Finite Group Databasebeta

← C2×#11737300 #14234274

Subgroups — C2×#11737300 #14234274

Order 1792.

2082 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90230C211yesmaximal, characteristic, complemented
2C2×D4×Dic14C211yesmaximal, characteristic, complemented
3C2×C7×#442C211yesmaximal, characteristic
4C2×#89924C211yesmaximal, characteristic
5C2×D8×Dic7C211yesmaximal, characteristic
6C2×#89781C211yesmaximal, characteristic, complemented
7C2×#89780C211yesmaximal, characteristic, complemented
8#11737300C2116yesmaximal, direct product factor
9C2×#89628C211yesmaximal, characteristic, complemented
10C2×#89627C211yesmaximal, characteristic, complemented
11C2×#89538C211yesmaximal, characteristic, complemented
12C2×#89533C211yesmaximal, characteristic, complemented
13C2×#89533C211yesmaximal, characteristic, complemented
14C2×#89531C211yesmaximal, characteristic, complemented
15C2×#89474C211yesmaximal, characteristic, complemented
16C2×#89473C211yesmaximal, characteristic, complemented
17C23×Dic14—21no—
18C22×C7×D8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×D4×Dic7C2211yescharacteristic
22C2×D4×Dic7C2211yescharacteristic
23C2×D4×Dic7C2211yescharacteristic
24C2×D4×Dic7C2211yescharacteristic
25C2×#6487—21no—
26C2×#6487—21no—
27C22×Dic7⋊C4—21no—
28#90230—24no—
29#90230C2218yescomplemented
30D4×Dic14—24no—
31D4×Dic14C2218yescomplemented
32C2×#6453C2211yescharacteristic
33C2×#6451C2211yescharacteristic
34C2×#6451C2211yescharacteristic
35C2×#6451C2211yescharacteristic
36C2×#6441—21no—
37C2×#6441—21no—
38C2×#6441—21no—
39C2×#6441—21no—
40C2×#6433C2211yescharacteristic
41C2×#6432C2211yescharacteristic
42C2×C4×Dic14C2211yescharacteristic
43C7×#442C2218yes—
44C2×C7×#106C2211yescharacteristic
45C2×C7×#102C2211yescharacteristic
46C2×C7×#102C2211yescharacteristic
47C2×C7×#97C2211yescharacteristic
48C2×#6406C2211yescharacteristic
49C2×#6406C2211yescharacteristic
50C2×#6406C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52#89924C2218yes—
53D8×Dic7C2218yes—
54C2×#6392C2211yescharacteristic
55C2×#6392C2211yescharacteristic
56C2×#6391C2211yescharacteristic
57C2×#6391C2211yescharacteristic
58C2×#6389C2211yescharacteristic
59C2×Dic7⋊C8C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×C8×Dic7C2211yescharacteristic
62#89781C2218yescomplemented
63#89780C2218yescomplemented
64C2×#6382C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×C4⋊(C7⋊C8)C2211yescharacteristic
69#89628C2218yescomplemented
70#89627C2218yescomplemented
71#89538C2218yescomplemented
72#89533C2218yescomplemented
73#89533C2218yescomplemented
74#89531C2218yescomplemented
75#89474C2218yescomplemented
76#89473C2218yescomplemented
77C2×#3384—71nomaximal, Sylow
78C22×C7×D4C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C23×C4×C7—21no—
82C23×Dic7—21no—
83C23×Dic7—21no—
84C23×Dic7—21no—
85C23×Dic7—21no—
86C22×Dic14—21no—
87C22×Dic14—21no—
88C22×Dic14—21no—
89C22×Dic14—21no—
90C22×Dic14—28no—
91C22×Dic14—48no—
92C22×Dic14D411yescharacteristic
93C2×C7×D8Q818yescomplemented
94C2×C7×D8C2314yes—
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C4×C7×D4—22no—
98C4×C7×D4—22no—
99C4×C7×D4C2314yes—
100C4×C7×D4C2314yes—
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C22⋊C4—21no—
104C2×C7×C22⋊C4—21no—
105C2×C42×C7C2311yescharacteristic
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109C2×C22⋊Dic7—21no—
110D4×Dic7—22no—
111D4×Dic7—22no—
112D4×Dic7—22no—
113D4×Dic7—22no—
114D4×Dic7C2314yes—
115D4×Dic7C2314yes—
116D4×Dic7C2314yes—
117D4×Dic7C2314yes—
118C2×C4⋊Dic7—21no—
119C2×C4⋊Dic7—21no—
120C2×C4⋊Dic7D411yescharacteristic
121C2×C4⋊Dic7C2311yescharacteristic
122C2×C4⋊Dic7C2311yescharacteristic
123C2×C4⋊Dic7C2311yescharacteristic
124C2×C4⋊Dic7C2311yescharacteristic
125#6487—28no—
126#6487—28no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—28no—
134C2×Dic7⋊C4D411yescharacteristic
135C2×Dic7⋊C4D411yescharacteristic
136C2×C4×Dic7C2311yescharacteristic
137C2×C4×Dic7C2311yescharacteristic
138C22×C7⋊C8C2311yescharacteristic
139C22×C7⋊C8C2311yescharacteristic
140#6453—22no—
141#6453C2314yes—
142#6451—22no—
143#6451—22no—
144#6451—22no—
145#6451C2314yes—
146#6451C2314yes—
147#6451C2314yes—
148#6441—28no—
149#6441—28no—
150#6441—28no—
151#6441—28no—
152#6433—22no—
153#6433C2314yes—
154#6432—22no—
155#6432C2314yes—
156C4×Dic14D414yes—
157C4×Dic14C2314yes—
158C7×#106C2314yes—
159C7×#102C2314yes—
160C7×#102C2314yes—
161C7×#97C2314yes—
162#6406C2314yes—
163#6406C2314yes—
164#6406C2314yes—
165#6406C2314yes—
166#6392C2314yes—
167#6392C2314yes—
168#6391C2314yes—
169#6391C2314yes—
170#6389C2314yes—
171Dic7⋊C8C2314yes—
172Dic7⋊C8C2314yes—
173C8×Dic7C2314yes—
174#6382C2314yes—
175#6382C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178C4⋊(C7⋊C8)C2314yes—
179C2×#554—71no—
180C2×D4×Q8—71no—
181#3384—716no—
182C2×#501—71no—
183C2×#501—71no—
184C2×#498—71no—
185C2×#478—71no—
186C2×#478—71no—
187C2×#476—71no—
188C2×#476—71no—
189C2×#476—71no—
190C2×#474—71no—
191C2×#446—71no—
192C2×#442—71no—
193C2×#442D711yescharacteristic
194C2×C4×D8—71no—
195C24×C7—21no—
196C24×C7—21no—
197C2×C7×D4—21no—
198C2×C7×D4—21no—
199C2×C7×D4—22no—
200C2×C7×D4—22no—
201C2×C7×D4C2×Q814yes—
202C2×C7×D4C2×Q814yescomplemented
203C2×C7×D4C2412yes—
204C2×C7×D4C2412yes—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—24no—
208C22×C4×C7—24no—
209C22×C4×C7—44no—
210C22×C4×C7—82no—
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2411yescharacteristic
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—24no—
219C22×Dic7—24no—
220C22×Dic7—24no—
221C22×Dic7—24no—
222C22×Dic7—44no—
223C22×Dic7—44no—
224C22×Dic7—44no—
225C22×Dic7—82no—
226C22×Dic7C2×D411yescharacteristic
227C22×Dic7C2×D411yescharacteristic
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230C2×Dic14—24no—
231C2×Dic14—24no—
232C2×Dic14—24no—
233C2×Dic14—24no—
234C2×Dic14—24no—
235C2×Dic14—432no—
236C2×Dic14—44no—
237C2×Dic14—44no—
238C2×Dic14—44no—
239C2×Dic14—82no—
240C2×Dic14C2×D414yes—
241C7×D8C2×Q8116yescomplemented
242C2×C7×C8—22no—
243C2×C7×C8C2×Q814yescomplemented
244C2×C7×C8C2412yes—
245C2×C7×C8C2412yes—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4C2412yes—
249C7×C4⋊C4C2412yes—
250C7×C22⋊C4—24no—
251C7×C22⋊C4—24no—
252C42×C7C2×D412yes—
253C42×C7C2412yes—
254C22⋊Dic7—24no—
255C22⋊Dic7—24no—
256C22⋊Dic7—24no—
257C22⋊Dic7—24no—
258C4⋊Dic7—21no—
259C4⋊Dic7—21no—
260C4⋊Dic7—24no—
261C4⋊Dic7—21no—
262C4⋊Dic7—21no—
263C4⋊Dic7—24no—
264C4⋊Dic7C2×D414yes—
265C4⋊Dic7C2412yes—
266C4⋊Dic7C2412yes—
267C4⋊Dic7C2412yes—
268C4⋊Dic7C2412yes—
269Dic7⋊C4—24no—
270Dic7⋊C4—24no—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4C2×D414yes—
276Dic7⋊C4C2×D414yes—
277C4×Dic7C2×D412yes—
278C4×Dic7C2×D412yes—
279C4×Dic7C2412yes—
280C4×Dic7C2412yes—
281C2×C7⋊C8—22no—
282C2×C7⋊C8—22no—
283C2×C7⋊C8C2412yes—
284C2×C7⋊C8C2412yes—
285C23×Q8—141no—
286C22×D8C2×D711yescharacteristic
287#554—78no—
288#554—144no—
289D4×Q8—78no—
290D4×Q8—144no—
291C2×C4⋊Q8—71no—
292C2×C4⋊Q8—71no—
293C2×C4⋊Q8—71no—
294C2×C4⋊Q8—71no—
295C2×#125—71no—
296C2×#125—71no—
297C2×C22⋊Q8—141no—
298C2×C22⋊Q8—141no—
299C2×C22⋊Q8—141no—
300C2×C22⋊Q8—141no—
301C2×C22⋊Q8—141no—
302C2×C22⋊Q8—141no—
303C2×C4×Q8—71no—
304C2×C4×D4—71no—
305C2×C4×D4—71no—
306C2×C4×D4—71no—
307C2×C4×D4—71no—
308C2×C4×D4C2×D711yescharacteristic
309C2×C4×D4C2×D711yescharacteristic
310C22×C4⋊C4—141no—
311#501—78no—
312#501—78no—
313#498—78no—
314#478—78no—
315#478—78no—
316#476—78no—
317#476—78no—
318#476—78no—
319#474—78no—
320#446—78no—
321#442—78no—
322#442C2×D718yes—
323C4×D8—78no—
324C2×#107—71no—
325C2×#107—71no—
326C2×#107—71no—
327C2×#106—71no—
328C2×#106—71no—
329C2×#106—71no—
330C2×#106—71no—
331C2×#106—71no—
332C2×#106C2×D711yescharacteristic
333C2×C4⋊C8—71no—
334C2×C4⋊C8—71no—
335C2×C4⋊C8—71no—
336C2×#102—71no—
337C2×#102—71no—
338C2×#102—71no—
339C2×#102—71no—
340C2×#102C2×D711yescharacteristic
341C2×#102C2×D711yescharacteristic
342C2×#97—71no—
343C2×#97C2×D711yescharacteristic
344C2×C4×C8—71no—
345C23×C7—24no—
346C23×C7—24no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—42no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7C22×D411yescharacteristic
354C7×D4—24no—
355C7×D4—24no—
356C7×D4—22no—
357C7×D4—22no—
358C7×D4C22×Q814yes—
359C7×D4C22×Q814yescomplemented
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—48no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—84no—
368C2×C4×C7C22×D412yes—
369C2×C4×C7C22×D412yes—
370C2×C4×C7C22×D411yescharacteristic
371C2×C4×C7C22×Q812yes—
372C2×C4×C72−1+412yes—
373C2×C4×C7C2511yescharacteristic
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—48no—
382C2×Dic7—42no—
383C2×Dic7—42no—
384C2×Dic7—42no—
385C2×Dic7—42no—
386C2×Dic7—48no—
387C2×Dic7—48no—
388C2×Dic7—84no—
389C2×Dic7AGL(1,ℤ/8)14yes—
390C2×Dic7C22×D412yes—
391C2×Dic7C22×D412yes—
392C2×Dic7C22×D412yes—
393C2×Dic7C22×D412yes—
394Dic14—28no—
395Dic14—48no—
396Dic14—48no—
397Dic14—48no—
398Dic14—84no—
399C7×C8—22no—
400C7×C8C22×Q814yescomplemented
401C7⋊C8—22no—
402C7⋊C8—22no—
403C22×Q8—71no—
404C22×Q8—141no—
405C22×Q8—141no—
406C22×Q8—141no—
407C22×Q8—148no—
408C22×Q8—141no—
409C22×Q8—288no—
410C22×D4C22×D711yescharacteristic
411C22×D4C22×D711yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—141no—
415C23×C4—141no—
416C23×C4—141no—
417C23×C4—141no—
418C2×D8Dic1418yescomplemented
419C2×D8C22×D714yes—
420C22×C8—71no—
421C22×C8—71no—
422C22×C8C22×D711yescharacteristic
423C22×C8C22×D711yescharacteristic
424C4⋊Q8—74no—
425C4⋊Q8—74no—
426C4⋊Q8—74no—
427C4⋊Q8—74no—
428C4⋊Q8—142no—
429C4⋊Q8—142no—
430C4⋊Q8—142no—
431C4⋊Q8—142no—
432#125—74no—
433#125—74no—
434#125—142no—
435#125—142no—
436C22⋊Q8—148no—
437C22⋊Q8—148no—
438C22⋊Q8—148no—
439C22⋊Q8—148no—
440C22⋊Q8—148no—
441C22⋊Q8—148no—
442C4×Q8—74no—
443C4×Q8—74no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—74no—
447C4×D4—74no—
448C4×D4—74no—
449C4×D4—74no—
450C4×D4—142no—
451C4×D4—142no—
452C4×D4—142no—
453C4×D4—142no—
454C4×D4C22×D714yes—
455C4×D4C22×D714yes—
456C2×C4⋊C4—71no—
457C2×C4⋊C4—71no—
458C2×C4⋊C4—71no—
459C2×C4⋊C4—71no—
460C2×C4⋊C4—71no—
461C2×C4⋊C4—71no—
462C2×C4⋊C4—71no—
463C2×C4⋊C4—148no—
464C2×C4⋊C4—141no—
465C2×C4⋊C4—141no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4C22×D711yescharacteristic
473C2×C4⋊C4C22×D711yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—141no—
477C2×C22⋊C4—141no—
478C2×C22⋊C4—141no—
479C2×C22⋊C4—141no—
480C2×C42—71no—
481C2×C42—71no—
482C2×C42C22×D711yescharacteristic
483#107—74no—
484#107—74no—
485#107—74no—
486#106—74no—
487#106—74no—
488#106—74no—
489#106—74no—
490#106—74no—
491#106C22×D714yes—
492C4⋊C8—74no—
493C4⋊C8—74no—
494C4⋊C8—74no—
495#102—74no—
496#102—74no—
497#102—74no—
498#102—74no—
499#102C22×D714yes—
500#102C22×D714yes—
501#97—74no—
502#97C22×D714yes—
503C4×C8—74no—
504C22×C7—24no—
505C22×C7—24no—
506C22×C7—48no—
507C22×C7—48no—
508C22×C7—42no—
509C22×C7—42no—
510C22×C7—42no—
511C22×C7—42no—
512C22×C7D4×Q812yes—
513C22×C7C2×AGL(1,ℤ/8)12yes—
514C22×C7#57712yes—
515C22×C7C23×D411yescharacteristic
516C4×C7—22no—
517C4×C7—22no—
518C4×C7—42no—
519C4×C7—42no—
520C4×C7D4×Q812yes—
521C4×C7C23×Q811yescharacteristic
522C4×C7C2×2−1+411yescharacteristic
523Dic7—22no—
524Dic7—22no—
525Dic7—22no—
526Dic7—42no—
527Dic7—42no—
528Dic7—42no—
529Dic7—42no—
530Dic7C2×AGL(1,ℤ/8)14yes—
531C24—21no—
532C24—21no—
533C2×Q8—74no—
534C2×Q8—144no—
535C2×Q8—144no—
536C2×Q8—144no—
537C2×Q8—144no—
538C2×Q8—144no—
539C2×Q8—284no—
540C2×Q8—284no—
541C2×Q8—284no—
542C2×Q8—2832no—
543C2×Q8—562no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4C2×Dic1414yes—
549C2×D4C2×Dic1414yescomplemented
550C2×D4C23×D712yes—
551C2×D4C23×D712yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—44no—
557C22×C4—71no—
558C22×C4—71no—
559C22×C4—71no—
560C22×C4—71no—
561C22×C4—82no—
562C22×C4—144no—
563C22×C4—144no—
564C22×C4—144no—
565C22×C4—144no—
566C22×C4—141no—
567C22×C4—141no—
568C22×C4—141no—
569C22×C4—141no—
570C22×C4—284no—
571C22×C4—284no—
572C22×C4—284no—
573C22×C4—562no—
574C22×C4D4×D711yescharacteristic
575C22×C4D4×D711yescharacteristic
576C22×C4C23×D711yescharacteristic
577D8C2×Dic14116yescomplemented
578C2×C8—22no—
579C2×C8—72no—
580C2×C8—72no—
581C2×C8—142no—
582C2×C8—142no—
583C2×C8C2×Dic1414yescomplemented
584C2×C8C23×D712yes—
585C2×C8C23×D712yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—74no—
589C4⋊C4—74no—
590C4⋊C4—74no—
591C4⋊C4—72no—
592C4⋊C4—72no—
593C4⋊C4—72no—
594C4⋊C4—72no—
595C4⋊C4—144no—
596C4⋊C4—144no—
597C4⋊C4—144no—
598C4⋊C4—144no—
599C4⋊C4—144no—
600C4⋊C4—144no—
601C4⋊C4—144no—
602C4⋊C4—141no—
603C4⋊C4—141no—
604C4⋊C4—141no—
605C4⋊C4—141no—
606C4⋊C4—144no—
607C4⋊C4C23×D712yes—
608C4⋊C4C23×D712yes—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—144no—
612C22⋊C4—144no—
613C22⋊C4—144no—
614C22⋊C4—144no—
615C42—72no—
616C42—72no—
617C42—72no—
618C42—72no—
619C42D4×D712yes—
620C42C23×D712yes—
621C2×C7—44no—
622C2×C7—44no—
623C2×C7#338414yescomplemented
624C2×C7C2×D4×Q811yescharacteristic
625C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
626C2×C7C2×#57711yescharacteristic
627C23—24no—
628C23—24no—
629C23—22no—
630C23—22no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23C2×D4×D711yescharacteristic
636Q8—148no—
637Q8—288no—
638Q8—288no—
639Q8—288no—
640Q8—564no—
641D4—24no—
642D4—24no—
643D4—22no—
644D4—22no—
645D4C22×Dic1414yes—
646D4C22×Dic1414yescomplemented
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—48no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—74no—
655C2×C4—72no—
656C2×C4—72no—
657C2×C4—72no—
658C2×C4—72no—
659C2×C4—84no—
660C2×C4—142no—
661C2×C4—142no—
662C2×C4—142no—
663C2×C4—142no—
664C2×C4—142no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—288no—
668C2×C4—288no—
669C2×C4—288no—
670C2×C4—282no—
671C2×C4—282no—
672C2×C4—282no—
673C2×C4—282no—
674C2×C4—564no—
675C2×C4C22×Dic1412yes—
676C2×C4C2×D4×D712yes—
677C2×C4C2×D4×D712yes—
678C2×C4C2×D4×D711yescharacteristic
679C2×C4#655412yes—
680C2×C4C24×D711yescharacteristic
681C8—22no—
682C8—142no—
683C8—142no—
684C8C22×Dic1414yescomplemented
685C7C2×#338411yescharacteristic, complemented, Sylow
686C22—24no—
687C22—24no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—48no—
693C22—48no—
694C22D4×Dic1412yes—
695C22D7×AGL(1,ℤ/8)12yes—
696C22#9046612yes—
697C22C22×D4×D711yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—74no—
703C4—142no—
704C4—142no—
705C4—142no—
706C4—282no—
707C4—282no—
708C4—282no—
709C4—282no—
710C4D4×Dic1412yes—
711C4C23×Dic1411yescharacteristic
712C4C2×#655411yescharacteristic
713C2—44no—
714C2—44no—
715C2#1173730014yesdirect product factor
716C2C2×D4×Dic1411yescharacteristic
717C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
718C2C2×#9046611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#442C2
socleC23×C7C22×D4
prime radicalC22×C7×D8C22
hypercenterC2×#442D7
hypocenterC7C2×#3384
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#90230C2semidirect
2. C2×D4×Dic14C2semidirect
6. C2×#89781C2semidirect
7. C2×#89780C2semidirect
8. #11737300C2direct (N × H)
9. C2×#89628C2semidirect
10. C2×#89627C2semidirect
11. C2×#89538C2semidirect
12. C2×#89533C2semidirect
13. C2×#89533C2semidirect
14. C2×#89531C2semidirect
15. C2×#89474C2semidirect
16. C2×#89473C2semidirect
29. #90230C22semidirect
31. D4×Dic14C22semidirect
62. #89781C22semidirect
63. #89780C22semidirect
69. #89628C22semidirect
70. #89627C22semidirect
71. #89538C22semidirect
72. #89533C22semidirect
73. #89533C22semidirect
74. #89531C22semidirect
75. #89474C22semidirect
76. #89473C22semidirect
93. C2×C7×D8Q8semidirect
202. C2×C7×D4C2×Q8semidirect
241. C7×D8C2×Q8semidirect
243. C2×C7×C8C2×Q8semidirect
359. C7×D4C22×Q8semidirect
400. C7×C8C22×Q8semidirect
418. C2×D8Dic14semidirect
549. C2×D4C2×Dic14semidirect
577. D8C2×Dic14semidirect
583. C2×C8C2×Dic14semidirect
623. C2×C7#3384semidirect
646. D4C22×Dic14semidirect
684. C8C22×Dic14semidirect
685. C7C2×#3384semidirect
715. C2#11737300direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902302
C2×D4×Dic142
C2×C7×#4422
C2×#899242
C2×D8×Dic72
C2×#897812
C2×#897802
#117373002
C2×#896282
C2×#896272
C2×#895382
C2×#895332
C2×#895312
C2×#894742
C2×#894732
C2×#33847