Finite Group Databasebeta

← C2×#11736859 #14232245

Subgroups — C2×#11736859 #14232245

Order 1792.

1930 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×#90256C211yesmaximal, characteristic
2C2×#90232C211yesmaximal, characteristic, complemented
3C2×C7×C8×D4C211yesmaximal, characteristic, complemented
4C2×#89886C211yesmaximal, characteristic, complemented
5C2×#89886C211yesmaximal, characteristic, complemented
6C2×#89878C211yesmaximal, characteristic, complemented
7C22×#6391C211yesmaximal, characteristic, complemented
8#11736859C2116yesmaximal, direct product factor
9C2×#89601C211yesmaximal, characteristic, complemented
10C2×#89619C211yesmaximal, characteristic, complemented
11C2×#89494C211yesmaximal, characteristic, complemented
12C2×#89495C211yesmaximal, characteristic, complemented
13C2×#89509C211yesmaximal, characteristic, complemented
14C2×#89508C211yesmaximal, characteristic, complemented
15C2×C4×#1132C211yesmaximal, characteristic, complemented
16C2×#89455C211yesmaximal, characteristic, complemented
17C23×C7×C8C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×#6502—21no—
21C2×#6498—21no—
22C2×#6493C2211yescharacteristic
23C2×#6493C2211yescharacteristic
24C2×#6489C2211yescharacteristic
25C2×#6489C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C2×#6487C2211yescharacteristic
29C2×#6487C2211yescharacteristic
30C22×#1132C2211yescharacteristic
31#90256—24no—
32#90256C2218yes—
33#90232—24no—
34#90232C2218yescomplemented
35C2×#6461—21no—
36C2×#6452—21no—
37C2×#6446—21no—
38C2×(C22⋊D7)⋊C4—21no—
39C2×#6442—21no—
40C2×#6440—21no—
41C2×C4×D28C2211yescharacteristic
42C2×#6433C2211yescharacteristic
43C2×#6433C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×C8×D4C2218yescomplemented
46C2×C7×C4⋊C8C2211yescharacteristic
47C2×C7×C22⋊C8C2211yescharacteristic
48C2×C7×C22⋊C8C2211yescharacteristic
49C2×C4×C7×C8C2211yescharacteristic
50#89886C2218yescomplemented
51#89886C2218yescomplemented
52C2×#6395C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55#89878C2218yescomplemented
56C2×#6392C2211yescharacteristic
57C2×#6392C2211yescharacteristic
58C2×#6392C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6391C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6391C2211yescharacteristic
63C2×#6391C2211yescharacteristic
64C2×#6391C2211yescharacteristic
65C2×#6391C2218yescomplemented
66C2×#6390C2211yescharacteristic
67C2×#6390C2211yescharacteristic
68C2×#6390C2211yescharacteristic
69#89619C2218yescomplemented
70#89601C2218yescomplemented
71#89509C2218yescomplemented
72#89508C2218yescomplemented
73#89495C2218yescomplemented
74#89494C2218yescomplemented
75C4×#1132C2218yescomplemented
76#89455C2218yescomplemented
77C2×#3337—71nomaximal, Sylow
78C22×C7×D4D411yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C23×Dic7—21no—
84C23×Dic7—21no—
85C22×D28C2311yescharacteristic
86C22×C4×D7—21no—
87C22×Dic14C2311yescharacteristic
88C22×C7×C8—24no—
89C22×C7×C8—24no—
90C22×C7×C8C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2314yes—
94C22×C7×C8C2314yes—
95C22×C7×C8C2311yescharacteristic
96C4×C7×D4D414yes—
97C4×C7×D4C2314yes—
98C2×C7×C4⋊C4D411yescharacteristic
99C2×C7×C22⋊C4D411yescharacteristic
100C2×C7×C22⋊C4D411yescharacteristic
101C2×C42×C7C2311yescharacteristic
102C2×C22⋊Dic7—21no—
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106#6502—28no—
107#6498—28no—
108#6493—22no—
109#6493—22no—
110#6493C2314yes—
111#6493C2314yes—
112C2×(C2×D7)⋊C4—21no—
113C2×(C2×D7)⋊C4—21no—
114C2×(C2×D7)⋊C4—21no—
115#6489—22no—
116#6489—22no—
117#6489C2314yes—
118#6489C2314yes—
119C2×C4⋊Dic7—21no—
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7—22no—
122C2×C4⋊Dic7—22no—
123C2×C4⋊Dic7C2311yescharacteristic
124C2×C4⋊Dic7C2311yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129C2×C4⋊Dic7C2314yes—
130C2×C4⋊Dic7C2314yes—
131#6487—22no—
132#6487—22no—
133#6487C2314yes—
134#6487C2314yes—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×C4×Dic7—21no—
143C2×C4×Dic7—21no—
144C2×C4×Dic7—21no—
145C2×#1132—24no—
146C2×#1132C2314yes—
147#6461—28no—
148#6452—28no—
149#6446—28no—
150(C22⋊D7)⋊C4—28no—
151#6442—28no—
152#6440—28no—
153C4×D28—22no—
154C4×D28C2314yes—
155#6433—22no—
156#6433—22no—
157#6433C2314yes—
158#6433C2314yes—
159C4×Dic14—22no—
160C4×Dic14C2314yes—
161C7×C4⋊C8C2314yes—
162C7×C22⋊C8C2314yes—
163C7×C22⋊C8C2314yes—
164C4×C7×C8C2314yes—
165#6395C2314yes—
166#6395C2314yes—
167#6395C2314yes—
168#6392C2314yes—
169#6392C2314yes—
170#6392C2314yes—
171#6392C2314yes—
172#6391C2314yes—
173#6391C2314yes—
174#6391C2314yes—
175#6391C2314yes—
176#6391C2314yes—
177#6390C2314yes—
178#6390C2314yes—
179#6390C2314yes—
180C2×#553—71no—
181C2×#552—71no—
182#3337—716no—
183C2×#499—71no—
184C2×#484—71no—
185C2×#485—71no—
186C2×#482—71no—
187C2×#480—71no—
188C2×#479—71no—
189C2×#478—71no—
190C2×#465—71no—
191C2×#465—71no—
192C2×C4×SD16—71no—
193C2×C8×D4D711yescharacteristic, complemented
194C2×#427—71no—
195C22×#106—71no—
196C24×C7C2×D411yescharacteristic
197C24×C7C2×D411yescharacteristic
198C23×D7—21no—
199C2×C7×D4—24no—
200C2×C7×D4C2×D414yes—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D412yes—
210C22×C4×C7C2×D412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2411yescharacteristic
214C2×C22⋊D7—24no—
215C2×C22⋊D7—24no—
216C2×C22⋊D7—44no—
217C2×C22⋊D7—82no—
218C22×Dic7—24no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—24no—
227C22×Dic7—44no—
228C22×Dic7—82no—
229C2×D28—22no—
230C2×D28—22no—
231C2×D28—21no—
232C2×D28C2412yes—
233C2×C4×D7—24no—
234C2×C4×D7—82no—
235C2×Dic14—22no—
236C2×Dic14—22no—
237C2×Dic14—21no—
238C2×Dic14C2412yes—
239C2×C7×C8—22no—
240C2×C7×C8—22no—
241C2×C7×C8—22no—
242C2×C7×C8—28no—
243C2×C7×C8—28no—
244C2×C7×C8#4114yes—
245C2×C7×C8C2412yes—
246C2×C7×C8C2412yes—
247C2×C7×C8C2412yes—
248C2×C7×C8C2412yes—
249C7×C4⋊C4C2×D414yes—
250C7×C22⋊C4C2×D414yes—
251C7×C22⋊C4C2×D414yes—
252C42×C7C2×D412yes—
253C42×C7C2412yes—
254C22⋊Dic7—24no—
255C22⋊Dic7—24no—
256C22⋊Dic7—24no—
257C22⋊Dic7—24no—
258(C2×D7)⋊C4—24no—
259(C2×D7)⋊C4—24no—
260(C2×D7)⋊C4—24no—
261C4⋊Dic7—21no—
262C4⋊Dic7—21no—
263C4⋊Dic7—21no—
264C4⋊Dic7—21no—
265C4⋊Dic7—21no—
266C4⋊Dic7—21no—
267C4⋊Dic7—24no—
268C4⋊Dic7—24no—
269C4⋊Dic7C2412yes—
270C4⋊Dic7C2412yes—
271C4⋊Dic7C2412yes—
272C4⋊Dic7C2412yes—
273C4⋊Dic7C2412yes—
274C4⋊Dic7C2412yes—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282C4×Dic7—24no—
283C4×Dic7—24no—
284C4×Dic7—24no—
285#1132—28no—
286C22×SD16—71no—
287C23×C8C2×D711yescharacteristic
288C23×C8C2×D711yescharacteristic
289#553—78no—
290#553—144no—
291#552—78no—
292#552—144no—
293C2×#126—141no—
294C2×#126—141no—
295C2×#125—71no—
296C2×#125—71no—
297C2×#125—141no—
298C2×#123—141no—
299C2×#123—141no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8—71no—
302C2×#121—71no—
303C2×#121—71no—
304C2×#121—141no—
305C2×C4×Q8—71no—
306C2×C4×D4—71no—
307C2×C4×D4—141no—
308C2×C4×D4C2×D711yescharacteristic
309C2×#117—71no—
310C2×#117—71no—
311C2×#117—141no—
312C22×C4⋊C4—71no—
313C22×C4⋊C4—71no—
314#499—78no—
315#485—78no—
316#484—78no—
317#482—78no—
318#480—78no—
319#479—78no—
320#478—78no—
321#465—78no—
322#465—78no—
323C4×SD16—78no—
324C8×D4C2×D718yescomplemented
325#427—78no—
326C2×#107—71no—
327C2×#107—71no—
328C2×#107—71no—
329C2×#107—71no—
330C2×#106—71no—
331C2×#106—71no—
332C2×#106—78no—
333C2×#106—71no—
334C2×#106—71no—
335C2×#106—71no—
336C2×C4⋊C8C2×D711yescharacteristic
337C2×#103—71no—
338C2×#103—71no—
339C2×#103—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×C22⋊C8C2×D711yescharacteristic
344C2×C22⋊C8C2×D711yescharacteristic
345C2×C4×C8C2×D711yescharacteristic
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7#13514yes—
352C23×C7C22×D412yes—
353C23×C7C22×D412yes—
354C23×C7C22×D411yescharacteristic
355C22×D7—22no—
356C22×D7—42no—
357C22×D7—42no—
358C22×D7—42no—
359C7×D4—28no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—24no—
365C2×C4×C7—24no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7C22×D412yes—
371C2×C4×C7C22×D412yes—
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—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—42no—
388C2×Dic7—48no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—84no—
396D28—22no—
397D28—22no—
398D28—42no—
399C4×D7—84no—
400Dic14—22no—
401Dic14—22no—
402Dic14—42no—
403C7×C8—22no—
404C7×C8—22no—
405C7×C8—22no—
406C7×C8C2×#4114yes—
407C22×Q8—71no—
408C22×D4—71no—
409C22×D4—141no—
410C22×D4—141no—
411C22×D4D2811yescharacteristic
412C23×C4—141no—
413C23×C4—141no—
414C23×C4—141no—
415C23×C4C22×D711yescharacteristic
416C23×C4C22×D711yescharacteristic
417C2×SD16—74no—
418C2×SD16—144no—
419C22×C8—24no—
420C22×C8—24no—
421C22×C8C22×D711yescharacteristic
422C22×C8C22×D711yescharacteristic
423C22×C8C22×D714yes—
424C22×C8C22×D714yes—
425C22×C8C22×D711yescharacteristic
426C22×C8C22×D711yescharacteristic
427#126—148no—
428#126—148no—
429#125—74no—
430#125—74no—
431#125—148no—
432#125—142no—
433#125—142no—
434#123—148no—
435#123—148no—
436C22⋊Q8—74no—
437C22⋊Q8—74no—
438C22⋊Q8—142no—
439C22⋊Q8—142no—
440#121—74no—
441#121—74no—
442#121—148no—
443#121—142no—
444#121—142no—
445C4×Q8—74no—
446C4×Q8—142no—
447C4×D4—74no—
448C4×D4—148no—
449C4×D4—142no—
450C4×D4D2814yes—
451C4×D4C22×D714yes—
452#117—74no—
453#117—74no—
454#117—142no—
455#117—142no—
456#117—148no—
457C2×C4⋊C4—71no—
458C2×C4⋊C4—71no—
459C2×C4⋊C4—71no—
460C2×C4⋊C4—71no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—74no—
463C2×C4⋊C4—71no—
464C2×C4⋊C4—71no—
465C2×C4⋊C4—141no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—142no—
468C2×C4⋊C4—142no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4—141no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4—141no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4D2811yescharacteristic
477C2×C22⋊C4—141no—
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⋊C4D2811yescharacteristic
485C2×C22⋊C4D2811yescharacteristic
486C2×C42—141no—
487C2×C42—141no—
488C2×C42—141no—
489C2×C42C22×D711yescharacteristic
490#107—74no—
491#107—74no—
492#107—74no—
493#107—74no—
494#106—74no—
495#106—74no—
496#106—74no—
497#106—74no—
498#106—74no—
499C4⋊C8C22×D714yes—
500#103—74no—
501#103—74no—
502#103—74no—
503#102—74no—
504#102—74no—
505#102—74no—
506C22⋊C8C22×D714yes—
507C22⋊C8C22×D714yes—
508C4×C8C22×D714yes—
509C22×C7—28no—
510C22×C7—22no—
511C22×C7—22no—
512C22×C7—22no—
513C22×C7—22no—
514C22×C7—22no—
515C22×C7—44no—
516C22×C7#54712yes—
517C22×C7C2×#13514yes—
518C22×C7C2×#13512yes—
519C22×C7#57712yes—
520C22×C7C23×D411yescharacteristic
521C2×D7—42no—
522C2×D7—42no—
523C2×D7—42no—
524C2×D7—84no—
525C4×C7—22no—
526C4×C7—22no—
527C4×C7—22no—
528C4×C7—22no—
529C4×C7#54712yes—
530C4×C7C22×#4111yescharacteristic
531C4×C7C2×2−1+411yescharacteristic
532Dic7—42no—
533Dic7—42no—
534Dic7—42no—
535Dic7—42no—
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539C24—141no—
540C24C2×D2811yescharacteristic
541C24C2×D2811yescharacteristic
542C2×Q8—72no—
543C2×Q8—141no—
544C2×Q8—142no—
545C2×Q8—142no—
546C2×D4—24no—
547C2×D4—72no—
548C2×D4—144no—
549C2×D4—144no—
550C2×D4—141no—
551C2×D4—142no—
552C2×D4—142no—
553C2×D4—284no—
554C2×D4—562no—
555C2×D4C2×D2814yes—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—144no—
561C22×C4—141no—
562C22×C4—141no—
563C22×C4—141no—
564C22×C4—141no—
565C22×C4—141no—
566C22×C4—141no—
567C22×C4—141no—
568C22×C4—144no—
569C22×C4—144no—
570C22×C4—284no—
571C22×C4—562no—
572C22×C4—562no—
573C22×C4C2×D2812yes—
574C22×C4C2×D2812yes—
575C22×C4C2×D2811yescharacteristic
576C22×C4C2×D2811yescharacteristic
577C22×C4C2×D2811yescharacteristic
578C22×C4C2×D2811yescharacteristic
579C22×C4C23×D712yes—
580C22×C4C23×D712yes—
581C22×C4C23×D711yescharacteristic
582SD16—148no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—28no—
587C2×C8—28no—
588C2×C8#115914yes—
589C2×C8C23×D712yes—
590C2×C8C23×D712yes—
591C2×C8C23×D712yes—
592C2×C8C23×D712yes—
593C4⋊C4—72no—
594C4⋊C4—72no—
595C4⋊C4—72no—
596C4⋊C4—72no—
597C4⋊C4—72no—
598C4⋊C4—72no—
599C4⋊C4—144no—
600C4⋊C4—144no—
601C4⋊C4—144no—
602C4⋊C4—144no—
603C4⋊C4—144no—
604C4⋊C4—144no—
605C4⋊C4—144no—
606C4⋊C4—141no—
607C4⋊C4—141no—
608C4⋊C4—141no—
609C4⋊C4—141no—
610C4⋊C4—144no—
611C4⋊C4—144no—
612C4⋊C4—141no—
613C4⋊C4—141no—
614C4⋊C4C2×D2814yes—
615C22⋊C4—144no—
616C22⋊C4—144no—
617C22⋊C4—144no—
618C22⋊C4—144no—
619C22⋊C4—144no—
620C22⋊C4—144no—
621C22⋊C4—144no—
622C22⋊C4C2×D2814yes—
623C22⋊C4C2×D2814yes—
624C42—144no—
625C42—144no—
626C42—144no—
627C42C2×D2812yes—
628C42C23×D712yes—
629C2×C7—24no—
630C2×C7—42no—
631C2×C7#333714yescomplemented
632C2×C7C2×#54711yescharacteristic
633C2×C7C22×#13511yescharacteristic
634C2×C7C2×#57711yescharacteristic
635D7—82no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—142no—
642C23—282no—
643C23—282no—
644C23—282no—
645C23#646714yes—
646C23C22×D2812yes—
647C23C22×D2812yes—
648C23C22×D2811yescharacteristic
649Q8—142no—
650Q8—142no—
651Q8—282no—
652D4—28no—
653D4—142no—
654D4—142no—
655D4—288no—
656D4—282no—
657D4—564no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—142no—
671C2×C4—142no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—142no—
675C2×C4—288no—
676C2×C4—282no—
677C2×C4—282no—
678C2×C4—282no—
679C2×C4—282no—
680C2×C4—282no—
681C2×C4—282no—
682C2×C4—282no—
683C2×C4—564no—
684C2×C4—564no—
685C2×C4C22×D2812yes—
686C2×C4C22×D2812yes—
687C2×C4C22×D2812yes—
688C2×C4C22×D2812yes—
689C2×C4C22×D2811yescharacteristic
690C2×C4C2×#115912yes—
691C2×C4#655412yes—
692C2×C4C24×D711yescharacteristic
693C8—22no—
694C8—22no—
695C8—22no—
696C8C2×#115914yes—
697C7C2×#333711yescharacteristic, complemented, Sylow
698C22—28no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—282no—
706C22—282no—
707C22—282no—
708C22—564no—
709C22#9024612yes—
710C22C2×#646714yes—
711C22C2×#646712yes—
712C22#9044212yes—
713C22C23×D2811yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—282no—
719C4—282no—
720C4—282no—
721C4—282no—
722C4—282no—
723C4—282no—
724C4—282no—
725C4#9024612yes—
726C4C22×#115911yescharacteristic
727C4C2×#655411yescharacteristic
728C2—24no—
729C2—42no—
730C2—562no—
731C2#1173685914yesdirect product factor
732C2C2×#9024611yescharacteristic
733C2C22×#646711yescharacteristic
734C2C2×#9044211yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×C8×D4C2
socleC23×C7C22×D4
prime radicalC2×#90256C2
hypercenterC2×C8×D4D7
hypocenterC7C2×#3337
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. C2×#90232C2semidirect
3. C2×C7×C8×D4C2semidirect
4. C2×#89886C2semidirect
5. C2×#89886C2semidirect
6. C2×#89878C2semidirect
7. C22×#6391C2semidirect
8. #11736859C2direct (N × H)
9. C2×#89601C2semidirect
10. C2×#89619C2semidirect
11. C2×#89494C2semidirect
12. C2×#89495C2semidirect
13. C2×#89509C2semidirect
14. C2×#89508C2semidirect
15. C2×C4×#1132C2semidirect
16. C2×#89455C2semidirect
34. #90232C22semidirect
45. C7×C8×D4C22semidirect
50. #89886C22semidirect
51. #89886C22semidirect
55. #89878C22semidirect
65. C2×#6391C22semidirect
69. #89619C22semidirect
70. #89601C22semidirect
71. #89509C22semidirect
72. #89508C22semidirect
73. #89495C22semidirect
74. #89494C22semidirect
75. C4×#1132C22semidirect
76. #89455C22semidirect
193. C2×C8×D4D7semidirect
324. C8×D4C2×D7semidirect
631. C2×C7#3337semidirect
697. C7C2×#3337semidirect
731. C2#11736859direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902562
C2×#902322
C2×C7×C8×D42
C2×#898862
C2×#898782
C22×#63912
#117368592
C2×#896012
C2×#896192
C2×#894942
C2×#894952
C2×#895092
C2×#895082
C2×C4×#11322
C2×#894552
C2×#33377