Finite Group Databasebeta

← #13277126

Subgroups — #13277126

Order 1792.

1462 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#383C211yesmaximal, characteristic, complemented
2C2×#89712C211yesmaximal, characteristic
3C2×#89441C211yesmaximal, characteristic
4C4×C7⋊#95C211yesmaximal, characteristic, complemented
5#11727183C211yesmaximal, characteristic
6#11727182C211yesmaximal, characteristic
7#11727172C211yesmaximal, characteristic, complemented
8#11727163C211yesmaximal, characteristic, complemented
9#11727162C211yesmaximal, characteristic
10#11727162C211yesmaximal, characteristic
11#11727162C211yesmaximal, characteristic
12#11727160C211yesmaximal, characteristic, complemented
13#11727159C211yesmaximal, characteristic, complemented
14Dic7⋊#95C211yesmaximal, characteristic, complemented
15Dic7×#95C211yesmaximal, characteristic, complemented
16C22×C42×C7C2211yescharacteristic
17C22×(C2×D7)⋊C4C2211yescharacteristic
18C22×(C2×D7)⋊C4C2211yescharacteristic
19C22×(C2×D7)⋊C4C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C7×#383—24no—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
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
51C2×C7⋊#95C2211yescharacteristic
52#89712C418yescomplemented
53#89441—24no—
54#14013—71nomaximal, Sylow
55C24×D7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×Dic7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C2×C42×C7—22no—
71C2×C42×C7—22no—
72C2×C42×C7C2×C414yes—
73C2×(C2×D7)⋊C4—22no—
74C2×(C2×D7)⋊C4—22no—
75C2×(C2×D7)⋊C4—22no—
76C2×(C2×D7)⋊C4—22no—
77C2×(C2×D7)⋊C4—22no—
78C2×(C2×D7)⋊C4—22no—
79C2×(C2×D7)⋊C4—22no—
80C2×(C2×D7)⋊C4—22no—
81C2×(C2×D7)⋊C4—22no—
82C2×(C2×D7)⋊C4—22no—
83C2×(C2×D7)⋊C4—22no—
84C2×(C2×D7)⋊C4—22no—
85C2×(C2×D7)⋊C4—41no—
86C2×(C2×D7)⋊C4—41no—
87C2×(C2×D7)⋊C4—41no—
88C2×(C2×D7)⋊C4—41no—
89C2×(C2×D7)⋊C4—41no—
90C2×(C2×D7)⋊C4—41no—
91C2×(C2×D7)⋊C4C2×C414yes—
92C2×(C2×D7)⋊C4C2×C414yes—
93C2×(C2×D7)⋊C4C2×C414yes—
94C2×Dic7⋊C4—22no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4—22no—
97C2×Dic7⋊C4—22no—
98C2×Dic7⋊C4—41no—
99C2×Dic7⋊C4—41no—
100C2×Dic7⋊C4—41no—
101C2×Dic7⋊C4—41no—
102C2×Dic7⋊C4C2×C414yes—
103C2×C4×Dic7—22no—
104C2×C4×Dic7—22no—
105C2×C4×Dic7—22no—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—22no—
110C2×C4×Dic7—41no—
111C2×C4×Dic7—41no—
112C2×C4×Dic7—41no—
113C2×C4×Dic7—41no—
114C2×C4×Dic7—41no—
115C7×#95—22no—
116C7×#95—22no—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95—22no—
120C7×#95D414yes—
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—41no—
131C7⋊#95—41no—
132C7⋊#95—41no—
133C7⋊#95C2×C414yes—
134C7⋊#95C2×C414yes—
135C2×#388—71no—
136C2×#388—71no—
137C2×#383D711yescharacteristic, complemented
138#1443—71no—
139#1441—71no—
140#1440—71no—
141#1439—71no—
142#1437—71no—
143#1437—71no—
144#1437—71no—
145#1436—71no—
146#1436—71no—
147C4⋊#95—71no—
148C4×#95—71no—
149C4×#95—71no—
150C24×C7C2411yescharacteristic
151C23×D7—21no—
152C23×D7—21no—
153C23×D7—21no—
154C23×D7—21no—
155C23×D7—21no—
156C23×D7—21no—
157C23×D7—21no—
158C23×D7—21no—
159C23×D7—21no—
160C23×D7—21no—
161C23×D7—21no—
162C23×D7—21no—
163C23×D7—21no—
164C23×D7—21no—
165C23×D7C22×C412yes—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
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—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7C22×C412yes—
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×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
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×Dic7C22×C412yes—
254C22×Dic7C22×C412yes—
255C22×Dic7C22×C412yes—
256C22×Dic7#4112yes—
257C22×Dic7#4112yes—
258C22×Dic7#4112yes—
259C22×Dic7#4112yes—
260C22×Dic7#4112yes—
261C22×Dic7#4112yes—
262C22×Dic7#4112yes—
263C22×Dic7#4112yes—
264C42×C7—28no—
265(C2×D7)⋊C4—28no—
266(C2×D7)⋊C4—28no—
267(C2×D7)⋊C4—44no—
268(C2×D7)⋊C4—44no—
269(C2×D7)⋊C4—44no—
270(C2×D7)⋊C4—44no—
271(C2×D7)⋊C4—44no—
272Dic7⋊C4—44no—
273Dic7⋊C4—44no—
274Dic7⋊C4—44no—
275C4×Dic7—44no—
276C4×Dic7—44no—
277C4×Dic7—44no—
278C4×Dic7—44no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4—71no—
282C22×C22⋊C4—71no—
283C22×C22⋊C4—71no—
284C22×C22⋊C4—71no—
285C22×C22⋊C4—71no—
286C22×C22⋊C4—71no—
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C42—71no—
290C22×C42—71no—
291C22×C42—71no—
292C22×C42—71no—
293C22×C42C2×D711yescharacteristic
294#388—78no—
295#388—144no—
296#383—24no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95C2×D711yescharacteristic
312C2×#95C2×D711yescharacteristic
313C2×#95C2×D711yescharacteristic
314C2×#95C2×D711yescharacteristic
315C2×#95C2×D711yescharacteristic
316C2×#95C2×D711yescharacteristic
317C23×C7C23×C411yescharacteristic
318C23×C7C22×D411yescharacteristic
319C23×C7C2×#4111yescharacteristic
320C23×C7C2×#4111yescharacteristic
321C23×C7C2×#4111yescharacteristic
322C23×C7C2×#4111yescharacteristic
323C23×C7C2×#4111yescharacteristic
324C23×C7C2×#4111yescharacteristic
325C23×C7C2×#4111yescharacteristic
326C23×C7C2×#4111yescharacteristic
327C23×C7C2×#4111yescharacteristic
328C23×C7H(5,𝔽2)11yescharacteristic
329C23×C7H(5,𝔽2)11yescharacteristic
330C23×C7H(5,𝔽2)11yescharacteristic
331C23×C72−1+411yescharacteristic
332C22×D7—22no—
333C22×D7—22no—
334C22×D7—22no—
335C22×D7—22no—
336C22×D7—22no—
337C22×D7—22no—
338C22×D7—22no—
339C22×D7—41no—
340C22×D7—41no—
341C22×D7—41no—
342C22×D7—41no—
343C22×D7—41no—
344C22×D7—41no—
345C22×D7—41no—
346C22×D7—41no—
347C22×D7—41no—
348C22×D7—41no—
349C22×D7—41no—
350C22×D7—41no—
351C22×D7—41no—
352C22×D7—41no—
353C22×D7—41no—
354C22×D7—41no—
355C22×D7—41no—
356C22×D7—41no—
357C22×D7—41no—
358C22×D7—41no—
359C22×D7—41no—
360C22×D7—41no—
361C22×D7—41no—
362C22×D7—41no—
363C22×D7—41no—
364C22×D7—41no—
365C22×D7—41no—
366C22×D7—41no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—41no—
386C2×C4×C7—41no—
387C2×C4×C7—41no—
388C2×C4×C7—41no—
389C2×C4×C7—41no—
390C2×C4×C7—41no—
391C2×C4×C7—41no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
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×C7C4×D414yes—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
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—41no—
444C2×Dic7—41no—
445C2×Dic7—41no—
446C2×Dic7—41no—
447C2×Dic7—41no—
448C2×Dic7—41no—
449C2×Dic7—41no—
450C2×Dic7—41no—
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#11714yes—
464C2×Dic7#12614yes—
465C25—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—71no—
472C23×C4—71no—
473C23×C4C22×D711yescharacteristic
474C23×C4C22×D711yescharacteristic
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480C2×C4⋊C4—74no—
481C2×C4⋊C4—142no—
482C2×C4⋊C4—142no—
483C2×C4⋊C4—142no—
484C2×C4⋊C4—142no—
485C2×C4⋊C4—281no—
486C2×C4⋊C4—281no—
487C2×C4⋊C4—281no—
488C2×C4⋊C4—281no—
489C2×C22⋊C4—74no—
490C2×C22⋊C4—74no—
491C2×C22⋊C4—74no—
492C2×C22⋊C4—142no—
493C2×C22⋊C4—142no—
494C2×C22⋊C4—142no—
495C2×C22⋊C4—142no—
496C2×C22⋊C4—142no—
497C2×C22⋊C4—142no—
498C2×C22⋊C4—142no—
499C2×C22⋊C4—142no—
500C2×C22⋊C4—142no—
501C2×C22⋊C4—142no—
502C2×C22⋊C4—142no—
503C2×C22⋊C4—142no—
504C2×C22⋊C4—281no—
505C2×C22⋊C4—281no—
506C2×C22⋊C4—281no—
507C2×C22⋊C4—281no—
508C2×C22⋊C4—281no—
509C2×C22⋊C4—281no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—142no—
513C2×C42—142no—
514C2×C42—142no—
515C2×C42—142no—
516C2×C42—142no—
517C2×C42—142no—
518C2×C42—142no—
519C2×C42—281no—
520C2×C42—281no—
521C2×C42—281no—
522C2×C42—281no—
523C2×C42—281no—
524C2×C42C4×D714yes—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—74no—
531#95—74no—
532#95—142no—
533#95—142no—
534#95—142no—
535#95—142no—
536#95—142no—
537#95—142no—
538#95—142no—
539#95—142no—
540#95—142no—
541#95—281no—
542#95—281no—
543#95—281no—
544#95C22⋊D714yes—
545C22×C7C2×#11711yescharacteristic
546C22×C7C2×C4×D411yescharacteristic
547C22×C7C4×#4111yescharacteristic
548C22×C7C4×#4111yescharacteristic
549C22×C7C4×#4111yescharacteristic
550C22×C7#51811yescharacteristic
551C22×C7#52011yescharacteristic
552C22×C7C2×#12611yescharacteristic
553C22×C7#52911yescharacteristic
554C22×C7#52911yescharacteristic
555C22×C7#52911yescharacteristic
556C22×C7#52911yescharacteristic
557C22×C7#52911yescharacteristic
558C22×C7#53211yescharacteristic
559C22×C7#53211yescharacteristic
560C22×C7#53811yescharacteristic
561C22×C7#53811yescharacteristic
562C22×C7#54211yescharacteristic
563C22×C7#54211yescharacteristic
564C22×C7#54611yescharacteristic
565C22×C7#54611yescharacteristic
566C22×C7#54711yescharacteristic
567C22×C7#55011yescharacteristic
568C22×C7#55111yescharacteristic
569C22×C7#55111yescharacteristic
570C22×C7#55111yescharacteristic
571C22×C7#55211yescharacteristic
572C22×C7#55311yescharacteristic
573C22×C7#55311yescharacteristic
574C22×C7#55311yescharacteristic
575C22×C7#55311yescharacteristic
576C22×C7#55311yescharacteristic
577C22×C7#55511yescharacteristic
578C22×C7#55611yescharacteristic
579C22×C7#55611yescharacteristic
580C2×D7—42no—
581C2×D7—42no—
582C2×D7—42no—
583C2×D7—42no—
584C2×D7—42no—
585C2×D7—42no—
586C2×D7—42no—
587C2×D7—81no—
588C2×D7—81no—
589C2×D7—81no—
590C2×D7—81no—
591C2×D7—81no—
592C2×D7—81no—
593C2×D7—81no—
594C2×D7—81no—
595C4×C7—24no—
596C4×C7—42no—
597C4×C7—42no—
598C4×C7—42no—
599C4×C7—42no—
600C4×C7—81no—
601C4×C7—81no—
602Dic7—24no—
603Dic7—24no—
604Dic7—42no—
605Dic7—42no—
606Dic7—42no—
607Dic7—42no—
608Dic7—42no—
609C24—72no—
610C24—141no—
611C24—141no—
612C24—141no—
613C24—141no—
614C24—141no—
615C24—141no—
616C24—141no—
617C24—141no—
618C24—141no—
619C24—141no—
620C24—141no—
621C24—141no—
622C24—141no—
623C24—141no—
624C24C23×D711yescharacteristic
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
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—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—72no—
671C22×C4—72no—
672C22×C4—72no—
673C22×C4—72no—
674C22×C4—72no—
675C22×C4—72no—
676C22×C4—72no—
677C22×C4—72no—
678C22×C4—141no—
679C22×C4—141no—
680C22×C4—141no—
681C22×C4—141no—
682C22×C4—141no—
683C22×C4—141no—
684C22×C4—141no—
685C22×C4—141no—
686C22×C4—141no—
687C22×C4—141no—
688C22×C4—141no—
689C22×C4—141no—
690C22×C4—141no—
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×C4C2×C4×D712yes—
717C22×C4C2×C4×D712yes—
718C22×C4C2×C4×D712yes—
719C22×C4#115712yes—
720C22×C4C2×C22⋊D712yes—
721C22×C4C2×C22⋊D712yes—
722C22×C4C2×C22⋊D712yes—
723C4⋊C4—284no—
724C4⋊C4—284no—
725C4⋊C4—284no—
726C22⋊C4—148no—
727C22⋊C4—148no—
728C22⋊C4—284no—
729C22⋊C4—284no—
730C22⋊C4—284no—
731C22⋊C4—284no—
732C22⋊C4—284no—
733C42—28no—
734C42—284no—
735C42—284no—
736C42—284no—
737C42—284no—
738C2×C7#229311yescharacteristic
739C2×C7C4×#12611yescharacteristic
740C2×C7#233711yescharacteristic
741C2×C7#234711yescharacteristic
742C2×C7#235311yescharacteristic
743C2×C7#235911yescharacteristic
744C2×C7#236311yescharacteristic
745C2×C7#251011yescharacteristic
746C2×C7#251211yescharacteristic
747C2×C7#251811yescharacteristic
748C2×C7#252111yescharacteristic
749C2×C7#252511yescharacteristic
750C2×C7#253211yescharacteristic
751C2×C7#255411yescharacteristic
752C2×C7#255911yescharacteristic
753D7—82no—
754C23—142no—
755C23—142no—
756C23—142no—
757C23—142no—
758C23—142no—
759C23—142no—
760C23—142no—
761C23—281no—
762C23—281no—
763C23—281no—
764C23—281no—
765C23—281no—
766C23—281no—
767C23—281no—
768C23—281no—
769C23—281no—
770C23—281no—
771C23—281no—
772C23—281no—
773C23—281no—
774C23—281no—
775C23—281no—
776C23—281no—
777C23—281no—
778C23—281no—
779C23—281no—
780C23—281no—
781C23—281no—
782C23—281no—
783C23—281no—
784C23—281no—
785C23—281no—
786C23—281no—
787C23—281no—
788C23—281no—
789C23C22×C4×D711yescharacteristic
790C23C2×#115711yescharacteristic
791C23D7×#4111yescharacteristic
792C23D7×#4111yescharacteristic
793C23D7×#4111yescharacteristic
794C23D7×#4111yescharacteristic
795C23D7×#4111yescharacteristic
796C23D7×#4111yescharacteristic
797C23D7×#4111yescharacteristic
798C23D7×#4111yescharacteristic
799C23#655311yescharacteristic
800C23#655311yescharacteristic
801C23#655311yescharacteristic
802C23#655411yescharacteristic
803C23C22×C22⋊D711yescharacteristic
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
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—74no—
853C2×C4—74no—
854C2×C4—142no—
855C2×C4—142no—
856C2×C4—142no—
857C2×C4—142no—
858C2×C4—142no—
859C2×C4—142no—
860C2×C4—142no—
861C2×C4—142no—
862C2×C4—142no—
863C2×C4—142no—
864C2×C4—142no—
865C2×C4—142no—
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—281no—
882C2×C4—281no—
883C2×C4—281no—
884C2×C4—281no—
885C2×C4—281no—
886C2×C4—281no—
887C2×C4—281no—
888C2×C4—281no—
889C2×C4—281no—
890C2×C4—281no—
891C2×C4—281no—
892C2×C4—281no—
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×C4C4×C22⋊D714yes—
902C7#1401311yescharacteristic, complemented, Sylow
903C22—282no—
904C22—282no—
905C22—282no—
906C22—282no—
907C22—282no—
908C22—282no—
909C22—282no—
910C22—561no—
911C22—561no—
912C22—561no—
913C22—561no—
914C22—561no—
915C22—561no—
916C22—561no—
917C22—561no—
918C22D7×#11711yescharacteristic
919C22#9021211yescharacteristic
920C22#9021311yescharacteristic
921C22#9021311yescharacteristic
922C22#9021311yescharacteristic
923C22#9021411yescharacteristic
924C22#9021811yescharacteristic
925C22#9021911yescharacteristic
926C22#9021911yescharacteristic
927C22#9022111yescharacteristic
928C22#9022211yescharacteristic
929C22#9022311yescharacteristic
930C22#9039311yescharacteristic
931C22#9039311yescharacteristic
932C22D7×#12611yescharacteristic
933C22#9039511yescharacteristic
934C22#9039511yescharacteristic
935C22#9039611yescharacteristic
936C22#9039611yescharacteristic
937C22#9039711yescharacteristic
938C22#9039711yescharacteristic
939C22#9039711yescharacteristic
940C22#9040011yescharacteristic
941C22#9040011yescharacteristic
942C22#9040011yescharacteristic
943C22#9040011yescharacteristic
944C22#9040111yescharacteristic
945C22#9040111yescharacteristic
946C22C2×C4×C22⋊D711yescharacteristic
947C22#9051511yescharacteristic
948C22#9052011yescharacteristic
949C22#9052011yescharacteristic
950C22#9052311yescharacteristic
951C22#9052311yescharacteristic
952C22#9052511yescharacteristic
953C4—24no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—81no—
959C4—81no—
960C4—144no—
961C4—144no—
962C4—282no—
963C4—282no—
964C4—282no—
965C4—282no—
966C4—282no—
967C2—562no—
968C2#1173170411yescharacteristic
969C2#1173170711yescharacteristic
970C2#1173170811yescharacteristic
971C2#1173171411yescharacteristic
972C2#1173171711yescharacteristic
973C2#1173171811yescharacteristic
974C2#1173174211yescharacteristic
975C2#1173174611yescharacteristic
976C2#1173967011yescharacteristic
977C2#1173968711yescharacteristic
978C2#1173968911yescharacteristic
979C2#1174052911yescharacteristic
980C2#1174053111yescharacteristic
981C2#1174055311yescharacteristic
982C2#1174055411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#383C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#383D7
hypocenterC7#14013
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
1. C2×C7×#383C2semidirect
4. C4×C7⋊#95C2semidirect
7. #11727172C2semidirect
8. #11727163C2semidirect
12. #11727160C2semidirect
13. #11727159C2semidirect
14. Dic7⋊#95C2semidirect
15. Dic7×#95C2semidirect
52. #89712C4semidirect
137. C2×#383D7semidirect
902. C7#14013semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3832
C2×#897122
C2×#894412
C4×C7⋊#952
#117271832
#117271822
#117271722
#117271632
#117271622
#117271602
#117271592
Dic7⋊#952
Dic7×#952
#140137