Finite Group Databasebeta

← C2×#11737196 #14233472

Subgroups — C2×#11737196 #14233472

Order 1792.

2070 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×#90259C211yesmaximal, characteristic, complemented
2C2×D4×Dic14C211yesmaximal, characteristic, complemented
3C2×C7×#440C211yesmaximal, characteristic, complemented
4C2×#89937C211yesmaximal, characteristic
5C2×#89934C211yesmaximal, characteristic, complemented
6C2×#89793C211yesmaximal, characteristic, complemented
7C2×#89788C211yesmaximal, characteristic
8#11737196C2116yesmaximal, direct product factor
9C2×#89647C211yesmaximal, characteristic, complemented
10C2×#89662C211yesmaximal, characteristic, complemented
11C2×#89567C211yesmaximal, characteristic, complemented
12C2×#89564C211yesmaximal, characteristic, complemented
13C2×#89529C211yesmaximal, characteristic, complemented
14C2×#89528C211yesmaximal, characteristic
15C2×#89486C211yesmaximal, characteristic, complemented
16C2×#89473C211yesmaximal, characteristic, complemented
17C23×Dic14—21no—
18C22×C7×SD16C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×#6510C2211yescharacteristic
22C2×#6507C2211yescharacteristic
23C2×D4×Dic7C2211yescharacteristic
24C2×D4×Dic7C2211yescharacteristic
25C22×#1142C2211yescharacteristic
26C22×#1141C2211yescharacteristic
27C2×#6487—21no—
28#90259—24no—
29#90259C2218yescomplemented
30D4×Dic14—24no—
31D4×Dic14C2218yescomplemented
32C2×#6461—21no—
33C2×#6459—21no—
34C2×#6456C2211yescharacteristic
35C2×#6451C2211yescharacteristic
36C2×#6451C2211yescharacteristic
37C2×#6450C2211yescharacteristic
38C2×#6441—21no—
39C2×#6441—21no—
40C2×#6439—21no—
41C2×#6438C2211yescharacteristic
42C2×#6435—21no—
43C2×#6432C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×#440C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#97C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52#89937C2218yes—
53#89934C2218yescomplemented
54C2×#6395C2211yescharacteristic
55C2×#6395C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×#6390C2211yescharacteristic
58C2×#6389C2211yescharacteristic
59C2×Dic7⋊C8C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×C8×Dic7C2211yescharacteristic
62#89793C2218yescomplemented
63#89788C2218yes—
64C2×#6384C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×C4⋊(C7⋊C8)C2211yescharacteristic
69#89662C2218yescomplemented
70#89647C2218yescomplemented
71#89567C2218yescomplemented
72#89564C2218yescomplemented
73#89529C2218yescomplemented
74#89528C2218yes—
75#89486C2218yescomplemented
76#89473C2218yescomplemented
77C2×#3367—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C23×Dic7—21no—
82C23×Dic7—21no—
83C22×D28C2311yescharacteristic
84C22×C4×D7—21no—
85C22×Dic14—21no—
86C22×Dic14—21no—
87C22×Dic14—21no—
88C22×Dic14—28no—
89C22×Dic14—48no—
90C22×Dic14D411yescharacteristic
91C22×Dic14C2311yescharacteristic
92C2×C7×SD16—24no—
93C2×C7×SD16C2314yes—
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C4×C7×Q8—22no—
97C4×C7×Q8C2314yes—
98C4×C7×D4—22no—
99C4×C7×D4C2314yes—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C22⋊C4—21no—
104C2×C42×C7—21no—
105C2×C42×C7C2311yescharacteristic
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108#6510—22no—
109#6510C2314yes—
110#6507—22no—
111#6507C2314yes—
112D4×Dic7—22no—
113D4×Dic7—22no—
114D4×Dic7C2314yes—
115D4×Dic7C2314yes—
116C2×#1142—24no—
117C2×#1142C2314yes—
118C2×#1141—24no—
119C2×#1141C2314yes—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4—21no—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7D411yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129#6487—28no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4D411yescharacteristic
136C2×Dic7⋊C4D411yescharacteristic
137C2×C4×Dic7—21no—
138C2×C4×Dic7C2311yescharacteristic
139C2×C4×Dic7C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141C22×C7⋊C8C2311yescharacteristic
142#6461—28no—
143#6459—28no—
144#6456—22no—
145#6456C2314yes—
146#6451—22no—
147#6451—22no—
148#6451C2314yes—
149#6451C2314yes—
150#6450—22no—
151#6450C2314yes—
152#6441—28no—
153#6441—28no—
154#6439—28no—
155#6438—22no—
156#6438C2314yes—
157#6435—28no—
158#6432—22no—
159#6432C2314yes—
160C4×Dic14D414yes—
161C4×Dic14C2314yes—
162C7×#107C2314yes—
163C7×#103C2314yes—
164C7×#102C2314yes—
165C7×#97C2314yes—
166#6409C2314yes—
167#6409C2314yes—
168#6395C2314yes—
169#6395C2314yes—
170#6390C2314yes—
171#6390C2314yes—
172#6389C2314yes—
173Dic7⋊C8C2314yes—
174Dic7⋊C8C2314yes—
175C8×Dic7C2314yes—
176#6384C2314yes—
177#6383C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180C4⋊(C7⋊C8)C2314yes—
181C2×#556—71no—
182C2×D4×Q8—71no—
183#3367—716no—
184C2×#489—71no—
185C2×#489—71no—
186C2×#487—71no—
187C2×#477—71no—
188C2×#477—71no—
189C2×#474—71no—
190C2×#463—71no—
191C2×#463—71no—
192C2×#461—71no—
193C2×#446—71no—
194C2×#440—71no—
195C2×#440D711yescharacteristic, complemented
196C2×C4×D8—71no—
197C24×C7—21no—
198C23×D7—21no—
199C2×C7×Q8—21no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8C2412yes—
203C2×C7×D4—21no—
204C2×C7×D4—22no—
205C2×C7×D4#4114yes—
206C2×C7×D4C2412yes—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—24no—
211C22×C4×C7—44no—
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2411yescharacteristic
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—24no—
219C22×Dic7—24no—
220C22×Dic7—44no—
221C22×Dic7—44no—
222C22×Dic7C2×D411yescharacteristic
223C22×Dic7C2×D411yescharacteristic
224C22×Dic7C2×D411yescharacteristic
225C22×Dic7C2×D411yescharacteristic
226C2×D28—22no—
227C2×D28—22no—
228C2×D28—21no—
229C2×D28C2412yes—
230C2×C4×D7—24no—
231C2×C4×D7—44no—
232C2×Dic14—24no—
233C2×Dic14—22no—
234C2×Dic14—22no—
235C2×Dic14—24no—
236C2×Dic14—21no—
237C2×Dic14—24no—
238C2×Dic14—24no—
239C2×Dic14—432no—
240C2×Dic14—44no—
241C2×Dic14—44no—
242C2×Dic14—44no—
243C2×Dic14C2×D414yes—
244C2×Dic14C2412yes—
245C7×SD16—28no—
246C2×C7×C8—22no—
247C2×C7×C8—22no—
248C2×C7×C8C2412yes—
249C2×C7×C8C2412yes—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—24no—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C22⋊C4—24no—
256C42×C7—24no—
257C42×C7C2×D412yes—
258C42×C7C2412yes—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261#1142—28no—
262#1141—28no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268C4⋊Dic7—21no—
269C4⋊Dic7—21no—
270C4⋊Dic7—24no—
271C4⋊Dic7C2×D414yes—
272C4⋊Dic7C2412yes—
273C4⋊Dic7C2412yes—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4C2×D414yes—
280Dic7⋊C4C2×D414yes—
281C4×Dic7—24no—
282C4×Dic7C2×D412yes—
283C4×Dic7C2×D412yes—
284C4×Dic7C2412yes—
285C4×Dic7C2412yes—
286C2×C7⋊C8—22no—
287C2×C7⋊C8—22no—
288C2×C7⋊C8C2412yes—
289C2×C7⋊C8C2412yes—
290C23×Q8—141no—
291C22×SD16—71no—
292C22×SD16C2×D711yescharacteristic
293C22×D8—71no—
294#556—78no—
295#556—144no—
296D4×Q8—78no—
297D4×Q8—144no—
298C2×C4⋊Q8—71no—
299C2×C4⋊Q8—71no—
300C2×C4⋊Q8—71no—
301C2×C4⋊Q8—71no—
302C2×#126—141no—
303C2×#126—141no—
304C2×#124—71no—
305C2×#124—71no—
306C2×C22⋊Q8—141no—
307C2×C22⋊Q8—141no—
308C2×C22⋊Q8—141no—
309C2×C22⋊Q8—141no—
310C2×C4×Q8—71no—
311C2×C4×Q8—71no—
312C2×C4×Q8C2×D711yescharacteristic
313C2×C4×D4—71no—
314C2×C4×D4—71no—
315C2×C4×D4—71no—
316C2×C4×D4C2×D711yescharacteristic
317C2×#117—141no—
318#489—78no—
319#489—78no—
320#487—78no—
321#477—78no—
322#477—78no—
323#474—78no—
324#463—78no—
325#463—78no—
326#461—78no—
327#446—78no—
328#440—78no—
329#440C2×D718yescomplemented
330C4×D8—78no—
331C2×#107—71no—
332C2×#107—71no—
333C2×#107C2×D711yescharacteristic
334C2×C4⋊C8—71no—
335C2×C4⋊C8—71no—
336C2×C4⋊C8—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#103—71no—
340C2×#103—71no—
341C2×#103—71no—
342C2×#103C2×D711yescharacteristic
343C2×#102—71no—
344C2×#102—71no—
345C2×#102—71no—
346C2×#102C2×D711yescharacteristic
347C2×#97—71no—
348C2×#97C2×D711yescharacteristic
349C2×C4×C8—71no—
350C23×C7—24no—
351C23×C7—22no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7C22×D411yescharacteristic
355C22×D7—22no—
356C22×D7—42no—
357C22×D7—42no—
358C22×D7—42no—
359C7×Q8—22no—
360C7×Q8—22no—
361C7×Q8—42no—
362C7×D4—24no—
363C7×D4—22no—
364C7×D4C2×#4114yes—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—48no—
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×C7C2×#4112yes—
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—48no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—48no—
391C2×Dic7AGL(1,ℤ/8)14yes—
392C2×Dic7C22×D412yes—
393C2×Dic7C22×D412yes—
394C2×Dic7C22×D412yes—
395C2×Dic7C22×D412yes—
396D28—22no—
397D28—22no—
398D28—42no—
399C4×D7—48no—
400Dic14—28no—
401Dic14—22no—
402Dic14—22no—
403Dic14—48no—
404Dic14—48no—
405Dic14—42no—
406Dic14—48no—
407C7×C8—22no—
408C7×C8—22no—
409C7⋊C8—22no—
410C7⋊C8—22no—
411C22×Q8—71no—
412C22×Q8—71no—
413C22×Q8—141no—
414C22×Q8—141no—
415C22×Q8—148no—
416C22×Q8—141no—
417C22×Q8—288no—
418C22×Q8C22×D711yescharacteristic
419C22×D4—71no—
420C22×D4C22×D711yescharacteristic
421C23×C4—21no—
422C23×C4—141no—
423C23×C4—141no—
424C23×C4—141no—
425C2×SD16—24no—
426C2×SD16—74no—
427C2×SD16—144no—
428C2×SD16C22×D714yes—
429C2×D8—74no—
430C2×D8—144no—
431C22×C8—71no—
432C22×C8—71no—
433C22×C8C22×D711yescharacteristic
434C22×C8C22×D711yescharacteristic
435C4⋊Q8—74no—
436C4⋊Q8—74no—
437C4⋊Q8—74no—
438C4⋊Q8—74no—
439C4⋊Q8—142no—
440C4⋊Q8—142no—
441C4⋊Q8—142no—
442C4⋊Q8—142no—
443#126—148no—
444#126—148no—
445#124—74no—
446#124—74no—
447#124—142no—
448#124—142no—
449C22⋊Q8—148no—
450C22⋊Q8—148no—
451C22⋊Q8—148no—
452C22⋊Q8—148no—
453C4×Q8—22no—
454C4×Q8—74no—
455C4×Q8—74no—
456C4×Q8—74no—
457C4×Q8—142no—
458C4×Q8C22×D714yes—
459C4×D4—22no—
460C4×D4—74no—
461C4×D4—74no—
462C4×D4—74no—
463C4×D4—142no—
464C4×D4—142no—
465C4×D4—142no—
466C4×D4C22×D714yes—
467#117—148no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—71no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—71no—
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⋊C4C22×D711yescharacteristic
481C2×C4⋊C4C22×D711yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—141no—
484C2×C22⋊C4—141no—
485C2×C22⋊C4—141no—
486C2×C22⋊C4—141no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C42—21no—
491C2×C42—71no—
492C2×C42—71no—
493C2×C42—141no—
494C2×C42C22×D711yescharacteristic
495#107—74no—
496#107—74no—
497#107C22×D714yes—
498C4⋊C8—74no—
499C4⋊C8—74no—
500C4⋊C8—74no—
501#103—74no—
502#103—74no—
503#103—74no—
504#103—74no—
505#103—74no—
506#103C22×D714yes—
507#102—74no—
508#102—74no—
509#102—74no—
510#102C22×D714yes—
511#97—74no—
512#97C22×D714yes—
513C4×C8—74no—
514C22×C7—24no—
515C22×C7—48no—
516C22×C7—42no—
517C22×C7—42no—
518C22×C7#54812yes—
519C22×C7C2×AGL(1,ℤ/8)12yes—
520C22×C7#57812yes—
521C22×C7C23×D411yescharacteristic
522C2×D7—42no—
523C2×D7—42no—
524C2×D7—42no—
525C2×D7—84no—
526C4×C7—22no—
527C4×C7—22no—
528C4×C7—42no—
529C4×C7—42no—
530C4×C7—42no—
531C4×C7#54812yes—
532C4×C7C22×#4111yescharacteristic
533C4×C7C2×2−1+411yescharacteristic
534Dic7—22no—
535Dic7—22no—
536Dic7—22no—
537Dic7—42no—
538Dic7—42no—
539Dic7—42no—
540Dic7C2×AGL(1,ℤ/8)14yes—
541C24—21no—
542C24—141no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—74no—
547C2×Q8—72no—
548C2×Q8—144no—
549C2×Q8—144no—
550C2×Q8—144no—
551C2×Q8—141no—
552C2×Q8—144no—
553C2×Q8—142no—
554C2×Q8—142no—
555C2×Q8—284no—
556C2×Q8—284no—
557C2×Q8—284no—
558C2×Q8—2832no—
559C2×Q8C23×D712yes—
560C2×D4—21no—
561C2×D4—22no—
562C2×D4—72no—
563C2×D4—142no—
564C2×D4—141no—
565C2×D4—142no—
566C2×D4#115714yes—
567C2×D4C23×D712yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—44no—
573C22×C4—71no—
574C22×C4—71no—
575C22×C4—71no—
576C22×C4—71no—
577C22×C4—144no—
578C22×C4—144no—
579C22×C4—144no—
580C22×C4—141no—
581C22×C4—141no—
582C22×C4—141no—
583C22×C4—284no—
584C22×C4—284no—
585C22×C4—284no—
586C22×C4D4×D711yescharacteristic
587C22×C4D4×D711yescharacteristic
588C22×C4C23×D711yescharacteristic
589SD16—28no—
590SD16—148no—
591D8—148no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—72no—
595C2×C8—72no—
596C2×C8—142no—
597C2×C8—142no—
598C2×C8C23×D712yes—
599C2×C8C23×D712yes—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—74no—
604C4⋊C4—74no—
605C4⋊C4—74no—
606C4⋊C4—72no—
607C4⋊C4—72no—
608C4⋊C4—144no—
609C4⋊C4—144no—
610C4⋊C4—144no—
611C4⋊C4—144no—
612C4⋊C4—144no—
613C4⋊C4—141no—
614C4⋊C4—141no—
615C4⋊C4—144no—
616C4⋊C4C23×D712yes—
617C4⋊C4C23×D712yes—
618C22⋊C4—24no—
619C22⋊C4—144no—
620C22⋊C4—144no—
621C22⋊C4—144no—
622C22⋊C4—144no—
623C22⋊C4—144no—
624C22⋊C4—144no—
625C22⋊C4—144no—
626C42—24no—
627C42—72no—
628C42—72no—
629C42—72no—
630C42—72no—
631C42—144no—
632C42D4×D712yes—
633C42C23×D712yes—
634C2×C7—44no—
635C2×C7#336714yescomplemented
636C2×C7C2×#54811yescharacteristic
637C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
638C2×C7C2×#57811yescharacteristic
639D7—82no—
640C23—24no—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—142no—
645C23—282no—
646C23—282no—
647C23—282no—
648C23C2×D4×D711yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—42no—
652Q8—148no—
653Q8—142no—
654Q8—142no—
655Q8—288no—
656Q8—288no—
657Q8—288no—
658Q8—282no—
659D4—24no—
660D4—22no—
661D4—142no—
662D4—142no—
663D4—282no—
664D4C2×#115714yes—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—48no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—74no—
675C2×C4—72no—
676C2×C4—72no—
677C2×C4—72no—
678C2×C4—72no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—288no—
686C2×C4—288no—
687C2×C4—288no—
688C2×C4—282no—
689C2×C4—282no—
690C2×C4—282no—
691C2×C4C2×#115712yes—
692C2×C4C2×D4×D712yes—
693C2×C4C2×D4×D712yes—
694C2×C4C2×D4×D711yescharacteristic
695C2×C4#655412yes—
696C2×C4C24×D711yescharacteristic
697C8—22no—
698C8—22no—
699C8—142no—
700C8—142no—
701C7C2×#336711yescharacteristic, complemented, Sylow
702C22—24no—
703C22—42no—
704C22—42no—
705C22—48no—
706C22—282no—
707C22—282no—
708C22—282no—
709C22—564no—
710C22#9024312yes—
711C22D7×AGL(1,ℤ/8)12yes—
712C22#9047012yes—
713C22C22×D4×D711yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—74no—
720C4—142no—
721C4—142no—
722C4—142no—
723C4—282no—
724C4—282no—
725C4—282no—
726C4#9024312yes—
727C4C22×#115711yescharacteristic
728C4C2×#655411yescharacteristic
729C2—44no—
730C2—562no—
731C2#1173719614yesdirect product factor
732C2C2×#9024311yescharacteristic
733C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
734C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#440C2
socleC23×C7C22×D4
prime radicalC22×#1141C22
hypercenterC2×#440D7
hypocenterC7C2×#3367
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#90259C2semidirect
2. C2×D4×Dic14C2semidirect
3. C2×C7×#440C2semidirect
5. C2×#89934C2semidirect
6. C2×#89793C2semidirect
8. #11737196C2direct (N × H)
9. C2×#89647C2semidirect
10. C2×#89662C2semidirect
11. C2×#89567C2semidirect
12. C2×#89564C2semidirect
13. C2×#89529C2semidirect
15. C2×#89486C2semidirect
16. C2×#89473C2semidirect
29. #90259C22semidirect
31. D4×Dic14C22semidirect
45. C7×#440C22semidirect
53. #89934C22semidirect
62. #89793C22semidirect
69. #89662C22semidirect
70. #89647C22semidirect
71. #89567C22semidirect
72. #89564C22semidirect
73. #89529C22semidirect
75. #89486C22semidirect
76. #89473C22semidirect
195. C2×#440D7semidirect
329. #440C2×D7semidirect
635. C2×C7#3367semidirect
701. C7C2×#3367semidirect
731. C2#11737196direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902592
C2×D4×Dic142
C2×C7×#4402
C2×#899372
C2×#899342
C2×#897932
C2×#897882
#117371962
C2×#896472
C2×#896622
C2×#895672
C2×#895642
C2×#895292
C2×#895282
C2×#894862
C2×#894732
C2×#33677