C2×C42—142no—
544#95—22no—
545#95—22no—
546#95—74no—
547#95—74no—
548#95—74no—
549#95—142no—
550#95—142no—
551#95—142no—
552#95—142no—
553#95—142no—
554#95—142no—
555#95—142no—
556#95—142no—
557#95—142no—
558#95—142no—
559#95—142no—
560#95—142no—
561#95—142no—
562#95—142no—
563#95—142no—
564C22×C7—24no—
565C22×C7—24no—
566C22×C7—24no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7—42no—
574C22×C7—42no—
575C22×C7—42no—
576C22×C7—42no—
577C22×C7—42no—
578C22×C7—42no—
579C22×C7C2×C4×D411yescharacteristic
580C22×C7C2×C4×D411yescharacteristic
581C22×C7C4×#4111yescharacteristic
582C22×C7C4×#4111yescharacteristic
583C22×C7C4×#4111yescharacteristic
584C22×C7C4×#4111yescharacteristic
585C22×C7C4×#4111yescharacteristic
586C22×C7C2×#12111yescharacteristic
587C22×C7C2×#12311yescharacteristic
588C22×C7C2×#12311yescharacteristic
589C22×C7C2×#12311yescharacteristic
590C22×C7#52511yescharacteristic
591C22×C7#52511yescharacteristic
592C22×C7#52511yescharacteristic
593C22×C7#52511yescharacteristic
594C22×C7C2×#12411yescharacteristic
595C22×C7C2×#12611yescharacteristic
596C22×C7C2×#12611yescharacteristic
597C22×C7#52911yescharacteristic
598C22×C7#52911yescharacteristic
599C22×C7#52911yescharacteristic
600C22×C7#52911yescharacteristic
601C22×C7#52911yescharacteristic
602C22×C7#52911yescharacteristic
603C22×C7#52911yescharacteristic
604C22×C7#52911yescharacteristic
605C22×C7#52911yescharacteristic
606C22×C7#52911yescharacteristic
607C22×C7#52911yescharacteristic
608C22×C7#52911yescharacteristic
609C22×C7#52911yescharacteristic
610C22×C7#52911yescharacteristic
611C22×C7#52911yescharacteristic
612C22×C7#53211yescharacteristic
613C22×C7#53211yescharacteristic
614C4×C7—42no—
615C4×C7—42no—
616C4×C7—42no—
617C4×C7—42no—
618C4×C7—42no—
619C4×C7#39718yescomplemented
620Dic7—24no—
621Dic7—42no—
622Dic7—42no—
623Dic7—42no—
624Dic7—42no—
625Dic7—42no—
626Dic7—42no—
627Dic7—42no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24C2×C4×D712yes—
641C24#115712yes—
642C24C2×C22⋊D712yes—
643C24C23×D711yescharacteristic
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—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—28no—
675C22×C4—28no—
676C22×C4—28no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—72no—
682C22×C4—72no—
683C22×C4—72no—
684C22×C4—72no—
685C22×C4—72no—
686C22×C4—72no—
687C22×C4—72no—
688C22×C4—72no—
689C22×C4—72no—
690C22×C4—72no—
691C22×C4—141no—
692C22×C4—141no—
693C22×C4—141no—
694C22×C4—141no—
695C22×C4—141no—
696C22×C4—141no—
697C22×C4—141no—
698C22×C4—141no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—141no—
703C22×C4—141no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—141no—
710C22×C4—141no—
711C22×C4—141no—
712C22×C4—141no—
713C22×C4—141no—
714C22×C4—141no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—141no—
720C22×C4—141no—
721C22×C4—141no—
722C22×C4—141no—
723C22×C4—141no—
724C22×C4—141no—
725C22×C4—141no—
726C22×C4—141no—
727C22×C4—141no—
728C22×C4—141no—
729C22×C4—141no—
730C22×C4—141no—
731C22×C4—141no—
732C22×C4—141no—
733C22×C4—141no—
734C22×C4—141no—
735C22×C4—141no—
736C22×C4—141no—
737C22×C4C2×C4×D712yes—
738C22×C4C2×C4×D712yes—
739C22×C4#115712yes—
740C22×C4#115712yes—
741C22×C4#115712yes—
742C22×C4#115712yes—
743C22×C4D4×D712yes—
744C22×C4#115912yes—
745C22×C4#115912yes—
746C22×C4#115912yes—
747C22×C4C2×C22⋊D712yes—
748C22×C4C2×C22⋊D712yes—
749C4⋊C4—148no—
750C4⋊C4—148no—
751C22⋊C4—28no—
752C22⋊C4—28no—
753C22⋊C4—148no—
754C22⋊C4—148no—
755C22⋊C4—148no—
756C22⋊C4—148no—
757C42—44no—
758C42—44no—
759C42—148no—
760C42—284no—
761C42—284no—
762C42—284no—
763C2×C7—44no—
764C2×C7C4×#12111yescharacteristic
765C2×C7C4×#12311yescharacteristic
766C2×C7C4×#12311yescharacteristic
767C2×C7C4×#12311yescharacteristic
768C2×C7C4×#12411yescharacteristic
769C2×C7C4×#12611yescharacteristic
770C2×C7C4×#12611yescharacteristic
771C2×C7C2×#39711yescharacteristic
772C2×C7#239211yescharacteristic
773C2×C7#239511yescharacteristic
774C2×C7#239511yescharacteristic
775C2×C7#239511yescharacteristic
776C2×C7#239811yescharacteristic
777C2×C7#240111yescharacteristic
778C2×C7#240111yescharacteristic
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23C4×C22⋊D714yes—
814C23C22×C4×D711yescharacteristic
815C23C2×#115711yescharacteristic
816C23C2×#115711yescharacteristic
817C23C2×#115711yescharacteristic
818C23C2×#115711yescharacteristic
819C23C2×#115711yescharacteristic
820C23C2×D4×D711yescharacteristic
821C23C2×#115911yescharacteristic
822C23C2×#115911yescharacteristic
823C23C2×#115911yescharacteristic
824C23D7×#4111yescharacteristic
825C23D7×#4111yescharacteristic
826C23D7×#4111yescharacteristic
827C23D7×#4111yescharacteristic
828C23C22×C22⋊D711yescharacteristic
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—416no—
865C2×C4—74no—
866C2×C4—142no—
867C2×C4—142no—
868C2×C4—142no—
869C2×C4—142no—
870C2×C4—142no—
871C2×C4—142no—
872C2×C4—142no—
873C2×C4—142no—
874C2×C4—142no—
875C2×C4—142no—
876C2×C4—142no—
877C2×C4—142no—
878C2×C4—142no—
879C2×C4—142no—
880C2×C4—142no—
881C2×C4—142no—
882C2×C4—142no—
883C2×C4—142no—
884C2×C4—142no—
885C2×C4—142no—
886C2×C4—142no—
887C2×C4—142no—
888C2×C4—142no—
889C2×C4—142no—
890C2×C4—142no—
891C2×C4—142no—
892C2×C4—142no—
893C2×C4—281no—
894C2×C4—281no—
895C2×C4—281no—
896C2×C4—281no—
897C2×C4—281no—
898C2×C4—281no—
899C2×C4—281no—
900C2×C4—281no—
901C2×C4—281no—
902C2×C4—281no—
903C2×C4—281no—
904C2×C4—281no—
905C2×C4—281no—
906C2×C4—281no—
907C2×C4—281no—
908C2×C4—281no—
909C2×C4—281no—
910C2×C4—281no—
911C2×C4—281no—
912C2×C4—281no—
913C2×C4—281no—
914C2×C4—281no—
915C2×C4—281no—
916C2×C4—281no—
917C2×C4—281no—
918C2×C4—281no—
919C2×C4—281no—
920C2×C4—281no—
921C2×C4#644214yes—
922C2×C4#644214yes—
923C2×C4#644614yes—
924C2×C4#644814yes—
925C2×C4#649214yes—
926C2×C4#649814yes—
927C2×C4#650214yes—
928C7C4×#39711yescharacteristic, complemented, Sylow
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C4×#115711yescharacteristic
945C22C4×#115711yescharacteristic
946C22#9017011yescharacteristic
947C22#9017011yescharacteristic
948C22C2×#644211yescharacteristic
949C22C2×#644211yescharacteristic
950C22C2×#644611yescharacteristic
951C22C2×#644811yescharacteristic
952C22#9021911yescharacteristic
953C22#9021911yescharacteristic
954C22#9021911yescharacteristic
955C22#9021911yescharacteristic
956C22C4×#115911yescharacteristic
957C22C4×#115911yescharacteristic
958C22C4×#115911yescharacteristic
959C22#9022911yescharacteristic
960C22#9022911yescharacteristic
961C22#9022911yescharacteristic
962C22#9022911yescharacteristic
963C22#9022911yescharacteristic
964C22#9022911yescharacteristic
965C22C4×D4×D711yescharacteristic
966C22#9023811yescharacteristic
967C22#9023811yescharacteristic
968C22#9023911yescharacteristic
969C22#9024811yescharacteristic
970C22#9024811yescharacteristic
971C22#9024811yescharacteristic
972C22C2×C4×C22⋊D711yescharacteristic
973C22C2×#649211yescharacteristic
974C22#9048211yescharacteristic
975C22C2×#649811yescharacteristic
976C22C2×#650211yescharacteristic
977C22#9051911yescharacteristic
978C22#9052311yescharacteristic
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—144no—
985C4—282no—
986C4—282no—
987C4—282no—
988C4—282no—
989C4—282no—
990C4—282no—
991C4—282no—
992C4#8972418yesdirect product factor
993C2—44no—
994C2C4×#644811yescharacteristic
995C2C4×#644211yescharacteristic
996C2C4×#644211yescharacteristic
997C2#1173092611yescharacteristic
998C2#1173092711yescharacteristic
999C2#1173092711yescharacteristic
1000C2C4×#644611yescharacteristic
1001C2#1173102711yescharacteristic
1002C2C4×#649211yescharacteristic
1003C2C2×#8972411yescharacteristic
1004C2#1173971911yescharacteristic
1005C2C4×#650211yescharacteristic
1006C2C4×#649811yescharacteristic
1007C2#1173979011yescharacteristic
1008C2#1173979111yescharacteristic
subgroupG/H
centerC23×C4C22×D7
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC2×C4×C7×C22⋊C4C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C4×#397
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. C2×C4×Dic7⋊C4C2semidirect
9. C4×C7⋊#95C2semidirect
10. C4×C7⋊#95C2semidirect
11. C4×C7⋊#95C2semidirect
12. #11727175C2semidirect
13. #11727172C2semidirect
14. #11727171C2semidirect
15. #11727167C2semidirect
54. #89724C4direct (N × H)
108. C2×Dic7⋊C4C2×C4semidirect
138. C7⋊#95C2×C4semidirect
139. C7⋊#95C2×C4semidirect
140. C7⋊#95C2×C4semidirect
619. C4×C7#397semidirect
928. C7C4×#397semidirect
992. C4#89724direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C7×C22⋊C42
C2×C4×C22⋊Dic72
C2×#897242
C2×C4×Dic7⋊C42
#117293032
#117293022
#117293012
C4×C7⋊#952
#117271752
#117271722
#117271712
#117271672
C4×#3977