Finite Group Databasebeta

← #13276471

Subgroups — #13276471

Order 1792.

1630 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C211yesmaximal, characteristic
2C2×#89757C211yesmaximal, characteristic
3C2×#89745C211yesmaximal, characteristic
4C2×#89749C211yesmaximal, characteristic
5C2×C4⋊C4×Dic7C211yesmaximal, characteristic
6C2×#89700C211yesmaximal, characteristic
7C2×C4×Dic7⋊C4C211yesmaximal, characteristic
8#11729322C212yesmaximal
9#11729317C212yesmaximal
10#11727174C212yesmaximal
11Dic7⋊#95C212yesmaximal
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2212yes—
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×C4⋊Dic7C2211yescharacteristic
17C22×C4⋊Dic7C2212yes—
18C22×C4⋊Dic7C2211yescharacteristic
19C22×Dic7⋊C4C2211yescharacteristic
20C22×Dic7⋊C4C2211yescharacteristic
21C22×Dic7⋊C4C2212yes—
22C22×Dic7⋊C4C2212yes—
23C22×C4×Dic7C2211yescharacteristic
24C22×C4×Dic7C2212yes—
25C22×C4×Dic7C2211yescharacteristic
26C7×#389—24no—
27C2×C7×#95C2212yes—
28C2×C7⋊#95C2211yescharacteristic
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36#89757—24no—
37#89749—24no—
38C4⋊C4×Dic7C418yescomplemented
39#89745—24no—
40C4×Dic7⋊C4—24no—
41#89700—24no—
42#13954—71nomaximal, Sylow
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2312yes—
47C23×C4×C7C2311yescharacteristic
48C23×Dic7C2312yes—
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2312yes—
53C23×Dic7C2311yescharacteristic
54C2×C7×C4⋊C4—22no—
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4—24no—
57C2×C7×C4⋊C4—22no—
58C2×C7×C4⋊C4—24no—
59C2×C7×C4⋊C4—42no—
60C2×C7×C4⋊C4C2×C414yes—
61C2×C7×C4⋊C4D414yes—
62C2×C7×C4⋊C4Q814yes—
63C2×C42×C7—22no—
64C2×C42×C7—22no—
65C2×C42×C7—22no—
66C2×C4⋊Dic7—22no—
67C2×C4⋊Dic7—22no—
68C2×C4⋊Dic7—24no—
69C2×C4⋊Dic7—22no—
70C2×C4⋊Dic7—24no—
71C2×C4⋊Dic7—42no—
72C2×C4⋊Dic7C2×C414yes—
73C2×C4⋊Dic7D414yes—
74C2×C4⋊Dic7Q814yes—
75C2×Dic7⋊C4—22no—
76C2×Dic7⋊C4—22no—
77C2×Dic7⋊C4—22no—
78C2×Dic7⋊C4—22no—
79C2×Dic7⋊C4—22no—
80C2×Dic7⋊C4—22no—
81C2×Dic7⋊C4—24no—
82C2×Dic7⋊C4—24no—
83C2×Dic7⋊C4—24no—
84C2×Dic7⋊C4—24no—
85C2×Dic7⋊C4—42no—
86C2×Dic7⋊C4—42no—
87C2×C4×Dic7—22no—
88C2×C4×Dic7—22no—
89C2×C4×Dic7—22no—
90C2×C4×Dic7—42no—
91C2×C4×Dic7—42no—
92C2×C4×Dic7C2×C418yes—
93C2×C4×Dic7C2×C414yes—
94C2×C4×Dic7D414yes—
95C2×C4×Dic7Q814yes—
96C7×#95—24no—
97C7⋊#95—24no—
98C7⋊#95—24no—
99C7⋊#95—22no—
100C7⋊#95—22no—
101C7⋊#95—24no—
102C7⋊#95—24no—
103C7⋊#95—24no—
104C7⋊#95C2×C418yes—
105C2×#389—71no—
106C2×#389—71no—
107C2×#389—71no—
108C2×#389D711yescharacteristic
109C2×#382—71no—
110C2×C4×C4⋊C4—71no—
111C2×C4×C4⋊C4—71no—
112#1444—72no—
113#1444—72no—
114C4⋊#95—72no—
115C4⋊#95—72no—
116C24×C7C2411yescharacteristic
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
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—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7C22×C414yes—
141C22×C4×C7C22×C412yes—
142C22×C4×C7C2×D414yes—
143C22×C4×C7C2×D412yes—
144C22×C4×C7C2×D412yes—
145C22×C4×C7C2×D412yes—
146C22×C4×C7C2×Q814yes—
147C22×C4×C7C2×Q812yes—
148C22×C4×C7C2×Q812yes—
149C22×C4×C7C2×Q812yes—
150C22×C4×C7#4112yes—
151C22×C4×C7#4112yes—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7—21no—
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7—21no—
168C22×Dic7—21no—
169C22×Dic7—21no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C22×Dic7—21no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7C22×C412yes—
184C22×Dic7C22×C414yes—
185C22×Dic7C22×C412yes—
186C22×Dic7C2×D412yes—
187C22×Dic7C2×D412yes—
188C22×Dic7C2×D414yes—
189C22×Dic7C2×Q812yes—
190C22×Dic7C2×Q812yes—
191C22×Dic7C2×Q814yes—
192C22×Dic7#4112yes—
193C22×Dic7#4112yes—
194C7×C4⋊C4—48no—
195C7×C4⋊C4—44no—
196C7×C4⋊C4C4⋊C4116yescomplemented
197C42×C7—44no—
198C4⋊Dic7—48no—
199C4⋊Dic7—44no—
200C4⋊Dic7C4⋊C4116yescomplemented
201Dic7⋊C4—28no—
202Dic7⋊C4—28no—
203Dic7⋊C4—48no—
204Dic7⋊C4—48no—
205C4×Dic7—48no—
206C4×Dic7—44no—
207C4×Dic7C4⋊C4116yescomplemented
208C22×C4⋊C4—71no—
209C22×C4⋊C4—71no—
210C22×C4⋊C4—71no—
211C22×C4⋊C4—71no—
212C22×C4⋊C4—72no—
213C22×C4⋊C4—72no—
214C22×C4⋊C4—72no—
215C22×C4⋊C4C2×D711yescharacteristic
216C22×C4⋊C4C2×D712yes—
217C22×C4⋊C4C2×D711yescharacteristic
218C22×C42—71no—
219C22×C42—72no—
220C22×C42—71no—
221C22×C42C2×D711yescharacteristic
222#389—24no—
223#389—144no—
224#389—144no—
225#389—144no—
226#382—144no—
227C4×C4⋊C4—78no—
228C4×C4⋊C4—144no—
229C2×#95—72no—
230C2×#95—71no—
231C2×#95—71no—
232C2×#95—72no—
233C2×#95—72no—
234C2×#95—72no—
235C2×#95—72no—
236C2×#95—72no—
237C2×#95C2×D712yes—
238C23×C7C23×C411yescharacteristic
239C23×C7C22×D411yescharacteristic
240C23×C7C22×D411yescharacteristic
241C23×C7C22×D411yescharacteristic
242C23×C7C22×Q811yescharacteristic
243C23×C7C22×Q811yescharacteristic
244C23×C7C22×Q811yescharacteristic
245C23×C7C2×#4111yescharacteristic
246C23×C7C2×#4111yescharacteristic
247C23×C7C2×#4111yescharacteristic
248C23×C7C2×#4111yescharacteristic
249C23×C7H(5,𝔽2)11yescharacteristic
250C23×C7H(5,𝔽2)11yescharacteristic
251C23×C72−1+411yescharacteristic
252C23×C72−1+411yescharacteristic
253C2×C4×C7—24no—
254C2×C4×C7—24no—
255C2×C4×C7—24no—
256C2×C4×C7—24no—
257C2×C4×C7—24no—
258C2×C4×C7—24no—
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—41no—
266C2×C4×C7—41no—
267C2×C4×C7—41no—
268C2×C4×C7—41no—
269C2×C4×C7—41no—
270C2×C4×C7—41no—
271C2×C4×C7—41no—
272C2×C4×C7—41no—
273C2×C4×C7—42no—
274C2×C4×C7—42no—
275C2×C4×C7—42no—
276C2×C4×C7—42no—
277C2×C4×C7—42no—
278C2×C4×C7—42no—
279C2×C4×C7—42no—
280C2×C4×C7C2×C4⋊C414yes—
281C2×C4×C7C2×C4⋊C414yes—
282C2×C4×C7C2×C4⋊C418yes—
283C2×C4×C7C2×C4⋊C414yes—
284C2×C4×C7#12714yes—
285C2×C4×C7C4⋊Q814yes—
286C2×C4×C7C4⋊Q814yes—
287C2×C4×C7C4⋊Q814yes—
288C2×Dic7—22no—
289C2×Dic7—24no—
290C2×Dic7—22no—
291C2×Dic7—22no—
292C2×Dic7—24no—
293C2×Dic7—22no—
294C2×Dic7—22no—
295C2×Dic7—22no—
296C2×Dic7—22no—
297C2×Dic7—22no—
298C2×Dic7—22no—
299C2×Dic7—22no—
300C2×Dic7—22no—
301C2×Dic7—22no—
302C2×Dic7—24no—
303C2×Dic7—24no—
304C2×Dic7—24no—
305C2×Dic7—24no—
306C2×Dic7—22no—
307C2×Dic7—22no—
308C2×Dic7—22no—
309C2×Dic7—22no—
310C2×Dic7—22no—
311C2×Dic7—22no—
312C2×Dic7—41no—
313C2×Dic7—41no—
314C2×Dic7—41no—
315C2×Dic7—41no—
316C2×Dic7—41no—
317C2×Dic7—41no—
318C2×Dic7—41no—
319C2×Dic7—41no—
320C2×Dic7—42no—
321C2×Dic7—42no—
322C2×Dic7—42no—
323C2×Dic7—42no—
324C2×Dic7—42no—
325C2×Dic7—42no—
326C2×Dic7—42no—
327C2×Dic7C2×C4⋊C414yes—
328C2×Dic7C2×C4⋊C414yes—
329C2×Dic7C2×C4⋊C418yes—
330C23×C4—72no—
331C23×C4—71no—
332C23×C4—71no—
333C23×C4—71no—
334C23×C4—71no—
335C23×C4—72no—
336C23×C4C22×D712yes—
337C23×C4C22×D711yescharacteristic
338C23×C4C22×D711yescharacteristic
339C23×C4C22×D712yes—
340C23×C4C22×D711yescharacteristic
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—74no—
348C2×C4⋊C4—74no—
349C2×C4⋊C4—74no—
350C2×C4⋊C4—142no—
351C2×C4⋊C4—142no—
352C2×C4⋊C4—142no—
353C2×C4⋊C4—142no—
354C2×C4⋊C4—142no—
355C2×C4⋊C4—142no—
356C2×C4⋊C4—144no—
357C2×C4⋊C4—144no—
358C2×C4⋊C4—144no—
359C2×C4⋊C4—144no—
360C2×C4⋊C4—142no—
361C2×C4⋊C4—142no—
362C2×C4⋊C4—144no—
363C2×C4⋊C4—144no—
364C2×C4⋊C4—142no—
365C2×C4⋊C4—282no—
366C2×C4⋊C4—282no—
367C2×C4⋊C4—282no—
368C2×C4⋊C4Dic1414yes—
369C2×C4⋊C4C4×D714yes—
370C2×C4⋊C4C22⋊D714yes—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—74no—
375C2×C42—74no—
376C2×C42—74no—
377C2×C42—78no—
378C2×C42—142no—
379C2×C42—142no—
380C2×C42—142no—
381C2×C42—282no—
382C2×C42—282no—
383#95—24no—
384#95—78no—
385#95—142no—
386#95—142no—
387#95—144no—
388#95—144no—
389#95—144no—
390#95—144no—
391#95—144no—
392C22×C7C22×C4⋊C411yescharacteristic
393C22×C7C22×C4⋊C411yescharacteristic
394C22×C7C22×C4⋊C411yescharacteristic
395C22×C7C4×#4111yescharacteristic
396C22×C7C4×#4111yescharacteristic
397C22×C7#51811yescharacteristic
398C22×C7#51911yescharacteristic
399C22×C7#52511yescharacteristic
400C22×C7#52511yescharacteristic
401C22×C7C2×#12711yescharacteristic
402C22×C7C2×C4⋊Q811yescharacteristic
403C22×C7C2×C4⋊Q811yescharacteristic
404C22×C7C2×C4⋊Q811yescharacteristic
405C22×C7#53311yescharacteristic
406C22×C7#53311yescharacteristic
407C22×C7#53711yescharacteristic
408C22×C7#53711yescharacteristic
409C22×C7#54411yescharacteristic
410C22×C7#54411yescharacteristic
411C22×C7#54611yescharacteristic
412C22×C7#54611yescharacteristic
413C22×C7#54611yescharacteristic
414C22×C7#54611yescharacteristic
415C22×C7#54811yescharacteristic
416C22×C7#54811yescharacteristic
417C22×C7#54811yescharacteristic
418C22×C7#54811yescharacteristic
419C22×C7#55411yescharacteristic
420C22×C7#55411yescharacteristic
421C22×C7#55411yescharacteristic
422C22×C7#55411yescharacteristic
423C22×C7#55711yescharacteristic
424C22×C7#55711yescharacteristic
425C22×C7#55711yescharacteristic
426C22×C7#55711yescharacteristic
427C4×C7—28no—
428C4×C7—42no—
429C4×C7—42no—
430C4×C7—82no—
431C4×C7#38418yes—
432Dic7—24no—
433Dic7—28no—
434Dic7—24no—
435Dic7—42no—
436Dic7—42no—
437Dic7—82no—
438C24C23×D711yescharacteristic
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
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—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—72no—
463C22×C4—74no—
464C22×C4—72no—
465C22×C4—72no—
466C22×C4—72no—
467C22×C4—74no—
468C22×C4—72no—
469C22×C4—72no—
470C22×C4—74no—
471C22×C4—72no—
472C22×C4—72no—
473C22×C4—141no—
474C22×C4—141no—
475C22×C4—142no—
476C22×C4—141no—
477C22×C4—142no—
478C22×C4—141no—
479C22×C4—141no—
480C22×C4—141no—
481C22×C4—142no—
482C22×C4—141no—
483C22×C4—142no—
484C22×C4—141no—
485C22×C4—141no—
486C22×C4—141no—
487C22×C4—141no—
488C22×C4—141no—
489C22×C4—141no—
490C22×C4—141no—
491C22×C4—141no—
492C22×C4—141no—
493C22×C4—141no—
494C22×C4—141no—
495C22×C4—141no—
496C22×C4—141no—
497C22×C4—142no—
498C22×C4—142no—
499C22×C4—142no—
500C22×C4—142no—
501C22×C4—142no—
502C22×C4—142no—
503C22×C4—142no—
504C22×C4C2×Dic1414yes—
505C22×C4C2×Dic1412yes—
506C22×C4C2×C4×D714yes—
507C22×C4C2×C4×D712yes—
508C22×C4D4×D712yes—
509C22×C4D4×D712yes—
510C22×C4#115912yes—
511C22×C4Q8×D712yes—
512C22×C4Q8×D712yes—
513C22×C4#116112yes—
514C22×C4C2×C22⋊D714yes—
515C22×C4C2×C22⋊D712yes—
516C4⋊C4—48no—
517C4⋊C4—44no—
518C4⋊C4—716no—
519C4⋊C4—148no—
520C4⋊C4—148no—
521C4⋊C4—288no—
522C4⋊C4—288no—
523C4⋊C4—288no—
524C4⋊C4—284no—
525C4⋊C4Dic7⋊C4116yescomplemented
526C42—44no—
527C42—716no—
528C42—288no—
529C42—284no—
530C2×C7C2×#38411yescharacteristic
531C2×C7#229611yescharacteristic
532C2×C7#231611yescharacteristic
533C2×C7#234911yescharacteristic
534C2×C7#234911yescharacteristic
535C2×C7#235111yescharacteristic
536C2×C7#235111yescharacteristic
537C2×C7#254011yescharacteristic
538C2×C7#254011yescharacteristic
539C2×C7#255011yescharacteristic
540C2×C7#255011yescharacteristic
541C2×C7#255011yescharacteristic
542C2×C7#255011yescharacteristic
543C2×C7#258411yescharacteristic
544C2×C7#258411yescharacteristic
545C23C22×Dic1411yescharacteristic
546C23C22×C4×D711yescharacteristic
547C23C2×D4×D711yescharacteristic
548C23C2×D4×D711yescharacteristic
549C23C2×#115911yescharacteristic
550C23#654811yescharacteristic
551C23C2×Q8×D711yescharacteristic
552C23C2×Q8×D711yescharacteristic
553C23C2×#116111yescharacteristic
554C23#655111yescharacteristic
555C23D7×#4111yescharacteristic
556C23D7×#4111yescharacteristic
557C23#655311yescharacteristic
558C23#655411yescharacteristic
559C23C22×C22⋊D711yescharacteristic
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—74no—
588C2×C4—74no—
589C2×C4—78no—
590C2×C4—142no—
591C2×C4—142no—
592C2×C4—144no—
593C2×C4—142no—
594C2×C4—142no—
595C2×C4—144no—
596C2×C4—142no—
597C2×C4—142no—
598C2×C4—144no—
599C2×C4—142no—
600C2×C4—144no—
601C2×C4—142no—
602C2×C4—142no—
603C2×C4—142no—
604C2×C4—144no—
605C2×C4—142no—
606C2×C4—142no—
607C2×C4—144no—
608C2×C4—142no—
609C2×C4—142no—
610C2×C4—142no—
611C2×C4—142no—
612C2×C4—142no—
613C2×C4—142no—
614C2×C4—281no—
615C2×C4—281no—
616C2×C4—281no—
617C2×C4—281no—
618C2×C4—281no—
619C2×C4—281no—
620C2×C4—281no—
621C2×C4—281no—
622C2×C4—282no—
623C2×C4—282no—
624C2×C4—282no—
625C2×C4—282no—
626C2×C4—282no—
627C2×C4—282no—
628C2×C4—282no—
629C2×C4#645114yes—
630C2×C4#645114yes—
631C2×C4D7×C4⋊C414yes—
632C2×C4D7×C4⋊C414yes—
633C2×C4C2×Dic7⋊C418yes—
634C2×C4C2×Dic7⋊C414yes—
635C2×C4#650314yes—
636C2×C4#650714yes—
637C7#1395411yescharacteristic, complemented, Sylow
638C22C2×#645111yescharacteristic
639C22C2×#645111yescharacteristic
640C22C2×D7×C4⋊C411yescharacteristic
641C22C2×D7×C4⋊C411yescharacteristic
642C22C4×#115911yescharacteristic
643C22#9023011yescharacteristic
644C22#9023411yescharacteristic
645C22#9023611yescharacteristic
646C22#9026011yescharacteristic
647C22#9026111yescharacteristic
648C22#9026311yescharacteristic
649C22C4×#116111yescharacteristic
650C22#9028911yescharacteristic
651C22#9029711yescharacteristic
652C22#9029911yescharacteristic
653C22#9030311yescharacteristic
654C22#9031811yescharacteristic
655C22#9032011yescharacteristic
656C22#9032111yescharacteristic
657C22#9032411yescharacteristic
658C22#9037611yescharacteristic
659C22#9037911yescharacteristic
660C22#9038011yescharacteristic
661C22#9038111yescharacteristic
662C22#9041211yescharacteristic
663C22#9041911yescharacteristic
664C22#9042011yescharacteristic
665C22#9042111yescharacteristic
666C22C22×Dic7⋊C411yescharacteristic
667C22C2×#650311yescharacteristic
668C22#9049711yescharacteristic
669C22C2×#650711yescharacteristic
670C22#9050811yescharacteristic
671C22#9052011yescharacteristic
672C22#9052211yescharacteristic
673C4—28no—
674C4—42no—
675C4—42no—
676C4—82no—
677C4—144no—
678C4—148no—
679C4—144no—
680C4—282no—
681C4—282no—
682C4—562no—
683C4#8974818yes—
684C2#1173340811yescharacteristic
685C2#1173342711yescharacteristic
686C2#1173350611yescharacteristic
687C2#1173350711yescharacteristic
688C2#1173352311yescharacteristic
689C2#1173352411yescharacteristic
690C2#1173364011yescharacteristic
691C2#1173364811yescharacteristic
692C2C2×#8974811yescharacteristic
693C2#1173977911yescharacteristic
694C2#1173990611yescharacteristic
695C2#1174011311yescharacteristic
696C2#1174022411yescharacteristic
697C2#1174048111yescharacteristic
698C2#1174068611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#389C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#389D7
hypocenterC7#13954
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
38. C4⋊C4×Dic7C4semidirect
196. C7×C4⋊C4C4⋊C4semidirect
200. C4⋊Dic7C4⋊C4semidirect
207. C4×Dic7C4⋊C4semidirect
525. C4⋊C4Dic7⋊C4semidirect
637. C7#13954semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×#897572
C2×#897452
C2×#897492
C2×C4⋊C4×Dic72
C2×#897002
C2×C4×Dic7⋊C42
#117293222
#117293172
#117271742
Dic7⋊#952
#139547