Finite Group Databasebeta

← #13277018

Subgroups — #13277018

Order 1792.

1614 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89700C211yesmaximal, characteristic
2C2×#89700C211yesmaximal, characteristic
3C2×#89700C211yesmaximal, characteristic
4C2×#89707C211yesmaximal, characteristic
5C2×C4×C4⋊Dic7C211yesmaximal, characteristic
6C2×#89419C212yesmaximal
7C4×C7×#95C211yesmaximal, characteristic
8#11729289C211yesmaximal, characteristic
9#11727174C212yesmaximal
10#11727164C212yesmaximal
11#11727161C212yesmaximal
12C22×C42×C7C2211yescharacteristic
13C22×C42×C7C2211yescharacteristic
14C22×C42×C7C2211yescharacteristic
15C22×C4⋊Dic7C2211yescharacteristic
16C22×C4⋊Dic7C2212yes—
17C22×C4⋊Dic7C2212yes—
18C22×C4⋊Dic7C2211yescharacteristic
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×Dic7⋊C4C2212yes—
22C22×Dic7⋊C4C2212yes—
23C22×Dic7⋊C4C2212yes—
24C22×C4×Dic7C2212yes—
25C2×C7×#95C2211yescharacteristic
26C2×C7×#95C2211yescharacteristic
27C2×C7×#95C2211yescharacteristic
28C2×C7×#95C2211yescharacteristic
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35#89707—24no—
36C4×C4⋊Dic7—24no—
37#89700—24no—
38#89700—24no—
39#89700C418yescomplemented
40#89419—28no—
41#14005—71nomaximal, Sylow
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×Dic7C2312yes—
50C23×Dic7C2312yes—
51C23×Dic7C2312yes—
52C23×Dic7C2312yes—
53C2×C42×C7—22no—
54C2×C42×C7—22no—
55C2×C42×C7—22no—
56C2×C42×C7—22no—
57C2×C42×C7—22no—
58C2×C42×C7—22no—
59C2×C42×C7—22no—
60C2×C42×C7C2×C414yes—
61C2×C42×C7Q814yes—
62C2×C4⋊Dic7—22no—
63C2×C4⋊Dic7—22no—
64C2×C4⋊Dic7—22no—
65C2×C4⋊Dic7—22no—
66C2×C4⋊Dic7—24no—
67C2×C4⋊Dic7—22no—
68C2×C4⋊Dic7—22no—
69C2×C4⋊Dic7—24no—
70C2×C4⋊Dic7—22no—
71C2×C4⋊Dic7—24no—
72C2×C4⋊Dic7—24no—
73C2×C4⋊Dic7—42no—
74C2×C4⋊Dic7—42no—
75C2×C4⋊Dic7C2×C414yes—
76C2×C4⋊Dic7C2×C414yes—
77C2×C4⋊Dic7D414yes—
78C2×C4⋊Dic7D414yes—
79C2×C4⋊Dic7Q814yes—
80C2×Dic7⋊C4—24no—
81C2×Dic7⋊C4—24no—
82C2×Dic7⋊C4—24no—
83C2×Dic7⋊C4—24no—
84C2×Dic7⋊C4—24no—
85C2×Dic7⋊C4—24no—
86C2×Dic7⋊C4—42no—
87C2×Dic7⋊C4—42no—
88C2×Dic7⋊C4C2×C418yes—
89C2×C4×Dic7—24no—
90C2×C4×Dic7—24no—
91C2×C4×Dic7—42no—
92C7×#95—22no—
93C7×#95—22no—
94C7×#95D414yes—
95C7×#95Q814yes—
96C7⋊#95—24no—
97C7⋊#95—24no—
98C7⋊#95—24no—
99C7⋊#95—24no—
100C7⋊#95—42no—
101C7⋊#95C2×C418yes—
102C2×#389—71no—
103C2×#389—71no—
104C2×#389—71no—
105C2×#389—72no—
106C2×#384—71no—
107C2×C4×C4⋊C4—71no—
108#1444—72no—
109#1441—72no—
110#1436—72no—
111C4⋊#95—71no—
112C4×#95D711yescharacteristic
113C24×C7C2411yescharacteristic
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—21no—
117C22×C4×C7—21no—
118C22×C4×C7—21no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—21no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—21no—
127C22×C4×C7—21no—
128C22×C4×C7—21no—
129C22×C4×C7—21no—
130C22×C4×C7—21no—
131C22×C4×C7—21no—
132C22×C4×C7—21no—
133C22×C4×C7—21no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7C22×C412yes—
145C22×C4×C7C22×C412yes—
146C22×C4×C7C22×C412yes—
147C22×C4×C7C2×D412yes—
148C22×C4×C7C2×D412yes—
149C22×C4×C7C2×D412yes—
150C22×C4×C7C2×D412yes—
151C22×C4×C7C2×D412yes—
152C22×C4×C7C2×Q812yes—
153C22×C4×C7C2×Q812yes—
154C22×C4×C7C2×Q812yes—
155C22×C4×C7C2×Q812yes—
156C22×C4×C7C2×Q812yes—
157C22×C4×C7C2×Q812yes—
158C22×C4×C7C2×Q812yes—
159C22×C4×C7#4112yes—
160C22×C4×C7#4112yes—
161C22×C4×C7#4112yes—
162C22×C4×C7#4112yes—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7C22×C414yes—
187C22×Dic7C22×C414yes—
188C22×Dic7C2×D414yes—
189C22×Dic7C2×D414yes—
190C22×Dic7C2×Q814yes—
191C42×C7—28no—
192C42×C7—28no—
193C42×C7—44no—
194C4⋊Dic7—28no—
195C4⋊Dic7—28no—
196C4⋊Dic7—48no—
197C4⋊Dic7—48no—
198C4⋊Dic7—44no—
199C4⋊Dic7C4⋊C4116yescomplemented
200Dic7⋊C4—216no—
201Dic7⋊C4—48no—
202Dic7⋊C4—48no—
203C4×Dic7—48no—
204C22×C4⋊C4—71no—
205C22×C4⋊C4—72no—
206C22×C4⋊C4—71no—
207C22×C4⋊C4—71no—
208C22×C4⋊C4—71no—
209C22×C4⋊C4—72no—
210C22×C4⋊C4—72no—
211C22×C4⋊C4—72no—
212C22×C4⋊C4—72no—
213C22×C42—72no—
214C22×C42C2×D711yescharacteristic
215C22×C42C2×D711yescharacteristic
216C22×C42C2×D711yescharacteristic
217#389—78no—
218#389—144no—
219#389—144no—
220#389—148no—
221#384—144no—
222C4×C4⋊C4—144no—
223C2×#95—72no—
224C2×#95—72no—
225C2×#95—72no—
226C2×#95—72no—
227C2×#95—72no—
228C2×#95—72no—
229C2×#95C2×D711yescharacteristic
230C2×#95C2×D711yescharacteristic
231C2×#95C2×D711yescharacteristic
232C2×#95C2×D711yescharacteristic
233C23×C7C23×C411yescharacteristic
234C23×C7C22×D411yescharacteristic
235C23×C7C22×D411yescharacteristic
236C23×C7C22×D411yescharacteristic
237C23×C7C22×Q811yescharacteristic
238C23×C7C22×Q811yescharacteristic
239C23×C7C22×Q811yescharacteristic
240C23×C7C2×#4111yescharacteristic
241C23×C7C2×#4111yescharacteristic
242C23×C7C2×#4111yescharacteristic
243C23×C7C2×#4111yescharacteristic
244C23×C7H(5,𝔽2)11yescharacteristic
245C23×C7H(5,𝔽2)11yescharacteristic
246C23×C72−1+411yescharacteristic
247C23×C72−1+411yescharacteristic
248C2×C4×C7—22no—
249C2×C4×C7—22no—
250C2×C4×C7—22no—
251C2×C4×C7—22no—
252C2×C4×C7—22no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—22no—
256C2×C4×C7—22no—
257C2×C4×C7—22no—
258C2×C4×C7—22no—
259C2×C4×C7—22no—
260C2×C4×C7—22no—
261C2×C4×C7—22no—
262C2×C4×C7—22no—
263C2×C4×C7—22no—
264C2×C4×C7—22no—
265C2×C4×C7—22no—
266C2×C4×C7—22no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—22no—
272C2×C4×C7—22no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—41no—
276C2×C4×C7—41no—
277C2×C4×C7—41no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—41no—
281C2×C4×C7—41no—
282C2×C4×C7—41no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7C2×C4⋊C414yes—
288C2×C4×C7C4×D414yes—
289C2×C4×C7C4×D414yes—
290C2×C4×C7C4×Q814yes—
291C2×C4×C7C4×Q814yes—
292C2×C4×C7#12114yes—
293C2×C4×C7C22⋊Q814yes—
294C2×C4×C7#12514yes—
295C2×C4×C7C4⋊Q814yes—
296C2×C4×C7C4⋊Q814yes—
297C2×Dic7—24no—
298C2×Dic7—24no—
299C2×Dic7—24no—
300C2×Dic7—24no—
301C2×Dic7—24no—
302C2×Dic7—24no—
303C2×Dic7—24no—
304C2×Dic7—24no—
305C2×Dic7—24no—
306C2×Dic7—24no—
307C2×Dic7—24no—
308C2×Dic7—24no—
309C2×Dic7—42no—
310C2×Dic7—42no—
311C2×Dic7—42no—
312C2×Dic7—42no—
313C2×Dic7—42no—
314C2×Dic7—42no—
315C2×Dic7—42no—
316C2×Dic7—42no—
317C2×Dic7—42no—
318C2×Dic7—42no—
319C2×Dic7—42no—
320C2×Dic7—42no—
321C2×Dic7—42no—
322C2×Dic7—42no—
323C2×Dic7—42no—
324C2×Dic7C2×C4⋊C418yes—
325C23×C4—72no—
326C23×C4—72no—
327C23×C4—72no—
328C23×C4—72no—
329C23×C4C22×D711yescharacteristic
330C23×C4C22×D711yescharacteristic
331C23×C4C22×D711yescharacteristic
332C23×C4C22×D711yescharacteristic
333C23×C4C22×D711yescharacteristic
334C23×C4C22×D711yescharacteristic
335C23×C4C22×D711yescharacteristic
336C2×C4⋊C4—74no—
337C2×C4⋊C4—74no—
338C2×C4⋊C4—74no—
339C2×C4⋊C4—78no—
340C2×C4⋊C4—74no—
341C2×C4⋊C4—74no—
342C2×C4⋊C4—144no—
343C2×C4⋊C4—144no—
344C2×C4⋊C4—142no—
345C2×C4⋊C4—142no—
346C2×C4⋊C4—142no—
347C2×C4⋊C4—142no—
348C2×C4⋊C4—144no—
349C2×C4⋊C4—144no—
350C2×C4⋊C4—144no—
351C2×C4⋊C4—144no—
352C2×C4⋊C4—144no—
353C2×C4⋊C4—144no—
354C2×C4⋊C4—144no—
355C2×C4⋊C4—144no—
356C2×C4⋊C4—142no—
357C2×C4⋊C4—142no—
358C2×C4⋊C4—142no—
359C2×C4⋊C4—282no—
360C2×C4⋊C4—282no—
361C2×C4⋊C4—282no—
362C2×C4⋊C4—282no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—144no—
371C2×C42—144no—
372C2×C42—282no—
373C2×C42Dic1414yes—
374C2×C42C4×D714yes—
375#95—22no—
376#95—22no—
377#95—78no—
378#95—144no—
379#95—144no—
380#95—144no—
381#95—144no—
382#95—282no—
383#95Dic1414yes—
384#95D2814yes—
385C22×C7C22×C4⋊C411yescharacteristic
386C22×C7C2×C4×D411yescharacteristic
387C22×C7C2×C4×D411yescharacteristic
388C22×C7C2×C4×Q811yescharacteristic
389C22×C7C2×C4×Q811yescharacteristic
390C22×C7#52011yescharacteristic
391C22×C7#52011yescharacteristic
392C22×C7C2×#12111yescharacteristic
393C22×C7C2×C22⋊Q811yescharacteristic
394C22×C7C2×#12511yescharacteristic
395C22×C7C2×C4⋊Q811yescharacteristic
396C22×C7C2×C4⋊Q811yescharacteristic
397C22×C7#53211yescharacteristic
398C22×C7#53311yescharacteristic
399C22×C7#53311yescharacteristic
400C22×C7#54011yescharacteristic
401C22×C7#54111yescharacteristic
402C22×C7#54411yescharacteristic
403C22×C7#54411yescharacteristic
404C22×C7D4211yescharacteristic
405C22×C7D4211yescharacteristic
406C22×C7#54611yescharacteristic
407C22×C7#54711yescharacteristic
408C22×C7#54711yescharacteristic
409C22×C7#54811yescharacteristic
410C22×C7D4×Q811yescharacteristic
411C22×C7D4×Q811yescharacteristic
412C22×C7D4×Q811yescharacteristic
413C22×C7#55011yescharacteristic
414C22×C7#55211yescharacteristic
415C22×C7#55311yescharacteristic
416C22×C7#55411yescharacteristic
417C22×C7#55411yescharacteristic
418C22×C7#55711yescharacteristic
419C22×C7Q8211yescharacteristic
420C4×C7—24no—
421C4×C7—24no—
422C4×C7—24no—
423C4×C7—42no—
424C4×C7—42no—
425C4×C7—42no—
426C4×C7#38918yescomplemented
427Dic7—28no—
428Dic7—44no—
429Dic7—44no—
430Dic7—82no—
431C24C23×D711yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—74no—
463C22×C4—74no—
464C22×C4—74no—
465C22×C4—74no—
466C22×C4—74no—
467C22×C4—142no—
468C22×C4—142no—
469C22×C4—142no—
470C22×C4—142no—
471C22×C4—142no—
472C22×C4—142no—
473C22×C4—142no—
474C22×C4—142no—
475C22×C4—142no—
476C22×C4—142no—
477C22×C4—142no—
478C22×C4—142no—
479C22×C4—142no—
480C22×C4—142no—
481C22×C4—142no—
482C22×C4—142no—
483C22×C4—142no—
484C22×C4—142no—
485C22×C4—142no—
486C22×C4—142no—
487C22×C4—142no—
488C22×C4—142no—
489C22×C4—142no—
490C22×C4C2×Dic1412yes—
491C22×C4C2×Dic1412yes—
492C22×C4C2×Dic1412yes—
493C22×C4C2×Dic1412yes—
494C22×C4C2×Dic1412yes—
495C22×C4C2×Dic1412yes—
496C22×C4C2×C4×D712yes—
497C22×C4C2×C4×D712yes—
498C22×C4C2×C4×D712yes—
499C22×C4C2×D2812yes—
500C22×C4C2×D2812yes—
501C22×C4C2×D2812yes—
502C22×C4#115712yes—
503C22×C4#115712yes—
504C22×C4#115712yes—
505C22×C4D4×D712yes—
506C22×C4D4×D712yes—
507C22×C4#115912yes—
508C22×C4Q8×D712yes—
509C4⋊C4—716no—
510C4⋊C4—1416no—
511C4⋊C4—148no—
512C4⋊C4—148no—
513C4⋊C4—288no—
514C4⋊C4—288no—
515C4⋊C4—288no—
516C4⋊C4—288no—
517C4⋊C4—284no—
518C42—28no—
519C42—28no—
520C42—44no—
521C42—288no—
522C2×C7C2×#38911yescharacteristic
523C2×C7C4×C4⋊Q811yescharacteristic
524C2×C7#233011yescharacteristic
525C2×C7D4×C4⋊C411yescharacteristic
526C2×C7Q8×C4⋊C411yescharacteristic
527C2×C7#236011yescharacteristic
528C2×C7#236111yescharacteristic
529C2×C7#242811yescharacteristic
530C2×C7#242911yescharacteristic
531C2×C7#244011yescharacteristic
532C2×C7#244111yescharacteristic
533C2×C7#250611yescharacteristic
534C2×C7#250711yescharacteristic
535C2×C7#255011yescharacteristic
536C2×C7#255111yescharacteristic
537C23C22×Dic1411yescharacteristic
538C23C22×Dic1411yescharacteristic
539C23C22×C4×D711yescharacteristic
540C23C22×D2811yescharacteristic
541C23C2×#115711yescharacteristic
542C23C2×#115711yescharacteristic
543C23C2×#115711yescharacteristic
544C23C2×D4×D711yescharacteristic
545C23C2×D4×D711yescharacteristic
546C23C2×#115911yescharacteristic
547C23C2×Q8×D711yescharacteristic
548C23#655311yescharacteristic
549C23#655311yescharacteristic
550C23#655411yescharacteristic
551C23#655411yescharacteristic
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—78no—
592C2×C4—144no—
593C2×C4—144no—
594C2×C4—144no—
595C2×C4—144no—
596C2×C4—144no—
597C2×C4—144no—
598C2×C4—144no—
599C2×C4—144no—
600C2×C4—144no—
601C2×C4—144no—
602C2×C4—144no—
603C2×C4—144no—
604C2×C4—282no—
605C2×C4—282no—
606C2×C4—282no—
607C2×C4—282no—
608C2×C4—282no—
609C2×C4—282no—
610C2×C4—282no—
611C2×C4—282no—
612C2×C4—282no—
613C2×C4—282no—
614C2×C4—282no—
615C2×C4—282no—
616C2×C4—282no—
617C2×C4—282no—
618C2×C4—282no—
619C2×C4C4×Dic1414yes—
620C2×C4C4×Dic1414yes—
621C2×C4#643214yes—
622C2×C4C4×D2814yes—
623C2×C4#644114yes—
624C2×C4(C22⋊D7)⋊C414yes—
625C2×C4#644714yes—
626C2×C4#645114yes—
627C2×C4#645214yes—
628C2×C4D7×C4⋊C414yes—
629C7#1400511yescharacteristic, complemented, Sylow
630C22C2×C4×Dic1411yescharacteristic
631C22C2×C4×Dic1411yescharacteristic
632C22C2×#643211yescharacteristic
633C22#9016111yescharacteristic
634C22#9016111yescharacteristic
635C22C2×C4×D2811yescharacteristic
636C22#9016811yescharacteristic
637C22C2×#644111yescharacteristic
638C22C2×(C22⋊D7)⋊C411yescharacteristic
639C22C2×#644711yescharacteristic
640C22C2×#645111yescharacteristic
641C22C2×#645211yescharacteristic
642C22C2×D7×C4⋊C411yescharacteristic
643C22#9020911yescharacteristic
644C22#9021011yescharacteristic
645C22#9021011yescharacteristic
646C22#9021411yescharacteristic
647C22#9021411yescharacteristic
648C22#9022611yescharacteristic
649C22D4×Dic1411yescharacteristic
650C22D4×Dic1411yescharacteristic
651C22#9023211yescharacteristic
652C22#9023411yescharacteristic
653C22D4×D2811yescharacteristic
654C22D4×D2811yescharacteristic
655C22#9024111yescharacteristic
656C22#9024211yescharacteristic
657C22#9024311yescharacteristic
658C22#9024411yescharacteristic
659C22#9024611yescharacteristic
660C22#9025611yescharacteristic
661C22Q8×Dic1411yescharacteristic
662C22#9025811yescharacteristic
663C22Q8×D2811yescharacteristic
664C22#9027011yescharacteristic
665C4—24no—
666C4—24no—
667C4—24no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—148no—
672C4—284no—
673C4—284no—
674C4—562no—
675C4#8941918yescomplemented
676C2C4×#643211yescharacteristic
677C2C2×#8941911yescharacteristic
678C2#1173083511yescharacteristic
679C2#1173091011yescharacteristic
680C2#1173091211yescharacteristic
681C2#1173093211yescharacteristic
682C2#1173093311yescharacteristic
683C2#1173093811yescharacteristic
684C2#1173093911yescharacteristic
685C2C4⋊C4×Dic1411yescharacteristic
686C2#1173112711yescharacteristic
687C2#1173112911yescharacteristic
688C2#1173115811yescharacteristic
689C2#1173116011yescharacteristic
690C2C4⋊C4×D2811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC4×C7×#95C2
socle, prime radical, cosocleC24×C7C24
hypercenterC4×#95D7
hypocenterC7#14005
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
39. #89700C4semidirect
199. C4⋊Dic7C4⋊C4semidirect
426. C4×C7#389semidirect
629. C7#14005semidirect
675. C4#89419semidirect

Maximal subgroups

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

subgroupindex
C2×#897002
C2×#897072
C2×C4×C4⋊Dic72
C2×#894192
C4×C7×#952
#117292892
#117271742
#117271642
#117271612
#140057