Finite Group Databasebeta

← #13275388

Subgroups — #13275388

Order 1792.

2022 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89761C211yesmaximal, characteristic
2C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
4C2×#89442C211yesmaximal, characteristic
5C2×#89441C211yesmaximal, characteristic
6C2×#89421C211yesmaximal, characteristic, complemented
7C2×#89438C211yesmaximal, characteristic
8C7×#1436C211yesmaximal, characteristic, complemented
9C4×C7⋊#95C211yesmaximal, characteristic, complemented
10#11727162C211yesmaximal, characteristic
11#11727162C211yesmaximal, characteristic
12#11727161C211yesmaximal, characteristic, complemented
13#11727160C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15Dic7×#95C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×(C2×D7)⋊C4C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
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
51#89761C418yescomplemented
52C4⋊C4×Dic7—24no—
53C4×(C2×D7)⋊C4—24no—
54#89442C418yescomplemented
55#89441C418yescomplemented
56#89438—24no—
57#89421—24no—
58#13823—71nomaximal, Sylow
59C24×D7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C22×C4×D7—22no—
75C22×C4×D7—22no—
76C22×C4×D7—22no—
77C22×C4×D7—22no—
78C22×C4×D7—41no—
79C22×C4×D7—41no—
80C22×C4×D7C2×C414yes—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4C2×C414yes—
84C2×C42×C7—22no—
85C2×C42×C7—22no—
86C2×C42×C7—41no—
87C2×(C2×D7)⋊C4—22no—
88C2×(C2×D7)⋊C4—22no—
89C2×(C2×D7)⋊C4—22no—
90C2×(C2×D7)⋊C4—22no—
91C2×(C2×D7)⋊C4—22no—
92C2×(C2×D7)⋊C4—22no—
93C2×(C2×D7)⋊C4—22no—
94C2×(C2×D7)⋊C4—22no—
95C2×(C2×D7)⋊C4—41no—
96C2×(C2×D7)⋊C4—41no—
97C2×(C2×D7)⋊C4C2×C414yes—
98C2×(C2×D7)⋊C4C2×C414yes—
99C2×(C2×D7)⋊C4C2×C414yes—
100C2×(C2×D7)⋊C4C2×C414yes—
101C2×(C2×D7)⋊C4C2×C414yes—
102C2×(C2×D7)⋊C4C2×C414yes—
103C2×(C2×D7)⋊C4C2×C414yes—
104C2×(C2×D7)⋊C4C2×C414yes—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7—22no—
107C2×C4⋊Dic7C2×C414yescomplemented
108C2×Dic7⋊C4—22no—
109C2×Dic7⋊C4—22no—
110C2×Dic7⋊C4—22no—
111C2×Dic7⋊C4—22no—
112C2×Dic7⋊C4C2×C414yes—
113C2×Dic7⋊C4C2×C414yescomplemented
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×Dic7—22no—
121C2×C4×Dic7—22no—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—22no—
124C2×C4×Dic7—22no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—22no—
127C2×C4×Dic7—22no—
128C2×C4×Dic7—41no—
129C2×C4×Dic7—41no—
130C2×C4×Dic7—41no—
131C2×C4×Dic7—41no—
132C2×C4×Dic7—41no—
133C2×C4×Dic7C2×C414yescomplemented
134C2×C4×Dic7C2×C414yescomplemented
135C7×#95—22no—
136C7×#95—22no—
137C7×#95—41no—
138C7×#95C2×C414yescomplemented
139C7×#95C2×C414yescomplemented
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C7⋊#95—41no—
145C7⋊#95C2×C414yes—
146C7⋊#95C2×C414yes—
147C7⋊#95C2×C414yescomplemented
148C7⋊#95C2×C414yescomplemented
149C7⋊#95D414yes—
150C7⋊#95D414yes—
151C2×#388—71no—
152C2×#388—71no—
153C2×#385—71no—
154C2×C4×C4⋊C4—71no—
155C2×C4×C4⋊C4—71no—
156C2×C4×C22⋊C4—71no—
157C2×C4×C22⋊C4—71no—
158#1437—71no—
159#1437—71no—
160#1436—71no—
161#1436—71no—
162#1436—71no—
163#1436D711yescharacteristic, complemented
164C4×#95—71no—
165C4×#95—71no—
166C24×C7C2411yescharacteristic
167C23×D7—21no—
168C23×D7—21no—
169C23×D7—21no—
170C23×D7—21no—
171C23×D7—21no—
172C23×D7—21no—
173C23×D7—21no—
174C23×D7—21no—
175C23×D7—21no—
176C23×D7—21no—
177C23×D7—21no—
178C23×D7—21no—
179C23×D7C22×C412yes—
180C23×D7C22×C412yes—
181C23×D7C22×C412yes—
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—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7C22×C412yes—
219C22×C4×C7C22×C412yes—
220C22×C4×C7C22×C412yes—
221C22×C4×C7C22×C412yes—
222C22×C4×C7C22×C412yes—
223C22×C4×C7C22×C412yes—
224C22×C4×C7C22×C412yes—
225C22×C4×C7C22×C412yes—
226C22×C4×C7C22×C412yes—
227C22×C4×C7C2×D412yes—
228C22×C4×C7C2×D412yes—
229C22×C4×C7#4112yes—
230C22×C4×C7#4112yes—
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×Dic7C22×C412yes—
264C22×Dic7C22×C412yes—
265C22×Dic7C22×C412yes—
266C22×Dic7C22×C412yes—
267C22×Dic7C22×C412yes—
268C22×Dic7C22×C412yes—
269C22×Dic7C22×C412yes—
270C22×Dic7C22×C412yes—
271C22×Dic7C22×C412yes—
272C22×Dic7C2×D412yes—
273C22×Dic7C2×D412yes—
274C22×Dic7C2×D412yes—
275C22×Dic7C2×D412yes—
276C22×Dic7#4112yes—
277C22×Dic7#4112yes—
278C22×Dic7#4112yes—
279C22×Dic7#4112yes—
280C2×C4×D7—28no—
281C2×C4×D7—28no—
282C2×C4×D7—44no—
283C2×C4×D7—44no—
284C2×C4×D7—44no—
285C2×C4×D7—44no—
286C2×C4×D7—44no—
287C7×C4⋊C4—28no—
288C42×C7—44no—
289(C2×D7)⋊C4—28no—
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—28no—
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—44no—
294(C2×D7)⋊C4C42116yescomplemented
295C4⋊Dic7—28no—
296Dic7⋊C4—28no—
297Dic7⋊C4—28no—
298C4×Dic7—28no—
299C4×Dic7—28no—
300C4×Dic7—44no—
301C4×Dic7—44no—
302C4×Dic7—44no—
303C4×Dic7—44no—
304C4×Dic7—44no—
305C24×C4—71no—
306C22×C4⋊C4—71no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4C2×D711yescharacteristic
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C42—71no—
317C22×C42—71no—
318C22×C42—71no—
319C22×C42—71no—
320C22×C42—71no—
321C22×C42—71no—
322C22×C42—71no—
323C22×C42C2×D711yescharacteristic
324#388—78no—
325#388—78no—
326#385—78no—
327C4×C4⋊C4—144no—
328C4×C4⋊C4—144no—
329C4×C22⋊C4—144no—
330C4×C22⋊C4—144no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95C2×D711yescharacteristic
343C2×#95C2×D711yescharacteristic
344C2×#95C2×D711yescharacteristic
345C2×#95C2×D711yescharacteristic
346C2×#95C2×D711yescharacteristic
347C23×C7C23×C411yescharacteristic
348C23×C7C23×C411yescharacteristic
349C23×C7C23×C411yescharacteristic
350C23×C7C22×D411yescharacteristic
351C23×C7C22×D411yescharacteristic
352C23×C7C2×#4111yescharacteristic
353C23×C7C2×#4111yescharacteristic
354C23×C7C2×#4111yescharacteristic
355C23×C7C2×#4111yescharacteristic
356C23×C7C2×#4111yescharacteristic
357C23×C7C2×#4111yescharacteristic
358C23×C7H(5,𝔽2)11yescharacteristic
359C23×C7H(5,𝔽2)11yescharacteristic
360C23×C72−1+411yescharacteristic
361C23×C72−1+411yescharacteristic
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—41no—
381C22×D7—41no—
382C22×D7—41no—
383C22×D7—41no—
384C22×D7—41no—
385C22×D7—41no—
386C22×D7—41no—
387C22×D7—41no—
388C22×D7—41no—
389C22×D7—41no—
390C22×D7—41no—
391C22×D7—41no—
392C22×D7—41no—
393C22×D7—41no—
394C22×D7—41no—
395C22×D7—41no—
396C22×D7C2×C4214yes—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
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—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7C2×C4214yes—
444C2×C4×C7C4×D414yes—
445C2×C4×C7C4×D414yes—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—22no—
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
470C2×Dic7—22no—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
478C2×Dic7—22no—
479C2×Dic7—22no—
480C2×Dic7—22no—
481C2×Dic7—22no—
482C2×Dic7—41no—
483C2×Dic7—41no—
484C2×Dic7—41no—
485C2×Dic7—41no—
486C2×Dic7—41no—
487C2×Dic7—41no—
488C2×Dic7—41no—
489C2×Dic7—41no—
490C2×Dic7C2×C4214yes—
491C2×Dic7C4×D414yes—
492C2×Dic7C4×D414yes—
493C2×Dic7C4×D414yes—
494C2×Dic7C4×D414yes—
495C4×D7—416no—
496C25—71no—
497C23×C4—71no—
498C23×C4—71no—
499C23×C4—71no—
500C23×C4—71no—
501C23×C4—71no—
502C23×C4—71no—
503C23×C4—71no—
504C23×C4—74no—
505C23×C4—142no—
506C23×C4—142no—
507C23×C4—142no—
508C23×C4—142no—
509C23×C4—281no—
510C23×C4—281no—
511C23×C4C22×D711yescharacteristic
512C23×C4C22×D711yescharacteristic
513C23×C4C22×D711yescharacteristic
514C23×C4C22×D711yescharacteristic
515C23×C4C22×D711yescharacteristic
516C23×C4C22×D711yescharacteristic
517C23×C4C22×D711yescharacteristic
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—74no—
521C2×C4⋊C4—74no—
522C2×C4⋊C4—74no—
523C2×C4⋊C4—142no—
524C2×C4⋊C4—142no—
525C2×C4⋊C4—142no—
526C2×C4⋊C4—142no—
527C2×C4⋊C4—142no—
528C2×C4⋊C4—142no—
529C2×C4⋊C4C4×D714yes—
530C2×C22⋊C4—74no—
531C2×C22⋊C4—74no—
532C2×C22⋊C4—74no—
533C2×C22⋊C4—74no—
534C2×C22⋊C4—74no—
535C2×C22⋊C4—74no—
536C2×C22⋊C4—74no—
537C2×C22⋊C4—74no—
538C2×C22⋊C4—142no—
539C2×C22⋊C4—142no—
540C2×C22⋊C4—142no—
541C2×C22⋊C4—142no—
542C2×C22⋊C4—142no—
543C2×C22⋊C4—142no—
544C2×C22⋊C4—142no—
545C2×C22⋊C4—142no—
546C2×C22⋊C4—281no—
547C2×C22⋊C4—281no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—41no—
551C2×C42—74no—
552C2×C42—74no—
553C2×C42—142no—
554C2×C42—142no—
555C2×C42—142no—
556C2×C42—142no—
557C2×C42—142no—
558C2×C42—142no—
559C2×C42—142no—
560C2×C42—142no—
561C2×C42—142no—
562C2×C42—142no—
563C2×C42—142no—
564C2×C42—142no—
565C2×C42—142no—
566C2×C42—142no—
567C2×C42—281no—
568C2×C42—281no—
569C2×C42—281no—
570C2×C42—281no—
571C2×C42—281no—
572#95—22no—
573#95—22no—
574#95—41no—
575#95—74no—
576#95—74no—
577#95—74no—
578#95—74no—
579#95—74no—
580#95—74no—
581#95—142no—
582#95—142no—
583#95—142no—
584#95—142no—
585#95—281no—
586#95C4×D714yescomplemented
587#95C4×D714yescomplemented
588C22×C7C22×C4211yescharacteristic
589C22×C7C2×C4×D411yescharacteristic
590C22×C7C2×C4×D411yescharacteristic
591C22×C7C2×C4×D411yescharacteristic
592C22×C7C2×C4×D411yescharacteristic
593C22×C7C2×C4×D411yescharacteristic
594C22×C7C2×C4×D411yescharacteristic
595C22×C7C4×#4111yescharacteristic
596C22×C7C4×#4111yescharacteristic
597C22×C7C4×#4111yescharacteristic
598C22×C7C4×#4111yescharacteristic
599C22×C7C4×#4111yescharacteristic
600C22×C7C4×#4111yescharacteristic
601C22×C7#51811yescharacteristic
602C22×C7#51911yescharacteristic
603C22×C7#52011yescharacteristic
604C22×C7#52011yescharacteristic
605C22×C7#52011yescharacteristic
606C22×C7#52011yescharacteristic
607C22×C7D4211yescharacteristic
608C22×C7#54611yescharacteristic
609C22×C7#54611yescharacteristic
610C22×C7#54711yescharacteristic
611C22×C7#54711yescharacteristic
612C22×C7#54811yescharacteristic
613C22×C7#54811yescharacteristic
614C22×C7#55111yescharacteristic
615C22×C7#55111yescharacteristic
616C22×C7#55211yescharacteristic
617C22×C7#55211yescharacteristic
618C22×C7#55311yescharacteristic
619C22×C7#55311yescharacteristic
620C22×C7#55611yescharacteristic
621C22×C7#55611yescharacteristic
622C22×C7#55911yescharacteristic
623C2×D7—24no—
624C2×D7—24no—
625C2×D7—24no—
626C2×D7—42no—
627C2×D7—42no—
628C2×D7—42no—
629C2×D7—42no—
630C2×D7—42no—
631C2×D7—42no—
632C2×D7—42no—
633C2×D7—42no—
634C2×D7—42no—
635C2×D7—42no—
636C2×D7—42no—
637C2×D7—42no—
638C4×C7—24no—
639C4×C7—24no—
640C4×C7—24no—
641C4×C7—42no—
642C4×C7—42no—
643C4×C7—42no—
644C4×C7—42no—
645Dic7—24no—
646Dic7—24no—
647Dic7—24no—
648Dic7—24no—
649Dic7—24no—
650Dic7—42no—
651Dic7—42no—
652C24—72no—
653C24—72no—
654C24—72no—
655C24—141no—
656C24—141no—
657C24—141no—
658C24—141no—
659C24—141no—
660C24—141no—
661C24—141no—
662C24—141no—
663C24—141no—
664C24—141no—
665C24—141no—
666C24—141no—
667C24C23×D711yescharacteristic
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—72no—
705C22×C4—72no—
706C22×C4—72no—
707C22×C4—72no—
708C22×C4—72no—
709C22×C4—72no—
710C22×C4—72no—
711C22×C4—72no—
712C22×C4—72no—
713C22×C4—72no—
714C22×C4—72no—
715C22×C4—72no—
716C22×C4—72no—
717C22×C4—72no—
718C22×C4—72no—
719C22×C4—72no—
720C22×C4—72no—
721C22×C4—148no—
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×C4—141no—
738C22×C4—141no—
739C22×C4—141no—
740C22×C4—141no—
741C22×C4—141no—
742C22×C4—141no—
743C22×C4—141no—
744C22×C4—141no—
745C22×C4—141no—
746C22×C4—141no—
747C22×C4—141no—
748C22×C4—141no—
749C22×C4—141no—
750C22×C4—141no—
751C22×C4—141no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—148no—
755C22×C4—284no—
756C22×C4—284no—
757C22×C4—284no—
758C22×C4—284no—
759C22×C4—284no—
760C22×C4C2×C4×D712yes—
761C22×C4C2×C4×D712yes—
762C22×C4C2×C4×D712yes—
763C22×C4C2×C4×D712yes—
764C22×C4C2×C4×D712yes—
765C22×C4C2×C4×D712yes—
766C22×C4C2×C4×D712yes—
767C22×C4C2×C4×D712yes—
768C22×C4C2×C4×D712yes—
769C22×C4D4×D712yes—
770C22×C4D4×D712yes—
771C22×C4#115912yes—
772C22×C4#116112yes—
773C4⋊C4—28no—
774C4⋊C4—148no—
775C4⋊C4—148no—
776C4⋊C4—148no—
777C22⋊C4—716no—
778C22⋊C4—148no—
779C22⋊C4—148no—
780C22⋊C4—148no—
781C22⋊C4—148no—
782C22⋊C4—284no—
783C42—44no—
784C42—148no—
785C42—148no—
786C42—284no—
787C42—284no—
788C42—284no—
789C42—284no—
790C42—284no—
791C2×C7C42×D411yescharacteristic
792C2×C7C42×D411yescharacteristic
793C2×C7#227411yescharacteristic
794C2×C7#235811yescharacteristic
795C2×C7#235911yescharacteristic
796C2×C7#235911yescharacteristic
797C2×C7#236111yescharacteristic
798C2×C7#236111yescharacteristic
799C2×C7#236211yescharacteristic
800C2×C7#236211yescharacteristic
801C2×C7#236711yescharacteristic
802C2×C7#236711yescharacteristic
803C2×C7#237311yescharacteristic
804C2×C7#237311yescharacteristic
805C2×C7#237411yescharacteristic
806D7—44no—
807C23—74no—
808C23—142no—
809C23—142no—
810C23—142no—
811C23—142no—
812C23—142no—
813C23—142no—
814C23—142no—
815C23—142no—
816C23—142no—
817C23—142no—
818C23—142no—
819C23—142no—
820C23—142no—
821C23—142no—
822C23—142no—
823C23—142no—
824C23—142no—
825C23—142no—
826C23—281no—
827C23—281no—
828C23—281no—
829C23—281no—
830C23—281no—
831C23—281no—
832C23—281no—
833C23—281no—
834C23—281no—
835C23—281no—
836C23—281no—
837C23—281no—
838C23—281no—
839C23—281no—
840C23—281no—
841C23—281no—
842C23C22×C4×D711yescharacteristic
843C23C22×C4×D711yescharacteristic
844C23C22×C4×D711yescharacteristic
845C23C2×D4×D711yescharacteristic
846C23C2×D4×D711yescharacteristic
847C23C2×#115911yescharacteristic
848C23#654811yescharacteristic
849C23C2×#116111yescharacteristic
850C23#655111yescharacteristic
851C23D7×#4111yescharacteristic
852C23D7×#4111yescharacteristic
853C23D7×#4111yescharacteristic
854C23D7×#4111yescharacteristic
855C23#655311yescharacteristic
856C23#655411yescharacteristic
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—74no—
904C2×C4—74no—
905C2×C4—74no—
906C2×C4—74no—
907C2×C4—74no—
908C2×C4—142no—
909C2×C4—142no—
910C2×C4—142no—
911C2×C4—142no—
912C2×C4—142no—
913C2×C4—142no—
914C2×C4—142no—
915C2×C4—142no—
916C2×C4—142no—
917C2×C4—142no—
918C2×C4—142no—
919C2×C4—142no—
920C2×C4—142no—
921C2×C4—142no—
922C2×C4—142no—
923C2×C4—142no—
924C2×C4—142no—
925C2×C4—142no—
926C2×C4—142no—
927C2×C4—142no—
928C2×C4—142no—
929C2×C4—142no—
930C2×C4—142no—
931C2×C4—142no—
932C2×C4—142no—
933C2×C4—142no—
934C2×C4—142no—
935C2×C4—142no—
936C2×C4—142no—
937C2×C4—142no—
938C2×C4—142no—
939C2×C4—142no—
940C2×C4—142no—
941C2×C4—142no—
942C2×C4—142no—
943C2×C4—142no—
944C2×C4—2816no—
945C2×C4—281no—
946C2×C4—281no—
947C2×C4—281no—
948C2×C4—281no—
949C2×C4—281no—
950C2×C4—281no—
951C2×C4—281no—
952C2×C4—281no—
953C2×C4C42×D714yes—
954C2×C4(C22⋊D7)⋊C414yes—
955C2×C4#645614yes—
956C7#1382311yescharacteristic, complemented, Sylow
957C22—144no—
958C22—144no—
959C22—144no—
960C22—282no—
961C22—282no—
962C22—282no—
963C22—282no—
964C22—282no—
965C22—282no—
966C22—282no—
967C22—282no—
968C22—282no—
969C22—282no—
970C22—282no—
971C22—282no—
972C22C2×C42×D711yescharacteristic
973C22C2×(C22⋊D7)⋊C411yescharacteristic
974C22C2×#645611yescharacteristic
975C22#9019511yescharacteristic
976C22#9021311yescharacteristic
977C22#9021311yescharacteristic
978C22#9021411yescharacteristic
979C22C4×#115911yescharacteristic
980C22C4×#115911yescharacteristic
981C22C4×D4×D711yescharacteristic
982C22C4×D4×D711yescharacteristic
983C22C4×D4×D711yescharacteristic
984C22C4×D4×D711yescharacteristic
985C22#9023611yescharacteristic
986C22#9023711yescharacteristic
987C22#9026311yescharacteristic
988C22C4×#116111yescharacteristic
989C22C4×#116111yescharacteristic
990C22#9026511yescharacteristic
991C22#9028211yescharacteristic
992C22#9030011yescharacteristic
993C22#9030111yescharacteristic
994C22#9032411yescharacteristic
995C22#9032811yescharacteristic
996C22#9033211yescharacteristic
997C22#9033311yescharacteristic
998C22#9034611yescharacteristic
999C22#9034911yescharacteristic
1000C22#9035511yescharacteristic
1001C22#9036811yescharacteristic
1002C22#9038411yescharacteristic
1003C22#9038611yescharacteristic
1004C22#9039311yescharacteristic
1005C22#9040011yescharacteristic
1006C22#9041711yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—144no—
1015C4—144no—
1016C4—144no—
1017C4—144no—
1018C4—144no—
1019C4—282no—
1020C4—282no—
1021C2—284no—
1022C2C4×(C22⋊D7)⋊C411yescharacteristic
1023C2C4×#645611yescharacteristic
1024C2#1173119511yescharacteristic
1025C2#1173184011yescharacteristic
1026C2#1173184311yescharacteristic
1027C2#1173232411yescharacteristic
1028C2#1173241111yescharacteristic
1029C2#1173241811yescharacteristic
1030C2#1173241911yescharacteristic
1031C2#1173242011yescharacteristic
1032C2#1173292211yescharacteristic
1033C2#1173292611yescharacteristic
1034C2#1173364911yescharacteristic
1035C2#1173365111yescharacteristic
1036C2#1173393611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC22×C7C22×C42
FittingC7×#1436C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1436D7
hypocenterC7#13823
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic7C2semidirect
6. C2×#89421C2semidirect
8. C7×#1436C2semidirect
9. C4×C7⋊#95C2semidirect
12. #11727161C2semidirect
13. #11727160C2semidirect
14. #11727160C2semidirect
15. Dic7×#95C2semidirect
51. #89761C4semidirect
54. #89442C4semidirect
55. #89441C4semidirect
107. C2×C4⋊Dic7C2×C4semidirect
113. C2×Dic7⋊C4C2×C4semidirect
133. C2×C4×Dic7C2×C4semidirect
134. C2×C4×Dic7C2×C4semidirect
138. C7×#95C2×C4semidirect
139. C7×#95C2×C4semidirect
147. C7⋊#95C2×C4semidirect
148. C7⋊#95C2×C4semidirect
163. #1436D7semidirect
294. (C2×D7)⋊C4C42semidirect
586. #95C4×D7semidirect
587. #95C4×D7semidirect
956. C7#13823semidirect

Maximal subgroups

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

subgroupindex
C2×#897612
C2×C4⋊C4×Dic72
C2×C4×(C2×D7)⋊C42
C2×#894422
C2×#894412
C2×#894212
C2×#894382
C7×#14362
C4×C7⋊#952
#117271622
#117271612
#117271602
Dic7×#952
#138237