Finite Group Databasebeta

← C2×#11737961 #14233363

Subgroups — C2×#11737961 #14233363

Order 1792.

1906 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90362C211yesmaximal, characteristic, complemented
2C2×#90230C211yesmaximal, characteristic, complemented
3C2×C7×#463C211yesmaximal, characteristic
4C2×#89934C211yesmaximal, characteristic, complemented
5C2×SD16×Dic7C211yesmaximal, characteristic, complemented
6C2×#89925C211yesmaximal, characteristic
7C2×D8×Dic7C211yesmaximal, characteristic
8C2×#89828C211yesmaximal, characteristic, complemented
9C2×C4×#1142C211yesmaximal, characteristic, complemented
10#11737961C2116yesmaximal, direct product factor
11C2×#89601C211yesmaximal, characteristic, complemented
12C2×#89602C211yesmaximal, characteristic, complemented
13C2×#89564C211yesmaximal, characteristic, complemented
14C2×#89568C211yesmaximal, characteristic, complemented
15C2×#89540C211yesmaximal, characteristic, complemented
16C2×#89533C211yesmaximal, characteristic, complemented
17C22×C7×SD16C2211yescharacteristic
18C22×C7×D8C2211yescharacteristic
19C2×C7×#124C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×Q8×Dic7C2211yescharacteristic
22C2×#6507C2211yescharacteristic
23C2×#6499C2211yescharacteristic
24C2×D4×Dic7C2211yescharacteristic
25C2×D4×Dic7C2211yescharacteristic
26C2×D4×Dic7C2211yescharacteristic
27C22×#1142C2211yescharacteristic
28C2×#6487—21no—
29C22×Dic7⋊C4—21no—
30#90362—24no—
31#90362C2218yescomplemented
32#90230—24no—
33#90230C2218yescomplemented
34C2×#6453C2211yescharacteristic
35C2×#6451C2211yescharacteristic
36C2×#6442—21no—
37C2×#6442—21no—
38C2×#6441—21no—
39C2×#6441—21no—
40C2×#6441—21no—
41C2×#6440—21no—
42C2×#6433C2211yescharacteristic
43C2×C4×Dic14C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×#463C2218yes—
46C2×C7×C4⋊C8C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×#6409C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54#89934C2218yescomplemented
55SD16×Dic7C2218yescomplemented
56#89925C2218yes—
57D8×Dic7C2218yes—
58C2×#6392C2211yescharacteristic
59C2×#6391C2211yescharacteristic
60C2×#6390C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×Dic7⋊C8C2211yescharacteristic
63C2×Dic7⋊C8C2211yescharacteristic
64C2×C8×Dic7C2211yescharacteristic
65C2×C8×Dic7C2211yescharacteristic
66#89828C2218yescomplemented
67C4×#1142C2218yescomplemented
68C2×#6384C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×C4×C7⋊C8C2211yescharacteristic
71#89602C2218yescomplemented
72#89601C2218yescomplemented
73#89568C2218yescomplemented
74#89564C2218yescomplemented
75#89540C2218yescomplemented
76#89533C2218yescomplemented
77C2×#3360—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7—21no—
82C23×Dic7—21no—
83C23×Dic7—21no—
84C23×Dic7—21no—
85C22×Dic14—21no—
86C22×Dic14D411yescharacteristic
87C22×Dic14C2311yescharacteristic
88C2×C7×SD16—24no—
89C2×C7×SD16C2314yes—
90C2×C7×D8—24no—
91C2×C7×D8C2314yes—
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C7×#124—22no—
95C7×#124C2314yes—
96C4×C7×D4—22no—
97C4×C7×D4C2314yes—
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C22⋊C4—21no—
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4—21no—
102C2×C42×C7C2311yescharacteristic
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108Q8×Dic7—22no—
109Q8×Dic7C2314yes—
110#6507—22no—
111#6507C2314yes—
112#6499—22no—
113#6499C2314yes—
114D4×Dic7—22no—
115D4×Dic7—22no—
116D4×Dic7—22no—
117D4×Dic7C2314yes—
118D4×Dic7C2314yes—
119D4×Dic7C2314yes—
120C2×#1142—24no—
121C2×#1142C2314yes—
122C2×C4⋊Dic7—21no—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7D411yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128#6487—28no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—28no—
137C2×Dic7⋊C4D411yescharacteristic
138C2×Dic7⋊C4D411yescharacteristic
139C2×C4×Dic7—21no—
140C2×C4×Dic7—21no—
141C2×C4×Dic7C2311yescharacteristic
142C2×C4×Dic7C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145#6453—22no—
146#6453C2314yes—
147#6451—22no—
148#6451C2314yes—
149#6442—28no—
150#6442—28no—
151#6441—28no—
152#6441—28no—
153#6441—28no—
154#6440—28no—
155#6433—22no—
156#6433C2314yes—
157C4×Dic14—22no—
158C4×Dic14D414yes—
159C4×Dic14C2314yes—
160C4×Dic14C2314yes—
161C7×C4⋊C8C2314yes—
162C7×#103C2314yes—
163C7×#102C2314yes—
164#6409C2314yes—
165#6409C2314yes—
166#6406C2314yes—
167#6406C2314yes—
168#6406C2314yes—
169#6392C2314yes—
170#6391C2314yes—
171#6390C2314yes—
172#6390C2314yes—
173Dic7⋊C8C2314yes—
174Dic7⋊C8C2314yes—
175C8×Dic7C2314yes—
176C8×Dic7C2314yes—
177#6384C2314yes—
178#6382C2314yes—
179C4×C7⋊C8C2314yes—
180C2×#556—71no—
181C2×#554—71no—
182#3360—716no—
183C2×#488—71no—
184C2×#488—71no—
185C2×#487—71no—
186C2×#479—71no—
187C2×#479—71no—
188C2×#476—71no—
189C2×#463—71no—
190C2×#463D711yescharacteristic
191C2×#461—71no—
192C2×C8×Q8—71no—
193C2×C4×SD16—71no—
194C2×C4×SD16—71no—
195C2×C4×D8—71no—
196C24×C7—21no—
197C24×C7—21no—
198C2×C7×Q8—21no—
199C2×C7×Q8—22no—
200C2×C7×Q8—22no—
201C2×C7×Q8C2412yes—
202C2×C7×D4—21no—
203C2×C7×D4—21no—
204C2×C7×D4—22no—
205C2×C7×D4—22no—
206C2×C7×D4—22no—
207C2×C7×D4#4114yes—
208C2×C7×D4C2412yes—
209C2×C7×D4C2412yes—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—24no—
213C22×C4×C7—82no—
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2411yescharacteristic
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—24no—
222C22×Dic7—24no—
223C22×Dic7—24no—
224C22×Dic7—44no—
225C22×Dic7—44no—
226C22×Dic7—82no—
227C22×Dic7C2×D411yescharacteristic
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230C22×Dic7C2×D411yescharacteristic
231C2×Dic14—24no—
232C2×Dic14—22no—
233C2×Dic14—22no—
234C2×Dic14—21no—
235C2×Dic14—24no—
236C2×Dic14—82no—
237C2×Dic14C2×D414yes—
238C2×Dic14C2412yes—
239C7×SD16—28no—
240C7×D8—28no—
241C2×C7×C8—22no—
242C2×C7×C8—22no—
243C2×C7×C8C2412yes—
244C2×C7×C8C2412yes—
245C7×C4⋊C4—21no—
246C7×C4⋊C4C2412yes—
247C7×C22⋊C4—24no—
248C7×C22⋊C4—24no—
249C7×C22⋊C4—24no—
250C42×C7C2×D412yes—
251C42×C7C2412yes—
252C22⋊Dic7—24no—
253C22⋊Dic7—24no—
254C22⋊Dic7—24no—
255C22⋊Dic7—24no—
256C22⋊Dic7—24no—
257#1142—28no—
258C4⋊Dic7—21no—
259C4⋊Dic7—21no—
260C4⋊Dic7—21no—
261C4⋊Dic7—24no—
262C4⋊Dic7—24no—
263C4⋊Dic7C2×D414yes—
264C4⋊Dic7C2412yes—
265C4⋊Dic7C2412yes—
266C4⋊Dic7C2412yes—
267Dic7⋊C4—24no—
268Dic7⋊C4—24no—
269Dic7⋊C4—24no—
270Dic7⋊C4—24no—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4C2×D414yes—
275Dic7⋊C4C2×D414yes—
276C4×Dic7—24no—
277C4×Dic7—24no—
278C4×Dic7C2×D412yes—
279C4×Dic7C2×D412yes—
280C4×Dic7C2412yes—
281C4×Dic7C2412yes—
282C2×C7⋊C8—22no—
283C2×C7⋊C8—22no—
284C2×C7⋊C8C2412yes—
285C2×C7⋊C8C2412yes—
286C22×SD16—71no—
287C22×SD16C2×D711yescharacteristic
288C22×D8C2×D711yescharacteristic
289#556—78no—
290#556—144no—
291#554—78no—
292#554—144no—
293C2×C4⋊Q8—71no—
294C2×C4⋊Q8—71no—
295C2×#126—141no—
296C2×#126—141no—
297C2×#125—71no—
298C2×#125—71no—
299C2×#124—71no—
300C2×#124C2×D711yescharacteristic
301C2×C22⋊Q8—141no—
302C2×C22⋊Q8—141no—
303C2×C22⋊Q8—141no—
304C2×C22⋊Q8—141no—
305C2×C4×Q8—71no—
306C2×C4×Q8—71no—
307C2×C4×Q8—71no—
308C2×C4×D4—71no—
309C2×C4×D4—71no—
310C2×C4×D4—71no—
311C2×C4×D4C2×D711yescharacteristic
312C2×#117—141no—
313C22×C4⋊C4—141no—
314#488—78no—
315#488—78no—
316#487—78no—
317#479—78no—
318#479—78no—
319#476—78no—
320#463—78no—
321#463C2×D718yes—
322#461—78no—
323C8×Q8—78no—
324C4×SD16—78no—
325C4×SD16—78no—
326C4×D8—78no—
327C2×#107—71no—
328C2×#106—71no—
329C2×#106—71no—
330C2×C4⋊C8—71no—
331C2×C4⋊C8—71no—
332C2×C4⋊C8C2×D711yescharacteristic
333C2×#103—71no—
334C2×#103—71no—
335C2×#103—71no—
336C2×#103—71no—
337C2×#103—71no—
338C2×#103C2×D711yescharacteristic
339C2×#102—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102C2×D711yescharacteristic
343C2×C4×C8—71no—
344C2×C4×C8—71no—
345C2×C4×C8—71no—
346C23×C7—24no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—42no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7C22×D411yescharacteristic
355C7×Q8—22no—
356C7×Q8—22no—
357C7×Q8—42no—
358C7×D4—24no—
359C7×D4—22no—
360C7×D4—22no—
361C7×D4—22no—
362C7×D4—42no—
363C7×D4C2×#4114yes—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7—84no—
371C2×C4×C7C22×D412yes—
372C2×C4×C7C22×D412yes—
373C2×C4×C7C22×D411yescharacteristic
374C2×C4×C7C2×#4112yes—
375C2×C4×C72−1+412yes—
376C2×C4×C7C2511yescharacteristic
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—42no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—48no—
389C2×Dic7—48no—
390C2×Dic7—84no—
391C2×Dic7#13514yes—
392C2×Dic7C22×D412yes—
393C2×Dic7C22×D412yes—
394C2×Dic7C22×D412yes—
395C2×Dic7C22×D412yes—
396Dic14—28no—
397Dic14—22no—
398Dic14—22no—
399Dic14—42no—
400Dic14—84no—
401C7×C8—22no—
402C7×C8—22no—
403C7⋊C8—22no—
404C7⋊C8—22no—
405C22×Q8—71no—
406C22×Q8—71no—
407C22×Q8—141no—
408C22×Q8C22×D711yescharacteristic
409C22×D4C22×D711yescharacteristic
410C22×D4C22×D711yescharacteristic
411C23×C4—21no—
412C23×C4—141no—
413C23×C4—141no—
414C23×C4—141no—
415C2×SD16—24no—
416C2×SD16—74no—
417C2×SD16—144no—
418C2×SD16C22×D714yes—
419C2×D8—24no—
420C2×D8C22×D714yes—
421C22×C8—71no—
422C22×C8—71no—
423C22×C8C22×D711yescharacteristic
424C22×C8C22×D711yescharacteristic
425C4⋊Q8—74no—
426C4⋊Q8—74no—
427C4⋊Q8—142no—
428C4⋊Q8—142no—
429#126—148no—
430#126—148no—
431#125—74no—
432#125—74no—
433#125—142no—
434#125—142no—
435#124—22no—
436#124—74no—
437#124—142no—
438#124C22×D714yes—
439C22⋊Q8—148no—
440C22⋊Q8—148no—
441C22⋊Q8—148no—
442C22⋊Q8—148no—
443C4×Q8—74no—
444C4×Q8—74no—
445C4×Q8—74no—
446C4×Q8—74no—
447C4×Q8—142no—
448C4×Q8—142no—
449C4×D4—22no—
450C4×D4—74no—
451C4×D4—74no—
452C4×D4—74no—
453C4×D4—142no—
454C4×D4—142no—
455C4×D4—142no—
456C4×D4C22×D714yes—
457#117—148no—
458C2×C4⋊C4—71no—
459C2×C4⋊C4—71no—
460C2×C4⋊C4—71no—
461C2×C4⋊C4—71no—
462C2×C4⋊C4—71no—
463C2×C4⋊C4—71no—
464C2×C4⋊C4—148no—
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⋊C4—141no—
474C2×C4⋊C4C22×D711yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—141no—
479C2×C22⋊C4—141no—
480C2×C22⋊C4—141no—
481C2×C22⋊C4—141no—
482C2×C22⋊C4—141no—
483C2×C42—71no—
484C2×C42—71no—
485C2×C42—141no—
486C2×C42—141no—
487C2×C42C22×D711yescharacteristic
488#107—74no—
489#106—74no—
490#106—74no—
491C4⋊C8—74no—
492C4⋊C8—74no—
493C4⋊C8C22×D714yes—
494#103—74no—
495#103—74no—
496#103—74no—
497#103—74no—
498#103—74no—
499#103C22×D714yes—
500#102—74no—
501#102—74no—
502#102—74no—
503#102C22×D714yes—
504C4×C8—74no—
505C4×C8—74no—
506C4×C8—74no—
507C22×C7—24no—
508C22×C7—48no—
509C22×C7—42no—
510C22×C7—42no—
511C22×C7—42no—
512C22×C7—42no—
513C22×C7—42no—
514C22×C7—84no—
515C22×C7#54812yes—
516C22×C7C2×#13512yes—
517C22×C7#57712yes—
518C22×C7C23×D411yescharacteristic
519C4×C7—22no—
520C4×C7—22no—
521C4×C7—42no—
522C4×C7—42no—
523C4×C7#54812yes—
524C4×C7C22×#4111yescharacteristic
525C4×C7C2×2−1+411yescharacteristic
526Dic7—22no—
527Dic7—22no—
528Dic7—22no—
529Dic7—42no—
530Dic7—42no—
531Dic7—42no—
532Dic7—42no—
533Dic7C2×#13514yes—
534C24—21no—
535C24—21no—
536C2×Q8—21no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—74no—
540C2×Q8—72no—
541C2×Q8—144no—
542C2×Q8—144no—
543C2×Q8—141no—
544C2×Q8—142no—
545C2×Q8—142no—
546C2×Q8—562no—
547C2×Q8C23×D712yes—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4#115914yes—
554C2×D4C23×D712yes—
555C2×D4C23×D712yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—71no—
560C22×C4—71no—
561C22×C4—71no—
562C22×C4—71no—
563C22×C4—82no—
564C22×C4—144no—
565C22×C4—144no—
566C22×C4—144no—
567C22×C4—141no—
568C22×C4—141no—
569C22×C4—141no—
570C22×C4—141no—
571C22×C4—284no—
572C22×C4—284no—
573C22×C4—562no—
574C22×C4D4×D711yescharacteristic
575C22×C4D4×D711yescharacteristic
576C22×C4C23×D711yescharacteristic
577SD16—28no—
578SD16—148no—
579D8—28no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—72no—
583C2×C8—72no—
584C2×C8—142no—
585C2×C8—142no—
586C2×C8C23×D712yes—
587C2×C8C23×D712yes—
588C4⋊C4—21no—
589C4⋊C4—74no—
590C4⋊C4—74no—
591C4⋊C4—74no—
592C4⋊C4—72no—
593C4⋊C4—72no—
594C4⋊C4—72no—
595C4⋊C4—144no—
596C4⋊C4—144no—
597C4⋊C4—144no—
598C4⋊C4—144no—
599C4⋊C4—144no—
600C4⋊C4—144no—
601C4⋊C4—144no—
602C4⋊C4—144no—
603C4⋊C4—144no—
604C4⋊C4—141no—
605C4⋊C4—141no—
606C4⋊C4—141no—
607C4⋊C4C23×D712yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—144no—
612C22⋊C4—144no—
613C22⋊C4—144no—
614C22⋊C4—144no—
615C22⋊C4—144no—
616C42—72no—
617C42—72no—
618C42—72no—
619C42—72no—
620C42—144no—
621C42—144no—
622C42D4×D712yes—
623C42C23×D712yes—
624C2×C7—44no—
625C2×C7—82no—
626C2×C7#336014yescomplemented
627C2×C7C2×#54811yescharacteristic
628C2×C7C22×#13511yescharacteristic
629C2×C7C2×#57711yescharacteristic
630C23—24no—
631C23—22no—
632C23—22no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23C2×D4×D711yescharacteristic
639Q8—22no—
640Q8—22no—
641Q8—42no—
642Q8—148no—
643Q8—142no—
644Q8—142no—
645Q8—282no—
646Q8—564no—
647D4—24no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—42no—
652D4C2×#115914yes—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—74no—
660C2×C4—72no—
661C2×C4—72no—
662C2×C4—72no—
663C2×C4—72no—
664C2×C4—84no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—142no—
671C2×C4—142no—
672C2×C4—288no—
673C2×C4—288no—
674C2×C4—282no—
675C2×C4—282no—
676C2×C4—282no—
677C2×C4—282no—
678C2×C4—564no—
679C2×C4C2×D4×D712yes—
680C2×C4C2×D4×D712yes—
681C2×C4C2×D4×D711yescharacteristic
682C2×C4C2×#115912yes—
683C2×C4#655412yes—
684C2×C4C24×D711yescharacteristic
685C8—22no—
686C8—22no—
687C8—142no—
688C8—142no—
689C7C2×#336011yescharacteristic, complemented, Sylow
690C22—24no—
691C22—42no—
692C22—48no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—84no—
698C22#9028912yes—
699C22D7×#13512yes—
700C22#9046612yes—
701C22C22×D4×D711yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—74no—
707C4—142no—
708C4—142no—
709C4—142no—
710C4—282no—
711C4—282no—
712C4—282no—
713C4—282no—
714C4#9028912yes—
715C4C22×#115911yescharacteristic
716C4C2×#655411yescharacteristic
717C2—44no—
718C2—82no—
719C2#1173796114yesdirect product factor
720C2C2×#9028911yescharacteristic
721C2C2×D7×#13511yescharacteristic
722C2C2×#9046611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#463C2
socleC23×C7C22×D4
prime radicalC22×C7×D8C22
hypercenterC2×#463D7
hypocenterC7C2×#3360
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#90362C2semidirect
2. C2×#90230C2semidirect
4. C2×#89934C2semidirect
5. C2×SD16×Dic7C2semidirect
8. C2×#89828C2semidirect
9. C2×C4×#1142C2semidirect
10. #11737961C2direct (N × H)
11. C2×#89601C2semidirect
12. C2×#89602C2semidirect
13. C2×#89564C2semidirect
14. C2×#89568C2semidirect
15. C2×#89540C2semidirect
16. C2×#89533C2semidirect
31. #90362C22semidirect
33. #90230C22semidirect
54. #89934C22semidirect
55. SD16×Dic7C22semidirect
66. #89828C22semidirect
67. C4×#1142C22semidirect
71. #89602C22semidirect
72. #89601C22semidirect
73. #89568C22semidirect
74. #89564C22semidirect
75. #89540C22semidirect
76. #89533C22semidirect
626. C2×C7#3360semidirect
689. C7C2×#3360semidirect
719. C2#11737961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903622
C2×#902302
C2×C7×#4632
C2×#899342
C2×SD16×Dic72
C2×#899252
C2×D8×Dic72
C2×#898282
C2×C4×#11422
#117379612
C2×#896012
C2×#896022
C2×#895642
C2×#895682
C2×#895402
C2×#895332
C2×#33607