Finite Group Databasebeta

← C2×#11738448 #14226729

Subgroups — C2×#11738448 #14226729

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×#90424C211yesmaximal, characteristic
2C2×#90274C211yesmaximal, characteristic, complemented
3C2×C7×#475C211yesmaximal, characteristic, complemented
4C2×#89863C211yesmaximal, characteristic, complemented
5C2×#89800C211yesmaximal, characteristic, complemented
6#11738448C2116yesmaximal, direct product factor
7C2×#89629C211yesmaximal, characteristic, complemented
8C2×#89643C211yesmaximal, characteristic, complemented
9C2×#89640C211yesmaximal, characteristic, complemented
10C2×#89636C211yesmaximal, characteristic
11C2×#89617C211yesmaximal, characteristic, complemented
12C2×#89611C211yesmaximal, characteristic, complemented
13C2×#89565C211yesmaximal, characteristic, complemented
14C2×#89590C211yesmaximal, characteristic, complemented
15C2×#89584C211yesmaximal, characteristic
16C2×#89585C211yesmaximal, characteristic, complemented
17C2×C7×C4⋊Q8C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C2×#6510—21no—
20C2×#6509—21no—
21C2×#6509C2211yescharacteristic
22C2×#6507C2211yescharacteristic
23C22×#1144C2211yescharacteristic
24C22×#1143C2211yescharacteristic
25C22×Dic28C2211yescharacteristic
26C22×#1132C2211yescharacteristic
27C22×#1131C2211yescharacteristic
28C22×C8×D7C2211yescharacteristic
29#90424—24no—
30#90424C2218yes—
31#90274—24no—
32#90274C2218yescomplemented
33C2×#6461—21no—
34C2×#6461—21no—
35C2×#6460C2211yescharacteristic
36C2×#6460C2211yescharacteristic
37C2×#6458C2211yescharacteristic
38C2×#6457—21no—
39C2×#6456C2211yescharacteristic
40C2×#6453C2211yescharacteristic
41C2×#6452—21no—
42C2×#6450C2211yescharacteristic
43C2×#6439—21no—
44C2×#6438C2211yescharacteristic
45C2×#6435C2211yescharacteristic
46C2×#6433—21no—
47C2×C4×Dic14C2211yescharacteristic
48C7×#475C2218yescomplemented
49C2×C7×#106C2211yescharacteristic
50C2×C7×#106C2211yescharacteristic
51C2×C7×C4⋊C8C2211yescharacteristic
52C2×C7×#103C2211yescharacteristic
53C2×C7×#103C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×Dic7⋊C8C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58#89863C2218yescomplemented
59#89800C2218yescomplemented
60C2×#6384C2211yescharacteristic
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×C4⋊(C7⋊C8)C2211yescharacteristic
67#89643C2218yescomplemented
68#89640C2218yescomplemented
69#89636C2218yes—
70#89629C2218yescomplemented
71#89617C2218yescomplemented
72#89611C2218yescomplemented
73#89590C2218yescomplemented
74#89585C2218yescomplemented
75#89584C2218yes—
76#89565C2218yescomplemented
77C2×#3258—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×D28—21no—
81C22×D28C2311yescharacteristic
82C22×C4×D7—21no—
83C22×C4×D7C2311yescharacteristic
84C22×Dic14C2311yescharacteristic
85C22×Dic14C2311yescharacteristic
86C22×C7×C8C2311yescharacteristic
87C22×C7×C8C2311yescharacteristic
88C7×C4⋊Q8—22no—
89C7×C4⋊Q8C2314yes—
90C4×C7×Q8—22no—
91C4×C7×Q8C2314yes—
92C2×C7×C4⋊C4—21no—
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4C2311yescharacteristic
95C2×C7×C4⋊C4C2311yescharacteristic
96C2×C7×C4⋊C4C2311yescharacteristic
97C2×C42×C7—21no—
98C2×C42×C7C2311yescharacteristic
99#6510—28no—
100#6509—22no—
101#6509—28no—
102#6509C2314yes—
103#6507—22no—
104#6507C2314yes—
105C2×#1144—42no—
106C2×#1144C2314yes—
107C2×#1143—42no—
108C2×#1143C2314yes—
109C2×(C2×D7)⋊C4—21no—
110C2×(C2×D7)⋊C4—21no—
111C2×(C2×D7)⋊C4—21no—
112C2×(C2×D7)⋊C4—21no—
113C2×(C2×D7)⋊C4—21no—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4D411yescharacteristic
117C2×(C2×D7)⋊C4D411yescharacteristic
118C2×C4⋊Dic7—21no—
119C2×C4⋊Dic7—21no—
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7C2311yescharacteristic
122C2×Dic7⋊C4—21no—
123C2×Dic7⋊C4—21no—
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4D411yescharacteristic
129C2×Dic7⋊C4D411yescharacteristic
130C2×C4×Dic7—21no—
131C2×C4×Dic7—21no—
132C2×C4×Dic7C2311yescharacteristic
133C22×C7⋊C8C2311yescharacteristic
134C22×C7⋊C8C2311yescharacteristic
135C2×Dic28—42no—
136C2×Dic28C2314yes—
137C2×#1132—42no—
138C2×#1132C2314yes—
139C2×#1131—42no—
140C2×#1131C2314yes—
141C2×C8×D7—42no—
142C2×C8×D7C2314yes—
143#6461—28no—
144#6461—28no—
145#6460—22no—
146#6460—22no—
147#6460C2314yes—
148#6460C2314yes—
149#6458—22no—
150#6458C2314yes—
151#6457—28no—
152#6456—22no—
153#6456C2314yes—
154#6453—22no—
155#6453C2314yes—
156#6452—28no—
157#6450—22no—
158#6450C2314yes—
159#6439—28no—
160#6438—22no—
161#6438C2314yes—
162#6435D414yes—
163#6435C2314yes—
164#6433—28no—
165C4×Dic14—22no—
166C4×Dic14C2314yes—
167C7×#106C2314yes—
168C7×#106C2314yes—
169C7×C4⋊C8C2314yes—
170C7×#103C2314yes—
171C7×#103C2314yes—
172#6395C2314yes—
173#6390C2314yes—
174Dic7⋊C8C2314yes—
175Dic7⋊C8C2314yes—
176#6384C2314yes—
177#6384C2314yes—
178#6384C2314yes—
179#6383C2314yes—
180#6381C2314yes—
181#6381C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183C2×#542—71no—
184C2×#541—71no—
185#3258—716no—
186C2×#479—71no—
187C2×#477—71no—
188C2×#475D711yescharacteristic, complemented
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×#424—71no—
199C23×D7—21no—
200C23×D7C2×D411yescharacteristic
201C2×C7×Q8—21no—
202C2×C7×Q8—24no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8—82no—
206C2×C7×Q8C2412yes—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2411yescharacteristic
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7C2×D411yescharacteristic
218C22×Dic7C2×D411yescharacteristic
219C22×Dic7C2×D411yescharacteristic
220C2×D28—22no—
221C2×D28—22no—
222C2×D28—21no—
223C2×D28—24no—
224C2×D28—82no—
225C2×D28C2412yes—
226C2×C4×D7—22no—
227C2×C4×D7—22no—
228C2×C4×D7—24no—
229C2×C4×D7—82no—
230C2×C4×D7C2×D412yes—
231C2×C4×D7C2412yes—
232C2×Dic14—22no—
233C2×Dic14—22no—
234C2×Dic14—22no—
235C2×Dic14—22no—
236C2×Dic14—21no—
237C2×Dic14—21no—
238C2×Dic14C2412yes—
239C2×Dic14C2412yes—
240C2×C7×C8—22no—
241C2×C7×C8—22no—
242C2×C7×C8C2412yes—
243C2×C7×C8C2412yes—
244C7×C4⋊C4—21no—
245C7×C4⋊C4—24no—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4C2412yes—
250C7×C4⋊C4C2412yes—
251C7×C4⋊C4C2412yes—
252C42×C7—24no—
253C42×C7C2×D412yes—
254C42×C7C2412yes—
255#1144—44no—
256#1143—44no—
257(C2×D7)⋊C4—24no—
258(C2×D7)⋊C4—24no—
259(C2×D7)⋊C4—24no—
260(C2×D7)⋊C4—24no—
261(C2×D7)⋊C4—24no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4C2×D414yes—
265(C2×D7)⋊C4C2×D414yes—
266C4⋊Dic7—21no—
267C4⋊Dic7—24no—
268C4⋊Dic7—24no—
269C4⋊Dic7—24no—
270C4⋊Dic7C2412yes—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4C2×D414yes—
278Dic7⋊C4C2×D414yes—
279C4×Dic7—24no—
280C4×Dic7—24no—
281C4×Dic7C2×D412yes—
282C4×Dic7C2412yes—
283C2×C7⋊C8—22no—
284C2×C7⋊C8—22no—
285C2×C7⋊C8C2412yes—
286C2×C7⋊C8C2412yes—
287Dic28—44no—
288#1132—44no—
289#1131—44no—
290C8×D7—44no—
291C22×Q16—71no—
292C22×Q16—71no—
293C22×SD16—71no—
294C22×SD16—71no—
295C22×M16—71no—
296C23×C8—71no—
297#542—78no—
298#542—144no—
299#541—78no—
300#541—144no—
301C2×C4⋊Q8—71no—
302C2×C4⋊Q8C2×D711yescharacteristic
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×Q8C2×D711yescharacteristic
320C2×C4×D4—71no—
321C2×#117—71no—
322#479—78no—
323#478—78no—
324#477—78no—
325#475C2×D718yescomplemented
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×#106C2×D711yescharacteristic
337C2×#106C2×D711yescharacteristic
338#424—78no—
339C2×C4⋊C8—71no—
340C2×C4⋊C8—71no—
341C2×C4⋊C8—71no—
342C2×C4⋊C8C2×D711yescharacteristic
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103C2×D711yescharacteristic
348C2×#103C2×D711yescharacteristic
349C2×#102—71no—
350C2×#102—71no—
351C23×C7C22×D411yescharacteristic
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—42no—
357C22×D7—42no—
358C22×D7—42no—
359C22×D7C22×D412yes—
360C7×Q8—22no—
361C7×Q8—22no—
362C7×Q8—42no—
363C7×Q8—84no—
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×C7C22×D412yes—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D411yescharacteristic
377C2×C4×C7H(5,𝔽2)12yes—
378C2×C4×C72−1+412yes—
379C2×C4×C7C2511yescharacteristic
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7C22×D412yes—
390C2×Dic7C22×D412yes—
391C2×Dic7C22×D412yes—
392D28—22no—
393D28—22no—
394D28—42no—
395D28—84no—
396C4×D7—24no—
397C4×D7—22no—
398C4×D7—22no—
399C4×D7—84no—
400Dic14—22no—
401Dic14—22no—
402Dic14—22no—
403Dic14—22no—
404Dic14—42no—
405Dic14—42no—
406C7×C8—22no—
407C7×C8—22no—
408C7⋊C8—22no—
409C7⋊C8—22no—
410C22×Q8—21no—
411C22×Q8—71no—
412C22×Q8—71no—
413C22×Q8C22×D711yescharacteristic
414C22×D4—71no—
415C22×D4—141no—
416C23×C4—71no—
417C23×C4—141no—
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—74no—
427C2×M16—282no—
428C22×C8—71no—
429C22×C8—71no—
430C22×C8—74no—
431C22×C8—282no—
432C22×C8C22×D711yescharacteristic
433C22×C8C22×D711yescharacteristic
434C4⋊Q8—22no—
435C4⋊Q8—74no—
436C4⋊Q8—142no—
437C4⋊Q8C22×D714yes—
438#126—148no—
439#126—148no—
440#126—148no—
441#125—74no—
442#125—148no—
443#125—142no—
444#125—148no—
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—148no—
455C22⋊Q8—142no—
456#121—74no—
457#121—142no—
458C4×Q8—22no—
459C4×Q8—74no—
460C4×Q8—74no—
461C4×Q8—142no—
462C4×Q8—142no—
463C4×Q8C22×D714yes—
464C4×D4—74no—
465C4×D4—142no—
466#117—74no—
467#117—74no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—71no—
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⋊C4C22×D711yescharacteristic
483C2×C4⋊C4C22×D711yescharacteristic
484C2×C4⋊C4C22×D711yescharacteristic
485C2×C22⋊C4—71no—
486C2×C22⋊C4—71no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C42—21no—
495C2×C42—71no—
496C2×C42—141no—
497C2×C42—141no—
498C2×C42C22×D711yescharacteristic
499#107—74no—
500#107—74no—
501#106C22×D714yes—
502#106C22×D714yes—
503C4⋊C8—74no—
504C4⋊C8—74no—
505C4⋊C8—74no—
506C4⋊C8C22×D714yes—
507#103—74no—
508#103—74no—
509#103—74no—
510#103—74no—
511#103C22×D714yes—
512#103C22×D714yes—
513#102—74no—
514#102—74no—
515C22×C7#53712yes—
516C22×C7#57712yes—
517C22×C7#57812yes—
518C22×C7C23×D411yescharacteristic
519C2×D7—22no—
520C2×D7—22no—
521C2×D7—22no—
522C2×D7—44no—
523C2×D7—42no—
524C2×D7—42no—
525C2×D7—42no—
526C2×D7—84no—
527C4×C7—22no—
528C4×C7—22no—
529C4×C7—42no—
530C4×C7—42no—
531C4×C7—42no—
532C4×C7—42no—
533C4×C7#53712yes—
534C4×C7C2×H(5,𝔽2)11yescharacteristic
535C4×C7C2×2−1+411yescharacteristic
536Dic7—22no—
537Dic7—22no—
538Dic7—22no—
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542C24—71no—
543C24—141no—
544C2×Q8—21no—
545C2×Q8—24no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—72no—
549C2×Q8—72no—
550C2×Q8—82no—
551C2×Q8—141no—
552C2×Q8—141no—
553C2×Q8—142no—
554C2×Q8—142no—
555C2×Q8—142no—
556C2×Q8—142no—
557C2×Q8C23×D712yes—
558C2×D4—72no—
559C2×D4—144no—
560C2×D4—141no—
561C2×D4—142no—
562C2×D4—142no—
563C2×D4—562no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—71no—
569C22×C4—71no—
570C22×C4—71no—
571C22×C4—72no—
572C22×C4—72no—
573C22×C4—144no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—141no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—562no—
580C22×C4D4×D711yescharacteristic
581C22×C4D4×D711yescharacteristic
582C22×C4C23×D711yescharacteristic
583Q16—284no—
584Q16—284no—
585SD16—284no—
586SD16—284no—
587M16—284no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—72no—
591C2×C8—72no—
592C2×C8—142no—
593C2×C8—142no—
594C2×C8—284no—
595C2×C8C23×D712yes—
596C2×C8C23×D712yes—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—74no—
603C4⋊C4—74no—
604C4⋊C4—72no—
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—144no—
614C4⋊C4—141no—
615C4⋊C4C23×D712yes—
616C4⋊C4C23×D712yes—
617C4⋊C4C23×D712yes—
618C22⋊C4—74no—
619C22⋊C4—74no—
620C22⋊C4—144no—
621C22⋊C4—144no—
622C22⋊C4—144no—
623C22⋊C4—144no—
624C22⋊C4—144no—
625C22⋊C4—144no—
626C22⋊C4—144no—
627C42—24no—
628C42—72no—
629C42—72no—
630C42—144no—
631C42—144no—
632C42D4×D712yes—
633C42C23×D712yes—
634C2×C7#325814yescomplemented
635C2×C7C2×#53711yescharacteristic
636C2×C7C2×#57711yescharacteristic
637C2×C7C2×#57811yescharacteristic
638D7—42no—
639D7—82no—
640C23—72no—
641C23—142no—
642C23—142no—
643C23—142no—
644C23—142no—
645C23—282no—
646C23—282no—
647C23—282no—
648C23C2×D4×D711yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—42no—
652Q8—84no—
653Q8—142no—
654Q8—142no—
655Q8—142no—
656Q8—142no—
657Q8—282no—
658Q8—282no—
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—22no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—72no—
674C2×C4—72no—
675C2×C4—72no—
676C2×C4—142no—
677C2×C4—142no—
678C2×C4—142no—
679C2×C4—144no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—282no—
686C2×C4—282no—
687C2×C4—282no—
688C2×C4—564no—
689C2×C4C2×D4×D712yes—
690C2×C4C2×D4×D712yes—
691C2×C4C2×D4×D711yescharacteristic
692C2×C4#655112yes—
693C2×C4#655312yes—
694C2×C4C24×D711yescharacteristic
695C8—22no—
696C8—22no—
697C8—142no—
698C8—142no—
699C7C2×#325811yescharacteristic, complemented, Sylow
700C22—142no—
701C22—142no—
702C22—142no—
703C22—284no—
704C22—282no—
705C22—282no—
706C22—282no—
707C22—564no—
708C22#9032012yes—
709C22#9045312yes—
710C22#9047012yes—
711C22C22×D4×D711yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—142no—
719C4—142no—
720C4—142no—
721C4—282no—
722C4—282no—
723C4—282no—
724C4#9032012yes—
725C4C2×#655111yescharacteristic
726C4C2×#655311yescharacteristic
727C2—282no—
728C2—562no—
729C2#1173844814yesdirect product factor
730C2C2×#9032011yescharacteristic
731C2C2×#9045311yescharacteristic
732C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#475C2
socleC23×C7C22×D4
prime radicalC2×#6458C22
hypercenterC2×#475D7
hypocenterC7C2×#3258
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×#90274C2semidirect
3. C2×C7×#475C2semidirect
4. C2×#89863C2semidirect
5. C2×#89800C2semidirect
6. #11738448C2direct (N × H)
7. C2×#89629C2semidirect
8. C2×#89643C2semidirect
9. C2×#89640C2semidirect
11. C2×#89617C2semidirect
12. C2×#89611C2semidirect
13. C2×#89565C2semidirect
14. C2×#89590C2semidirect
16. C2×#89585C2semidirect
32. #90274C22semidirect
48. C7×#475C22semidirect
58. #89863C22semidirect
59. #89800C22semidirect
67. #89643C22semidirect
68. #89640C22semidirect
70. #89629C22semidirect
71. #89617C22semidirect
72. #89611C22semidirect
73. #89590C22semidirect
74. #89585C22semidirect
76. #89565C22semidirect
188. C2×#475D7semidirect
325. #475C2×D7semidirect
634. C2×C7#3258semidirect
699. C7C2×#3258semidirect
729. C2#11738448direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904242
C2×#902742
C2×C7×#4752
C2×#898632
C2×#898002
#117384482
C2×#896292
C2×#896432
C2×#896402
C2×#896362
C2×#896172
C2×#896112
C2×#895652
C2×#895902
C2×#895842
C2×#895852
C2×#32587