Finite Group Databasebeta

← C2×#11739120 #14233528

Subgroups — C2×#11739120 #14233528

Order 1792.

1906 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90413C211yesmaximal, characteristic, complemented
2C2×#90372C211yesmaximal, characteristic
3C2×C7×#489C211yesmaximal, characteristic, complemented
4C2×#89859C211yesmaximal, characteristic, complemented
5C2×#89826C211yesmaximal, characteristic, complemented
6#11739120C2116yesmaximal, direct product factor
7C2×#89570C211yesmaximal, characteristic, complemented
8C2×#89567C211yesmaximal, characteristic, complemented
9C2×#89566C211yesmaximal, characteristic, complemented
10C2×#89562C211yesmaximal, characteristic, complemented
11C2×#89534C211yesmaximal, characteristic
12C2×#89532C211yesmaximal, characteristic
13C2×#89531C211yesmaximal, characteristic, complemented
14C2×#89529C211yesmaximal, characteristic, complemented
15C2×#89482C211yesmaximal, characteristic, complemented
16C2×#89473C211yesmaximal, characteristic, complemented
17C2×C7×C4⋊Q8C2211yescharacteristic
18C2×C7×#124C2211yescharacteristic
19C2×#6510C2211yescharacteristic
20C2×Q8×Dic7C2211yescharacteristic
21C2×#6507—21no—
22C2×#6507—21no—
23C22×#1144C2211yescharacteristic
24C2×#6503C2211yescharacteristic
25C2×D4×Dic7C2211yescharacteristic
26C22×#1142C2211yescharacteristic
27C22×#1132C2211yescharacteristic
28#90413—24no—
29#90413C2218yescomplemented
30#90372—24no—
31#90372C2218yes—
32C2×#6451—21no—
33C2×#6451C2211yescharacteristic
34C2×#6451C2211yescharacteristic
35C2×#6450—21no—
36C2×#6450C2211yescharacteristic
37C2×#6450C2211yescharacteristic
38C2×#6449—21no—
39C2×#6448—21no—
40C2×#6446—21no—
41C2×(C22⋊D7)⋊C4—21no—
42C2×C4×D28C2211yescharacteristic
43C2×C4×Dic14C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×#489C2218yescomplemented
46C2×C7×#103C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×#97C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×#6392C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×#6389C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×Dic7⋊C8C2211yescharacteristic
59C2×C8×Dic7C2211yescharacteristic
60#89859C2218yescomplemented
61#89826C2218yescomplemented
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×C4⋊(C7⋊C8)C2211yescharacteristic
67#89570C2218yescomplemented
68#89567C2218yescomplemented
69#89566C2218yescomplemented
70#89562C2218yescomplemented
71#89534C2218yes—
72#89532C2218yes—
73#89531C2218yescomplemented
74#89529C2218yescomplemented
75#89482C2218yescomplemented
76#89473C2218yescomplemented
77C2×#3375—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C23×Dic7—21no—
84C22×D28C2311yescharacteristic
85C22×C4×D7—21no—
86C22×Dic14—21no—
87C22×Dic14—21no—
88C22×Dic14D411yescharacteristic
89C22×Dic14C2311yescharacteristic
90C22×C7×C8C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C7×C4⋊Q8—22no—
93C7×C4⋊Q8C2314yes—
94C7×#124—22no—
95C7×#124C2314yes—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C22⋊C4—21no—
100C2×C7×C22⋊C4—21no—
101C2×C42×C7C2311yescharacteristic
102C2×C22⋊Dic7—21no—
103#6510—22no—
104#6510C2314yes—
105Q8×Dic7—22no—
106Q8×Dic7C2314yes—
107#6507—28no—
108#6507—28no—
109C2×#1144—24no—
110C2×#1144C2314yes—
111#6503—22no—
112#6503C2314yes—
113D4×Dic7—22no—
114D4×Dic7C2314yes—
115C2×#1142—24no—
116C2×#1142C2314yes—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7D411yescharacteristic
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×Dic7⋊C4D411yescharacteristic
130C2×Dic7⋊C4D411yescharacteristic
131C2×C4×Dic7—21no—
132C2×C4×Dic7—21no—
133C2×C4×Dic7—21no—
134C2×C4×Dic7—21no—
135C2×C4×Dic7C2311yescharacteristic
136C2×C4×Dic7C2311yescharacteristic
137C22×C7⋊C8C2311yescharacteristic
138C22×C7⋊C8C2311yescharacteristic
139C2×#1132—24no—
140C2×#1132C2314yes—
141#6451—28no—
142#6451—22no—
143#6451—22no—
144#6451C2314yes—
145#6451C2314yes—
146#6450—28no—
147#6450—22no—
148#6450—22no—
149#6450C2314yes—
150#6450C2314yes—
151#6449—28no—
152#6448—28no—
153#6446—28no—
154(C22⋊D7)⋊C4—28no—
155C4×D28—22no—
156C4×D28C2314yes—
157C4×Dic14—22no—
158C4×Dic14D414yes—
159C4×Dic14C2314yes—
160C4×Dic14C2314yes—
161C7×#103C2314yes—
162C7×#103C2314yes—
163C7×#102C2314yes—
164C7×#102C2314yes—
165C7×#97C2314yes—
166#6409C2314yes—
167#6406C2314yes—
168#6395C2314yes—
169#6392C2314yes—
170#6390C2314yes—
171#6389C2314yes—
172Dic7⋊C8C2314yes—
173Dic7⋊C8C2314yes—
174C8×Dic7C2314yes—
175#6383C2314yes—
176#6383C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179C4⋊(C7⋊C8)C2314yes—
180C2×#559—71no—
181C2×Q82—71no—
182#3375—716no—
183C2×#489—71no—
184C2×#489D711yescharacteristic, complemented
185C2×#486—71no—
186C2×#477—71no—
187C2×#474—71no—
188C2×#474—71no—
189C2×#464—71no—
190C2×#464—71no—
191C2×#460—71no—
192C2×#446—71no—
193C2×#440—71no—
194C2×#440—71no—
195C2×C4×Q16—71no—
196C24×C7—21no—
197C23×D7—21no—
198C2×C7×Q8—21no—
199C2×C7×Q8—24no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8—82no—
203C2×C7×Q8C2412yes—
204C2×C7×D4—21no—
205C2×C7×D4—22no—
206C2×C7×D4—22no—
207C2×C7×D4C2412yes—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2411yescharacteristic
214C2×C22⋊D7—24no—
215C2×C22⋊D7—24no—
216C2×C22⋊D7—44no—
217C2×C22⋊D7—82no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—24no—
222C22×Dic7—82no—
223C22×Dic7C2×D411yescharacteristic
224C22×Dic7C2×D411yescharacteristic
225C22×Dic7C2×D411yescharacteristic
226C22×Dic7C2×D411yescharacteristic
227C2×D28—22no—
228C2×D28—22no—
229C2×D28—21no—
230C2×D28C2412yes—
231C2×C4×D7—24no—
232C2×C4×D7—82no—
233C2×Dic14—21no—
234C2×Dic14—22no—
235C2×Dic14—24no—
236C2×Dic14—24no—
237C2×Dic14—24no—
238C2×Dic14—82no—
239C2×Dic14—82no—
240C2×Dic14C2×D414yes—
241C2×Dic14#4114yes—
242C2×Dic14C2412yes—
243C2×C7×C8—22no—
244C2×C7×C8—22no—
245C2×C7×C8C2412yes—
246C2×C7×C8C2412yes—
247C7×C4⋊C4—24no—
248C7×C4⋊C4—21no—
249C7×C4⋊C4—21no—
250C7×C4⋊C4C2412yes—
251C7×C4⋊C4C2412yes—
252C7×C22⋊C4—24no—
253C7×C22⋊C4—24no—
254C42×C7C2×D412yes—
255C42×C7C2412yes—
256C22⋊Dic7—24no—
257#1144—28no—
258#1142—28no—
259(C2×D7)⋊C4—24no—
260(C2×D7)⋊C4—24no—
261(C2×D7)⋊C4—24no—
262C4⋊Dic7—21no—
263C4⋊Dic7—21no—
264C4⋊Dic7—24no—
265C4⋊Dic7C2×D414yes—
266C4⋊Dic7C2412yes—
267C4⋊Dic7C2412yes—
268Dic7⋊C4—24no—
269Dic7⋊C4—24no—
270Dic7⋊C4—24no—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4C2×D414yes—
274Dic7⋊C4C2×D414yes—
275C4×Dic7—24no—
276C4×Dic7—24no—
277C4×Dic7—24no—
278C4×Dic7—24no—
279C4×Dic7C2×D412yes—
280C4×Dic7C2×D412yes—
281C4×Dic7C2412yes—
282C4×Dic7C2412yes—
283C2×C7⋊C8—22no—
284C2×C7⋊C8—22no—
285C2×C7⋊C8C2412yes—
286C2×C7⋊C8C2412yes—
287#1132—28no—
288C22×Q16—71no—
289C22×SD16—71no—
290C22×SD16—71no—
291#559—78no—
292#559—144no—
293Q82—78no—
294Q82—144no—
295C2×C4⋊Q8—71no—
296C2×C4⋊Q8—71no—
297C2×C4⋊Q8—141no—
298C2×C4⋊Q8—141no—
299C2×C4⋊Q8—141no—
300C2×C4⋊Q8C2×D711yescharacteristic
301C2×#127—71no—
302C2×#124—71no—
303C2×#124—141no—
304C2×#124C2×D711yescharacteristic
305C2×#123—141no—
306C2×#123—141no—
307C2×C4×Q8—71no—
308C2×C4×Q8—71no—
309C2×C4×Q8—71no—
310C2×C4×Q8—71no—
311C2×C4×Q8—71no—
312C2×C4×Q8—141no—
313C2×C4×D4—71no—
314C2×C4×D4—71no—
315C2×C4×D4—141no—
316#489—78no—
317#489C2×D718yescomplemented
318#486—78no—
319#477—78no—
320#474—78no—
321#474—78no—
322#464—78no—
323#464—78no—
324#460—78no—
325#446—78no—
326#440—78no—
327#440—78no—
328C4×Q16—78no—
329C2×#107—71no—
330C2×#107—71no—
331C2×#107—71no—
332C2×C4⋊C8—71no—
333C2×C4⋊C8—71no—
334C2×C4⋊C8—71no—
335C2×#103—71no—
336C2×#103—71no—
337C2×#103C2×D711yescharacteristic
338C2×#103C2×D711yescharacteristic
339C2×#102—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×#102C2×D711yescharacteristic
344C2×#102C2×D711yescharacteristic
345C2×#97—71no—
346C2×#97C2×D711yescharacteristic
347C2×C4×C8—71no—
348C23×C7—22no—
349C23×C7—42no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7C22×D411yescharacteristic
353C22×D7—22no—
354C22×D7—42no—
355C22×D7—42no—
356C22×D7—42no—
357C7×Q8—22no—
358C7×Q8—22no—
359C7×Q8—42no—
360C7×Q8—84no—
361C7×D4—22no—
362C7×D4—22no—
363C7×D4—42no—
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×D412yes—
374C2×C4×C7C22×D411yescharacteristic
375C2×C4×C7C2×#4112yes—
376C2×C4×C72−1+412yes—
377C2×C4×C7C2511yescharacteristic
378C22⋊D7—48no—
379C22⋊D7—84no—
380C2×Dic7—24no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7—84no—
390C2×Dic7#13714yes—
391C2×Dic7C22×D412yes—
392C2×Dic7C22×D412yes—
393C2×Dic7C22×D412yes—
394C2×Dic7C22×D412yes—
395D28—22no—
396D28—22no—
397D28—42no—
398C4×D7—84no—
399Dic14—24no—
400Dic14—22no—
401Dic14—28no—
402Dic14—84no—
403Dic14—84no—
404Dic14C2×#4114yes—
405C7×C8—22no—
406C7×C8—22no—
407C7⋊C8—22no—
408C7⋊C8—22no—
409C22×Q8—21no—
410C22×Q8—71no—
411C22×Q8—71no—
412C22×Q8—141no—
413C22×Q8—141no—
414C22×Q8C22×D711yescharacteristic
415C22×D4—71no—
416C22×D4—141no—
417C22×D4—141no—
418C22×D4C22×D711yescharacteristic
419C23×C4—141no—
420C23×C4—141no—
421C2×Q16—74no—
422C2×Q16—144no—
423C2×SD16—74no—
424C2×SD16—74no—
425C2×SD16—144no—
426C2×SD16—144no—
427C22×C8—71no—
428C22×C8—71no—
429C22×C8C22×D711yescharacteristic
430C22×C8C22×D711yescharacteristic
431C4⋊Q8—22no—
432C4⋊Q8—74no—
433C4⋊Q8—74no—
434C4⋊Q8—142no—
435C4⋊Q8—142no—
436C4⋊Q8—148no—
437C4⋊Q8—148no—
438C4⋊Q8—148no—
439C4⋊Q8C22×D714yes—
440#127—74no—
441#127—142no—
442#124—22no—
443#124—74no—
444#124—142no—
445#124—148no—
446#124C22×D714yes—
447#123—148no—
448#123—148no—
449C4×Q8—74no—
450C4×Q8—74no—
451C4×Q8—74no—
452C4×Q8—74no—
453C4×Q8—74no—
454C4×Q8—74no—
455C4×Q8—142no—
456C4×Q8—142no—
457C4×Q8—142no—
458C4×Q8—148no—
459C4×Q8—142no—
460C4×D4—74no—
461C4×D4—74no—
462C4×D4—142no—
463C4×D4—148no—
464C4×D4—142no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—71no—
467C2×C4⋊C4—71no—
468C2×C4⋊C4—71no—
469C2×C4⋊C4—71no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4—141no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4—141no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4C22×D711yescharacteristic
478C2×C4⋊C4C22×D711yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—141no—
482C2×C22⋊C4—141no—
483C2×C22⋊C4—141no—
484C2×C22⋊C4—141no—
485C2×C42—71no—
486C2×C42—71no—
487C2×C42—141no—
488C2×C42—141no—
489C2×C42—141no—
490C2×C42—141no—
491C2×C42C22×D711yescharacteristic
492#107—74no—
493#107—74no—
494#107—74no—
495C4⋊C8—74no—
496C4⋊C8—74no—
497C4⋊C8—74no—
498#103—74no—
499#103—74no—
500#103C22×D714yes—
501#103C22×D714yes—
502#102—74no—
503#102—74no—
504#102—74no—
505#102—74no—
506#102C22×D714yes—
507#102C22×D714yes—
508#97—74no—
509#97C22×D714yes—
510C4×C8—74no—
511C22×C7—42no—
512C22×C7—42no—
513C22×C7—42no—
514C22×C7—84no—
515C22×C7#54812yes—
516C22×C7C2×#13712yes—
517C22×C7#57612yes—
518C22×C7C23×D411yescharacteristic
519C2×D7—42no—
520C2×D7—42no—
521C2×D7—42no—
522C2×D7—84no—
523C4×C7—22no—
524C4×C7—22no—
525C4×C7—42no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7#54812yes—
529C4×C7C22×#4111yescharacteristic
530C4×C7C2×2−1+411yescharacteristic
531Dic7—24no—
532Dic7—22no—
533Dic7—22no—
534Dic7—22no—
535Dic7—42no—
536Dic7—42no—
537Dic7C2×#13714yes—
538C24—21no—
539C24—141no—
540C2×Q8—21no—
541C2×Q8—24no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—74no—
545C2×Q8—74no—
546C2×Q8—72no—
547C2×Q8—82no—
548C2×Q8—144no—
549C2×Q8—144no—
550C2×Q8—144no—
551C2×Q8—141no—
552C2×Q8—142no—
553C2×Q8—562no—
554C2×Q8—562no—
555C2×Q8C23×D712yes—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—72no—
560C2×D4—144no—
561C2×D4—144no—
562C2×D4—141no—
563C2×D4—142no—
564C2×D4—142no—
565C2×D4—284no—
566C2×D4—562no—
567C2×D4C23×D712yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—71no—
572C22×C4—71no—
573C22×C4—71no—
574C22×C4—71no—
575C22×C4—144no—
576C22×C4—141no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—144no—
580C22×C4—562no—
581C22×C4—562no—
582C22×C4D4×D711yescharacteristic
583C22×C4D4×D711yescharacteristic
584C22×C4C23×D711yescharacteristic
585Q16—148no—
586SD16—148no—
587SD16—148no—
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—24no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—74no—
600C4⋊C4—74no—
601C4⋊C4—74no—
602C4⋊C4—72no—
603C4⋊C4—72no—
604C4⋊C4—144no—
605C4⋊C4—144no—
606C4⋊C4—144no—
607C4⋊C4—144no—
608C4⋊C4—144no—
609C4⋊C4—144no—
610C4⋊C4—141no—
611C4⋊C4—141no—
612C4⋊C4C23×D712yes—
613C4⋊C4C23×D712yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—144no—
617C22⋊C4—144no—
618C22⋊C4—144no—
619C22⋊C4—144no—
620C42—72no—
621C42—72no—
622C42—72no—
623C42—72no—
624C42—144no—
625C42—144no—
626C42—144no—
627C42—144no—
628C42D4×D712yes—
629C42C23×D712yes—
630C2×C7—82no—
631C2×C7#337514yescomplemented
632C2×C7C2×#54811yescharacteristic
633C2×C7C22×#13711yescharacteristic
634C2×C7C2×#57611yescharacteristic
635D7—82no—
636C23—22no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—142no—
641C23—282no—
642C23—282no—
643C23—282no—
644C23C2×D4×D711yescharacteristic
645Q8—22no—
646Q8—22no—
647Q8—42no—
648Q8—74no—
649Q8—84no—
650Q8—148no—
651Q8—144no—
652Q8—142no—
653Q8—564no—
654Q8—564no—
655D4—22no—
656D4—22no—
657D4—42no—
658D4—142no—
659D4—142no—
660D4—288no—
661D4—282no—
662D4—564no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—74no—
672C2×C4—72no—
673C2×C4—72no—
674C2×C4—72no—
675C2×C4—72no—
676C2×C4—144no—
677C2×C4—142no—
678C2×C4—142no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—282no—
684C2×C4—282no—
685C2×C4—564no—
686C2×C4—564no—
687C2×C4C2×D4×D712yes—
688C2×C4C2×D4×D712yes—
689C2×C4C2×D4×D711yescharacteristic
690C2×C4D7×#4112yes—
691C2×C4#655412yes—
692C2×C4C24×D711yescharacteristic
693C8—22no—
694C8—22no—
695C8—142no—
696C8—142no—
697C7C2×#337511yescharacteristic, complemented, Sylow
698C22—42no—
699C22—42no—
700C22—42no—
701C22—84no—
702C22—282no—
703C22—282no—
704C22—282no—
705C22—564no—
706C22#9036812yes—
707C22#9046512yes—
708C22D7×#13712yes—
709C22C22×D4×D711yescharacteristic
710C4—22no—
711C4—22no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—74no—
716C4—142no—
717C4—142no—
718C4—142no—
719C4—144no—
720C4—282no—
721C4—282no—
722C4#9036812yes—
723C4C2×D7×#4111yescharacteristic
724C4C2×#655411yescharacteristic
725C2—82no—
726C2—562no—
727C2#1173912014yesdirect product factor
728C2C2×#9036811yescharacteristic
729C2C2×#9046511yescharacteristic
730C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#489C2
socleC23×C7C22×D4
prime radicalC2×#6503C22
hypercenterC2×#489D7
hypocenterC7C2×#3375
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#90413C2semidirect
3. C2×C7×#489C2semidirect
4. C2×#89859C2semidirect
5. C2×#89826C2semidirect
6. #11739120C2direct (N × H)
7. C2×#89570C2semidirect
8. C2×#89567C2semidirect
9. C2×#89566C2semidirect
10. C2×#89562C2semidirect
13. C2×#89531C2semidirect
14. C2×#89529C2semidirect
15. C2×#89482C2semidirect
16. C2×#89473C2semidirect
29. #90413C22semidirect
45. C7×#489C22semidirect
60. #89859C22semidirect
61. #89826C22semidirect
67. #89570C22semidirect
68. #89567C22semidirect
69. #89566C22semidirect
70. #89562C22semidirect
73. #89531C22semidirect
74. #89529C22semidirect
75. #89482C22semidirect
76. #89473C22semidirect
184. C2×#489D7semidirect
317. #489C2×D7semidirect
631. C2×C7#3375semidirect
697. C7C2×#3375semidirect
727. C2#11739120direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904132
C2×#903722
C2×C7×#4892
C2×#898592
C2×#898262
#117391202
C2×#895702
C2×#895672
C2×#895662
C2×#895622
C2×#895342
C2×#895322
C2×#895312
C2×#895292
C2×#894822
C2×#894732
C2×#33757