Finite Group Databasebeta

← #13277613

Subgroups — #13277613

Order 1792.

1838 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6451C211yesmaximal, characteristic
2C2×C7×#389C211yesmaximal, characteristic
3C2×#89746C212yesmaximal
4C2×C4⋊C4×Dic7C211yesmaximal, characteristic
5#11729320C212yesmaximal
6#11729317C211yesmaximal, characteristic
7#11729317C211yesmaximal, characteristic
8#11729289C211yesmaximal, characteristic
9C4×C7⋊#95C211yesmaximal, characteristic
10#11727178C212yesmaximal
11#11727159C212yesmaximal
12C23×Dic14C2212yes—
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2212yes—
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×C4⋊Dic7C2211yescharacteristic
18C22×C4⋊Dic7C2211yescharacteristic
19C22×Dic7⋊C4C2212yes—
20C22×C4×Dic7C2212yes—
21C22×C4×Dic7C2211yescharacteristic
22C22×C4×Dic7C2211yescharacteristic
23C2×#6451—24no—
24C2×#6451—24no—
25C2×#6451C418yescomplemented
26C7×#389—24no—
27C2×C7×#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2211yescharacteristic
39C4⋊C4×Dic7—24no—
40#89746—28no—
41#14053—71nomaximal, Sylow
42C23×C4×C7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2312yes—
46C23×C4×C7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2312yes—
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2311yescharacteristic
53C22×Dic14—24no—
54C22×Dic14—24no—
55C22×Dic14—24no—
56C22×Dic14—24no—
57C22×Dic14—42no—
58C22×Dic14—42no—
59C22×Dic14C2×C418yes—
60C2×C7×C4⋊C4—24no—
61C2×C7×C4⋊C4—24no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—42no—
66C2×C7×C4⋊C4C2×C414yes—
67C2×C7×C4⋊C4D414yes—
68C2×C7×C4⋊C4D414yes—
69C2×C42×C7—22no—
70C2×C42×C7—22no—
71C2×C42×C7—22no—
72C2×C4⋊Dic7—22no—
73C2×C4⋊Dic7—22no—
74C2×C4⋊Dic7—22no—
75C2×C4⋊Dic7—22no—
76C2×C4⋊Dic7C2×C414yes—
77C2×C4⋊Dic7Q814yescomplemented
78C2×Dic7⋊C4—24no—
79C2×Dic7⋊C4—24no—
80C2×Dic7⋊C4C2×C418yes—
81C2×C4×Dic7—22no—
82C2×C4×Dic7—22no—
83C2×C4×Dic7—22no—
84C2×C4×Dic7—22no—
85C2×C4×Dic7—24no—
86C2×C4×Dic7—24no—
87C2×C4×Dic7—42no—
88C2×C4×Dic7C2×C414yes—
89C2×C4×Dic7Q814yescomplemented
90#6451—232no—
91C7×#95—24no—
92C7⋊#95—24no—
93C7⋊#95—24no—
94C7⋊#95—24no—
95C7⋊#95—24no—
96C7⋊#95—22no—
97C7⋊#95—22no—
98C7⋊#95—24no—
99C7⋊#95—42no—
100C7⋊#95—42no—
101C7⋊#95D414yes—
102C7⋊#95Q814yescomplemented
103C22×C4⋊Q8—71no—
104C2×#391—72no—
105C2×#389D711yescharacteristic
106C2×C4×C4⋊C4—71no—
107#1446—72no—
108#1441—72no—
109#1436—72no—
110C4⋊#95—71no—
111C4⋊#95—71no—
112C4⋊#95—71no—
113C4×#95—71no—
114C24×C7C2411yescharacteristic
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
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—22no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7C22×C414yes—
139C22×C4×C7C22×C412yes—
140C22×C4×C7C2×D412yes—
141C22×C4×C7C2×D414yes—
142C22×C4×C7C2×D414yes—
143C22×C4×C7C2×D412yes—
144C22×C4×C7C2×D412yes—
145C22×C4×C7C2×Q812yes—
146C22×C4×C7C2×Q812yes—
147C22×C4×C7C2×Q812yes—
148C22×C4×C7#4112yes—
149C22×C4×C7#4112yes—
150C22×Dic7—21no—
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—21no—
169C22×Dic7—21no—
170C22×Dic7—22no—
171C22×Dic7—21no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—21no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—21no—
179C22×Dic7—22no—
180C22×Dic7C22×C414yes—
181C22×Dic7C22×C412yes—
182C22×Dic7C22×C412yes—
183C22×Dic7C2×D412yes—
184C22×Dic7C2×D412yes—
185C22×Dic7C2×Q812yes—
186C22×Dic7C2×Q814yes—
187C22×Dic7C2×Q812yes—
188C22×Dic7C2×Q812yes—
189C22×Dic7C2×Q812yes—
190C22×Dic7#4112yes—
191C22×Dic7#4112yes—
192C2×Dic14—216no—
193C2×Dic14—216no—
194C2×Dic14—48no—
195C2×Dic14—48no—
196C2×Dic14—48no—
197C2×Dic14—48no—
198C2×Dic14—48no—
199C7×C4⋊C4—48no—
200C7×C4⋊C4—44no—
201C7×C4⋊C4C22⋊C4116yes—
202C42×C7—44no—
203C4⋊Dic7—28no—
204C4⋊Dic7—28no—
205Dic7⋊C4—216no—
206C4×Dic7—28no—
207C4×Dic7—28no—
208C4×Dic7—48no—
209C23×Q8—72no—
210C2×C4⋊Q8—78no—
211C2×C4⋊Q8—144no—
212C2×C4⋊Q8—144no—
213C22×C4⋊C4—72no—
214C22×C4⋊C4—71no—
215C22×C4⋊C4—71no—
216C22×C4⋊C4C2×D711yescharacteristic
217C22×C4⋊C4C2×D712yes—
218C22×C4⋊C4C2×D711yescharacteristic
219C22×C42—71no—
220C22×C42—71no—
221C22×C42—72no—
222C22×C42C2×D711yescharacteristic
223#391—148no—
224#389—24no—
225C4×C4⋊C4—144no—
226C2×#95—71no—
227C2×#95—71no—
228C2×#95—71no—
229C2×#95—71no—
230C2×#95—72no—
231C2×#95—72no—
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×C22⋊C418yes—
281C2×C4×C7C2×C22⋊C414yes—
282C2×C4×C7C4×Q814yes—
283C2×C4×C7C4×Q814yes—
284C2×C4×C7C22⋊Q814yes—
285C2×C4×C7C22⋊Q814yes—
286C2×C4×C7#12414yes—
287C2×C4×C7C4⋊Q814yes—
288C2×Dic7—22no—
289C2×Dic7—22no—
290C2×Dic7—22no—
291C2×Dic7—22no—
292C2×Dic7—22no—
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—22no—
303C2×Dic7—22no—
304C2×Dic7—22no—
305C2×Dic7—22no—
306C2×Dic7—24no—
307C2×Dic7—24no—
308C2×Dic7—24no—
309C2×Dic7—22no—
310C2×Dic7—24no—
311C2×Dic7—22no—
312C2×Dic7—22no—
313C2×Dic7—24no—
314C2×Dic7—24no—
315C2×Dic7—42no—
316C2×Dic7—42no—
317C2×Dic7—42no—
318C2×Dic7—42no—
319C2×Dic7—42no—
320C2×Dic7—42no—
321C2×Dic7—42no—
322C2×Dic7—41no—
323C2×Dic7—41no—
324C2×Dic7—42no—
325C2×Dic7—41no—
326C2×Dic7—41no—
327C2×Dic7C4×D414yes—
328C2×Dic7C4×Q814yes—
329C2×Dic7C4⋊Q814yescomplemented
330Dic14—432no—
331C22×Q8—78no—
332C22×Q8—144no—
333C22×Q8—144no—
334C22×Q8—144no—
335C22×Q8—144no—
336C22×Q8—282no—
337C22×Q8—282no—
338C23×C4—71no—
339C23×C4—71no—
340C23×C4—71no—
341C23×C4—72no—
342C23×C4—72no—
343C23×C4—71no—
344C23×C4C22×D712yes—
345C23×C4C22×D711yescharacteristic
346C23×C4C22×D711yescharacteristic
347C23×C4C22×D712yes—
348C23×C4C22×D711yescharacteristic
349C4⋊Q8—1432no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—78no—
357C2×C4⋊C4—74no—
358C2×C4⋊C4—74no—
359C2×C4⋊C4—144no—
360C2×C4⋊C4—142no—
361C2×C4⋊C4—142no—
362C2×C4⋊C4—142no—
363C2×C4⋊C4—144no—
364C2×C4⋊C4—142no—
365C2×C4⋊C4C4×D714yes—
366C2×C4⋊C4D2814yes—
367C2×C4⋊C4C22⋊D714yes—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—74no—
372C2×C42—74no—
373C2×C42—142no—
374C2×C42—142no—
375C2×C42—142no—
376C2×C42—142no—
377C2×C42—144no—
378C2×C42—144no—
379C2×C42—282no—
380#95—24no—
381#95—74no—
382#95—74no—
383#95—142no—
384#95—142no—
385#95—144no—
386#95—144no—
387#95—144no—
388#95—144no—
389#95—144no—
390#95—282no—
391#95—282no—
392C22×C7C22×C22⋊C411yescharacteristic
393C22×C7C2×C4×D411yescharacteristic
394C22×C7C2×C4×Q811yescharacteristic
395C22×C7C2×C4×Q811yescharacteristic
396C22×C7C2×C4×Q811yescharacteristic
397C22×C7#51811yescharacteristic
398C22×C7#51911yescharacteristic
399C22×C7C2×C22⋊Q811yescharacteristic
400C22×C7C2×C22⋊Q811yescharacteristic
401C22×C7C2×#12411yescharacteristic
402C22×C7C2×C4⋊Q811yescharacteristic
403C22×C7C2×C4⋊Q811yescharacteristic
404C22×C7#53211yescharacteristic
405C22×C7#53311yescharacteristic
406C22×C7#53311yescharacteristic
407C22×C7#54211yescharacteristic
408C22×C7#54211yescharacteristic
409C22×C7#54411yescharacteristic
410C22×C7#54411yescharacteristic
411C22×C7D4211yescharacteristic
412C22×C7D4211yescharacteristic
413C22×C7#54611yescharacteristic
414C22×C7#54611yescharacteristic
415C22×C7#54711yescharacteristic
416C22×C7#54811yescharacteristic
417C22×C7#54811yescharacteristic
418C22×C7D4×Q811yescharacteristic
419C22×C7D4×Q811yescharacteristic
420C22×C7D4×Q811yescharacteristic
421C22×C7#55411yescharacteristic
422C22×C7#55411yescharacteristic
423C22×C7#55511yescharacteristic
424C22×C7#55611yescharacteristic
425C22×C7#55711yescharacteristic
426C22×C7Q8211yescharacteristic
427C4×C7—28no—
428C4×C7—42no—
429C4×C7—42no—
430C4×C7—82no—
431C4×C7#39118yescomplemented
432Dic7—24no—
433Dic7—24no—
434Dic7—24no—
435Dic7—44no—
436Dic7—42no—
437Dic7—44no—
438C24C23×D711yescharacteristic
439C2×Q8—1416no—
440C2×Q8—1416no—
441C2×Q8—288no—
442C2×Q8—288no—
443C2×Q8—288no—
444C2×Q8—288no—
445C2×Q8—288no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
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—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—72no—
470C22×C4—72no—
471C22×C4—72no—
472C22×C4—72no—
473C22×C4—72no—
474C22×C4—72no—
475C22×C4—72no—
476C22×C4—72no—
477C22×C4—72no—
478C22×C4—74no—
479C22×C4—72no—
480C22×C4—74no—
481C22×C4—141no—
482C22×C4—141no—
483C22×C4—141no—
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—142no—
495C22×C4—142no—
496C22×C4—142no—
497C22×C4—142no—
498C22×C4—141no—
499C22×C4—142no—
500C22×C4—141no—
501C22×C4—142no—
502C22×C4—142no—
503C22×C4—141no—
504C22×C4—141no—
505C22×C4—141no—
506C22×C4—142no—
507C22×C4—142no—
508C22×C4—142no—
509C22×C4—142no—
510C22×C4—142no—
511C22×C4C2×C4×D714yes—
512C22×C4C2×C4×D712yes—
513C22×C4C2×D2814yes—
514C22×C4C2×D2812yes—
515C22×C4D4×D712yes—
516C22×C4#115912yes—
517C22×C4#115912yes—
518C22×C4Q8×D712yes—
519C22×C4Q8×D712yes—
520C22×C4Q8×D712yes—
521C22×C4C2×C22⋊D714yes—
522C22×C4C2×C22⋊D712yes—
523C4⋊C4—48no—
524C4⋊C4—44no—
525C4⋊C4—148no—
526C4⋊C4—1416no—
527C4⋊C4—148no—
528C4⋊C4(C2×D7)⋊C4116yes—
529C42—44no—
530C42—148no—
531C42—148no—
532C42—288no—
533C2×C7C2×#39111yescharacteristic
534C2×C7C4×C4⋊Q811yescharacteristic
535C2×C7#233111yescharacteristic
536C2×C7D4×C22⋊C411yescharacteristic
537C2×C7Q8×C22⋊C411yescharacteristic
538C2×C7#236511yescharacteristic
539C2×C7#236911yescharacteristic
540C2×C7#243911yescharacteristic
541C2×C7#244011yescharacteristic
542C2×C7#245111yescharacteristic
543C2×C7#245211yescharacteristic
544C2×C7#249111yescharacteristic
545C2×C7#249211yescharacteristic
546C2×C7#255011yescharacteristic
547C2×C7#255111yescharacteristic
548C23C22×C4×D711yescharacteristic
549C23C22×D2811yescharacteristic
550C23C2×D4×D711yescharacteristic
551C23C2×#115911yescharacteristic
552C23C2×#115911yescharacteristic
553C23#654811yescharacteristic
554C23C2×Q8×D711yescharacteristic
555C23C2×Q8×D711yescharacteristic
556C23C2×Q8×D711yescharacteristic
557C23#655111yescharacteristic
558C23D7×#4111yescharacteristic
559C23D7×#4111yescharacteristic
560C23#655311yescharacteristic
561C23#655411yescharacteristic
562C23C22×C22⋊D711yescharacteristic
563Q8—2832no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—74no—
592C2×C4—74no—
593C2×C4—74no—
594C2×C4—142no—
595C2×C4—142no—
596C2×C4—142no—
597C2×C4—142no—
598C2×C4—142no—
599C2×C4—142no—
600C2×C4—142no—
601C2×C4—142no—
602C2×C4—142no—
603C2×C4—142no—
604C2×C4—142no—
605C2×C4—142no—
606C2×C4—142no—
607C2×C4—142no—
608C2×C4—142no—
609C2×C4—142no—
610C2×C4—142no—
611C2×C4—142no—
612C2×C4—142no—
613C2×C4—144no—
614C2×C4—144no—
615C2×C4—142no—
616C2×C4—142no—
617C2×C4—144no—
618C2×C4—144no—
619C2×C4—144no—
620C2×C4—144no—
621C2×C4—282no—
622C2×C4—282no—
623C2×C4—282no—
624C2×C4—281no—
625C2×C4—282no—
626C2×C4—282no—
627C2×C4—281no—
628C2×C4—282no—
629C2×C4—282no—
630C2×C4—281no—
631C2×C4—281no—
632C2×C4—282no—
633C2×C4#645014yes—
634C2×C4#645014yes—
635C2×C4#646014yes—
636C2×C4#646014yes—
637C2×C4C2×(C2×D7)⋊C418yes—
638C2×C4C2×(C2×D7)⋊C414yes—
639C2×C4#649914yes—
640C2×C4#650714yes—
641C7#1405311yescharacteristic, complemented, Sylow
642C22C2×#645011yescharacteristic
643C22C2×#645011yescharacteristic
644C22C2×#646011yescharacteristic
645C22C2×#646011yescharacteristic
646C22C4×D4×D711yescharacteristic
647C22#9023611yescharacteristic
648C22D4×D2811yescharacteristic
649C22#9024511yescharacteristic
650C22C4×Q8×D711yescharacteristic
651C22#9026311yescharacteristic
652C22Q8×D2811yescharacteristic
653C22#9026711yescharacteristic
654C22#9028711yescharacteristic
655C22#9029411yescharacteristic
656C22#9030211yescharacteristic
657C22#9030711yescharacteristic
658C22#9031311yescharacteristic
659C22#9032611yescharacteristic
660C22#9033211yescharacteristic
661C22#9033411yescharacteristic
662C22#9037611yescharacteristic
663C22#9037911yescharacteristic
664C22#9038011yescharacteristic
665C22#9038111yescharacteristic
666C22#9041311yescharacteristic
667C22D7×C4⋊Q811yescharacteristic
668C22#9041811yescharacteristic
669C22#9042011yescharacteristic
670C22C22×(C2×D7)⋊C411yescharacteristic
671C22C2×#649911yescharacteristic
672C22D4×C22⋊D711yescharacteristic
673C22C2×#650711yescharacteristic
674C22Q8×C22⋊D711yescharacteristic
675C22#9052011yescharacteristic
676C22#9052211yescharacteristic
677C4—28no—
678C4—42no—
679C4—42no—
680C4—82no—
681C4—144no—
682C4—144no—
683C4—144no—
684C4—282no—
685C4—284no—
686C4—284no—
687C4#8974618yescomplemented
688C2#1173341211yescharacteristic
689C2#1173341911yescharacteristic
690C2#1173343111yescharacteristic
691C2#1173343211yescharacteristic
692C2#1173344211yescharacteristic
693C2#1173344411yescharacteristic
694C2#1173345411yescharacteristic
695C2#1173345611yescharacteristic
696C2C2×#8974611yescharacteristic
697C2D4×(C2×D7)⋊C411yescharacteristic
698C2Q8×(C2×D7)⋊C411yescharacteristic
699C2#1174010711yescharacteristic
700C2#1174021811yescharacteristic
701C2#1174048111yescharacteristic
702C2#1174068711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#389C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#389D7
hypocenterC7#14053
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
25. C2×#6451C4semidirect
77. C2×C4⋊Dic7Q8semidirect
89. C2×C4×Dic7Q8semidirect
102. C7⋊#95Q8semidirect
329. C2×Dic7C4⋊Q8semidirect
431. C4×C7#391semidirect
641. C7#14053semidirect
687. C4#89746semidirect

Maximal subgroups

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

subgroupindex
C22×#64512
C2×C7×#3892
C2×#897462
C2×C4⋊C4×Dic72
#117293202
#117293172
#117292892
C4×C7⋊#952
#117271782
#117271592
#140537