Finite Group Databasebeta

← C2×#11736539 #14226724

Subgroups — C2×#11736539 #14226724

Order 1792.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90225C211yesmaximal, characteristic
2C2×#90209C211yesmaximal, characteristic, complemented
3C2×C7×#424C211yesmaximal, characteristic, complemented
4C2×#89909C211yesmaximal, characteristic, complemented
5C2×#89906C211yesmaximal, characteristic
6C2×#89888C211yesmaximal, characteristic, complemented
7C2×#89886C211yesmaximal, characteristic
8#11736539C2116yesmaximal, direct product factor
9C2×#89601C211yesmaximal, characteristic, complemented
10C2×#89622C211yesmaximal, characteristic, complemented
11C2×#89623C211yesmaximal, characteristic, complemented
12C2×#89617C211yesmaximal, characteristic, complemented
13C2×#89617C211yesmaximal, characteristic, complemented
14C2×#89621C211yesmaximal, characteristic, complemented
15C2×#89619C211yesmaximal, characteristic, complemented
16C2×#89613C211yesmaximal, characteristic, complemented
17C22×C7×M16C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C7×#117C2211yescharacteristic
20C2×#6493C2211yescharacteristic
21C2×#6487C2211yescharacteristic
22C2×#6487C2211yescharacteristic
23C2×#6487C2211yescharacteristic
24C22×Dic28C2211yescharacteristic
25C22×Dic28C2211yescharacteristic
26C22×#1132C2211yescharacteristic
27C22×#1132C2211yescharacteristic
28#90225—24no—
29#90225C2218yes—
30#90209—24no—
31#90209C2218yescomplemented
32C2×#6461—21no—
33C2×#6459—21no—
34C2×#6452—21no—
35C2×#6452—21no—
36C2×#6448—21no—
37C2×#6446—21no—
38C2×#6442—21no—
39C2×#6442—21no—
40C2×#6438C2211yescharacteristic
41C2×C4×D28C2211yescharacteristic
42C2×#6433C2211yescharacteristic
43C2×#6432C2211yescharacteristic
44C2×#6432C2211yescharacteristic
45C2×C4×Dic14C2211yescharacteristic
46C2×C4×Dic14C2211yescharacteristic
47C2×C4×Dic14C2211yescharacteristic
48C7×#424C2218yescomplemented
49C2×C7×C4⋊C8C2211yescharacteristic
50C2×C7×C4⋊C8C2211yescharacteristic
51C2×C7×C4⋊C8C2211yescharacteristic
52C2×C7×C4⋊C8C2211yescharacteristic
53#89909C2218yescomplemented
54#89906C2218yes—
55#89888C2218yescomplemented
56#89886C2218yes—
57C2×#6395C2211yescharacteristic
58C2×#6395C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6391C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×#6390C2211yescharacteristic
65C2×#6390C2211yescharacteristic
66C2×#6390C2211yescharacteristic
67C2×#6390C2211yescharacteristic
68C2×#6390C2211yescharacteristic
69#89623C2218yescomplemented
70#89622C2218yescomplemented
71#89621C2218yescomplemented
72#89619C2218yescomplemented
73#89617C2218yescomplemented
74#89617C2218yescomplemented
75#89613C2218yescomplemented
76#89601C2218yescomplemented
77C2×#3258—71nomaximal, Sylow
78C23×C4×C7C2311yescharacteristic
79C22×C22⋊D7—21no—
80C22×D28C2311yescharacteristic
81C22×C4×D7—21no—
82C22×Dic14—21no—
83C22×Dic14C2311yescharacteristic
84C22×Dic14C2311yescharacteristic
85C22×Dic14C2311yescharacteristic
86C2×C7×M16—42no—
87C2×C7×M16C2314yes—
88C22×C7×C8—42no—
89C22×C7×C8C2311yescharacteristic
90C22×C7×C8C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2314yes—
94C7×#117D414yes—
95C7×#117C2314yes—
96C2×C7×C4⋊C4D411yescharacteristic
97C2×C7×C4⋊C4D411yescharacteristic
98C2×C7×C22⋊C4D411yescharacteristic
99C2×C7×C22⋊C4D411yescharacteristic
100C2×C42×C7C2311yescharacteristic
101C2×C42×C7C2311yescharacteristic
102C2×C22⋊Dic7—21no—
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7—21no—
105#6493—22no—
106#6493C2314yes—
107C2×(C2×D7)⋊C4—21no—
108C2×(C2×D7)⋊C4—21no—
109C2×(C2×D7)⋊C4—21no—
110C2×(C2×D7)⋊C4—21no—
111C2×C4⋊Dic7—21no—
112C2×C4⋊Dic7—21no—
113C2×C4⋊Dic7—21no—
114C2×C4⋊Dic7C2311yescharacteristic
115C2×C4⋊Dic7C2311yescharacteristic
116C2×C4⋊Dic7C2311yescharacteristic
117C2×C4⋊Dic7C2311yescharacteristic
118#6487—22no—
119#6487—22no—
120#6487—22no—
121#6487C2314yes—
122#6487C2314yes—
123#6487C2314yes—
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×C4×Dic7—21no—
133C2×C4×Dic7—21no—
134C2×C4×Dic7—21no—
135C2×Dic28—42no—
136C2×Dic28—42no—
137C2×Dic28C2314yes—
138C2×Dic28C2314yes—
139C2×#1132—42no—
140C2×#1132—42no—
141C2×#1132C2314yes—
142C2×#1132C2314yes—
143#6461—28no—
144#6459—28no—
145#6452—28no—
146#6452—28no—
147#6448—28no—
148#6446—28no—
149#6442—28no—
150#6442—28no—
151#6438—22no—
152#6438C2314yes—
153C4×D28—22no—
154C4×D28C2314yes—
155#6433—22no—
156#6433C2314yes—
157#6432—22no—
158#6432—22no—
159#6432C2314yes—
160#6432C2314yes—
161C4×Dic14—22no—
162C4×Dic14—22no—
163C4×Dic14—22no—
164C4×Dic14C2314yes—
165C4×Dic14C2314yes—
166C4×Dic14C2314yes—
167C7×C4⋊C8C2314yes—
168C7×C4⋊C8C2314yes—
169C7×C4⋊C8C2314yes—
170C7×C4⋊C8C2314yes—
171#6395C2314yes—
172#6395C2314yes—
173#6392C2314yes—
174#6392C2314yes—
175#6391C2314yes—
176#6391C2314yes—
177#6390C2314yes—
178#6390C2314yes—
179#6390C2314yes—
180#6390C2314yes—
181#6390C2314yes—
182#6390C2314yes—
183C2×#542—71no—
184C2×#541—71no—
185#3258—716no—
186C2×#479—71no—
187C2×#477—71no—
188C2×#475—71no—
189C2×#478—71no—
190C2×#470—71no—
191C2×#468—71no—
192C2×#467—71no—
193C2×#465—71no—
194C2×#464—71no—
195C2×#464—71no—
196C2×#462—71no—
197C2×#461—71no—
198C2×#424D711yescharacteristic, complemented
199C24×C7C2×D411yescharacteristic
200C23×D7—21no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7C2×D411yescharacteristic
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2411yescharacteristic
211C2×C22⋊D7—24no—
212C2×C22⋊D7—82no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C2×D28—22no—
221C2×D28—22no—
222C2×D28—21no—
223C2×D28C2412yes—
224C2×C4×D7—24no—
225C2×C4×D7—82no—
226C2×Dic14—22no—
227C2×Dic14—22no—
228C2×Dic14—22no—
229C2×Dic14—22no—
230C2×Dic14—22no—
231C2×Dic14—22no—
232C2×Dic14—21no—
233C2×Dic14—21no—
234C2×Dic14—21no—
235C2×Dic14—24no—
236C2×Dic14—82no—
237C2×Dic14C2412yes—
238C2×Dic14C2412yes—
239C2×Dic14C2412yes—
240C7×M16—44no—
241C2×C7×C8—22no—
242C2×C7×C8—22no—
243C2×C7×C8—22no—
244C2×C7×C8—22no—
245C2×C7×C8—44no—
246C2×C7×C8C2412yes—
247C2×C7×C8C2412yes—
248C2×C7×C8C2412yes—
249C2×C7×C8C2412yes—
250C7×C4⋊C4C2×D414yes—
251C7×C4⋊C4C2×D414yes—
252C7×C22⋊C4C2×D414yes—
253C7×C22⋊C4C2×D414yes—
254C42×C7C2×D412yes—
255C42×C7C2×D412yes—
256C42×C7C2412yes—
257C42×C7C2412yes—
258C22⋊Dic7—24no—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261(C2×D7)⋊C4—24no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265C4⋊Dic7—21no—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—24no—
270C4⋊Dic7—24no—
271C4⋊Dic7—24no—
272C4⋊Dic7C2412yes—
273C4⋊Dic7C2412yes—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284C4×Dic7—24no—
285C4×Dic7—24no—
286C4×Dic7—24no—
287Dic28—44no—
288Dic28—44no—
289#1132—44no—
290#1132—44no—
291C22×Q16—71no—
292C22×Q16—71no—
293C22×SD16—71no—
294C22×SD16—71no—
295C22×M16C2×D711yescharacteristic
296C23×C8C2×D711yescharacteristic
297#542—78no—
298#542—144no—
299#541—78no—
300#541—144no—
301C2×C4⋊Q8—71no—
302C2×C4⋊Q8—71no—
303C2×#126—141no—
304C2×#126—141no—
305C2×#126—141no—
306C2×#125—71no—
307C2×#125—141no—
308C2×#125—141no—
309C2×#124—71no—
310C2×#124—141no—
311C2×#123—141no—
312C2×C22⋊Q8—71no—
313C2×C22⋊Q8—71no—
314C2×C22⋊Q8—71no—
315C2×C22⋊Q8—141no—
316C2×#121—71no—
317C2×C4×Q8—71no—
318C2×C4×Q8—71no—
319C2×C4×Q8—71no—
320C2×C4×D4—71no—
321C2×#117C2×D711yescharacteristic
322#479—78no—
323#478—78no—
324#477—78no—
325#475—78no—
326#470—78no—
327#468—78no—
328#467—78no—
329#465—78no—
330#464—78no—
331#464—78no—
332#462—78no—
333#461—78no—
334C2×#107—71no—
335C2×#107—71no—
336C2×#106—71no—
337C2×#106—71no—
338#424C2×D718yescomplemented
339C2×C4⋊C8C2×D711yescharacteristic
340C2×C4⋊C8C2×D711yescharacteristic
341C2×C4⋊C8C2×D711yescharacteristic
342C2×C4⋊C8C2×D711yescharacteristic
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103—71no—
349C2×#102—71no—
350C2×#102—71no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7C22×D412yes—
355C23×C7C22×D411yescharacteristic
356C22×D7—22no—
357C22×D7—42no—
358C22×D7—42no—
359C22×D7—42no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—24no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7C22×D412yes—
369C2×C4×C7C22×D412yes—
370C2×C4×C7C22×D412yes—
371C2×C4×C7C22×D412yes—
372C2×C4×C7C22×D412yes—
373C2×C4×C7C22×D411yescharacteristic
374C2×C4×C7H(5,𝔽2)12yes—
375C2×C4×C72−1+412yes—
376C2×C4×C7C2511yescharacteristic
377C22⋊D7—84no—
378C2×Dic7—22no—
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×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7—42no—
392D28—22no—
393D28—22no—
394D28—42no—
395C4×D7—84no—
396Dic14—22no—
397Dic14—22no—
398Dic14—22no—
399Dic14—22no—
400Dic14—22no—
401Dic14—22no—
402Dic14—42no—
403Dic14—42no—
404Dic14—42no—
405Dic14—84no—
406C7×C8—22no—
407C7×C8—22no—
408C7×C8—22no—
409C7×C8—22no—
410C22×Q8—71no—
411C22×Q8—71no—
412C22×Q8—71no—
413C22×Q8—141no—
414C22×D4—71no—
415C22×D4—141no—
416C23×C4—141no—
417C23×C4C22×D711yescharacteristic
418C2×Q16—74no—
419C2×Q16—74no—
420C2×Q16—282no—
421C2×Q16—282no—
422C2×SD16—74no—
423C2×SD16—74no—
424C2×SD16—282no—
425C2×SD16—282no—
426C2×M16—42no—
427C2×M16C22×D714yes—
428C22×C8—42no—
429C22×C8C22×D711yescharacteristic
430C22×C8C22×D711yescharacteristic
431C22×C8C22×D711yescharacteristic
432C22×C8C22×D711yescharacteristic
433C22×C8C22×D714yes—
434C4⋊Q8—74no—
435C4⋊Q8—74no—
436C4⋊Q8—142no—
437C4⋊Q8—142no—
438#126—148no—
439#126—148no—
440#126—148no—
441#125—74no—
442#125—148no—
443#125—148no—
444#125—142no—
445#124—74no—
446#124—148no—
447#124—142no—
448#123—148no—
449C22⋊Q8—74no—
450C22⋊Q8—74no—
451C22⋊Q8—74no—
452C22⋊Q8—142no—
453C22⋊Q8—142no—
454C22⋊Q8—142no—
455C22⋊Q8—148no—
456#121—74no—
457#121—142no—
458C4×Q8—74no—
459C4×Q8—74no—
460C4×Q8—74no—
461C4×Q8—142no—
462C4×Q8—142no—
463C4×Q8—142no—
464C4×D4—74no—
465C4×D4—142no—
466#117D2814yes—
467#117C22×D714yes—
468C2×C4⋊C4—71no—
469C2×C4⋊C4—71no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—141no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4—141no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4D2811yescharacteristic
484C2×C4⋊C4D2811yescharacteristic
485C2×C22⋊C4—141no—
486C2×C22⋊C4—141no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4D2811yescharacteristic
493C2×C22⋊C4D2811yescharacteristic
494C2×C42—141no—
495C2×C42—141no—
496C2×C42—141no—
497C2×C42C22×D711yescharacteristic
498C2×C42C22×D711yescharacteristic
499#107—74no—
500#107—74no—
501#106—74no—
502#106—74no—
503C4⋊C8C22×D714yes—
504C4⋊C8C22×D714yes—
505C4⋊C8C22×D714yes—
506C4⋊C8C22×D714yes—
507#103—74no—
508#103—74no—
509#103—74no—
510#103—74no—
511#103—74no—
512#103—74no—
513#102—74no—
514#102—74no—
515C22×C7—22no—
516C22×C7—22no—
517C22×C7—22no—
518C22×C7—44no—
519C22×C7#53712yes—
520C22×C7#57712yes—
521C22×C7#57812yes—
522C22×C7C23×D411yescharacteristic
523C2×D7—42no—
524C2×D7—42no—
525C2×D7—42no—
526C2×D7—84no—
527C4×C7—22no—
528C4×C7—22no—
529C4×C7—22no—
530C4×C7—22no—
531C4×C7—22no—
532C4×C7#53712yes—
533C4×C7C2×H(5,𝔽2)11yescharacteristic
534C4×C7C2×2−1+411yescharacteristic
535Dic7—42no—
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542C24—141no—
543C24C2×D2811yescharacteristic
544C2×Q8—72no—
545C2×Q8—72no—
546C2×Q8—72no—
547C2×Q8—141no—
548C2×Q8—141no—
549C2×Q8—141no—
550C2×Q8—144no—
551C2×Q8—142no—
552C2×Q8—142no—
553C2×Q8—142no—
554C2×Q8—142no—
555C2×Q8—142no—
556C2×Q8—142no—
557C2×Q8—562no—
558C2×D4—72no—
559C2×D4—144no—
560C2×D4—141no—
561C2×D4—142no—
562C2×D4—142no—
563C2×D4—562no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—141no—
567C22×C4—141no—
568C22×C4—141no—
569C22×C4—141no—
570C22×C4—141no—
571C22×C4—141no—
572C22×C4—141no—
573C22×C4—144no—
574C22×C4—562no—
575C22×C4C2×D2812yes—
576C22×C4C2×D2811yescharacteristic
577C22×C4C2×D2811yescharacteristic
578C22×C4C2×D2811yescharacteristic
579C22×C4C2×D2811yescharacteristic
580C22×C4C2×D2811yescharacteristic
581C22×C4C23×D712yes—
582C22×C4C23×D711yescharacteristic
583Q16—284no—
584Q16—284no—
585SD16—284no—
586SD16—284no—
587M16—44no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—44no—
593C2×C8C23×D712yes—
594C2×C8C23×D712yes—
595C2×C8C23×D712yes—
596C2×C8C23×D712yes—
597C4⋊C4—72no—
598C4⋊C4—72no—
599C4⋊C4—72no—
600C4⋊C4—72no—
601C4⋊C4—144no—
602C4⋊C4—144no—
603C4⋊C4—144no—
604C4⋊C4—144no—
605C4⋊C4—144no—
606C4⋊C4—144no—
607C4⋊C4—144no—
608C4⋊C4—144no—
609C4⋊C4—141no—
610C4⋊C4—141no—
611C4⋊C4—141no—
612C4⋊C4—141no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4C2×D2814yes—
617C4⋊C4C2×D2814yes—
618C22⋊C4—144no—
619C22⋊C4—144no—
620C22⋊C4—144no—
621C22⋊C4—144no—
622C22⋊C4—144no—
623C22⋊C4—144no—
624C22⋊C4—144no—
625C22⋊C4C2×D2814yes—
626C22⋊C4C2×D2814yes—
627C42—144no—
628C42—144no—
629C42—144no—
630C42C2×D2812yes—
631C42C2×D2812yes—
632C42C23×D712yes—
633C42C23×D712yes—
634C2×C7—42no—
635C2×C7#325814yescomplemented
636C2×C7C2×#53711yescharacteristic
637C2×C7C2×#57711yescharacteristic
638C2×C7C2×#57811yescharacteristic
639D7—82no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—142no—
644C23—282no—
645C23—282no—
646C23—282no—
647C23C22×D2812yes—
648C23C22×D2811yescharacteristic
649Q8—142no—
650Q8—142no—
651Q8—142no—
652Q8—142no—
653Q8—142no—
654Q8—142no—
655Q8—282no—
656Q8—282no—
657Q8—282no—
658Q8—564no—
659D4—142no—
660D4—142no—
661D4—282no—
662D4—564no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—142no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—142no—
675C2×C4—142no—
676C2×C4—142no—
677C2×C4—142no—
678C2×C4—282no—
679C2×C4—282no—
680C2×C4—282no—
681C2×C4—282no—
682C2×C4—282no—
683C2×C4—282no—
684C2×C4—282no—
685C2×C4—564no—
686C2×C4C22×D2812yes—
687C2×C4C22×D2812yes—
688C2×C4C22×D2812yes—
689C2×C4C22×D2812yes—
690C2×C4C22×D2812yes—
691C2×C4C22×D2811yescharacteristic
692C2×C4#654812yes—
693C2×C4#655112yes—
694C2×C4C24×D711yescharacteristic
695C8—22no—
696C8—22no—
697C8—22no—
698C8—22no—
699C7C2×#325811yescharacteristic, complemented, Sylow
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—282no—
705C22—282no—
706C22—282no—
707C22—564no—
708C22#9020112yes—
709C22#9044212yes—
710C22#9044412yes—
711C22C23×D2811yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—282no—
718C4—282no—
719C4—282no—
720C4—282no—
721C4—282no—
722C4—282no—
723C4—282no—
724C4#9020112yes—
725C4C2×#654811yescharacteristic
726C4C2×#655111yescharacteristic
727C2—42no—
728C2—562no—
729C2#1173653914yesdirect product factor
730C2C2×#9020111yescharacteristic
731C2C2×#9044211yescharacteristic
732C2C2×#9044411yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#424C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
hypercenterC2×#424D7
hypocenterC7C2×#3258
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. C2×#90209C2semidirect
3. C2×C7×#424C2semidirect
4. C2×#89909C2semidirect
6. C2×#89888C2semidirect
8. #11736539C2direct (N × H)
9. C2×#89601C2semidirect
10. C2×#89622C2semidirect
11. C2×#89623C2semidirect
12. C2×#89617C2semidirect
13. C2×#89617C2semidirect
14. C2×#89621C2semidirect
15. C2×#89619C2semidirect
16. C2×#89613C2semidirect
31. #90209C22semidirect
48. C7×#424C22semidirect
53. #89909C22semidirect
55. #89888C22semidirect
69. #89623C22semidirect
70. #89622C22semidirect
71. #89621C22semidirect
72. #89619C22semidirect
73. #89617C22semidirect
74. #89617C22semidirect
75. #89613C22semidirect
76. #89601C22semidirect
198. C2×#424D7semidirect
338. #424C2×D7semidirect
635. C2×C7#3258semidirect
699. C7C2×#3258semidirect
729. C2#11736539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902252
C2×#902092
C2×C7×#4242
C2×#899092
C2×#899062
C2×#898882
C2×#898862
#117365392
C2×#896012
C2×#896222
C2×#896232
C2×#896172
C2×#896212
C2×#896192
C2×#896132
C2×#32587