Finite Group Databasebeta

← C2×#11738619 #14225899

Subgroups — C2×#11738619 #14225899

Order 1792.

2050 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×#125C211yesmaximal, characteristic, complemented
2C2×#90239C211yesmaximal, characteristic
3C2×C7×#478C211yesmaximal, characteristic, complemented
4C2×#89838C211yesmaximal, characteristic, complemented
5C2×#89781C211yesmaximal, characteristic, complemented
6#11738619C2116yesmaximal, direct product factor
7C2×#89654C211yesmaximal, characteristic, complemented
8C2×#89648C211yesmaximal, characteristic, complemented
9C2×#89635C211yesmaximal, characteristic, complemented
10C2×#89628C211yesmaximal, characteristic, complemented
11C2×#89619C211yesmaximal, characteristic, complemented
12C2×#89607C211yesmaximal, characteristic, complemented
13C2×#89549C211yesmaximal, characteristic, complemented
14C2×#89546C211yesmaximal, characteristic, complemented
15C2×#89536C211yesmaximal, characteristic, complemented
16C2×#89536C211yesmaximal, characteristic, complemented
17C22×#1157—21no—
18C2×C7×#125C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×#6503C2211yescharacteristic
21C2×#6501C2211yescharacteristic
22C2×C4×C22⋊D7—21no—
23D7×#125—24no—
24D7×#125C2218yescomplemented
25#90239—24no—
26#90239C2218yes—
27C2×#6458C2211yescharacteristic
28C2×D7×C4⋊C4—21no—
29C2×D7×C4⋊C4—21no—
30C2×D7×C4⋊C4C2211yescharacteristic
31C2×D7×C4⋊C4C2211yescharacteristic
32C2×#6453C2211yescharacteristic
33C2×#6453C2211yescharacteristic
34C2×#6452—21no—
35C2×#6452—21no—
36C2×#6451C2211yescharacteristic
37C2×#6448—21no—
38C2×#6447—21no—
39C2×C4×D28C2211yescharacteristic
40C2×C42×D7C2211yescharacteristic
41C2×#6433C2211yescharacteristic
42C7×#478C2218yescomplemented
43C2×C7×#107C2211yescharacteristic
44C2×C7×#106C2211yescharacteristic
45C2×C7×C4⋊C8C2211yescharacteristic
46C2×C7×#102C2211yescharacteristic
47C2×C7×#102C2211yescharacteristic
48C2×#6406C2211yescharacteristic
49C2×#6406C2211yescharacteristic
50C2×#6395C2211yescharacteristic
51C2×#6395C2211yescharacteristic
52C2×(C2×D7)⋊C8C2211yescharacteristic
53C2×(C2×D7)⋊C8C2211yescharacteristic
54C2×#6392C2211yescharacteristic
55C2×#6391C2211yescharacteristic
56C2×#6389C2211yescharacteristic
57C2×#6389C2211yescharacteristic
58#89838C2218yescomplemented
59#89781C2218yescomplemented
60C2×#6383C2211yescharacteristic
61C2×#6383C2211yescharacteristic
62C2×#6382C2211yescharacteristic
63C2×#6382C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×C4⋊(C7⋊C8)C2211yescharacteristic
67#89654C2218yescomplemented
68#89648C2218yescomplemented
69#89635C2218yescomplemented
70#89628C2218yescomplemented
71#89619C2218yescomplemented
72#89607C2218yescomplemented
73#89549C2218yescomplemented
74#89546C2218yescomplemented
75#89536C2218yescomplemented
76#89536C2218yescomplemented
77C2×#3234—71nomaximal, Sylow
78C22×C7×D4C2311yescharacteristic
79C23×C4×C7—21no—
80C22×C22⋊D7—21no—
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C2×#1157—28no—
84C2×#1157—48no—
85C22×D28—21no—
86C22×D28C2311yescharacteristic
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×C4×D7D411yescharacteristic
91C22×C4×D7D411yescharacteristic
92C22×C4×D7C2311yescharacteristic
93C22×Dic14—21no—
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C7×#125—22no—
97C7×#125C2314yes—
98C4×C7×D4—22no—
99C4×C7×D4C2314yes—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C22⋊C4—21no—
106C2×C42×C7C2311yescharacteristic
107C2×C22⋊Dic7—21no—
108#6503—22no—
109#6503C2314yes—
110#6501—22no—
111#6501C2314yes—
112C4×C22⋊D7—28no—
113C2×(C2×D7)⋊C4—21no—
114C2×(C2×D7)⋊C4—21no—
115C2×C4⋊Dic7—21no—
116C2×C4⋊Dic7—21no—
117C2×C4⋊Dic7C2311yescharacteristic
118C2×C4⋊Dic7C2311yescharacteristic
119C2×C4⋊Dic7C2311yescharacteristic
120C2×Dic7⋊C4—21no—
121C2×Dic7⋊C4—21no—
122C2×Dic7⋊C4—21no—
123C2×Dic7⋊C4—21no—
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×C4×Dic7D411yescharacteristic
128C2×C4×Dic7D411yescharacteristic
129C2×C4×Dic7C2311yescharacteristic
130C22×C7⋊C8C2311yescharacteristic
131C22×C7⋊C8C2311yescharacteristic
132#6458—22no—
133#6458C2314yes—
134D7×C4⋊C4—22no—
135D7×C4⋊C4—22no—
136D7×C4⋊C4—28no—
137D7×C4⋊C4—28no—
138D7×C4⋊C4C2314yes—
139D7×C4⋊C4C2314yes—
140#6453—22no—
141#6453—22no—
142#6453C2314yes—
143#6453C2314yes—
144#6452—28no—
145#6452—28no—
146#6451—22no—
147#6451C2314yes—
148#6448—28no—
149#6447—28no—
150C4×D28—22no—
151C4×D28C2314yes—
152C42×D7D414yes—
153C42×D7C2314yes—
154#6433—22no—
155#6433C2314yes—
156C7×#107C2314yes—
157C7×#106C2314yes—
158C7×C4⋊C8C2314yes—
159C7×#102C2314yes—
160C7×#102C2314yes—
161#6406C2314yes—
162#6406C2314yes—
163#6395C2314yes—
164#6395C2314yes—
165(C2×D7)⋊C8C2314yes—
166(C2×D7)⋊C8C2314yes—
167#6392C2314yes—
168#6391C2314yes—
169#6389C2314yes—
170#6389C2314yes—
171#6383C2314yes—
172#6383C2314yes—
173#6382C2314yes—
174#6382C2314yes—
175#6381C2314yes—
176#6381C2314yes—
177C4⋊(C7⋊C8)C2314yes—
178C2×#532—71no—
179C22×#125—71no—
180#3234—716no—
181C2×#501—71no—
182C2×#501—71no—
183C2×#490—71no—
184C2×#490—71no—
185C2×#481—71no—
186C2×#481—71no—
187C2×#480—71no—
188C2×#480—71no—
189C2×#478—71no—
190C2×#478—71no—
191C2×#478—71no—
192C2×#478D711yescharacteristic, complemented
193C2×#432—71no—
194C24×C7—21no—
195C23×D7—21no—
196C23×D7C2×D411yescharacteristic
197C2×C7×D4—21no—
198C2×C7×D4—22no—
199C2×C7×D4—22no—
200C2×C7×D4C2412yes—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—24no—
205C22×C4×C7—44no—
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2411yescharacteristic
209C2×C22⋊D7—24no—
210C2×C22⋊D7—24no—
211C2×C22⋊D7—24no—
212C2×C22⋊D7—44no—
213C2×C22⋊D7—44no—
214C2×C22⋊D7—44no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7C2×D411yescharacteristic
219C22×Dic7C2×D411yescharacteristic
220C22×Dic7C2×D411yescharacteristic
221#1157—432no—
222C2×D28—22no—
223C2×D28—22no—
224C2×D28—24no—
225C2×D28—21no—
226C2×D28—44no—
227C2×D28C2412yes—
228C2×C4×D7—24no—
229C2×C4×D7—22no—
230C2×C4×D7—22no—
231C2×C4×D7—24no—
232C2×C4×D7—24no—
233C2×C4×D7—24no—
234C2×C4×D7—42no—
235C2×C4×D7—44no—
236C2×C4×D7—44no—
237C2×C4×D7—44no—
238C2×C4×D7C2×D412yes—
239C2×C4×D7C2×D414yes—
240C2×C4×D7C2×D414yes—
241C2×C4×D7C2412yes—
242C2×Dic14—24no—
243C2×Dic14—44no—
244C2×C7×C8—22no—
245C2×C7×C8—22no—
246C2×C7×C8C2412yes—
247C2×C7×C8C2412yes—
248C7×C4⋊C4—21no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C4⋊C4C2412yes—
256C7×C22⋊C4—24no—
257C42×C7C2×D412yes—
258C42×C7C2412yes—
259C22⋊Dic7—24no—
260(C2×D7)⋊C4—24no—
261(C2×D7)⋊C4—24no—
262C4⋊Dic7—21no—
263C4⋊Dic7—21no—
264C4⋊Dic7—21no—
265C4⋊Dic7—24no—
266C4⋊Dic7—24no—
267C4⋊Dic7C2412yes—
268C4⋊Dic7C2412yes—
269C4⋊Dic7C2412yes—
270Dic7⋊C4—24no—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277C4×Dic7C2×D412yes—
278C4×Dic7C2×D414yes—
279C4×Dic7C2×D414yes—
280C4×Dic7C2412yes—
281C2×C7⋊C8—22no—
282C2×C7⋊C8—22no—
283C2×C7⋊C8C2412yes—
284C2×C7⋊C8C2412yes—
285C22×#41—141no—
286#532—78no—
287#532—144no—
288C2×C4⋊Q8—71no—
289C2×#127—71no—
290C2×#125—78no—
291C2×#125—71no—
292C2×#125—71no—
293C2×#125—71no—
294C2×#125—141no—
295C2×#125—141no—
296C2×#125—144no—
297C2×#125C2×D711yescharacteristic
298C2×#124—141no—
299C2×#121—71no—
300C2×#121—71no—
301C2×#121—141no—
302C2×C4×D4—71no—
303C2×C4×D4—141no—
304C2×C4×D4C2×D711yescharacteristic
305C22×C4⋊C4—71no—
306C22×C4⋊C4—71no—
307C22×C4⋊C4—141no—
308C22×C4⋊C4—141no—
309C22×C42—71no—
310#501—78no—
311#501—78no—
312#490—78no—
313#490—78no—
314#481—78no—
315#481—78no—
316#480—78no—
317#480—78no—
318#478—78no—
319#478—78no—
320#478—78no—
321#478C2×D718yescomplemented
322#432—78no—
323C2×#107—71no—
324C2×#107—71no—
325C2×#107—71no—
326C2×#107C2×D711yescharacteristic
327C2×#106—71no—
328C2×#106—71no—
329C2×#106—71no—
330C2×#106C2×D711yescharacteristic
331C2×C4⋊C8—71no—
332C2×C4⋊C8C2×D711yescharacteristic
333C2×#102—71no—
334C2×#102—71no—
335C2×#102—71no—
336C2×#102—71no—
337C2×#102—71no—
338C2×#102—71no—
339C2×#102C2×D711yescharacteristic
340C2×#102C2×D711yescharacteristic
341C2×C22⋊C8—71no—
342C2×C22⋊C8—71no—
343C2×#97—71no—
344C2×#97—71no—
345C23×C7—22no—
346C23×C7—42no—
347C23×C7—42no—
348C23×C7—42no—
349C23×C7C22×D411yescharacteristic
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—42no—
354C22×D7—42no—
355C22×D7—42no—
356C22×D7AGL(1,ℤ/8)14yes—
357C22×D7C22×D412yes—
358C7×D4—22no—
359C7×D4—22no—
360C7×D4—42no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—48no—
367C2×C4×C7—42no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7C22×D412yes—
371C2×C4×C7C22×D412yes—
372C2×C4×C7C22×D411yescharacteristic
373C2×C4×C72−1+412yes—
374C2×C4×C72−1+412yes—
375C2×C4×C7C2511yescharacteristic
376C22⋊D7—48no—
377C22⋊D7—48no—
378C22⋊D7—48no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7C22×D412yes—
389C2×Dic7C22×D412yes—
390C2×Dic7C22×D412yes—
391D28—22no—
392D28—22no—
393D28—48no—
394D28—42no—
395C4×D7—28no—
396C4×D7—24no—
397C4×D7—22no—
398C4×D7—22no—
399C4×D7—44no—
400C4×D7—48no—
401C4×D7—48no—
402C4×D7—48no—
403Dic14—48no—
404C7×C8—22no—
405C7×C8—22no—
406C7⋊C8—22no—
407C7⋊C8—22no—
408C2×#41—148no—
409C2×#41—288no—
410C22×Q8—141no—
411C22×D4—71no—
412C22×D4—141no—
413C22×D4—141no—
414C22×D4—141no—
415C22×D4—141no—
416C22×D4C22×D711yescharacteristic
417C23×C4—21no—
418C23×C4—71no—
419C23×C4—71no—
420C23×C4—71no—
421C23×C4—141no—
422C23×C4—141no—
423C23×C4—141no—
424C22×C8—71no—
425C22×C8—71no—
426C22×C8C22×D711yescharacteristic
427C22×C8C22×D711yescharacteristic
428C4⋊Q8—74no—
429C4⋊Q8—142no—
430#127—74no—
431#127—142no—
432#125—22no—
433#125—74no—
434#125—74no—
435#125—74no—
436#125—148no—
437#125—148no—
438#125—142no—
439#125—142no—
440#125—142no—
441#125C22×D714yes—
442#124—148no—
443#121—74no—
444#121—74no—
445#121—148no—
446#121—142no—
447#121—142no—
448C4×D4—22no—
449C4×D4—74no—
450C4×D4—148no—
451C4×D4—142no—
452C4×D4C22×D714yes—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—71no—
456C2×C4⋊C4—71no—
457C2×C4⋊C4—71no—
458C2×C4⋊C4—74no—
459C2×C4⋊C4—74no—
460C2×C4⋊C4—142no—
461C2×C4⋊C4—142no—
462C2×C4⋊C4—148no—
463C2×C4⋊C4—148no—
464C2×C4⋊C4—141no—
465C2×C4⋊C4—141no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4—141no—
473C2×C4⋊C4C22×D711yescharacteristic
474C2×C4⋊C4C22×D711yescharacteristic
475C2×C4⋊C4C22×D711yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—141no—
478C2×C22⋊C4—141no—
479C2×C22⋊C4—141no—
480C2×C42—71no—
481C2×C42—71no—
482C2×C42—71no—
483C2×C42—74no—
484C2×C42—74no—
485C2×C42C22×D711yescharacteristic
486#107—74no—
487#107—74no—
488#107—74no—
489#107C22×D714yes—
490#106—74no—
491#106—74no—
492#106—74no—
493#106C22×D714yes—
494C4⋊C8—74no—
495C4⋊C8C22×D714yes—
496#102—74no—
497#102—74no—
498#102—74no—
499#102—74no—
500#102—74no—
501#102—74no—
502#102C22×D714yes—
503#102C22×D714yes—
504C22⋊C8—74no—
505C22⋊C8—74no—
506#97—74no—
507#97—74no—
508C22×C7—42no—
509C22×C7—42no—
510C22×C7—42no—
511C22×C7—84no—
512C22×C7#53612yes—
513C22×C7C2×AGL(1,ℤ/8)12yes—
514C22×C7#57512yes—
515C22×C7C23×D411yescharacteristic
516C2×D7—22no—
517C2×D7—28no—
518C2×D7—22no—
519C2×D7—42no—
520C2×D7—42no—
521C2×D7—42no—
522C2×D7—84no—
523C2×D7C2×AGL(1,ℤ/8)14yes—
524C4×C7—22no—
525C4×C7—22no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7—42no—
529C4×C7#53612yes—
530C4×C7C2×2−1+411yescharacteristic
531C4×C7C2×2−1+411yescharacteristic
532Dic7—22no—
533Dic7—22no—
534Dic7—22no—
535Dic7—42no—
536Dic7—42no—
537Dic7—42no—
538C24—21no—
539C24—71no—
540C24—141no—
541#41—2832no—
542C2×Q8—144no—
543C2×Q8—284no—
544C2×D4—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—72no—
548C2×D4—144no—
549C2×D4—144no—
550C2×D4—144no—
551C2×D4—144no—
552C2×D4—141no—
553C2×D4—142no—
554C2×D4—142no—
555C2×D4—284no—
556C2×D4—284no—
557C2×D4—284no—
558C2×D4—284no—
559C2×D4C23×D712yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—24no—
564C22×C4—44no—
565C22×C4—71no—
566C22×C4—71no—
567C22×C4—71no—
568C22×C4—72no—
569C22×C4—74no—
570C22×C4—72no—
571C22×C4—74no—
572C22×C4—144no—
573C22×C4—144no—
574C22×C4—144no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—141no—
580C22×C4—144no—
581C22×C4—282no—
582C22×C4—284no—
583C22×C4—284no—
584C22×C4—284no—
585C22×C4D4×D711yescharacteristic
586C22×C4D4×D711yescharacteristic
587C22×C4C23×D711yescharacteristic
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—72no—
591C2×C8—72no—
592C2×C8—142no—
593C2×C8—142no—
594C2×C8C23×D712yes—
595C2×C8C23×D712yes—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—72no—
602C4⋊C4—72no—
603C4⋊C4—72no—
604C4⋊C4—144no—
605C4⋊C4—144no—
606C4⋊C4—144no—
607C4⋊C4—144no—
608C4⋊C4—144no—
609C4⋊C4—144no—
610C4⋊C4—144no—
611C4⋊C4—144no—
612C4⋊C4—144no—
613C4⋊C4—141no—
614C4⋊C4—141no—
615C4⋊C4—141no—
616C4⋊C4C23×D712yes—
617C4⋊C4C23×D712yes—
618C4⋊C4C23×D712yes—
619C22⋊C4—24no—
620C22⋊C4—144no—
621C22⋊C4—144no—
622C22⋊C4—144no—
623C42—74no—
624C42—74no—
625C42—72no—
626C42—72no—
627C42D4×D712yes—
628C42C23×D712yes—
629C2×C7—82no—
630C2×C7#323414yescomplemented
631C2×C7C2×#53611yescharacteristic
632C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
633C2×C7C2×#57511yescharacteristic
634D7—24no—
635D7—82no—
636C23—22no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—74no—
641C23—72no—
642C23—142no—
643C23—142no—
644C23—142no—
645C23—282no—
646C23—282no—
647C23—282no—
648C23C2×D4×D711yescharacteristic
649Q8—288no—
650D4—22no—
651D4—22no—
652D4—42no—
653D4—142no—
654D4—142no—
655D4—288no—
656D4—288no—
657D4—288no—
658D4—288no—
659D4—282no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—48no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—72no—
670C2×C4—72no—
671C2×C4—72no—
672C2×C4—148no—
673C2×C4—142no—
674C2×C4—142no—
675C2×C4—142no—
676C2×C4—144no—
677C2×C4—142no—
678C2×C4—142no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—284no—
683C2×C4—288no—
684C2×C4—288no—
685C2×C4—288no—
686C2×C4—282no—
687C2×C4—282no—
688C2×C4—282no—
689C2×C4C2×D4×D712yes—
690C2×C4C2×D4×D712yes—
691C2×C4C2×D4×D711yescharacteristic
692C2×C4#655112yes—
693C2×C4#655412yes—
694C2×C4C24×D711yescharacteristic
695C8—22no—
696C8—22no—
697C8—142no—
698C8—142no—
699C7C2×#323411yescharacteristic, complemented, Sylow
700C22—42no—
701C22—42no—
702C22—42no—
703C22—74no—
704C22—84no—
705C22—142no—
706C22—148no—
707C22—142no—
708C22—282no—
709C22—282no—
710C22—282no—
711C22—564no—
712C22#9031912yes—
713C22#9045912yes—
714C22D7×AGL(1,ℤ/8)12yes—
715C22C22×D4×D711yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—142no—
722C4—142no—
723C4—142no—
724C4—282no—
725C4—282no—
726C4—282no—
727C4#9031912yes—
728C4C2×#655111yescharacteristic
729C4C2×#655411yescharacteristic
730C2—82no—
731C2—144no—
732C2—562no—
733C2#1173861914yesdirect product factor
734C2C2×#9031911yescharacteristic
735C2C2×#9045911yescharacteristic
736C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#478C2
socleC23×C7C22×D4
prime radicalC2×#90239C2
hypercenterC2×#478D7
hypocenterC7C2×#3234
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×D7×#125C2semidirect
3. C2×C7×#478C2semidirect
4. C2×#89838C2semidirect
5. C2×#89781C2semidirect
6. #11738619C2direct (N × H)
7. C2×#89654C2semidirect
8. C2×#89648C2semidirect
9. C2×#89635C2semidirect
10. C2×#89628C2semidirect
11. C2×#89619C2semidirect
12. C2×#89607C2semidirect
13. C2×#89549C2semidirect
14. C2×#89546C2semidirect
15. C2×#89536C2semidirect
16. C2×#89536C2semidirect
24. D7×#125C22semidirect
42. C7×#478C22semidirect
58. #89838C22semidirect
59. #89781C22semidirect
67. #89654C22semidirect
68. #89648C22semidirect
69. #89635C22semidirect
70. #89628C22semidirect
71. #89619C22semidirect
72. #89607C22semidirect
73. #89549C22semidirect
74. #89546C22semidirect
75. #89536C22semidirect
76. #89536C22semidirect
192. C2×#478D7semidirect
321. #478C2×D7semidirect
630. C2×C7#3234semidirect
699. C7C2×#3234semidirect
733. C2#11738619direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D7×#1252
C2×#902392
C2×C7×#4782
C2×#898382
C2×#897812
#117386192
C2×#896542
C2×#896482
C2×#896352
C2×#896282
C2×#896192
C2×#896072
C2×#895492
C2×#895462
C2×#895362
C2×#32347