Finite Group Databasebeta

← C2×#11739117 #14233544

Subgroups — C2×#11739117 #14233544

Order 1792.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90421C211yesmaximal, characteristic, complemented
2C2×#90372C211yesmaximal, characteristic, complemented
3C2×C7×#489C211yesmaximal, characteristic, complemented
4C2×#89859C211yesmaximal, characteristic, complemented
5C2×#89829C211yesmaximal, characteristic, complemented
6#11739117C2116yesmaximal, direct product factor
7C2×#89591C211yesmaximal, characteristic, complemented
8C2×#89572C211yesmaximal, characteristic, complemented
9C2×#89571C211yesmaximal, characteristic, complemented
10C2×#89589C211yesmaximal, characteristic, complemented
11C2×#89558C211yesmaximal, characteristic
12C2×#89536C211yesmaximal, characteristic, complemented
13C2×#89535C211yesmaximal, characteristic, complemented
14C2×#89528C211yesmaximal, characteristic, complemented
15C2×#89483C211yesmaximal, characteristic, complemented
16C2×#89473C211yesmaximal, characteristic, complemented
17C2×C7×C4⋊Q8C2211yescharacteristic
18C2×C7×#124C2211yescharacteristic
19C2×#6510C2211yescharacteristic
20C2×#6509—21no—
21C2×#6509—21no—
22C2×Q8×Dic7C2211yescharacteristic
23C22×#1143C2211yescharacteristic
24C2×#6503C2211yescharacteristic
25C2×D4×Dic7C2211yescharacteristic
26C22×#1141C2211yescharacteristic
27C22×D56C2211yescharacteristic
28#90421—24no—
29#90421C2218yescomplemented
30#90372—24no—
31#90372C2218yescomplemented
32C2×#6460—21no—
33C2×#6456C2211yescharacteristic
34C2×#6456C2211yescharacteristic
35C2×D7×C4⋊C4—21no—
36C2×#6453C2211yescharacteristic
37C2×#6453C2211yescharacteristic
38C2×#6449—21no—
39C2×#6448—21no—
40C2×#6446—21no—
41C2×(C22⋊D7)⋊C4—21no—
42C2×C4×D28C2211yescharacteristic
43C2×C4×D28C2211yescharacteristic
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×#6395C2211yescharacteristic
55C2×#6391C2211yescharacteristic
56C2×#6389C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×Dic7⋊C8C2211yescharacteristic
59C2×C8×Dic7C2211yescharacteristic
60#89859C2218yescomplemented
61#89829C2218yescomplemented
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×C4⋊(C7⋊C8)C2211yescharacteristic
67#89591C2218yescomplemented
68#89589C2218yescomplemented
69#89572C2218yescomplemented
70#89571C2218yescomplemented
71#89558C2218yes—
72#89536C2218yescomplemented
73#89535C2218yescomplemented
74#89528C2218yescomplemented
75#89483C2218yescomplemented
76#89473C2218yescomplemented
77C2×#3370—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×D28C2311yescharacteristic
86C22×C4×D7—21no—
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×Dic14D411yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C7×C4⋊Q8—22no—
94C7×C4⋊Q8C2314yes—
95C7×#124—22no—
96C7×#124C2314yes—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4—21no—
102C2×C42×C7C2311yescharacteristic
103C2×C22⋊Dic7—21no—
104#6510—22no—
105#6510C2314yes—
106#6509—28no—
107#6509—28no—
108Q8×Dic7—22no—
109Q8×Dic7C2314yes—
110C2×#1143—24no—
111C2×#1143C2314yes—
112#6503—22no—
113#6503C2314yes—
114D4×Dic7—22no—
115D4×Dic7C2314yes—
116C2×#1141—24no—
117C2×#1141C2314yes—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×C4⋊Dic7—21no—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7D411yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129C2×C4⋊Dic7C2311yescharacteristic
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4D411yescharacteristic
133C2×Dic7⋊C4D411yescharacteristic
134C2×C4×Dic7—21no—
135C2×C4×Dic7C2311yescharacteristic
136C2×C4×Dic7C2311yescharacteristic
137C22×C7⋊C8C2311yescharacteristic
138C22×C7⋊C8C2311yescharacteristic
139C2×D56—24no—
140C2×D56C2314yes—
141#6460—28no—
142#6456—22no—
143#6456—22no—
144#6456C2314yes—
145#6456C2314yes—
146D7×C4⋊C4—28no—
147#6453—22no—
148#6453—22no—
149#6453C2314yes—
150#6453C2314yes—
151#6449—28no—
152#6448—28no—
153#6446—28no—
154(C22⋊D7)⋊C4—28no—
155C4×D28—22no—
156C4×D28—22no—
157C4×D28C2314yes—
158C4×D28C2314yes—
159C4×Dic14D414yes—
160C4×Dic14C2314yes—
161C7×#103C2314yes—
162C7×#103C2314yes—
163C7×#102C2314yes—
164C7×#102C2314yes—
165C7×#97C2314yes—
166#6409C2314yes—
167#6406C2314yes—
168#6395C2314yes—
169#6395C2314yes—
170#6391C2314yes—
171#6389C2314yes—
172Dic7⋊C8C2314yes—
173Dic7⋊C8C2314yes—
174C8×Dic7C2314yes—
175#6383C2314yes—
176#6383C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179C4⋊(C7⋊C8)C2314yes—
180C2×#559—71no—
181C2×#554—71no—
182#3370—716no—
183C2×#490—71no—
184C2×#489D711yescharacteristic, complemented
185C2×#488—71no—
186C2×#479—71no—
187C2×#478—71no—
188C2×#474—71no—
189C2×#463—71no—
190C2×#463—71no—
191C2×#459—71no—
192C2×#446—71no—
193C2×#442—71no—
194C2×#440—71no—
195C2×C4×D8—71no—
196C24×C7—21no—
197C23×D7—21no—
198C23×D7—21no—
199C2×C7×Q8—21no—
200C2×C7×Q8—24no—
201C2×C7×Q8—22no—
202C2×C7×Q8—22no—
203C2×C7×Q8—82no—
204C2×C7×Q8C2412yes—
205C2×C7×D4—21no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4C2412yes—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2411yescharacteristic
215C2×C22⋊D7—24no—
216C2×C22⋊D7—24no—
217C2×C22⋊D7—44no—
218C2×C22⋊D7—82no—
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—21no—
228C2×D28—22no—
229C2×D28—22no—
230C2×D28—22no—
231C2×D28—21no—
232C2×D28#4114yes—
233C2×D28C2412yes—
234C2×D28C2412yes—
235C2×C4×D7—24no—
236C2×C4×D7—24no—
237C2×C4×D7—24no—
238C2×C4×D7—24no—
239C2×C4×D7—44no—
240C2×C4×D7—82no—
241C2×C4×D7—82no—
242C2×C4×D7—82no—
243C2×Dic14—42no—
244C2×Dic14C2×D414yes—
245C2×C7×C8—22no—
246C2×C7×C8—22no—
247C2×C7×C8C2412yes—
248C2×C7×C8C2412yes—
249C7×C4⋊C4—21no—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—24no—
252C7×C4⋊C4C2412yes—
253C7×C4⋊C4C2412yes—
254C7×C22⋊C4—24no—
255C7×C22⋊C4—24no—
256C42×C7C2×D412yes—
257C42×C7C2412yes—
258C22⋊Dic7—24no—
259#1143—28no—
260#1141—28no—
261(C2×D7)⋊C4—24no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—24no—
270C4⋊Dic7—24no—
271C4⋊Dic7—24no—
272C4⋊Dic7C2×D414yes—
273C4⋊Dic7C2412yes—
274C4⋊Dic7C2412yes—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4C2×D414yes—
278Dic7⋊C4C2×D414yes—
279C4×Dic7—24no—
280C4×Dic7C2×D412yes—
281C4×Dic7C2×D412yes—
282C4×Dic7C2412yes—
283C4×Dic7C2412yes—
284C2×C7⋊C8—22no—
285C2×C7⋊C8—22no—
286C2×C7⋊C8C2412yes—
287C2×C7⋊C8C2412yes—
288D56—28no—
289C22×SD16—71no—
290C22×D8—71no—
291C22×D8—71no—
292#559—78no—
293#559—144no—
294#554—78no—
295#554—144no—
296C2×C4⋊Q8C2×D711yescharacteristic
297C2×#127—71no—
298C2×#125—71no—
299C2×#125—71no—
300C2×#124—71no—
301C2×#124—141no—
302C2×#124C2×D711yescharacteristic
303C2×#123—141no—
304C2×#123—141no—
305C2×C22⋊Q8—141no—
306C2×C22⋊Q8—141no—
307C2×C22⋊Q8—141no—
308C2×C4×Q8—71no—
309C2×C4×Q8—71no—
310C2×C4×D4—71no—
311C2×C4×D4—71no—
312C2×C4×D4—71no—
313C2×C4×D4—71no—
314C2×C4×D4—71no—
315C2×C4×D4—141no—
316C22×C4⋊C4—141no—
317#490—78no—
318#489C2×D718yescomplemented
319#488—78no—
320#479—78no—
321#478—78no—
322#474—78no—
323#463—78no—
324#463—78no—
325#459—78no—
326#446—78no—
327#442—78no—
328#440—78no—
329C4×D8—78no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#106—71no—
333C2×C4⋊C8—71no—
334C2×C4⋊C8—71no—
335C2×C4⋊C8—71no—
336C2×#103—71no—
337C2×#103C2×D711yescharacteristic
338C2×#103C2×D711yescharacteristic
339C2×#102—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×#102—71no—
344C2×#102C2×D711yescharacteristic
345C2×#102C2×D711yescharacteristic
346C2×#97—71no—
347C2×#97C2×D711yescharacteristic
348C2×C4×C8—71no—
349C23×C7—22no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7C22×D411yescharacteristic
354C22×D7—24no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—42no—
358C22×D7—42no—
359C22×D7—42no—
360C22×D7—42no—
361C22×D7—42no—
362C7×Q8—22no—
363C7×Q8—22no—
364C7×Q8—42no—
365C7×Q8—84no—
366C7×D4—22no—
367C7×D4—22no—
368C7×D4—42no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D411yescharacteristic
380C2×C4×C7C2×#4112yes—
381C2×C4×C72−1+412yes—
382C2×C4×C7C2511yescharacteristic
383C22⋊D7—48no—
384C22⋊D7—84no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—84no—
394C2×Dic7C22×D412yes—
395C2×Dic7C22×D412yes—
396C2×Dic7C22×D412yes—
397C2×Dic7C22×D412yes—
398D28—24no—
399D28—22no—
400D28—22no—
401D28—22no—
402D28—42no—
403D28C2×#4114yes—
404C4×D7—48no—
405C4×D7—84no—
406C4×D7—84no—
407C4×D7—84no—
408Dic14—44no—
409C7×C8—22no—
410C7×C8—22no—
411C7⋊C8—22no—
412C7⋊C8—22no—
413C22×Q8—21no—
414C22×Q8—71no—
415C22×Q8C22×D711yescharacteristic
416C22×D4—71no—
417C22×D4—71no—
418C22×D4—141no—
419C22×D4—141no—
420C22×D4C22×D711yescharacteristic
421C23×C4—141no—
422C23×C4—141no—
423C23×C4—141no—
424C23×C4—141no—
425C23×C4—141no—
426C2×SD16—74no—
427C2×SD16—144no—
428C2×D8—74no—
429C2×D8—74no—
430C2×D8—144no—
431C2×D8—144no—
432C22×C8—71no—
433C22×C8—71no—
434C22×C8C22×D711yescharacteristic
435C22×C8C22×D711yescharacteristic
436C4⋊Q8—22no—
437C4⋊Q8C22×D714yes—
438#127—74no—
439#127—142no—
440#125—74no—
441#125—74no—
442#125—142no—
443#125—142no—
444#124—22no—
445#124—74no—
446#124—142no—
447#124—148no—
448#124C22×D714yes—
449#123—148no—
450#123—148no—
451C22⋊Q8—148no—
452C22⋊Q8—148no—
453C22⋊Q8—148no—
454C4×Q8—74no—
455C4×Q8—74no—
456C4×Q8—74no—
457C4×Q8—142no—
458C4×D4—74no—
459C4×D4—74no—
460C4×D4—74no—
461C4×D4—74no—
462C4×D4—74no—
463C4×D4—142no—
464C4×D4—142no—
465C4×D4—142no—
466C4×D4—148no—
467C4×D4—142no—
468C4×D4—142no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—148no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4C22×D711yescharacteristic
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—141no—
486C2×C22⋊C4—141no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C42—71no—
493C2×C42—71no—
494C2×C42—141no—
495C2×C42C22×D711yescharacteristic
496#107—74no—
497#107—74no—
498#106—74no—
499C4⋊C8—74no—
500C4⋊C8—74no—
501C4⋊C8—74no—
502#103—74no—
503#103C22×D714yes—
504#103C22×D714yes—
505#102—74no—
506#102—74no—
507#102—74no—
508#102—74no—
509#102—74no—
510#102C22×D714yes—
511#102C22×D714yes—
512#97—74no—
513#97C22×D714yes—
514C4×C8—74no—
515C22×C7—42no—
516C22×C7—42no—
517C22×C7—42no—
518C22×C7—84no—
519C22×C7#54812yes—
520C22×C7#57512yes—
521C22×C7#57612yes—
522C22×C7C23×D411yescharacteristic
523C2×D7—24no—
524C2×D7—48no—
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—42no—
528C2×D7—42no—
529C2×D7—42no—
530C2×D7—84no—
531C4×C7—22no—
532C4×C7—22no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7#54812yes—
537C4×C7C22×#4111yescharacteristic
538C4×C7C2×2−1+411yescharacteristic
539Dic7—22no—
540Dic7—22no—
541Dic7—22no—
542Dic7—22no—
543Dic7—42no—
544Dic7—42no—
545C24—21no—
546C24—141no—
547C24—141no—
548C2×Q8—21no—
549C2×Q8—24no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—74no—
553C2×Q8—82no—
554C2×Q8—282no—
555C2×Q8C23×D712yes—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—74no—
560C2×D4—72no—
561C2×D4—72no—
562C2×D4—144no—
563C2×D4—144no—
564C2×D4—141no—
565C2×D4—141no—
566C2×D4—142no—
567C2×D4—142no—
568C2×D4—142no—
569C2×D4—284no—
570C2×D4—562no—
571C2×D4C23×D712yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—71no—
576C22×C4—71no—
577C22×C4—71no—
578C22×C4—71no—
579C22×C4—144no—
580C22×C4—144no—
581C22×C4—144no—
582C22×C4—141no—
583C22×C4—141no—
584C22×C4—144no—
585C22×C4—144no—
586C22×C4—284no—
587C22×C4—562no—
588C22×C4—562no—
589C22×C4—562no—
590C22×C4—562no—
591C22×C4D4×D711yescharacteristic
592C22×C4D4×D711yescharacteristic
593C22×C4C23×D711yescharacteristic
594SD16—148no—
595D8—148no—
596D8—148no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—72no—
600C2×C8—72no—
601C2×C8—142no—
602C2×C8—142no—
603C2×C8C23×D712yes—
604C2×C8C23×D712yes—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—74no—
609C4⋊C4—74no—
610C4⋊C4—74no—
611C4⋊C4—72no—
612C4⋊C4—72no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—141no—
619C4⋊C4—141no—
620C4⋊C4C23×D712yes—
621C4⋊C4C23×D712yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—144no—
625C22⋊C4—144no—
626C22⋊C4—144no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C42—72no—
632C42—72no—
633C42—72no—
634C42—72no—
635C42—144no—
636C42D4×D712yes—
637C42C23×D712yes—
638C2×C7—82no—
639C2×C7#337014yescomplemented
640C2×C7C2×#54811yescharacteristic
641C2×C7C2×#57511yescharacteristic
642C2×C7C2×#57611yescharacteristic
643D7—44no—
644D7—82no—
645C23—22no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—144no—
650C23—142no—
651C23—142no—
652C23—282no—
653C23—282no—
654C23—282no—
655C23—282no—
656C23—282no—
657C23C2×D4×D711yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—84no—
662Q8—284no—
663D4—22no—
664D4—22no—
665D4—42no—
666D4—74no—
667D4—144no—
668D4—142no—
669D4—142no—
670D4—142no—
671D4—288no—
672D4—282no—
673D4—564no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—72no—
683C2×C4—72no—
684C2×C4—72no—
685C2×C4—72no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—288no—
693C2×C4—282no—
694C2×C4—282no—
695C2×C4—564no—
696C2×C4—564no—
697C2×C4—564no—
698C2×C4—564no—
699C2×C4C2×D4×D712yes—
700C2×C4C2×D4×D712yes—
701C2×C4C2×D4×D711yescharacteristic
702C2×C4D7×#4112yes—
703C2×C4#655412yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—22no—
707C8—142no—
708C8—142no—
709C7C2×#337011yescharacteristic, complemented, Sylow
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—144no—
715C22—282no—
716C22—282no—
717C22—288no—
718C22—282no—
719C22—282no—
720C22—282no—
721C22—564no—
722C22#9036812yes—
723C22#9046512yes—
724C22#9046812yes—
725C22C22×D4×D711yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—142no—
732C4—142no—
733C4—142no—
734C4—142no—
735C4—282no—
736C4—282no—
737C4#9036812yes—
738C4C2×D7×#4111yescharacteristic
739C4C2×#655411yescharacteristic
740C2—82no—
741C2—284no—
742C2—562no—
743C2#1173911714yesdirect product factor
744C2C2×#9036811yescharacteristic
745C2C2×#9046511yescharacteristic
746C2C2×#9046811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#489C2
socleC23×C7C22×D4
prime radicalC2×#89558C2
hypercenterC2×#489D7
hypocenterC7C2×#3370
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×#90421C2semidirect
2. C2×#90372C2semidirect
3. C2×C7×#489C2semidirect
4. C2×#89859C2semidirect
5. C2×#89829C2semidirect
6. #11739117C2direct (N × H)
7. C2×#89591C2semidirect
8. C2×#89572C2semidirect
9. C2×#89571C2semidirect
10. C2×#89589C2semidirect
12. C2×#89536C2semidirect
13. C2×#89535C2semidirect
14. C2×#89528C2semidirect
15. C2×#89483C2semidirect
16. C2×#89473C2semidirect
29. #90421C22semidirect
31. #90372C22semidirect
45. C7×#489C22semidirect
60. #89859C22semidirect
61. #89829C22semidirect
67. #89591C22semidirect
68. #89589C22semidirect
69. #89572C22semidirect
70. #89571C22semidirect
72. #89536C22semidirect
73. #89535C22semidirect
74. #89528C22semidirect
75. #89483C22semidirect
76. #89473C22semidirect
184. C2×#489D7semidirect
318. #489C2×D7semidirect
639. C2×C7#3370semidirect
709. C7C2×#3370semidirect
743. C2#11739117direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904212
C2×#903722
C2×C7×#4892
C2×#898592
C2×#898292
#117391172
C2×#895912
C2×#895722
C2×#895712
C2×#895892
C2×#895582
C2×#895362
C2×#895352
C2×#895282
C2×#894832
C2×#894732
C2×#33707