Finite Group Databasebeta

← C2×#11738884 #14232442

Subgroups — C2×#11738884 #14232442

Order 1792.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90332C211yesmaximal, characteristic, complemented
2C2×#90205C211yesmaximal, characteristic
3C2×C7×#483C211yesmaximal, characteristic, complemented
4C2×#89821C211yesmaximal, characteristic, complemented
5C2×#89736C211yesmaximal, characteristic, complemented
6#11738884C2116yesmaximal, direct product factor
7C2×#89642C211yesmaximal, characteristic, complemented
8C2×#89638C211yesmaximal, characteristic, complemented
9C2×#89632C211yesmaximal, characteristic, complemented
10C2×#89628C211yesmaximal, characteristic, complemented
11C2×#89579C211yesmaximal, characteristic, complemented
12C2×#89586C211yesmaximal, characteristic, complemented
13C2×#89571C211yesmaximal, characteristic, complemented
14C2×#89589C211yesmaximal, characteristic, complemented
15C2×#89500C211yesmaximal, characteristic, complemented
16C2×#89509C211yesmaximal, characteristic, complemented
17C2×C7×C22⋊Q8C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C2×#6509C2211yescharacteristic
20C2×Q8×Dic7C2211yescharacteristic
21C22×#1143C2211yescharacteristic
22C2×#6493—21no—
23C2×#6493C2211yescharacteristic
24C2×C4×C22⋊D7—21no—
25C2×C4×C22⋊D7C2211yescharacteristic
26C2×#6489C2211yescharacteristic
27C22×#1136C2211yescharacteristic
28C22×C8×D7C2211yescharacteristic
29#90332—24no—
30#90332C2218yescomplemented
31#90205—24no—
32#90205C2218yes—
33C2×#6461—21no—
34C2×#6461—21no—
35C2×#6458C2211yescharacteristic
36C2×#6457—21no—
37C2×#6456C2211yescharacteristic
38C2×#6455C2211yescharacteristic
39C2×#6455C2211yescharacteristic
40C2×#6453C2211yescharacteristic
41C2×#6451C2211yescharacteristic
42C2×#6450—21no—
43C2×#6448—21no—
44C2×#6442—21no—
45C7×#483C2218yescomplemented
46C2×C7×#106C2211yescharacteristic
47C2×C7×#106C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6392C2211yescharacteristic
56C2×#6391C2211yescharacteristic
57C2×#6389C2211yescharacteristic
58C2×Dic7⋊C8C2211yescharacteristic
59#89821C2218yescomplemented
60C2×#6383C2211yescharacteristic
61#89736C2218yescomplemented
62C2×#6382C2211yescharacteristic
63C2×#6382C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67#89642C2218yescomplemented
68#89638C2218yescomplemented
69#89632C2218yescomplemented
70#89628C2218yescomplemented
71#89589C2218yescomplemented
72#89586C2218yescomplemented
73#89579C2218yescomplemented
74#89571C2218yescomplemented
75#89509C2218yescomplemented
76#89500C2218yescomplemented
77C2×#3350—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C23×C4×C7—21no—
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7D411yescharacteristic
83C22×D28—21no—
84C22×D28C2311yescharacteristic
85C22×C4×D7—21no—
86C22×C4×D7C2311yescharacteristic
87C22×Dic14—21no—
88C22×C7×C8C2311yescharacteristic
89C22×C7×C8C2311yescharacteristic
90C7×C22⋊Q8—22no—
91C7×C22⋊Q8C2314yes—
92C2×C7×C4⋊C4—21no—
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4C2314yes—
96C2×C7×C4⋊C4C2311yescharacteristic
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C22⋊C4—21no—
100C2×C22⋊Dic7—21no—
101C2×C22⋊Dic7D411yescharacteristic
102#6509—22no—
103#6509C2314yes—
104Q8×Dic7—22no—
105Q8×Dic7C2314yes—
106C2×#1143—24no—
107C2×#1143C2314yes—
108#6493—22no—
109#6493—28no—
110#6493C2314yes—
111C4×C22⋊D7—28no—
112C4×C22⋊D7D414yes—
113C4×C22⋊D7C2314yes—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4D411yescharacteristic
121#6489—22no—
122#6489C2314yes—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7—21no—
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4D411yescharacteristic
132C2×C4×Dic7—21no—
133C2×C4×Dic7—21no—
134C2×C4×Dic7—21no—
135C2×C4×Dic7—21no—
136C2×C4×Dic7C2311yescharacteristic
137C2×#1136—24no—
138C2×#1136C2314yes—
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141C2×C8×D7—24no—
142C2×C8×D7C2314yes—
143#6461—28no—
144#6461—28no—
145#6458—22no—
146#6458C2314yes—
147#6457—28no—
148#6456—22no—
149#6456C2314yes—
150#6455—22no—
151#6455—22no—
152#6455C2314yes—
153#6455C2314yes—
154#6453—22no—
155#6453C2314yes—
156#6451—22no—
157#6451C2314yes—
158#6450—28no—
159#6448—28no—
160#6442—28no—
161C7×#106C2314yes—
162C7×#106C2314yes—
163C7×#103C2314yes—
164C7×#103C2314yes—
165C7×C22⋊C8C2314yes—
166#6409C2314yes—
167#6395C2314yes—
168#6395C2314yes—
169(C2×D7)⋊C8C2314yes—
170#6392C2314yes—
171#6391C2314yes—
172#6389C2314yes—
173Dic7⋊C8C2314yes—
174#6383C2314yes—
175#6382C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180C2×#556—71no—
181C2×#553—71no—
182#3350—716no—
183C2×#501—71no—
184C2×#485—71no—
185C2×#482—71no—
186C2×#482—71no—
187C2×#483D711yescharacteristic, complemented
188C2×#479—71no—
189C2×#476—71no—
190C2×#468—71no—
191C2×#465—71no—
192C2×#440—71no—
193C2×#435—71no—
194C2×#428—71no—
195C2×#427—71no—
196C24×C7C2×D411yescharacteristic
197C23×D7—21no—
198C23×D7C2×D411yescharacteristic
199C2×C7×Q8—21no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8C2412yes—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—24no—
210C22×C4×C7—82no—
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2411yescharacteristic
215C2×C22⋊D7—24no—
216C2×C22⋊D7—42no—
217C2×C22⋊D7—44no—
218C2×C22⋊D7C2×D414yes—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7C2×D411yescharacteristic
223C22×Dic7C2×D411yescharacteristic
224C22×Dic7C2×D411yescharacteristic
225C2×D28—22no—
226C2×D28—22no—
227C2×D28—21no—
228C2×D28—24no—
229C2×D28—82no—
230C2×D28C2412yes—
231C2×C4×D7—22no—
232C2×C4×D7—22no—
233C2×C4×D7—24no—
234C2×C4×D7—82no—
235C2×C4×D7C2×D412yes—
236C2×C4×D7C2412yes—
237C2×Dic14—24no—
238C2×Dic14—44no—
239C2×C7×C8—22no—
240C2×C7×C8—22no—
241C2×C7×C8C2412yes—
242C2×C7×C8C2412yes—
243C7×C4⋊C4—24no—
244C7×C4⋊C4—21no—
245C7×C4⋊C4—21no—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—24no—
248C7×C4⋊C4C2412yes—
249C7×C4⋊C4C2412yes—
250C7×C4⋊C4C2412yes—
251C7×C22⋊C4—24no—
252C22⋊Dic7—24no—
253C22⋊Dic7C2×D414yes—
254#1143—28no—
255(C2×D7)⋊C4—24no—
256(C2×D7)⋊C4—24no—
257(C2×D7)⋊C4—24no—
258(C2×D7)⋊C4—24no—
259(C2×D7)⋊C4—24no—
260(C2×D7)⋊C4—24no—
261(C2×D7)⋊C4C2×D414yes—
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⋊C4C2×D414yes—
274C4×Dic7—24no—
275C4×Dic7—24no—
276C4×Dic7—24no—
277C4×Dic7—24no—
278C4×Dic7C2×D412yes—
279C4×Dic7C2412yes—
280#1136—28no—
281C2×C7⋊C8—22no—
282C2×C7⋊C8#4114yes—
283C2×C7⋊C8C2412yes—
284C2×C7⋊C8C2412yes—
285C8×D7—28no—
286C22×SD16—71no—
287C22×M16—71no—
288C23×C8—71no—
289#556—78no—
290#556—144no—
291#553—78no—
292#553—144no—
293C2×C4⋊Q8—71no—
294C2×#126—141no—
295C2×#126—141no—
296C2×#126—141no—
297C2×#125—71no—
298C2×#124—141no—
299C2×#123—141no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8C2×D711yescharacteristic
302C2×#121—71no—
303C2×#121—71no—
304C2×#121—141no—
305C2×C4×Q8—71no—
306C2×C4×Q8—141no—
307C2×C4×D4—71no—
308C2×C4×D4—71no—
309C2×C4×D4—141no—
310C2×#117—71no—
311C2×#117—71no—
312C2×#117—71no—
313C22×C4⋊C4C2×D711yescharacteristic
314#501—78no—
315#485—78no—
316#483C2×D718yescomplemented
317#482—78no—
318#482—78no—
319#479—78no—
320#476—78no—
321#468—78no—
322#465—78no—
323#440—78no—
324#435—78no—
325#428—78no—
326#427—78no—
327C2×#107—71no—
328C2×#107—71no—
329C2×#107—71no—
330C2×#107—71no—
331C2×#106—71no—
332C2×#106—71no—
333C2×#106—71no—
334C2×#106C2×D711yescharacteristic
335C2×#106C2×D711yescharacteristic
336C2×C4⋊C8—71no—
337C2×#103—71no—
338C2×#103C2×D711yescharacteristic
339C2×#103C2×D711yescharacteristic
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×C22⋊C8—71no—
344C2×C22⋊C8C2×D711yescharacteristic
345C2×#97—71no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7C22×D412yes—
350C23×C7C22×D411yescharacteristic
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—42no—
356C22×D7—42no—
357C22×D7—42no—
358C22×D7C22×D412yes—
359C7×Q8—22no—
360C7×Q8—22no—
361C7×Q8—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—22no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—42no—
374C2×C4×C7—84no—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D411yescharacteristic
377C2×C4×C7C2×#4112yes—
378C2×C4×C72−1+412yes—
379C2×C4×C7C2511yescharacteristic
380C22⋊D7—44no—
381C22⋊D7—48no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7C22×D412yes—
392C2×Dic7C22×D412yes—
393C2×Dic7C22×D412yes—
394D28—22no—
395D28—22no—
396D28—42no—
397D28—84no—
398C4×D7—24no—
399C4×D7—22no—
400C4×D7—22no—
401C4×D7—84no—
402Dic14—48no—
403C7×C8—22no—
404C7×C8—22no—
405C7⋊C8—22no—
406C7⋊C8C2×#4114yes—
407C22×Q8—141no—
408C22×Q8C22×D711yescharacteristic
409C22×D4—71no—
410C22×D4—71no—
411C22×D4—141no—
412C22×D4—141no—
413C23×C4—21no—
414C23×C4—71no—
415C23×C4—141no—
416C23×C4C22×D711yescharacteristic
417C2×SD16—74no—
418C2×SD16—144no—
419C2×M16—74no—
420C2×M16—144no—
421C22×C8—71no—
422C22×C8—71no—
423C22×C8—74no—
424C22×C8—144no—
425C22×C8C22×D711yescharacteristic
426C22×C8C22×D711yescharacteristic
427C4⋊Q8—74no—
428C4⋊Q8—142no—
429#126—148no—
430#126—148no—
431#126—148no—
432#125—74no—
433#125—142no—
434#124—148no—
435#123—148no—
436C22⋊Q8—22no—
437C22⋊Q8—74no—
438C22⋊Q8—142no—
439C22⋊Q8C22×D714yes—
440#121—74no—
441#121—74no—
442#121—142no—
443#121—148no—
444#121—142no—
445C4×Q8—74no—
446C4×Q8—142no—
447C4×Q8—148no—
448C4×D4—74no—
449C4×D4—74no—
450C4×D4—74no—
451C4×D4—142no—
452C4×D4—148no—
453#117—74no—
454#117—74no—
455#117—74no—
456#117—142no—
457#117—142no—
458#117—142no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—71no—
463C2×C4⋊C4—71no—
464C2×C4⋊C4—71no—
465C2×C4⋊C4—71no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4C22×D711yescharacteristic
472C2×C4⋊C4C22×D711yescharacteristic
473C2×C4⋊C4C22×D714yes—
474C2×C4⋊C4C22×D711yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—71no—
477C2×C22⋊C4—71no—
478C2×C22⋊C4—141no—
479C2×C22⋊C4—141no—
480C2×C22⋊C4—141no—
481C2×C22⋊C4—141no—
482C2×C22⋊C4—141no—
483C2×C22⋊C4—141no—
484C2×C22⋊C4—141no—
485C2×C42—71no—
486C2×C42—141no—
487C2×C42—141no—
488C2×C42—141no—
489C2×C42—141no—
490#107—74no—
491#107—74no—
492#107—74no—
493#107—74no—
494#106—74no—
495#106—74no—
496#106—74no—
497#106C22×D714yes—
498#106C22×D714yes—
499C4⋊C8—74no—
500#103—74no—
501#103C22×D714yes—
502#103C22×D714yes—
503#102—74no—
504#102—74no—
505#102—74no—
506C22⋊C8—74no—
507C22⋊C8C22×D714yes—
508#97—74no—
509C22×C7—22no—
510C22×C7—22no—
511C22×C7—22no—
512C22×C7—44no—
513C22×C7#54712yes—
514C22×C7#57512yes—
515C22×C7#57712yes—
516C22×C7C23×D411yescharacteristic
517C2×D7—22no—
518C2×D7—22no—
519C2×D7—22no—
520C2×D7—44no—
521C2×D7—42no—
522C2×D7—42no—
523C2×D7—42no—
524C2×D7—84no—
525C4×C7—22no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7—42no—
529C4×C7—42no—
530C4×C7#54712yes—
531C4×C7C22×#4111yescharacteristic
532C4×C7C2×2−1+411yescharacteristic
533Dic7—22no—
534Dic7—22no—
535Dic7—22no—
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539C24—71no—
540C24—141no—
541C24D4×D711yescharacteristic
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—144no—
546C2×Q8—284no—
547C2×Q8C23×D712yes—
548C2×D4—74no—
549C2×D4—72no—
550C2×D4—144no—
551C2×D4—144no—
552C2×D4—141no—
553C2×D4—142no—
554C2×D4—142no—
555C2×D4—282no—
556C2×D4—284no—
557C2×D4—562no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—71no—
566C22×C4—71no—
567C22×C4—71no—
568C22×C4—72no—
569C22×C4—72no—
570C22×C4—82no—
571C22×C4—144no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—141no—
575C22×C4—141no—
576C22×C4—141no—
577C22×C4—562no—
578C22×C4D4×D712yes—
579C22×C4D4×D711yescharacteristic
580C22×C4C23×D712yes—
581C22×C4C23×D711yescharacteristic
582SD16—148no—
583M16—148no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—74no—
587C2×C8—72no—
588C2×C8—72no—
589C2×C8—148no—
590C2×C8—142no—
591C2×C8C23×D712yes—
592C2×C8C23×D712yes—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—74no—
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—141no—
608C4⋊C4—141no—
609C4⋊C4—141no—
610C4⋊C4C23×D712yes—
611C4⋊C4C23×D712yes—
612C4⋊C4C23×D712yes—
613C22⋊C4—24no—
614C22⋊C4—74no—
615C22⋊C4—74no—
616C22⋊C4—144no—
617C22⋊C4—144no—
618C22⋊C4—144no—
619C22⋊C4—144no—
620C22⋊C4—144no—
621C22⋊C4—144no—
622C22⋊C4—144no—
623C42—72no—
624C42—72no—
625C42—144no—
626C42—144no—
627C42—144no—
628C42—144no—
629C2×C7—42no—
630C2×C7#335014yescomplemented
631C2×C7C2×#54711yescharacteristic
632C2×C7C2×#57511yescharacteristic
633C2×C7C2×#57711yescharacteristic
634D7—42no—
635D7—82no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—72no—
640C23—142no—
641C23—142no—
642C23—142no—
643C23—142no—
644C23—282no—
645C23—282no—
646C23—282no—
647C23C2×D4×D712yes—
648C23C2×D4×D711yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—42no—
652Q8—288no—
653D4—142no—
654D4—142no—
655D4—284no—
656D4—288no—
657D4—282no—
658D4—564no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—72no—
672C2×C4—72no—
673C2×C4—72no—
674C2×C4—84no—
675C2×C4—142no—
676C2×C4—142no—
677C2×C4—142no—
678C2×C4—144no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—282no—
685C2×C4—282no—
686C2×C4—282no—
687C2×C4—564no—
688C2×C4C2×D4×D712yes—
689C2×C4C2×D4×D711yescharacteristic
690C2×C4D7×#4112yes—
691C2×C4#655412yes—
692C2×C4C24×D711yescharacteristic
693C8—22no—
694C8—22no—
695C8—74no—
696C8—142no—
697C7C2×#335011yescharacteristic, complemented, Sylow
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—142no—
703C22—142no—
704C22—142no—
705C22—284no—
706C22—282no—
707C22—282no—
708C22—282no—
709C22—564no—
710C22#9034612yes—
711C22#9045312yes—
712C22#9046812yes—
713C22C22×D4×D711yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—142no—
720C4—142no—
721C4—142no—
722C4—282no—
723C4—282no—
724C4—282no—
725C4#9034612yes—
726C4C2×D7×#4111yescharacteristic
727C4C2×#655411yescharacteristic
728C2—42no—
729C2—282no—
730C2—562no—
731C2#1173888414yesdirect product factor
732C2C2×#9034611yescharacteristic
733C2C2×#9045311yescharacteristic
734C2C2×#9046811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#483C2
socleC23×C7C22×D4
prime radicalC2×#90205C2
hypercenterC2×#483D7
hypocenterC7C2×#3350
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#90332C2semidirect
3. C2×C7×#483C2semidirect
4. C2×#89821C2semidirect
5. C2×#89736C2semidirect
6. #11738884C2direct (N × H)
7. C2×#89642C2semidirect
8. C2×#89638C2semidirect
9. C2×#89632C2semidirect
10. C2×#89628C2semidirect
11. C2×#89579C2semidirect
12. C2×#89586C2semidirect
13. C2×#89571C2semidirect
14. C2×#89589C2semidirect
15. C2×#89500C2semidirect
16. C2×#89509C2semidirect
30. #90332C22semidirect
45. C7×#483C22semidirect
59. #89821C22semidirect
61. #89736C22semidirect
67. #89642C22semidirect
68. #89638C22semidirect
69. #89632C22semidirect
70. #89628C22semidirect
71. #89589C22semidirect
72. #89586C22semidirect
73. #89579C22semidirect
74. #89571C22semidirect
75. #89509C22semidirect
76. #89500C22semidirect
187. C2×#483D7semidirect
316. #483C2×D7semidirect
630. C2×C7#3350semidirect
697. C7C2×#3350semidirect
731. C2#11738884direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903322
C2×#902052
C2×C7×#4832
C2×#898212
C2×#897362
#117388842
C2×#896422
C2×#896382
C2×#896322
C2×#896282
C2×#895792
C2×#895862
C2×#895712
C2×#895892
C2×#895002
C2×#895092
C2×#33507