Finite Group Databasebeta

← C2×#11738801 #14225852

Subgroups — C2×#11738801 #14225852

Order 1792.

2058 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×#90287C211yesmaximal, characteristic
2C2×#90208C211yesmaximal, characteristic, complemented
3C2×C7×#482C211yesmaximal, characteristic, complemented
4C2×#89807C211yesmaximal, characteristic, complemented
5C2×#89775C211yesmaximal, characteristic, complemented
6#11738801C2116yesmaximal, direct product factor
7C2×#89663C211yesmaximal, characteristic, complemented
8C2×#89646C211yesmaximal, characteristic, complemented
9C2×#89643C211yesmaximal, characteristic, complemented
10C2×#89627C211yesmaximal, characteristic, complemented
11C2×#89532C211yesmaximal, characteristic, complemented
12C2×#89532C211yesmaximal, characteristic, complemented
13C2×#89535C211yesmaximal, characteristic, complemented
14C2×#89538C211yesmaximal, characteristic, complemented
15C2×#89509C211yesmaximal, characteristic, complemented
16C2×#89490C211yesmaximal, characteristic, complemented
17C22×#1159—21no—
18C2×C7×#121C2211yescharacteristic
19C2×C7×#117C2211yescharacteristic
20C2×#6503C2211yescharacteristic
21C2×#6502—21no—
22C2×D4×Dic7C2211yescharacteristic
23C2×#6493C2211yescharacteristic
24C2×#6489C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26#90287—24no—
27#90287C2218yes—
28#90208—24no—
29#90208C2218yescomplemented
30C2×#6456C2211yescharacteristic
31C2×#6453C2211yescharacteristic
32C2×#6453C2211yescharacteristic
33C2×#6451C2211yescharacteristic
34C2×#6451C2211yescharacteristic
35C2×#6451C2211yescharacteristic
36C2×#6448—21no—
37C2×(C22⋊D7)⋊C4—21no—
38C2×#6441—21no—
39C2×#6441—21no—
40C2×C4×Dic14—21no—
41C2×C4×Dic14—21no—
42C7×#482C2218yescomplemented
43C2×C7×#107C2211yescharacteristic
44C2×C7×#106C2211yescharacteristic
45C2×C7×#102C2211yescharacteristic
46C2×C7×#102C2211yescharacteristic
47C2×C7×C22⋊C8C2211yescharacteristic
48C2×#6406C2211yescharacteristic
49C2×#6406C2211yescharacteristic
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51C2×#6395C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×#6392C2211yescharacteristic
54C2×#6391C2211yescharacteristic
55C2×Dic7⋊C8C2211yescharacteristic
56C2×Dic7⋊C8C2211yescharacteristic
57C2×C8×Dic7C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89807C2218yescomplemented
60#89775C2218yescomplemented
61C2×#6383C2211yescharacteristic
62C2×#6383C2211yescharacteristic
63C2×#6382C2211yescharacteristic
64C2×#6382C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67#89663C2218yescomplemented
68#89646C2218yescomplemented
69#89643C2218yescomplemented
70#89627C2218yescomplemented
71#89538C2218yescomplemented
72#89535C2218yescomplemented
73#89532C2218yescomplemented
74#89532C2218yescomplemented
75#89509C2218yescomplemented
76#89490C2218yescomplemented
77C2×#3228—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C23×Dic7—21no—
85C23×Dic7D411yescharacteristic
86C23×Dic7D411yescharacteristic
87C2×#1159—28no—
88C2×#1159—48no—
89C22×D28C2311yescharacteristic
90C22×C4×D7—21no—
91C22×Dic14—21no—
92C22×Dic14—21no—
93C22×Dic14—21no—
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C7×#121—22no—
97C7×#121C2314yes—
98C7×#117—22no—
99C7×#117C2314yes—
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C22⋊C4—21no—
104C2×C7×C22⋊C4—21no—
105C2×C42×C7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108#6503—22no—
109#6503C2314yes—
110#6502—28no—
111D4×Dic7—22no—
112D4×Dic7C2314yes—
113#6493—22no—
114#6493C2314yes—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117#6489—22no—
118#6489C2314yes—
119C2×C4⋊Dic7—21no—
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7C2311yescharacteristic
122C2×C4⋊Dic7C2311yescharacteristic
123C2×C4⋊Dic7C2311yescharacteristic
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×C4×Dic7—21no—
130C2×C4×Dic7D411yescharacteristic
131C2×C4×Dic7D411yescharacteristic
132C2×C4×Dic7D414yes—
133C2×C4×Dic7C2311yescharacteristic
134C2×C4×Dic7C2311yescharacteristic
135C2×C4×Dic7C2314yes—
136C22×C7⋊C8C2311yescharacteristic
137C22×C7⋊C8C2311yescharacteristic
138#6456—22no—
139#6456C2314yes—
140#6453—22no—
141#6453—22no—
142#6453C2314yes—
143#6453C2314yes—
144#6451—22no—
145#6451—22no—
146#6451—22no—
147#6451C2314yes—
148#6451C2314yes—
149#6451C2314yes—
150#6448—28no—
151(C22⋊D7)⋊C4—28no—
152#6441—28no—
153#6441—28no—
154C4×Dic14—28no—
155C4×Dic14—28no—
156C7×#107C2314yes—
157C7×#106C2314yes—
158C7×#102C2314yes—
159C7×#102C2314yes—
160C7×C22⋊C8C2314yes—
161#6406C2314yes—
162#6406C2314yes—
163C22⋊(C7⋊C8)C2314yes—
164#6395C2314yes—
165#6395C2314yes—
166#6392C2314yes—
167#6391C2314yes—
168Dic7⋊C8C2314yes—
169Dic7⋊C8C2314yes—
170C8×Dic7C2314yes—
171C8×Dic7C2314yes—
172#6383C2314yes—
173#6383C2314yes—
174#6382C2314yes—
175#6382C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178C2×#533—71no—
179C2×#532—71no—
180#3228—716no—
181C2×#500—71no—
182C2×#498—71no—
183C2×#486—71no—
184C2×#486—71no—
185C2×#482—71no—
186C2×#482—71no—
187C2×#482—71no—
188C2×#482D711yescharacteristic, complemented
189C2×#478—71no—
190C2×#478—71no—
191C2×#478—71no—
192C2×#478—71no—
193C2×#431—71no—
194C24×C7—21no—
195C24×C7C2×D411yescharacteristic
196C23×D7—21no—
197C2×C7×D4—24no—
198C2×C7×D4—21no—
199C2×C7×D4—22no—
200C2×C7×D4—22no—
201C2×C7×D4—44no—
202C2×C7×D4C2412yes—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2411yescharacteristic
212C2×C22⋊D7—24no—
213C2×C22⋊D7—24no—
214C2×C22⋊D7—24no—
215C2×C22⋊D7—44no—
216C2×C22⋊D7—44no—
217C2×C22⋊D7—44no—
218C22×Dic7—24no—
219C22×Dic7—24no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—24no—
224C22×Dic7—44no—
225C22×Dic7C2×D414yes—
226C22×Dic7C2×D414yes—
227C22×Dic7C2×D411yescharacteristic
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230C22×Dic7C2×D411yescharacteristic
231#1159—432no—
232C2×D28—22no—
233C2×D28—22no—
234C2×D28—21no—
235C2×D28C2412yes—
236C2×C4×D7—24no—
237C2×C4×D7—44no—
238C2×Dic14—24no—
239C2×Dic14—24no—
240C2×Dic14—24no—
241C2×Dic14—44no—
242C2×Dic14—44no—
243C2×Dic14—44no—
244C2×C7×C8—22no—
245C2×C7×C8—22no—
246C2×C7×C8C2412yes—
247C2×C7×C8C2412yes—
248C7×C4⋊C4—21no—
249C7×C4⋊C4—21no—
250C7×C4⋊C4—21no—
251C7×C4⋊C4C2412yes—
252C7×C4⋊C4C2412yes—
253C7×C4⋊C4C2412yes—
254C7×C22⋊C4—24no—
255C7×C22⋊C4—24no—
256C42×C7—24no—
257C22⋊Dic7—24no—
258C22⋊Dic7—24no—
259(C2×D7)⋊C4—24no—
260(C2×D7)⋊C4—24no—
261C4⋊Dic7—21no—
262C4⋊Dic7—21no—
263C4⋊Dic7—21no—
264C4⋊Dic7—24no—
265C4⋊Dic7—24no—
266C4⋊Dic7C2412yes—
267C4⋊Dic7C2412yes—
268C4⋊Dic7C2412yes—
269Dic7⋊C4—24no—
270Dic7⋊C4—24no—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274C4×Dic7—24no—
275C4×Dic7C2×D414yes—
276C4×Dic7C2×D414yes—
277C4×Dic7C2×D412yes—
278C4×Dic7C2×D412yes—
279C4×Dic7C2412yes—
280C4×Dic7C2412yes—
281C2×C7⋊C8—22no—
282C2×C7⋊C8—22no—
283C2×C7⋊C8C2412yes—
284C2×C7⋊C8C2412yes—
285C22×#41—141no—
286#533—78no—
287#533—144no—
288#532—78no—
289#532—144no—
290C2×C4⋊Q8—71no—
291C2×C4⋊Q8—71no—
292C2×C4⋊Q8—71no—
293C2×#127—71no—
294C2×#125—71no—
295C2×#125—71no—
296C2×#124—141no—
297C2×C22⋊Q8—141no—
298C2×C22⋊Q8—141no—
299C2×#121—71no—
300C2×#121—141no—
301C2×#121C2×D711yescharacteristic
302C2×C4×Q8—141no—
303C2×C4×Q8—141no—
304C2×C4×D4—71no—
305C2×C4×D4—71no—
306C2×C4×D4—141no—
307C2×#117—71no—
308C2×#117C2×D711yescharacteristic
309C22×C42—71no—
310#500—78no—
311#498—78no—
312#486—78no—
313#486—78no—
314#482—78no—
315#482—78no—
316#482—78no—
317#482C2×D718yescomplemented
318#478—78no—
319#478—78no—
320#478—78no—
321#478—78no—
322#431—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⋊C8—71no—
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⋊C8C2×D711yescharacteristic
343C2×C4×C8—71no—
344C2×C4×C8—71no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—42no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7C22×D412yes—
353C23×C7C22×D411yescharacteristic
354C22×D7—22no—
355C22×D7—42no—
356C22×D7—42no—
357C22×D7—42no—
358C7×D4—22no—
359C7×D4—22no—
360C7×D4—48no—
361C7×D4—42no—
362C2×C4×C7—22no—
363C2×C4×C7—24no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7C22×D412yes—
373C2×C4×C7C22×D411yescharacteristic
374C2×C4×C72−1+412yes—
375C2×C4×C72−1+412yes—
376C2×C4×C7C2511yescharacteristic
377C22⋊D7—48no—
378C22⋊D7—48no—
379C22⋊D7—48no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—28no—
383C2×Dic7—28no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—48no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7#13514yes—
392C2×Dic7AGL(1,ℤ/8)14yes—
393C2×Dic7C22×D412yes—
394C2×Dic7C22×D412yes—
395C2×Dic7C22×D412yes—
396C2×Dic7C22×D412yes—
397D28—22no—
398D28—22no—
399D28—42no—
400C4×D7—48no—
401Dic14—48no—
402Dic14—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×Q8—141no—
412C22×Q8—141no—
413C22×D4—21no—
414C22×D4—71no—
415C22×D4—141no—
416C22×D4—141no—
417C22×D4—141no—
418C22×D4C22×D711yescharacteristic
419C23×C4—71no—
420C23×C4—71no—
421C23×C4—141no—
422C23×C4—141no—
423C23×C4C22×D711yescharacteristic
424C22×C8—71no—
425C22×C8—71no—
426C22×C8C22×D711yescharacteristic
427C22×C8C22×D711yescharacteristic
428C4⋊Q8—74no—
429C4⋊Q8—74no—
430C4⋊Q8—74no—
431C4⋊Q8—142no—
432C4⋊Q8—142no—
433C4⋊Q8—142no—
434#127—74no—
435#127—142no—
436#125—74no—
437#125—74no—
438#125—142no—
439#125—142no—
440#124—148no—
441C22⋊Q8—148no—
442C22⋊Q8—148no—
443#121—22no—
444#121—74no—
445#121—148no—
446#121—142no—
447#121C22×D714yes—
448C4×Q8—148no—
449C4×Q8—148no—
450C4×D4—74no—
451C4×D4—74no—
452C4×D4—148no—
453C4×D4—142no—
454C4×D4—142no—
455#117—22no—
456#117—74no—
457#117—142no—
458#117C22×D714yes—
459C2×C4⋊C4—71no—
460C2×C4⋊C4—71no—
461C2×C4⋊C4—71no—
462C2×C4⋊C4—141no—
463C2×C4⋊C4—141no—
464C2×C4⋊C4—141no—
465C2×C4⋊C4—141no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4C22×D711yescharacteristic
470C2×C4⋊C4C22×D711yescharacteristic
471C2×C4⋊C4C22×D711yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—141no—
475C2×C22⋊C4—141no—
476C2×C22⋊C4—141no—
477C2×C22⋊C4—141no—
478C2×C42—21no—
479C2×C42—71no—
480C2×C42—71no—
481C2×C42—74no—
482C2×C42—71no—
483C2×C42—71no—
484C2×C42—74no—
485C2×C42—141no—
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⋊C8—74no—
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⋊C8C22×D714yes—
506C4×C8—74no—
507C4×C8—74no—
508C22×C7—22no—
509C22×C7—22no—
510C22×C7—22no—
511C22×C7—44no—
512C22×C7—42no—
513C22×C7—42no—
514C22×C7—42no—
515C22×C7—84no—
516C22×C7#53612yes—
517C22×C7C2×#13512yes—
518C22×C7C2×AGL(1,ℤ/8)12yes—
519C22×C7C23×D411yescharacteristic
520C2×D7—42no—
521C2×D7—42no—
522C2×D7—42no—
523C2×D7—84no—
524C4×C7—22no—
525C4×C7—42no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7#53612yes—
529C4×C7C2×2−1+411yescharacteristic
530C4×C7C2×2−1+411yescharacteristic
531Dic7—22no—
532Dic7—22no—
533Dic7—42no—
534Dic7—42no—
535Dic7—42no—
536Dic7C2×#13514yes—
537Dic7C2×AGL(1,ℤ/8)14yes—
538C24—21no—
539C24—141no—
540C24D4×D711yescharacteristic
541#41—2832no—
542C2×Q8—144no—
543C2×Q8—144no—
544C2×Q8—144no—
545C2×Q8—284no—
546C2×Q8—284no—
547C2×Q8—284no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—44no—
553C2×D4—72no—
554C2×D4—144no—
555C2×D4—144no—
556C2×D4—144no—
557C2×D4—141no—
558C2×D4—142no—
559C2×D4—142no—
560C2×D4—284no—
561C2×D4—284no—
562C2×D4—284no—
563C2×D4C23×D712yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—71no—
570C22×C4—71no—
571C22×C4—74no—
572C22×C4—74no—
573C22×C4—71no—
574C22×C4—71no—
575C22×C4—144no—
576C22×C4—144no—
577C22×C4—144no—
578C22×C4—144no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—141no—
582C22×C4—284no—
583C22×C4—284no—
584C22×C4D4×D712yes—
585C22×C4D4×D711yescharacteristic
586C22×C4C23×D712yes—
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—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—72no—
600C4⋊C4—72no—
601C4⋊C4—72no—
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⋊C4C23×D712yes—
613C4⋊C4C23×D712yes—
614C4⋊C4C23×D712yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—144no—
618C22⋊C4—144no—
619C22⋊C4—144no—
620C22⋊C4—144no—
621C42—24no—
622C42—74no—
623C42—72no—
624C42—74no—
625C42—72no—
626C42—72no—
627C42—72no—
628C42—144no—
629C2×C7—42no—
630C2×C7—82no—
631C2×C7#322814yescomplemented
632C2×C7C2×#53611yescharacteristic
633C2×C7C22×#13511yescharacteristic
634C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
635D7—82no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—142no—
644C23—282no—
645C23—282no—
646C23—282no—
647C23C2×D4×D712yes—
648C23C2×D4×D711yescharacteristic
649Q8—288no—
650Q8—288no—
651Q8—288no—
652D4—22no—
653D4—22no—
654D4—48no—
655D4—42no—
656D4—142no—
657D4—142no—
658D4—288no—
659D4—288no—
660D4—288no—
661D4—282no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—74no—
673C2×C4—74no—
674C2×C4—72no—
675C2×C4—72no—
676C2×C4—72no—
677C2×C4—72no—
678C2×C4—148no—
679C2×C4—148no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—288no—
686C2×C4—288no—
687C2×C4—282no—
688C2×C4—282no—
689C2×C4—282no—
690C2×C4C2×D4×D712yes—
691C2×C4C2×D4×D711yescharacteristic
692C2×C4#655412yes—
693C2×C4#655412yes—
694C2×C4C24×D711yescharacteristic
695C8—22no—
696C8—22no—
697C8—142no—
698C8—142no—
699C7C2×#322811yescharacteristic, complemented, Sylow
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22—282no—
709C22—282no—
710C22—282no—
711C22—564no—
712C22#9033912yes—
713C22D7×#13512yes—
714C22D7×AGL(1,ℤ/8)12yes—
715C22C22×D4×D711yescharacteristic
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—74no—
721C4—74no—
722C4—142no—
723C4—142no—
724C4—282no—
725C4—282no—
726C4—282no—
727C4#9033912yes—
728C4C2×#655411yescharacteristic
729C4C2×#655411yescharacteristic
730C2—42no—
731C2—82no—
732C2—562no—
733C2#1173880114yesdirect product factor
734C2C2×#9033911yescharacteristic
735C2C2×D7×#13511yescharacteristic
736C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#482C2
socleC23×C7C22×D4
prime radicalC2×#90287C2
hypercenterC2×#482D7
hypocenterC7C2×#3228
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#90208C2semidirect
3. C2×C7×#482C2semidirect
4. C2×#89807C2semidirect
5. C2×#89775C2semidirect
6. #11738801C2direct (N × H)
7. C2×#89663C2semidirect
8. C2×#89646C2semidirect
9. C2×#89643C2semidirect
10. C2×#89627C2semidirect
11. C2×#89532C2semidirect
12. C2×#89532C2semidirect
13. C2×#89535C2semidirect
14. C2×#89538C2semidirect
15. C2×#89509C2semidirect
16. C2×#89490C2semidirect
29. #90208C22semidirect
42. C7×#482C22semidirect
59. #89807C22semidirect
60. #89775C22semidirect
67. #89663C22semidirect
68. #89646C22semidirect
69. #89643C22semidirect
70. #89627C22semidirect
71. #89538C22semidirect
72. #89535C22semidirect
73. #89532C22semidirect
74. #89532C22semidirect
75. #89509C22semidirect
76. #89490C22semidirect
188. C2×#482D7semidirect
317. #482C2×D7semidirect
631. C2×C7#3228semidirect
699. C7C2×#3228semidirect
733. C2#11738801direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902872
C2×#902082
C2×C7×#4822
C2×#898072
C2×#897752
#117388012
C2×#896632
C2×#896462
C2×#896432
C2×#896272
C2×#895322
C2×#895352
C2×#895382
C2×#895092
C2×#894902
C2×#32287