Finite Group Databasebeta

← #13277430

Subgroups — #13277430

Order 1792.

1478 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×#388C211yesmaximal, characteristic
2C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
3C2×#89723C211yesmaximal, characteristic
4#11729318C211yesmaximal, characteristic, complemented
5#11729302C211yesmaximal, characteristic
6#11729300C211yesmaximal, characteristic
7#11729299C211yesmaximal, characteristic
8#11729299C211yesmaximal, characteristic
9#11729299C211yesmaximal, characteristic
10#11729288C211yesmaximal, characteristic, complemented
11C4×C7⋊#95C211yesmaximal, characteristic, complemented
12#11727166C211yesmaximal, characteristic, complemented
13#11727166C211yesmaximal, characteristic, complemented
14#11727161C211yesmaximal, characteristic, complemented
15#11727155C211yesmaximal, characteristic, complemented
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C7×#388C418yescomplemented
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
52C4⋊C4×Dic7—24no—
53#89723—24no—
54#14037—71nomaximal, Sylow
55C25×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×Dic7C2311yescharacteristic
63C23×Dic7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4C2×C414yes—
73C2×C7×C22⋊C4—22no—
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—41no—
78C2×C7×C22⋊C4—41no—
79C2×C7×C22⋊C4C2×C414yes—
80C2×C7×C22⋊C4C2×C414yes—
81C2×C7×C22⋊C4C2×C414yes—
82C2×C42×C7—41no—
83C2×C42×C7—41no—
84C2×C42×C7C2×C414yes—
85C2×C22⋊Dic7—22no—
86C2×C22⋊Dic7—22no—
87C2×C22⋊Dic7—22no—
88C2×C22⋊Dic7—22no—
89C2×C22⋊Dic7—22no—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7—22no—
93C2×C22⋊Dic7—41no—
94C2×C22⋊Dic7—41no—
95C2×C22⋊Dic7—41no—
96C2×C22⋊Dic7—41no—
97C2×C4⋊Dic7—22no—
98C2×C4⋊Dic7—22no—
99C2×C4⋊Dic7—22no—
100C2×C4⋊Dic7—22no—
101C2×C4⋊Dic7—22no—
102C2×C4⋊Dic7—41no—
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—22no—
111C2×C4×Dic7—22no—
112C2×C4×Dic7—41no—
113C2×C4×Dic7—41no—
114C2×C4×Dic7—41no—
115C7×#95C2×C414yes—
116C7×#95C2×C414yes—
117C7⋊#95—22no—
118C7⋊#95—22no—
119C7⋊#95—22no—
120C7⋊#95—22no—
121C7⋊#95—22no—
122C7⋊#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—41no—
129C7⋊#95—41no—
130C7⋊#95—41no—
131C7⋊#95—41no—
132C7⋊#95—41no—
133C7⋊#95—41no—
134C7⋊#95D414yes—
135C2×#388—71no—
136C2×#388D711yescharacteristic
137C2×C4×C4⋊C4—71no—
138#1442—71no—
139#1442—71no—
140#1440—71no—
141#1439—71no—
142#1437—71no—
143#1437—71no—
144#1437—71no—
145#1436—71no—
146#1436—71no—
147#1434—71no—
148#1434—71no—
149C4×#95—71no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—21no—
154C24×C7—21no—
155C24×C7—21no—
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×C7C22×C412yes—
165C24×C7C2411yescharacteristic
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×C7C22×C412yes—
199C22×C4×C7C22×C412yes—
200C22×C4×C7C22×C412yes—
201C22×C4×C7C22×C412yes—
202C22×C4×C7C22×C412yes—
203C22×C4×C7C22×C412yes—
204C22×C4×C7C2×D412yes—
205C22×C4×C7#4112yes—
206C22×C4×C7#4112yes—
207C22×C4×C7#4112yes—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
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×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7C2×D412yes—
257C22×Dic7C2×D412yes—
258C22×Dic7#4112yes—
259C22×Dic7#4112yes—
260C22×Dic7#4112yes—
261C22×Dic7#4112yes—
262C22×Dic7#4112yes—
263C22×Dic7#4112yes—
264C7×C4⋊C4—28no—
265C7×C22⋊C4—28no—
266C7×C22⋊C4—28no—
267C7×C22⋊C4—44no—
268C42×C7—44no—
269C22⋊Dic7—44no—
270C22⋊Dic7—44no—
271C22⋊Dic7—44no—
272C22⋊Dic7—44no—
273C4⋊Dic7—28no—
274C4⋊Dic7—44no—
275C4×Dic7—28no—
276C4×Dic7—44no—
277C4×Dic7—44no—
278C4×Dic7—44no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4C2×D711yescharacteristic
282C22×C22⋊C4—71no—
283C22×C22⋊C4—71no—
284C22×C22⋊C4—71no—
285C22×C22⋊C4—71no—
286C22×C22⋊C4C2×D711yescharacteristic
287C22×C22⋊C4C2×D711yescharacteristic
288C22×C22⋊C4C2×D711yescharacteristic
289C22×C42—71no—
290C22×C42—71no—
291C22×C42—71no—
292C22×C42—71no—
293C22×C42C2×D711yescharacteristic
294#388—144no—
295#388Dic718yescomplemented
296C4×C4⋊C4—144no—
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×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95C2×D711yescharacteristic
316C2×#95C2×D711yescharacteristic
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—22no—
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—41no—
331C23×C7—41no—
332C23×C7—41no—
333C23×C7—41no—
334C23×C7—41no—
335C23×C7—41no—
336C23×C7—41no—
337C23×C7—41no—
338C23×C7—41no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—41no—
344C23×C7—41no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7C23×C411yescharacteristic
353C23×C7C22×D411yescharacteristic
354C23×C7C2×#4111yescharacteristic
355C23×C7C2×#4111yescharacteristic
356C23×C7C2×#4111yescharacteristic
357C23×C7C2×#4111yescharacteristic
358C23×C7C2×#4111yescharacteristic
359C23×C7C2×#4111yescharacteristic
360C23×C7C2×#4111yescharacteristic
361C23×C7C2×#4111yescharacteristic
362C23×C7C2×#4111yescharacteristic
363C23×C7H(5,𝔽2)11yescharacteristic
364C23×C7H(5,𝔽2)11yescharacteristic
365C23×C7H(5,𝔽2)11yescharacteristic
366C23×C72−1+411yescharacteristic
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—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
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#11714yes—
408C2×C4×C7C4×D414yes—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
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—41no—
431C2×Dic7—41no—
432C2×Dic7—41no—
433C2×Dic7—41no—
434C2×Dic7—41no—
435C2×Dic7—41no—
436C2×Dic7—41no—
437C2×Dic7—41no—
438C2×Dic7—41no—
439C2×Dic7—41no—
440C2×Dic7—41no—
441C2×Dic7—41no—
442C2×Dic7—41no—
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—41no—
464C2×Dic7#12614yes—
465C25C22×D711yescharacteristic
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—71no—
472C23×C4—71no—
473C23×C4—71no—
474C23×C4C22×D711yescharacteristic
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—142no—
483C2×C4⋊C4—142no—
484C2×C4⋊C4—142no—
485C2×C4⋊C4—142no—
486C2×C4⋊C4—142no—
487C2×C4⋊C4—281no—
488C2×C4⋊C4C2×Dic714yes—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—41no—
494C2×C22⋊C4—41no—
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—281no—
504C2×C22⋊C4—281no—
505C2×C22⋊C4—281no—
506C2×C22⋊C4—281no—
507C2×C22⋊C4C2×Dic714yes—
508C2×C22⋊C4C2×Dic714yes—
509C2×C22⋊C4C2×Dic714yes—
510C2×C42—41no—
511C2×C42—41no—
512C2×C42—142no—
513C2×C42—142no—
514C2×C42—142no—
515C2×C42—142no—
516C2×C42—142no—
517C2×C42—142no—
518C2×C42—142no—
519C2×C42—142no—
520C2×C42—142no—
521C2×C42—281no—
522C2×C42—281no—
523C2×C42—281no—
524C2×C42C2×Dic714yes—
525#95—74no—
526#95—142no—
527#95—142no—
528#95—142no—
529#95—142no—
530#95—142no—
531#95—142no—
532#95—142no—
533#95—142no—
534#95—142no—
535#95—142no—
536#95—142no—
537#95—281no—
538#95—281no—
539#95—281no—
540#95—281no—
541#95—281no—
542#95—281no—
543#95C2×Dic714yes—
544#95C2×Dic714yes—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—81no—
553C22×C7—81no—
554C22×C7—81no—
555C22×C7—81no—
556C22×C7—81no—
557C22×C7—81no—
558C22×C7—81no—
559C22×C7—81no—
560C22×C7C2×#11711yescharacteristic
561C22×C7C2×C4×D411yescharacteristic
562C22×C7C4×#4111yescharacteristic
563C22×C7C4×#4111yescharacteristic
564C22×C7C4×#4111yescharacteristic
565C22×C7#51811yescharacteristic
566C22×C7#52011yescharacteristic
567C22×C7#52511yescharacteristic
568C22×C7#52511yescharacteristic
569C22×C7C2×#12611yescharacteristic
570C22×C7#52911yescharacteristic
571C22×C7#52911yescharacteristic
572C22×C7#52911yescharacteristic
573C22×C7#52911yescharacteristic
574C22×C7#52911yescharacteristic
575C22×C7#53811yescharacteristic
576C22×C7#53911yescharacteristic
577C22×C7#54011yescharacteristic
578C22×C7#54211yescharacteristic
579C22×C7#54611yescharacteristic
580C22×C7#54611yescharacteristic
581C22×C7#54611yescharacteristic
582C22×C7#54811yescharacteristic
583C22×C7#55211yescharacteristic
584C22×C7#55211yescharacteristic
585C22×C7#55311yescharacteristic
586C22×C7#55311yescharacteristic
587C22×C7#55311yescharacteristic
588C22×C7#55311yescharacteristic
589C22×C7#55511yescharacteristic
590C22×C7#55511yescharacteristic
591C22×C7#55611yescharacteristic
592C22×C7#55911yescharacteristic
593C22×C7#55911yescharacteristic
594C22×C7#55911yescharacteristic
595C4×C7—24no—
596C4×C7—24no—
597C4×C7—42no—
598C4×C7—42no—
599C4×C7—42no—
600C4×C7—42no—
601Dic7—24no—
602Dic7—42no—
603Dic7—42no—
604Dic7—42no—
605Dic7—42no—
606Dic7—42no—
607Dic7—81no—
608Dic7—81no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24C22×Dic712yes—
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—72no—
658C22×C4—72no—
659C22×C4—72no—
660C22×C4—72no—
661C22×C4—72no—
662C22×C4—72no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—141no—
666C22×C4—141no—
667C22×C4—141no—
668C22×C4—141no—
669C22×C4—141no—
670C22×C4—141no—
671C22×C4—141no—
672C22×C4—141no—
673C22×C4—141no—
674C22×C4—141no—
675C22×C4—141no—
676C22×C4—141no—
677C22×C4—141no—
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#115712yes—
714C22×C4#115712yes—
715C22×C4D4×D712yes—
716C22×C4#115912yes—
717C22×C4C22×Dic712yes—
718C22×C4C22×Dic712yes—
719C22×C4C22×Dic712yes—
720C22×C4C22×Dic712yes—
721C22×C4C22×Dic712yes—
722C22×C4C22×Dic712yes—
723C4⋊C4—28no—
724C4⋊C4—148no—
725C4⋊C4—284no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—44no—
729C22⋊C4—284no—
730C22⋊C4—284no—
731C22⋊C4—284no—
732C22⋊C4—284no—
733C42—44no—
734C42—148no—
735C42—284no—
736C42—284no—
737C42—284no—
738C2×C7—82no—
739C2×C7#229011yescharacteristic
740C2×C7C4×#12611yescharacteristic
741C2×C7#233511yescharacteristic
742C2×C7#234611yescharacteristic
743C2×C7#235711yescharacteristic
744C2×C7#236411yescharacteristic
745C2×C7#236711yescharacteristic
746C2×C7#245811yescharacteristic
747C2×C7#245911yescharacteristic
748C2×C7#247611yescharacteristic
749C2×C7#248111yescharacteristic
750C2×C7#251311yescharacteristic
751C2×C7#252511yescharacteristic
752C2×C7#259311yescharacteristic
753C2×C7#259611yescharacteristic
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23C2×#115711yescharacteristic
790C23C2×#115711yescharacteristic
791C23C2×D4×D711yescharacteristic
792C23C2×#115911yescharacteristic
793C23#654811yescharacteristic
794C23#654811yescharacteristic
795C23D7×#4111yescharacteristic
796C23D7×#4111yescharacteristic
797C23D7×#4111yescharacteristic
798C23D7×#4111yescharacteristic
799C23D7×#4111yescharacteristic
800C23D7×#4111yescharacteristic
801C23#655311yescharacteristic
802C23#655411yescharacteristic
803C23C23×Dic711yescharacteristic
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—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
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—74no—
845C2×C4—142no—
846C2×C4—142no—
847C2×C4—142no—
848C2×C4—142no—
849C2×C4—142no—
850C2×C4—142no—
851C2×C4—142no—
852C2×C4—142no—
853C2×C4—142no—
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—281no—
867C2×C4—281no—
868C2×C4—281no—
869C2×C4—281no—
870C2×C4—281no—
871C2×C4—281no—
872C2×C4—281no—
873C2×C4—281no—
874C2×C4—281no—
875C2×C4—281no—
876C2×C4—281no—
877C2×C4—281no—
878C2×C4—281no—
879C2×C4—281no—
880C2×C4—281no—
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#648914yes—
901C2×C4D4×Dic714yes—
902C7#1403711yescharacteristic, complemented, Sylow
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22#9022011yescharacteristic
919C22#9022011yescharacteristic
920C22#9022311yescharacteristic
921C22#9022311yescharacteristic
922C22#9022911yescharacteristic
923C22#9022911yescharacteristic
924C22#9023811yescharacteristic
925C22#9023811yescharacteristic
926C22#9024911yescharacteristic
927C22#9024911yescharacteristic
928C22#9025011yescharacteristic
929C22#9025011yescharacteristic
930C22#9029211yescharacteristic
931C22#9029211yescharacteristic
932C22#9030111yescharacteristic
933C22#9030111yescharacteristic
934C22#9034811yescharacteristic
935C22#9035111yescharacteristic
936C22#9035311yescharacteristic
937C22#9035411yescharacteristic
938C22#9036211yescharacteristic
939C22#9036711yescharacteristic
940C22#9036811yescharacteristic
941C22#9037211yescharacteristic
942C22D7×#12611yescharacteristic
943C22#9039711yescharacteristic
944C22#9039711yescharacteristic
945C22#9039711yescharacteristic
946C22C2×#648911yescharacteristic
947C22C2×D4×Dic711yescharacteristic
948C22#9048911yescharacteristic
949C22#41×Dic711yescharacteristic
950C22#41×Dic711yescharacteristic
951C22#41×Dic711yescharacteristic
952C22#9051811yescharacteristic
953C4—24no—
954C4—24no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—144no—
960C4—282no—
961C4—282no—
962C4—282no—
963C4—282no—
964C4—282no—
965C4—561no—
966C4—561no—
967C2—82no—
968C2#1173295311yescharacteristic
969C2#1173298711yescharacteristic
970C2#1173299811yescharacteristic
971C2#1173301811yescharacteristic
972C2#1173306811yescharacteristic
973C2#1173308011yescharacteristic
974C2#1173329911yescharacteristic
975C2#1173330911yescharacteristic
976C2#1173968411yescharacteristic
977C2#1173976311yescharacteristic
978C2#1173978311yescharacteristic
979C2#1174008311yescharacteristic
980C2#1174028211yescharacteristic
981C2#1174040011yescharacteristic
982C2Dic7×#12611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#388C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#388D7
hypocenterC7#14037
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic7C2semidirect
4. #11729318C2semidirect
10. #11729288C2semidirect
11. C4×C7⋊#95C2semidirect
12. #11727166C2semidirect
13. #11727166C2semidirect
14. #11727161C2semidirect
15. #11727155C2semidirect
31. C7×#388C4semidirect
295. #388Dic7semidirect
902. C7#14037semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×C4⋊C4×Dic72
C2×#897232
#117293182
#117293022
#117293002
#117292992
#117292882
C4×C7⋊#952
#117271662
#117271612
#117271552
#140377