Finite Group Databasebeta

← #13278098

Subgroups — #13278098

Order 1792.

1586 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89442C211yesmaximal, characteristic
2C2×#89425C211yesmaximal, characteristic, complemented
3C2×#89438C211yesmaximal, characteristic
4C7×#1443C211yesmaximal, characteristic, complemented
5#11727183C211yesmaximal, characteristic
6#11727182C211yesmaximal, characteristic
7(C2×D7)⋊#95C211yesmaximal, characteristic
8(C2×D7)⋊#95C211yesmaximal, characteristic
9#11727168C211yesmaximal, characteristic, complemented
10#11727162C211yesmaximal, characteristic
11#11727161C211yesmaximal, characteristic, complemented
12#11727155C211yesmaximal, characteristic, complemented
13#11727155C211yesmaximal, characteristic, complemented
14#11727155C211yesmaximal, characteristic, complemented
15Dic7×#95C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
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×C4⋊Dic7C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
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
51#89442C418yescomplemented
52#89438—24no—
53#89425—24no—
54#14086—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
70C22×C4×D7—22no—
71C22×C4×D7—22no—
72C22×C4×D7—22no—
73C22×C4×D7—22no—
74C22×C4×D7—22no—
75C22×C4×D7—41no—
76C22×C4×D7—41no—
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—22no—
86C2×(C2×D7)⋊C4—22no—
87C2×(C2×D7)⋊C4—22no—
88C2×(C2×D7)⋊C4—41no—
89C2×(C2×D7)⋊C4—41no—
90C2×(C2×D7)⋊C4—41no—
91C2×(C2×D7)⋊C4—41no—
92C2×(C2×D7)⋊C4C2×C414yes—
93C2×(C2×D7)⋊C4C2×C414yes—
94C2×(C2×D7)⋊C4C2×C414yes—
95C2×C4⋊Dic7—22no—
96C2×C4⋊Dic7—22no—
97C2×C4⋊Dic7C2×C414yescomplemented
98C2×Dic7⋊C4—22no—
99C2×Dic7⋊C4—41no—
100C2×Dic7⋊C4—41no—
101C2×C4×Dic7—22no—
102C2×C4×Dic7—22no—
103C2×C4×Dic7—22no—
104C2×C4×Dic7—22no—
105C2×C4×Dic7—41no—
106C2×C4×Dic7—41no—
107C2×C4×Dic7—41no—
108C2×C4×Dic7—41no—
109C2×C4×Dic7—41no—
110C2×C4×Dic7—41no—
111C2×C4×Dic7C2×C414yescomplemented
112C2×C4×Dic7D414yes—
113C7×#95—22no—
114C7×#95—22no—
115C7×#95—22no—
116C7×#95—22no—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95C2×C414yescomplemented
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—22no—
129C7⋊#95—22no—
130C7⋊#95—41no—
131C7⋊#95—41no—
132C7⋊#95—41no—
133C7⋊#95—41no—
134C7⋊#95C2×C414yescomplemented
135C2×#388—71no—
136C2×#387—71no—
137C2×C4×C22⋊C4—71no—
138#1443D711yescharacteristic, complemented
139#1442—71no—
140#1440—71no—
141#1439—71no—
142#1437—71no—
143#1436—71no—
144#1434—71no—
145#1434—71no—
146#1434—71no—
147C22⋊#95—71no—
148C22⋊#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×D7C22×C412yes—
164C23×D7#4112yes—
165C23×D7#4112yes—
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×C7—21no—
209C22×C4×C7C22×C412yes—
210C22×C4×C7C22×C412yes—
211C22×C4×C7C22×C412yes—
212C22×C4×C7C2×D412yes—
213C22×C4×C7#4112yes—
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×Dic7—21no—
254C22×Dic7C22×C412yes—
255C22×Dic7C22×C412yes—
256C22×Dic7C22×C412yes—
257C22×Dic7C2×D412yes—
258C22×Dic7C2×D412yes—
259C22×Dic7#4112yes—
260C22×Dic7#4112yes—
261C22×Dic7#4112yes—
262C22×Dic7#4112yes—
263C22×Dic7#4112yes—
264C2×C4×D7—28no—
265C2×C4×D7—44no—
266C2×C4×D7—44no—
267C2×C4×D7—44no—
268C2×C4×D7—44no—
269C2×C4×D7—44no—
270C2×C4×D7—44no—
271(C2×D7)⋊C4—28no—
272(C2×D7)⋊C4—28no—
273(C2×D7)⋊C4—28no—
274(C2×D7)⋊C4—44no—
275(C2×D7)⋊C4—44no—
276(C2×D7)⋊C4—44no—
277C4⋊Dic7—28no—
278Dic7⋊C4—44no—
279C4×Dic7—44no—
280C4×Dic7—44no—
281C4×Dic7—44no—
282C4×Dic7—44no—
283C24×C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C22⋊C4—71no—
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C22⋊C4—71no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C42—71no—
293C22×C42—71no—
294C22×C42—71no—
295C22×C42—71no—
296#388—78no—
297#387—144no—
298C4×C22⋊C4—144no—
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×#95C2×D711yescharacteristic
315C2×#95C2×D711yescharacteristic
316C2×#95C2×D711yescharacteristic
317C2×#95C2×D711yescharacteristic
318C2×#95C2×D711yescharacteristic
319C2×#95C2×D711yescharacteristic
320C2×#95C2×D711yescharacteristic
321C23×C7C23×C411yescharacteristic
322C23×C7C22×D411yescharacteristic
323C23×C7C2×#4111yescharacteristic
324C23×C7C2×#4111yescharacteristic
325C23×C7C2×#4111yescharacteristic
326C23×C7C2×#4111yescharacteristic
327C23×C7C2×#4111yescharacteristic
328C23×C7C2×#4111yescharacteristic
329C23×C7C2×#4111yescharacteristic
330C23×C7C2×#4111yescharacteristic
331C23×C7C2×#4111yescharacteristic
332C23×C7H(5,𝔽2)11yescharacteristic
333C23×C7H(5,𝔽2)11yescharacteristic
334C23×C7H(5,𝔽2)11yescharacteristic
335C23×C72−1+411yescharacteristic
336C22×D7—22no—
337C22×D7—22no—
338C22×D7—22no—
339C22×D7—22no—
340C22×D7—22no—
341C22×D7—22no—
342C22×D7—22no—
343C22×D7—22no—
344C22×D7—22no—
345C22×D7—22no—
346C22×D7—22no—
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
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—
367C22×D7—41no—
368C22×D7—41no—
369C22×D7—41no—
370C22×D7#11714yes—
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—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×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
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—22no—
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—41no—
465C2×Dic7—41no—
466C2×Dic7—41no—
467C2×Dic7C4×D414yes—
468C2×Dic7#12414yes—
469C4×D7—416no—
470C25—71no—
471C23×C4—71no—
472C23×C4—71no—
473C23×C4—71no—
474C23×C4—71no—
475C23×C4—71no—
476C23×C4—71no—
477C23×C4—71no—
478C23×C4—142no—
479C23×C4—142no—
480C23×C4—142no—
481C23×C4—142no—
482C23×C4—142no—
483C23×C4—281no—
484C23×C4—281no—
485C23×C4C22×D711yescharacteristic
486C23×C4C22×D711yescharacteristic
487C23×C4C22×D711yescharacteristic
488C23×C4C22×D711yescharacteristic
489C23×C4C22×D711yescharacteristic
490C23×C4C22×D711yescharacteristic
491C23×C4C22×D711yescharacteristic
492C2×C4⋊C4—74no—
493C2×C4⋊C4—142no—
494C2×C4⋊C4—142no—
495C2×C4⋊C4—142no—
496C2×C4⋊C4—281no—
497C2×C4⋊C4—281no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—74no—
500C2×C22⋊C4—74no—
501C2×C22⋊C4—142no—
502C2×C22⋊C4—142no—
503C2×C22⋊C4—142no—
504C2×C22⋊C4—142no—
505C2×C22⋊C4—142no—
506C2×C22⋊C4—142no—
507C2×C22⋊C4—142no—
508C2×C22⋊C4—142no—
509C2×C22⋊C4—142no—
510C2×C22⋊C4—142no—
511C2×C22⋊C4—142no—
512C2×C22⋊C4—281no—
513C2×C22⋊C4—281no—
514C2×C22⋊C4—281no—
515C2×C22⋊C4—281no—
516C2×C42—74no—
517C2×C42—74no—
518C2×C42—142no—
519C2×C42—142no—
520C2×C42—142no—
521C2×C42—142no—
522C2×C42—281no—
523C2×C42—281no—
524C2×C42—281no—
525C2×C42—281no—
526C2×C42—281no—
527C2×C42—281no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—74no—
535#95—142no—
536#95—142no—
537#95—142no—
538#95—142no—
539#95—142no—
540#95—142no—
541#95—142no—
542#95—142no—
543#95—142no—
544#95—142no—
545#95—281no—
546#95—281no—
547#95—281no—
548#95—281no—
549#95C4×D714yescomplemented
550C22×C7C2×#11711yescharacteristic
551C22×C7C2×C4×D411yescharacteristic
552C22×C7C4×#4111yescharacteristic
553C22×C7C4×#4111yescharacteristic
554C22×C7C4×#4111yescharacteristic
555C22×C7#51811yescharacteristic
556C22×C7#52011yescharacteristic
557C22×C7#52511yescharacteristic
558C22×C7#52511yescharacteristic
559C22×C7C2×#12411yescharacteristic
560C22×C7#52911yescharacteristic
561C22×C7#52911yescharacteristic
562C22×C7#52911yescharacteristic
563C22×C7#52911yescharacteristic
564C22×C7#53211yescharacteristic
565C22×C7#53411yescharacteristic
566C22×C7#53711yescharacteristic
567C22×C7#53811yescharacteristic
568C22×C7#53911yescharacteristic
569C22×C7#55111yescharacteristic
570C22×C7#55111yescharacteristic
571C22×C7#55111yescharacteristic
572C22×C7#55111yescharacteristic
573C22×C7#55111yescharacteristic
574C22×C7#55111yescharacteristic
575C22×C7#55211yescharacteristic
576C22×C7#55211yescharacteristic
577C22×C7#55211yescharacteristic
578C22×C7#55311yescharacteristic
579C22×C7#55311yescharacteristic
580C22×C7#55311yescharacteristic
581C22×C7#55311yescharacteristic
582C22×C7#55311yescharacteristic
583C22×C7#55611yescharacteristic
584C22×C7#55911yescharacteristic
585C2×D7—24no—
586C2×D7—24no—
587C2×D7—24no—
588C2×D7—42no—
589C2×D7—42no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—42no—
593C2×D7—42no—
594C2×D7—42no—
595C2×D7—42no—
596C2×D7—42no—
597C2×D7—42no—
598C2×D7—42no—
599C2×D7—42no—
600C4×C7—42no—
601C4×C7—42no—
602C4×C7—42no—
603C4×C7—42no—
604C4×C7—42no—
605C4×C7—42no—
606C4×C7—81no—
607Dic7—24no—
608Dic7—24no—
609Dic7—42no—
610Dic7—42no—
611Dic7—42no—
612Dic7—42no—
613Dic7—81no—
614C24—72no—
615C24—72no—
616C24—72no—
617C24—141no—
618C24—141no—
619C24—141no—
620C24—141no—
621C24—141no—
622C24—141no—
623C24—141no—
624C24—141no—
625C24—141no—
626C24—141no—
627C24—141no—
628C24—141no—
629C24C23×D711yescharacteristic
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—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—72no—
674C22×C4—72no—
675C22×C4—72no—
676C22×C4—72no—
677C22×C4—72no—
678C22×C4—72no—
679C22×C4—72no—
680C22×C4—72no—
681C22×C4—72no—
682C22×C4—72no—
683C22×C4—148no—
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×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—141no—
720C22×C4—141no—
721C22×C4—141no—
722C22×C4—141no—
723C22×C4—284no—
724C22×C4—284no—
725C22×C4—284no—
726C22×C4—284no—
727C22×C4—284no—
728C22×C4—284no—
729C22×C4C2×C4×D712yes—
730C22×C4C2×C4×D712yes—
731C22×C4C2×C4×D712yes—
732C22×C4D4×D712yes—
733C22×C4#115912yes—
734C22×C4#115912yes—
735C4⋊C4—148no—
736C4⋊C4—284no—
737C22⋊C4—148no—
738C22⋊C4—148no—
739C22⋊C4—148no—
740C22⋊C4—284no—
741C22⋊C4—284no—
742C22⋊C4—284no—
743C42—284no—
744C42—284no—
745C42—284no—
746C42—284no—
747C2×C7#229011yescharacteristic
748C2×C7C4×#12411yescharacteristic
749C2×C7#232511yescharacteristic
750C2×C7#234311yescharacteristic
751C2×C7#235311yescharacteristic
752C2×C7#237311yescharacteristic
753C2×C7#237411yescharacteristic
754C2×C7#256111yescharacteristic
755C2×C7#256211yescharacteristic
756C2×C7#257511yescharacteristic
757C2×C7#257611yescharacteristic
758C2×C7#257711yescharacteristic
759C2×C7#257811yescharacteristic
760C2×C7#260111yescharacteristic
761C2×C7#260211yescharacteristic
762D7—44no—
763C23—74no—
764C23—142no—
765C23—142no—
766C23—142no—
767C23—142no—
768C23—142no—
769C23—142no—
770C23—142no—
771C23—142no—
772C23—142no—
773C23—142no—
774C23—142no—
775C23—142no—
776C23—142no—
777C23—142no—
778C23—142no—
779C23—142no—
780C23—142no—
781C23—142no—
782C23—281no—
783C23—281no—
784C23—281no—
785C23—281no—
786C23—281no—
787C23—281no—
788C23—281no—
789C23—281no—
790C23—281no—
791C23—281no—
792C23—281no—
793C23—281no—
794C23—281no—
795C23—281no—
796C23—281no—
797C23—281no—
798C23C22×C4×D711yescharacteristic
799C23C2×D4×D711yescharacteristic
800C23C2×#115911yescharacteristic
801C23C2×#115911yescharacteristic
802C23#655111yescharacteristic
803C23D7×#4111yescharacteristic
804C23D7×#4111yescharacteristic
805C23D7×#4111yescharacteristic
806C23D7×#4111yescharacteristic
807C23D7×#4111yescharacteristic
808C23D7×#4111yescharacteristic
809C23D7×#4111yescharacteristic
810C23#655311yescharacteristic
811C23#655311yescharacteristic
812C23#655311yescharacteristic
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—22no—
829C2×C4—22no—
830C2×C4—22no—
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—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—74no—
863C2×C4—74no—
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—142no—
882C2×C4—142no—
883C2×C4—142no—
884C2×C4—142no—
885C2×C4—142no—
886C2×C4—142no—
887C2×C4—142no—
888C2×C4—2816no—
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×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—
912C7#1408611yescharacteristic, complemented, Sylow
913C22—144no—
914C22—144no—
915C22—144no—
916C22—282no—
917C22—282no—
918C22—282no—
919C22—282no—
920C22—282no—
921C22—282no—
922C22—282no—
923C22—282no—
924C22—282no—
925C22—282no—
926C22—282no—
927C22—282no—
928C22D7×#11711yescharacteristic
929C22#9021211yescharacteristic
930C22#9021311yescharacteristic
931C22C4×#115911yescharacteristic
932C22C4×#115911yescharacteristic
933C22C4×D4×D711yescharacteristic
934C22#9026511yescharacteristic
935C22#9028711yescharacteristic
936C22#9029711yescharacteristic
937C22#9030911yescharacteristic
938C22#9032011yescharacteristic
939C22#9033011yescharacteristic
940C22#9033211yescharacteristic
941C22#9034011yescharacteristic
942C22#9034411yescharacteristic
943C22#9034711yescharacteristic
944C22#9034911yescharacteristic
945C22#9034911yescharacteristic
946C22#9034911yescharacteristic
947C22D7×#12411yescharacteristic
948C22#9037111yescharacteristic
949C22#9037211yescharacteristic
950C22#9038311yescharacteristic
951C22#9038411yescharacteristic
952C22#9038411yescharacteristic
953C22#9039511yescharacteristic
954C22#9039611yescharacteristic
955C22#9039611yescharacteristic
956C22#9039611yescharacteristic
957C22#9039711yescharacteristic
958C22#9039711yescharacteristic
959C22#9040011yescharacteristic
960C22#9040011yescharacteristic
961C22#9040011yescharacteristic
962C22#9040011yescharacteristic
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—81no—
970C4—144no—
971C4—144no—
972C4—282no—
973C4—282no—
974C4—282no—
975C4—282no—
976C4—561no—
977C2—284no—
978C2#1173174211yescharacteristic
979C2#1173241811yescharacteristic
980C2#1173274311yescharacteristic
981C2#1173274811yescharacteristic
982C2#1173289411yescharacteristic
983C2#1173289911yescharacteristic
984C2#1173293311yescharacteristic
985C2#1173477311yescharacteristic
986C2#1173497011yescharacteristic
987C2#1173498011yescharacteristic
988C2#1173512811yescharacteristic
989C2#1173562511yescharacteristic
990C2#1173563311yescharacteristic
991C2#1173563411yescharacteristic
992C2#1173585911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1443C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1443D7
hypocenterC7#14086
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
2. C2×#89425C2semidirect
4. C7×#1443C2semidirect
9. #11727168C2semidirect
11. #11727161C2semidirect
12. #11727155C2semidirect
13. #11727155C2semidirect
14. #11727155C2semidirect
15. Dic7×#95C2semidirect
51. #89442C4semidirect
97. C2×C4⋊Dic7C2×C4semidirect
111. C2×C4×Dic7C2×C4semidirect
119. C7×#95C2×C4semidirect
134. C7⋊#95C2×C4semidirect
138. #1443D7semidirect
549. #95C4×D7semidirect
912. C7#14086semidirect

Maximal subgroups

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

subgroupindex
C2×#894422
C2×#894252
C2×#894382
C7×#14432
#117271832
#117271822
(C2×D7)⋊#952
#117271682
#117271622
#117271612
#117271552
Dic7×#952
#140867