Finite Group Databasebeta

← #13259104

Subgroups — #13259104

Order 1792.

1374 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×#117C211yesmaximal, characteristic
2C2×#89898C211yesmaximal, characteristic
3C2×#89898C211yesmaximal, characteristic
4C2×C7×#344C211yesmaximal, characteristic, complemented
5C2×#89354C211yesmaximal, characteristic, complemented
6C2×#89351C211yesmaximal, characteristic, complemented
7C2×#89328C211yesmaximal, characteristic, complemented
8C23×C4×D7C2211yescharacteristic
9C22×C7×M16C2211yescharacteristic
10C22×C7×M16C2211yescharacteristic
11C2×C7×#117C2211yescharacteristic
12C2×#6489C2211yescharacteristic
13C22×#1136C2211yescharacteristic
14C22×#1136C2211yescharacteristic
15D7×#117—22no—
16D7×#117—22no—
17D7×#117—22no—
18D7×#117—22no—
19C2×#6455—21no—
20C2×D7×C4⋊C4—21no—
21C2×D7×C22⋊C4C412yes—
22C2×#6440C412yes—
23C2×#6435—21no—
24C2×C42×D7—21no—
25#89898—22no—
26#89898—21no—
27#89898—21no—
28#89898—21no—
29#89898—21no—
30#89898C414yescomplemented
31C2×(C2×D7)⋊C8—22no—
32C2×(C2×D7)⋊C8C414yescomplemented
33C7×#344—22no—
34#89354—22no—
35#89351—22no—
36#89328—22no—
37#10738—71nomaximal, Sylow
38C24×D7C2×C411yescharacteristic
39C23×C4×C7C2311yescharacteristic
40C23×Dic7C2×C411yescharacteristic
41C22×C4×D7—21no—
42C22×C4×D7—21no—
43C22×C4×D7—21no—
44C22×C4×D7—21no—
45C22×C4×D7—21no—
46C22×C4×D7—21no—
47C22×C4×D7—21no—
48C22×C4×D7—21no—
49C22×C4×D7—22no—
50C22×C4×D7C2×C412yes—
51C22×C4×D7C2×C412yes—
52C22×C4×D7D412yes—
53C22×C4×D7D411yescharacteristic
54C22×C4×D7D411yescharacteristic
55C22×C4×D7D411yescharacteristic
56C22×C4×D7D411yescharacteristic
57C22×C4×D7Q812yes—
58C2×C7×M16—21no—
59C2×C7×M16—21no—
60C2×C7×M16—21no—
61C2×C7×M16—21no—
62C2×C7×M16—21no—
63C2×C7×M16—21no—
64C2×C7×M16—21no—
65C2×C7×M16—21no—
66C2×C7×M16—21no—
67C2×C7×M16—21no—
68C2×C7×M16—21no—
69C2×C7×M16C2×C412yescomplemented
70C22×C7×C8—21no—
71C22×C7×C8C2×C412yescomplemented
72C7×#117—21no—
73C7×#117—21no—
74C7×#117D412yes—
75C7×#117D412yes—
76C2×C7×C4⋊C4—21no—
77C2×C7×C22⋊C4C2×C412yes—
78C2×C42×C7—21no—
79C2×C22⋊Dic7C2×C412yes—
80C2×(C2×D7)⋊C4—22no—
81#6489—21no—
82#6489—21no—
83#6489D412yes—
84#6489D412yes—
85C2×C4⋊Dic7—21no—
86C2×Dic7⋊C4—22no—
87C2×C4×Dic7—21no—
88C2×C4×Dic7—22no—
89C2×#1136—21no—
90C2×#1136—21no—
91C2×#1136—21no—
92C2×#1136—21no—
93C2×#1136—21no—
94C2×#1136—21no—
95C2×#1136—21no—
96C2×#1136—21no—
97C2×#1136—21no—
98C2×#1136—21no—
99C2×#1136—21no—
100C2×#1136C2×C412yescomplemented
101C22×C7⋊C8—21no—
102C22×C7⋊C8C2×C412yescomplemented
103#6455—24no—
104#6455—24no—
105D7×C4⋊C4—24no—
106D7×C4⋊C4—24no—
107D7×C22⋊C4—24no—
108D7×C22⋊C4—24no—
109#6440—24no—
110#6440—24no—
111#6435—24no—
112#6435—24no—
113C42×D7—24no—
114C42×D7—24no—
115(C2×D7)⋊C8—24no—
116(C2×D7)⋊C8—24no—
117(C2×D7)⋊C8—24no—
118(C2×D7)⋊C8—24no—
119C22×#117—71no—
120C2×#407—71no—
121C2×#407—71no—
122C2×#344—71no—
123C2×#344—71no—
124C2×#344—71no—
125C2×#344D711yescharacteristic, complemented
126C24×C7C22×C411yescharacteristic
127C23×D7—21no—
128C23×D7—21no—
129C23×D7—21no—
130C23×D7—21no—
131C23×D7—44no—
132C23×D7C4212yes—
133C23×D7C22⋊C411yescharacteristic
134C23×D7C22⋊C411yescharacteristic
135C23×D7C4⋊C412yes—
136C22×C4×C7—22no—
137C22×C4×C7C22×C411yescharacteristic
138C22×C4×C7C22×C411yescharacteristic
139C22×C4×C7C2×D411yescharacteristic
140C22×C4×C7C2×D411yescharacteristic
141C22×C4×C7C2×D411yescharacteristic
142C22×C4×C7C2×D411yescharacteristic
143C22×C4×C7C2×D411yescharacteristic
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2×Q811yescharacteristic
147C22×C4×C7#4111yescharacteristic
148C22×C4×C7#4111yescharacteristic
149C22×C4×C7#4111yescharacteristic
150C22×C4×C7#4111yescharacteristic
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—22no—
156C22×Dic7C4212yes—
157C22×Dic7C22⋊C411yescharacteristic
158C22×Dic7C22⋊C411yescharacteristic
159C22×Dic7C4⋊C412yes—
160C2×C4×D7—22no—
161C2×C4×D7—22no—
162C2×C4×D7—22no—
163C2×C4×D7—22no—
164C2×C4×D7—22no—
165C2×C4×D7—22no—
166C2×C4×D7—22no—
167C2×C4×D7—22no—
168C2×C4×D7—21no—
169C2×C4×D7—21no—
170C2×C4×D7—21no—
171C2×C4×D7—21no—
172C2×C4×D7—21no—
173C2×C4×D7—21no—
174C2×C4×D7—21no—
175C2×C4×D7—21no—
176C2×C4×D7—22no—
177C2×C4×D7—22no—
178C2×C4×D7—22no—
179C2×C4×D7—22no—
180C2×C4×D7—22no—
181C2×C4×D7—22no—
182C2×C4×D7—22no—
183C2×C4×D7—22no—
184C2×C4×D7—21no—
185C2×C4×D7—21no—
186C2×C4×D7—21no—
187C2×C4×D7—21no—
188C2×C4×D7—21no—
189C2×C4×D7—21no—
190C2×C4×D7—21no—
191C2×C4×D7—21no—
192C2×C4×D7—28no—
193C2×C4×D7—48no—
194C2×C4×D7C22⋊C412yes—
195C2×C4×D7C22⋊C412yes—
196C2×C4×D7C22⋊C412yes—
197C2×C4×D7C22⋊C412yes—
198C2×C4×D7C4⋊C412yes—
199C2×C4×D7C4⋊C412yes—
200C2×C4×D7C4⋊C412yes—
201C2×C4×D7C4⋊C412yes—
202C7×M16—22no—
203C7×M16—22no—
204C7×M16—41no—
205C7×M16—41no—
206C7×M16—41no—
207C7×M16—41no—
208C7×M16—41no—
209C7×M16—41no—
210C2×C7×C8—22no—
211C2×C7×C8—22no—
212C2×C7×C8—22no—
213C2×C7×C8—22no—
214C2×C7×C8—41no—
215C2×C7×C8—41no—
216C7×C4⋊C4—22no—
217C7×C4⋊C4—22no—
218C7×C22⋊C4—22no—
219C7×C22⋊C4C22⋊C414yes—
220C42×C7—22no—
221C42×C7—22no—
222C22⋊Dic7—22no—
223C22⋊Dic7C22⋊C414yes—
224(C2×D7)⋊C4—28no—
225C4⋊Dic7—22no—
226C4⋊Dic7—22no—
227Dic7⋊C4—28no—
228C4×Dic7—28no—
229C4×Dic7—22no—
230C4×Dic7—22no—
231#1136—22no—
232#1136—22no—
233#1136—41no—
234#1136—41no—
235#1136—41no—
236#1136—41no—
237#1136—41no—
238#1136—41no—
239C2×C7⋊C8—22no—
240C2×C7⋊C8—22no—
241C2×C7⋊C8—22no—
242C2×C7⋊C8—22no—
243C2×C7⋊C8—41no—
244C2×C7⋊C8—41no—
245C24×C4—71no—
246C22×M16—71no—
247C22×M16—71no—
248C22×M16C2×D711yescharacteristic
249C22×M16C2×D711yescharacteristic
250C2×#117—71no—
251C2×#117—72no—
252C2×#117—141no—
253C2×#117—141no—
254C2×#117—142no—
255C2×#117—142no—
256C2×#117—142no—
257C2×#117—142no—
258C2×#117C2×D711yescharacteristic
259C22×C4⋊C4—141no—
260C22×C22⋊C4—72no—
261C22×C42—141no—
262#407—74no—
263#407—141no—
264#407—142no—
265#407—141no—
266#407—141no—
267#407—141no—
268C2×C22⋊C8—74no—
269C2×C22⋊C8—142no—
270#344—22no—
271#344—142no—
272#344—142no—
273#344—142no—
274C23×C7—42no—
275C23×C7C2×C4211yescharacteristic
276C23×C7C2×C22⋊C411yescharacteristic
277C23×C7C2×C22⋊C411yescharacteristic
278C23×C7C2×C22⋊C411yescharacteristic
279C23×C7C2×C4⋊C411yescharacteristic
280C23×C7#11711yescharacteristic
281C23×C7#11711yescharacteristic
282C22×D7—21no—
283C22×D7—21no—
284C22×D7—24no—
285C22×D7—22no—
286C22×D7—22no—
287C22×D7—21no—
288C22×D7—22no—
289C22×D7—22no—
290C22×D7—21no—
291C22×D7—24no—
292C22×D7—24no—
293C22×D7—42no—
294C22×D7—42no—
295C22×D7—42no—
296C22×D7—44no—
297C22×D7—44no—
298C22×D7—44no—
299C22×D7—44no—
300C22×D7#9512yes—
301C22×D7#9512yes—
302C2×C4×C7—24no—
303C2×C4×C7—44no—
304C2×C4×C7C2×C22⋊C411yescharacteristic
305C2×C4×C7C2×C22⋊C411yescharacteristic
306C2×C4×C7C2×C4⋊C411yescharacteristic
307C2×C4×C7C2×C4⋊C411yescharacteristic
308C2×C4×C7C4×D411yescharacteristic
309C2×C4×C7C4×D411yescharacteristic
310C2×C4×C7C4×D411yescharacteristic
311C2×C4×C7C4×D411yescharacteristic
312C2×C4×C7C4×D411yescharacteristic
313C2×C4×C7C4×D411yescharacteristic
314C2×C4×C7C4×D411yescharacteristic
315C2×C4×C7C4×D411yescharacteristic
316C2×C4×C7#12011yescharacteristic
317C2×C4×C7#12011yescharacteristic
318C2×C4×C7#12011yescharacteristic
319C2×C4×C7#12011yescharacteristic
320C2×C4×C7#12111yescharacteristic
321C2×C4×C7#12111yescharacteristic
322C2×C4×C7#12111yescharacteristic
323C2×C4×C7#12111yescharacteristic
324C2×C4×C7C22⋊Q811yescharacteristic
325C2×C4×C7C22⋊Q811yescharacteristic
326C2×C4×C7C22⋊Q811yescharacteristic
327C2×C4×C7C22⋊Q811yescharacteristic
328C2×C4×C7#12311yescharacteristic
329C2×C4×C7#12311yescharacteristic
330C2×C4×C7#12311yescharacteristic
331C2×C4×C7#12311yescharacteristic
332C2×Dic7—22no—
333C2×Dic7—22no—
334C2×Dic7—21no—
335C2×Dic7—21no—
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—21no—
339C2×Dic7—21no—
340C2×Dic7—24no—
341C2×Dic7—44no—
342C2×Dic7#9512yes—
343C2×Dic7#9512yes—
344C4×D7—22no—
345C4×D7—22no—
346C4×D7—22no—
347C4×D7—22no—
348C4×D7—22no—
349C4×D7—22no—
350C4×D7—22no—
351C4×D7—22no—
352C4×D7—22no—
353C4×D7—22no—
354C4×D7—22no—
355C4×D7—22no—
356C4×D7—22no—
357C4×D7—22no—
358C4×D7—22no—
359C4×D7—22no—
360C4×D7—416no—
361C7×C8—42no—
362C7×C8—42no—
363C7⋊C8—42no—
364C7⋊C8—42no—
365C25—71no—
366C23×C4—71no—
367C23×C4—72no—
368C23×C4—72no—
369C23×C4—71no—
370C23×C4—71no—
371C23×C4—71no—
372C23×C4—72no—
373C23×C4—71no—
374C23×C4—72no—
375C23×C4—142no—
376C23×C4—141no—
377C23×C4—141no—
378C23×C4—141no—
379C23×C4—141no—
380C23×C4—141no—
381C23×C4—141no—
382C23×C4—141no—
383C23×C4—141no—
384C23×C4C22×D711yescharacteristic
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—21no—
389C2×M16—21no—
390C2×M16—21no—
391C2×M16—21no—
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C2×M16—21no—
396C2×M16—72no—
397C2×M16—141no—
398C2×M16—141no—
399C2×M16—141no—
400C2×M16—141no—
401C2×M16—141no—
402C2×M16—141no—
403C2×M16—141no—
404C2×M16—141no—
405C2×M16—141no—
406C2×M16—141no—
407C2×M16—141no—
408C2×M16C4×D712yescomplemented
409C22×C8—21no—
410C22×C8—72no—
411C22×C8—141no—
412C22×C8C4×D712yescomplemented
413#117—21no—
414#117—21no—
415#117—72no—
416#117—72no—
417#117—144no—
418#117—144no—
419#117—144no—
420#117—144no—
421#117—144no—
422#117—141no—
423#117—141no—
424#117—144no—
425#117D2812yes—
426#117C22⋊D712yes—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—144no—
429C2×C4⋊C4—144no—
430C2×C4⋊C4—142no—
431C2×C4⋊C4—141no—
432C2×C22⋊C4—72no—
433C2×C22⋊C4—144no—
434C2×C22⋊C4—142no—
435C2×C22⋊C4—144no—
436C2×C22⋊C4C4×D712yes—
437C2×C42—21no—
438C2×C42—144no—
439C2×C42—144no—
440C2×C42—142no—
441C2×C42—141no—
442C22⋊C8—144no—
443C22⋊C8—144no—
444C22⋊C8—144no—
445C22⋊C8—144no—
446C22×C7—22no—
447C22×C7—22no—
448C22×C7—22no—
449C22×C7—41no—
450C22×C7—41no—
451C22×C7—41no—
452C22×C7—41no—
453C22×C7C2×#9511yescharacteristic
454C22×C7C4×C22⋊C411yescharacteristic
455C22×C7C4×C22⋊C411yescharacteristic
456C22×C7#37911yescharacteristic
457C22×C7#38011yescharacteristic
458C22×C7#38011yescharacteristic
459C22×C7#38111yescharacteristic
460C2×D7—24no—
461C2×D7—24no—
462C2×D7—22no—
463C2×D7—22no—
464C2×D7—22no—
465C2×D7—22no—
466C2×D7—22no—
467C2×D7—44no—
468C2×D7—44no—
469C2×D7—44no—
470C2×D7—44no—
471C2×D7—42no—
472C2×D7—42no—
473C2×D7#34414yescomplemented
474C4×C7—44no—
475C4×C7#38511yescharacteristic
476C4×C7#38511yescharacteristic
477C4×C7#38511yescharacteristic
478C4×C7#38511yescharacteristic
479C4×C7#38611yescharacteristic
480C4×C7#38611yescharacteristic
481C4×C7#38611yescharacteristic
482C4×C7#38611yescharacteristic
483Dic7—22no—
484Dic7—22no—
485Dic7—44no—
486C24—71no—
487C24—72no—
488C24—72no—
489C24—71no—
490C24—141no—
491C24—141no—
492C24—141no—
493C24—141no—
494C24—284no—
495C24C2×C4×D711yescharacteristic
496C22×C4—22no—
497C22×C4—72no—
498C22×C4—71no—
499C22×C4—71no—
500C22×C4—72no—
501C22×C4—72no—
502C22×C4—72no—
503C22×C4—72no—
504C22×C4—72no—
505C22×C4—72no—
506C22×C4—72no—
507C22×C4—72no—
508C22×C4—72no—
509C22×C4—148no—
510C22×C4—141no—
511C22×C4—141no—
512C22×C4—141no—
513C22×C4—141no—
514C22×C4—142no—
515C22×C4—142no—
516C22×C4—142no—
517C22×C4—142no—
518C22×C4—141no—
519C22×C4—141no—
520C22×C4—141no—
521C22×C4—141no—
522C22×C4—141no—
523C22×C4—141no—
524C22×C4—141no—
525C22×C4—141no—
526C22×C4—142no—
527C22×C4—142no—
528C22×C4—142no—
529C22×C4—142no—
530C22×C4—141no—
531C22×C4—141no—
532C22×C4—141no—
533C22×C4—141no—
534C22×C4—142no—
535C22×C4—142no—
536C22×C4—142no—
537C22×C4—142no—
538C22×C4—142no—
539C22×C4—142no—
540C22×C4—141no—
541C22×C4—141no—
542C22×C4—141no—
543C22×C4—141no—
544C22×C4—142no—
545C22×C4—142no—
546C22×C4—142no—
547C22×C4—288no—
548C22×C4C2×C4×D711yescharacteristic
549C22×C4C2×C4×D711yescharacteristic
550C22×C4C2×D2811yescharacteristic
551C22×C4#115711yescharacteristic
552C22×C4#115711yescharacteristic
553C22×C4D4×D711yescharacteristic
554C22×C4D4×D711yescharacteristic
555C22×C4D4×D711yescharacteristic
556C22×C4D4×D711yescharacteristic
557C22×C4D4×D711yescharacteristic
558C22×C4#115911yescharacteristic
559C22×C4Q8×D711yescharacteristic
560C22×C4#116111yescharacteristic
561C22×C4C2×C22⋊D711yescharacteristic
562M16—22no—
563M16—22no—
564M16—41no—
565M16—41no—
566M16—41no—
567M16—41no—
568M16—41no—
569M16—41no—
570M16—142no—
571M16—142no—
572M16—281no—
573M16—281no—
574M16—281no—
575M16—281no—
576M16—281no—
577M16—281no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—142no—
585C2×C8—142no—
586C2×C8—142no—
587C2×C8—142no—
588C2×C8—281no—
589C2×C8—281no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—148no—
593C4⋊C4—142no—
594C4⋊C4—142no—
595C22⋊C4—22no—
596C22⋊C4—74no—
597C22⋊C4—148no—
598C22⋊C4—142no—
599C22⋊C4(C2×D7)⋊C414yes—
600C42—22no—
601C42—22no—
602C42—148no—
603C42—142no—
604C42—142no—
605C2×C7—21no—
606C2×C7—21no—
607C2×C7—21no—
608C2×C7—21no—
609C2×C7—21no—
610C2×C7—21no—
611C2×C7C22⋊#9511yescharacteristic
612C2×C7C2×#34412yes—
613D7—24no—
614D7—42no—
615C23—42no—
616C23—72no—
617C23—72no—
618C23—144no—
619C23—144no—
620C23—144no—
621C23—141no—
622C23—141no—
623C23—141no—
624C23—142no—
625C23—142no—
626C23—142no—
627C23—141no—
628C23—142no—
629C23—282no—
630C23—282no—
631C23—282no—
632C23—284no—
633C23—284no—
634C23—284no—
635C23—284no—
636C23C42×D711yescharacteristic
637C23#643511yescharacteristic
638C23D7×C22⋊C411yescharacteristic
639C23D7×C22⋊C411yescharacteristic
640C23D7×C4⋊C411yescharacteristic
641C23#645511yescharacteristic
642C23C2×(C2×D7)⋊C411yescharacteristic
643C2×C4—24no—
644C2×C4—44no—
645C2×C4—72no—
646C2×C4—72no—
647C2×C4—141no—
648C2×C4—141no—
649C2×C4—142no—
650C2×C4—142no—
651C2×C4—142no—
652C2×C4—141no—
653C2×C4—141no—
654C2×C4—142no—
655C2×C4—142no—
656C2×C4—142no—
657C2×C4—142no—
658C2×C4—142no—
659C2×C4—142no—
660C2×C4—142no—
661C2×C4—142no—
662C2×C4—142no—
663C2×C4—142no—
664C2×C4—142no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—142no—
671C2×C4—144no—
672C2×C4—2816no—
673C2×C4—284no—
674C2×C4C4×D2811yescharacteristic
675C2×C4C4×D2811yescharacteristic
676C2×C4D7×C22⋊C411yescharacteristic
677C2×C4D7×C22⋊C411yescharacteristic
678C2×C4(C22⋊D7)⋊C411yescharacteristic
679C2×C4(C22⋊D7)⋊C411yescharacteristic
680C2×C4#644511yescharacteristic
681C2×C4#644511yescharacteristic
682C2×C4#644611yescharacteristic
683C2×C4#644611yescharacteristic
684C2×C4#644711yescharacteristic
685C2×C4#644711yescharacteristic
686C2×C4D7×C4⋊C411yescharacteristic
687C2×C4D7×C4⋊C411yescharacteristic
688C2×C4#645611yescharacteristic
689C2×C4#645611yescharacteristic
690C2×C4#645711yescharacteristic
691C2×C4#645711yescharacteristic
692C2×C4#645811yescharacteristic
693C2×C4#645911yescharacteristic
694C2×C4#645911yescharacteristic
695C2×C4#646011yescharacteristic
696C2×C4C4×C22⋊D711yescharacteristic
697C2×C4C4×C22⋊D711yescharacteristic
698C2×C4#650011yescharacteristic
699C2×C4#650011yescharacteristic
700C2×C4#650111yescharacteristic
701C2×C4#650911yescharacteristic
702C8—42no—
703C8—42no—
704C8—282no—
705C8—282no—
706C7#1073811yescharacteristic, complemented, Sylow
707C22—22no—
708C22—22no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—74no—
715C22—144no—
716C22—144no—
717C22—142no—
718C22—142no—
719C22—142no—
720C22—142no—
721C22—142no—
722C22—284no—
723C22—284no—
724C22—284no—
725C22—284no—
726C22—282no—
727C22—282no—
728C22D7×#9511yescharacteristic
729C22#8943611yescharacteristic
730C22#8943811yescharacteristic
731C22#8943911yescharacteristic
732C22C4×(C2×D7)⋊C411yescharacteristic
733C22#8972711yescharacteristic
734C22#8975911yescharacteristic
735C4—44no—
736C4—142no—
737C4—142no—
738C4—284no—
739C4#8943711yescharacteristic
740C4#8943711yescharacteristic
741C4#8944011yescharacteristic
742C4#8944011yescharacteristic
743C4#8972811yescharacteristic
744C4#8972811yescharacteristic
745C4#8976111yescharacteristic
746C4#8976111yescharacteristic
747C2—21no—
748C2—21no—
749C2—21no—
750C2—21no—
751C2—21no—
752C2—21no—
753C2—144no—
754C2—282no—
755C2D7×#34412yes—
756C2(C2×D7)⋊#9511yescharacteristic
subgroupG/H
centerC2×C4D7×C22⋊C4
commutatorC23×C7C2×C42
FrattiniC23×C4C22×D7
FittingC2×C7×#344C2
socleC22×C7C2×#95
prime radicalC24×D7C2×C4
cosocleC23×C4×C7C23
hypercenterC2×#344D7
hypocenterC7#10738
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C2×C7×#344C2semidirect
5. C2×#89354C2semidirect
6. C2×#89351C2semidirect
7. C2×#89328C2semidirect
30. #89898C4semidirect
32. C2×(C2×D7)⋊C8C4semidirect
69. C2×C7×M16C2×C4semidirect
71. C22×C7×C8C2×C4semidirect
100. C2×#1136C2×C4semidirect
102. C22×C7⋊C8C2×C4semidirect
125. C2×#344D7semidirect
408. C2×M16C4×D7semidirect
412. C22×C8C4×D7semidirect
473. C2×D7#344semidirect
706. C7#10738semidirect

Maximal subgroups

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

subgroupindex
C2×D7×#1172
C2×#898982
C2×C7×#3442
C2×#893542
C2×#893512
C2×#893282
#107387