Finite Group Databasebeta

← C2×#11736915 #14232345

Subgroups — C2×#11736915 #14232345

Order 1792.

1878 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×#90234C211yesmaximal, characteristic
2C2×#90232C211yesmaximal, characteristic
3C2×C7×#435C211yesmaximal, characteristic
4C2×#89909C211yesmaximal, characteristic, complemented
5C2×#89893C211yesmaximal, characteristic, complemented
6C2×#89888C211yesmaximal, characteristic, complemented
7C22×#6391C211yesmaximal, characteristic, complemented
8#11736915C2116yesmaximal, direct product factor
9C2×#89601C211yesmaximal, characteristic, complemented
10C2×#89623C211yesmaximal, characteristic, complemented
11C2×#89494C211yesmaximal, characteristic, complemented
12C2×#89495C211yesmaximal, characteristic, complemented
13C2×#89493C211yesmaximal, characteristic, complemented
14C2×#89493C211yesmaximal, characteristic, complemented
15C2×#89488C211yesmaximal, characteristic, complemented
16C2×#89474C211yesmaximal, characteristic, complemented
17C22×C7×M16C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×#6498—21no—
21C2×D4×Dic7—21no—
22C2×#6489C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C2×#6487C2211yescharacteristic
27C2×#6487C2211yescharacteristic
28C2×#6487C2211yescharacteristic
29C2×#6487C2211yescharacteristic
30C22×Dic28C2211yescharacteristic
31#90234—24no—
32#90234C2218yes—
33#90232—24no—
34#90232C2218yes—
35C2×#6453—21no—
36C2×#6452—21no—
37C2×#6442—21no—
38C2×#6441—21no—
39C2×#6441—21no—
40C2×#6440—21no—
41C2×#6433C2211yescharacteristic
42C2×#6432C2211yescharacteristic
43C2×C4×Dic14C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×#435C2218yes—
46C2×C7×C4⋊C8C2211yescharacteristic
47C2×C7×C22⋊C8C2211yescharacteristic
48C2×C7×C22⋊C8C2211yescharacteristic
49C2×C7×#97C2211yescharacteristic
50#89909C2218yescomplemented
51#89893C2218yescomplemented
52#89888C2218yescomplemented
53C2×#6392C2211yescharacteristic
54C2×#6392C2211yescharacteristic
55C2×#6392C2211yescharacteristic
56C2×#6391C2211yescharacteristic
57C2×#6391C2211yescharacteristic
58C2×#6391C2211yescharacteristic
59C2×#6391C2211yescharacteristic
60C2×#6391C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6391C2218yescomplemented
63C2×#6390C2211yescharacteristic
64C2×#6390C2211yescharacteristic
65C2×#6390C2211yescharacteristic
66C2×#6390C2211yescharacteristic
67C2×#6390C2211yescharacteristic
68C2×#6390C2211yescharacteristic
69#89623C2218yescomplemented
70#89601C2218yescomplemented
71#89495C2218yescomplemented
72#89494C2218yescomplemented
73#89493C2218yescomplemented
74#89493C2218yescomplemented
75#89488C2218yescomplemented
76#89474C2218yescomplemented
77C2×#3344—71nomaximal, Sylow
78C22×C7×D4D411yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×Dic7—21no—
82C23×Dic7—21no—
83C23×Dic7—21no—
84C22×Dic14—21no—
85C22×Dic14C2311yescharacteristic
86C22×Dic14C2311yescharacteristic
87C2×C7×M16—24no—
88C2×C7×M16C2314yes—
89C22×C7×C8—24no—
90C22×C7×C8C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2314yes—
94C22×C7×C8C2311yescharacteristic
95C4×C7×D4D414yes—
96C4×C7×D4C2314yes—
97C2×C7×C4⋊C4D411yescharacteristic
98C2×C7×C22⋊C4D411yescharacteristic
99C2×C7×C22⋊C4D411yescharacteristic
100C2×C42×C7C2311yescharacteristic
101C2×C22⋊Dic7—21no—
102C2×C22⋊Dic7—21no—
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106#6498—28no—
107D4×Dic7—28no—
108#6489—22no—
109#6489C2314yes—
110C2×C4⋊Dic7—21no—
111C2×C4⋊Dic7—21no—
112C2×C4⋊Dic7—21no—
113C2×C4⋊Dic7—21no—
114C2×C4⋊Dic7—22no—
115C2×C4⋊Dic7—22no—
116C2×C4⋊Dic7—22no—
117C2×C4⋊Dic7C2311yescharacteristic
118C2×C4⋊Dic7C2311yescharacteristic
119C2×C4⋊Dic7C2311yescharacteristic
120C2×C4⋊Dic7C2311yescharacteristic
121C2×C4⋊Dic7C2311yescharacteristic
122C2×C4⋊Dic7C2311yescharacteristic
123C2×C4⋊Dic7C2314yes—
124C2×C4⋊Dic7C2314yes—
125C2×C4⋊Dic7C2314yes—
126#6487—22no—
127#6487—22no—
128#6487—22no—
129#6487—22no—
130#6487C2314yes—
131#6487C2314yes—
132#6487C2314yes—
133#6487C2314yes—
134C2×Dic7⋊C4—21no—
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×Dic28—24no—
146C2×Dic28C2314yes—
147#6453—28no—
148#6452—28no—
149#6442—28no—
150#6441—28no—
151#6441—28no—
152#6440—28no—
153#6433—22no—
154#6433C2314yes—
155#6432—22no—
156#6432C2314yes—
157C4×Dic14—22no—
158C4×Dic14—22no—
159C4×Dic14C2314yes—
160C4×Dic14C2314yes—
161C7×C4⋊C8C2314yes—
162C7×C22⋊C8C2314yes—
163C7×C22⋊C8C2314yes—
164C7×#97C2314yes—
165#6392C2314yes—
166#6392C2314yes—
167#6392C2314yes—
168#6391C2314yes—
169#6391C2314yes—
170#6391C2314yes—
171#6391C2314yes—
172#6391C2314yes—
173#6391C2314yes—
174#6390C2314yes—
175#6390C2314yes—
176#6390C2314yes—
177#6390C2314yes—
178#6390C2314yes—
179#6390C2314yes—
180C2×#554—71no—
181C2×#552—71no—
182#3344—716no—
183C2×#501—71no—
184C2×#484—71no—
185C2×#485—71no—
186C2×#483—71no—
187C2×#483—71no—
188C2×#479—71no—
189C2×#475—71no—
190C2×#470—71no—
191C2×#467—71no—
192C2×#441—71no—
193C2×#435D711yescharacteristic
194C2×#428—71no—
195C22×#106—71no—
196C24×C7C2×D411yescharacteristic
197C24×C7C2×D411yescharacteristic
198C2×C7×D4—24no—
199C2×C7×D4C2×D414yes—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D412yes—
209C22×C4×C7C2×D412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2411yescharacteristic
213C22×Dic7—24no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—24no—
223C22×Dic7—24no—
224C22×Dic7—44no—
225C22×Dic7—82no—
226C22×Dic7—82no—
227C2×Dic14—22no—
228C2×Dic14—22no—
229C2×Dic14—22no—
230C2×Dic14—22no—
231C2×Dic14—21no—
232C2×Dic14—21no—
233C2×Dic14—24no—
234C2×Dic14—82no—
235C2×Dic14C2412yes—
236C2×Dic14C2412yes—
237C7×M16—28no—
238C2×C7×C8—22no—
239C2×C7×C8—22no—
240C2×C7×C8—22no—
241C2×C7×C8—28no—
242C2×C7×C8#4114yes—
243C2×C7×C8C2412yes—
244C2×C7×C8C2412yes—
245C2×C7×C8C2412yes—
246C2×C7×C8C2412yes—
247C7×C4⋊C4C2×D414yes—
248C7×C22⋊C4C2×D414yes—
249C7×C22⋊C4C2×D414yes—
250C42×C7C2×D412yes—
251C42×C7C2412yes—
252C22⋊Dic7—24no—
253C22⋊Dic7—24no—
254C22⋊Dic7—24no—
255C22⋊Dic7—24no—
256C22⋊Dic7—24no—
257C4⋊Dic7—21no—
258C4⋊Dic7—21no—
259C4⋊Dic7—21no—
260C4⋊Dic7—21no—
261C4⋊Dic7—24no—
262C4⋊Dic7—21no—
263C4⋊Dic7—21no—
264C4⋊Dic7—24no—
265C4⋊Dic7—24no—
266C4⋊Dic7—24no—
267C4⋊Dic7C2412yes—
268C4⋊Dic7C2412yes—
269C4⋊Dic7C2412yes—
270C4⋊Dic7C2412yes—
271C4⋊Dic7C2412yes—
272C4⋊Dic7C2412yes—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281C4×Dic7—24no—
282C4×Dic7—24no—
283C4×Dic7—24no—
284Dic28—28no—
285C22×Q16—71no—
286C22×M16C2×D711yescharacteristic
287C23×C8C2×D711yescharacteristic
288#554—78no—
289#554—144no—
290#552—78no—
291#552—144no—
292C2×C4⋊Q8—71no—
293C2×#126—141no—
294C2×#125—71no—
295C2×#125—141no—
296C2×#125—141no—
297C2×#123—141no—
298C2×C22⋊Q8—71no—
299C2×C22⋊Q8—71no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8—71no—
302C2×C22⋊Q8—141no—
303C2×C22⋊Q8—141no—
304C2×C4×Q8—71no—
305C2×C4×Q8—71no—
306C2×C4×D4—141no—
307C2×C4×D4C2×D711yescharacteristic
308C2×#117—71no—
309C2×#117—141no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4—71no—
313#501—78no—
314#485—78no—
315#484—78no—
316#483—78no—
317#483—78no—
318#479—78no—
319#475—78no—
320#470—78no—
321#467—78no—
322#441—78no—
323#435C2×D718yes—
324#428—78no—
325C2×#107—71no—
326C2×#107—71no—
327C2×#107—71no—
328C2×#106—71no—
329C2×#106—71no—
330C2×#106—71no—
331C2×#106—71no—
332C2×#106—78no—
333C2×#106—71no—
334C2×#106—71no—
335C2×C4⋊C8C2×D711yescharacteristic
336C2×#103—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#103—71no—
340C2×#103—71no—
341C2×#103—71no—
342C2×C22⋊C8C2×D711yescharacteristic
343C2×C22⋊C8C2×D711yescharacteristic
344C2×#97C2×D711yescharacteristic
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7#13714yes—
351C23×C7C22×D412yes—
352C23×C7C22×D412yes—
353C23×C7C22×D411yescharacteristic
354C7×D4—28no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—24no—
360C2×C4×C7—24no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7C22×D412yes—
366C2×C4×C7C22×D412yes—
367C2×C4×C7C22×D412yes—
368C2×C4×C7C22×D412yes—
369C2×C4×C7C22×D411yescharacteristic
370C2×C4×C7C2×#4112yes—
371C2×C4×C72−1+412yes—
372C2×C4×C7C2511yescharacteristic
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—42no—
382C2×Dic7—42no—
383C2×Dic7—48no—
384C2×Dic7—42no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—84no—
391C2×Dic7—84no—
392Dic14—22no—
393Dic14—22no—
394Dic14—22no—
395Dic14—22no—
396Dic14—42no—
397Dic14—42no—
398Dic14—84no—
399C7×C8—22no—
400C7×C8—22no—
401C7×C8—22no—
402C7×C8C2×#4114yes—
403C22×Q8—71no—
404C22×Q8—71no—
405C22×Q8—141no—
406C22×D4D2811yescharacteristic
407C23×C4—141no—
408C23×C4—141no—
409C23×C4—141no—
410C23×C4C22×D711yescharacteristic
411C23×C4C22×D711yescharacteristic
412C2×Q16—74no—
413C2×Q16—144no—
414C2×M16—24no—
415C2×M16C22×D714yes—
416C22×C8—24no—
417C22×C8C22×D711yescharacteristic
418C22×C8C22×D714yes—
419C22×C8C22×D711yescharacteristic
420C22×C8C22×D711yescharacteristic
421C22×C8C22×D711yescharacteristic
422C4⋊Q8—74no—
423C4⋊Q8—142no—
424#126—148no—
425#125—74no—
426#125—148no—
427#125—148no—
428#125—142no—
429#123—148no—
430C22⋊Q8—74no—
431C22⋊Q8—74no—
432C22⋊Q8—74no—
433C22⋊Q8—74no—
434C22⋊Q8—142no—
435C22⋊Q8—142no—
436C22⋊Q8—142no—
437C22⋊Q8—142no—
438C22⋊Q8—148no—
439C22⋊Q8—148no—
440C4×Q8—74no—
441C4×Q8—74no—
442C4×Q8—142no—
443C4×Q8—142no—
444C4×D4—148no—
445C4×D4D2814yes—
446C4×D4C22×D714yes—
447#117—74no—
448#117—142no—
449#117—148no—
450C2×C4⋊C4—71no—
451C2×C4⋊C4—71no—
452C2×C4⋊C4—71no—
453C2×C4⋊C4—71no—
454C2×C4⋊C4—71no—
455C2×C4⋊C4—74no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—74no—
458C2×C4⋊C4—71no—
459C2×C4⋊C4—141no—
460C2×C4⋊C4—141no—
461C2×C4⋊C4—141no—
462C2×C4⋊C4—142no—
463C2×C4⋊C4—142no—
464C2×C4⋊C4—142no—
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⋊C4—141no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4D2811yescharacteristic
475C2×C22⋊C4—141no—
476C2×C22⋊C4—141no—
477C2×C22⋊C4—141no—
478C2×C22⋊C4—141no—
479C2×C22⋊C4—141no—
480C2×C22⋊C4D2811yescharacteristic
481C2×C22⋊C4D2811yescharacteristic
482C2×C42—141no—
483C2×C42—141no—
484C2×C42—141no—
485C2×C42C22×D711yescharacteristic
486#107—74no—
487#107—74no—
488#107—74no—
489#106—74no—
490#106—74no—
491#106—74no—
492#106—74no—
493#106—74no—
494#106—74no—
495C4⋊C8C22×D714yes—
496#103—74no—
497#103—74no—
498#103—74no—
499#103—74no—
500#103—74no—
501#103—74no—
502C22⋊C8C22×D714yes—
503C22⋊C8C22×D714yes—
504#97C22×D714yes—
505C22×C7—28no—
506C22×C7—22no—
507C22×C7—22no—
508C22×C7—22no—
509C22×C7—22no—
510C22×C7—22no—
511C22×C7—44no—
512C22×C7#54712yes—
513C22×C7C2×#13714yes—
514C22×C7C2×#13712yes—
515C22×C7#57712yes—
516C22×C7C23×D411yescharacteristic
517C4×C7—22no—
518C4×C7—22no—
519C4×C7—22no—
520C4×C7—22no—
521C4×C7#54712yes—
522C4×C7C22×#4111yescharacteristic
523C4×C7C2×2−1+411yescharacteristic
524Dic7—42no—
525Dic7—42no—
526Dic7—42no—
527Dic7—42no—
528Dic7—42no—
529Dic7—42no—
530Dic7—42no—
531Dic7—42no—
532C24C2×D2811yescharacteristic
533C24C2×D2811yescharacteristic
534C2×Q8—72no—
535C2×Q8—72no—
536C2×Q8—141no—
537C2×Q8—141no—
538C2×Q8—144no—
539C2×Q8—142no—
540C2×Q8—142no—
541C2×Q8—142no—
542C2×Q8—142no—
543C2×Q8—562no—
544C2×D4—24no—
545C2×D4C2×D2814yes—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—144no—
551C22×C4—141no—
552C22×C4—141no—
553C22×C4—141no—
554C22×C4—141no—
555C22×C4—141no—
556C22×C4—141no—
557C22×C4—141no—
558C22×C4—141no—
559C22×C4—144no—
560C22×C4—144no—
561C22×C4—284no—
562C22×C4—562no—
563C22×C4—562no—
564C22×C4C2×D2812yes—
565C22×C4C2×D2812yes—
566C22×C4C2×D2811yescharacteristic
567C22×C4C2×D2811yescharacteristic
568C22×C4C2×D2811yescharacteristic
569C22×C4C2×D2811yescharacteristic
570C22×C4C23×D712yes—
571C22×C4C23×D712yes—
572C22×C4C23×D711yescharacteristic
573Q16—148no—
574M16—28no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—28no—
579C2×C8#115914yes—
580C2×C8C23×D712yes—
581C2×C8C23×D712yes—
582C2×C8C23×D712yes—
583C2×C8C23×D712yes—
584C4⋊C4—72no—
585C4⋊C4—72no—
586C4⋊C4—72no—
587C4⋊C4—72no—
588C4⋊C4—72no—
589C4⋊C4—72no—
590C4⋊C4—144no—
591C4⋊C4—144no—
592C4⋊C4—144no—
593C4⋊C4—144no—
594C4⋊C4—144no—
595C4⋊C4—144no—
596C4⋊C4—144no—
597C4⋊C4—144no—
598C4⋊C4—141no—
599C4⋊C4—141no—
600C4⋊C4—144no—
601C4⋊C4—144no—
602C4⋊C4—141no—
603C4⋊C4—141no—
604C4⋊C4—141no—
605C4⋊C4—144no—
606C4⋊C4—141no—
607C4⋊C4—144no—
608C4⋊C4C2×D2814yes—
609C22⋊C4—144no—
610C22⋊C4—144no—
611C22⋊C4—144no—
612C22⋊C4—144no—
613C22⋊C4—144no—
614C22⋊C4C2×D2814yes—
615C22⋊C4C2×D2814yes—
616C42—144no—
617C42—144no—
618C42—144no—
619C42C2×D2812yes—
620C42C23×D712yes—
621C2×C7—24no—
622C2×C7—42no—
623C2×C7#334414yescomplemented
624C2×C7C2×#54711yescharacteristic
625C2×C7C22×#13711yescharacteristic
626C2×C7C2×#57711yescharacteristic
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23#647214yes—
633C23C22×D2812yes—
634C23C22×D2812yes—
635C23C22×D2811yescharacteristic
636Q8—142no—
637Q8—142no—
638Q8—142no—
639Q8—142no—
640Q8—282no—
641Q8—282no—
642Q8—564no—
643D4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—142no—
655C2×C4—142no—
656C2×C4—142no—
657C2×C4—142no—
658C2×C4—142no—
659C2×C4—142no—
660C2×C4—142no—
661C2×C4—142no—
662C2×C4—288no—
663C2×C4—282no—
664C2×C4—282no—
665C2×C4—282no—
666C2×C4—282no—
667C2×C4—282no—
668C2×C4—282no—
669C2×C4—282no—
670C2×C4—282no—
671C2×C4—564no—
672C2×C4—564no—
673C2×C4C22×D2812yes—
674C2×C4C22×D2812yes—
675C2×C4C22×D2812yes—
676C2×C4C22×D2812yes—
677C2×C4C22×D2811yescharacteristic
678C2×C4C2×#115912yes—
679C2×C4#655412yes—
680C2×C4C24×D711yescharacteristic
681C8—22no—
682C8—22no—
683C8—22no—
684C8C2×#115914yes—
685C7C2×#334411yescharacteristic, complemented, Sylow
686C22—28no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#9024612yes—
694C22C2×#647214yes—
695C22C2×#647212yes—
696C22#9044212yes—
697C22C23×D2811yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—282no—
703C4—282no—
704C4—282no—
705C4—282no—
706C4—282no—
707C4—282no—
708C4—282no—
709C4—282no—
710C4#9024612yes—
711C4C22×#115911yescharacteristic
712C4C2×#655411yescharacteristic
713C2—24no—
714C2—42no—
715C2#1173691514yesdirect product factor
716C2C2×#9024611yescharacteristic
717C2C22×#647211yescharacteristic
718C2C2×#9044211yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#435C2
socleC23×C7C22×D4
prime radicalC22×C7×D4D4
hypercenterC2×#435D7
hypocenterC7C2×#3344
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
4. C2×#89909C2semidirect
5. C2×#89893C2semidirect
6. C2×#89888C2semidirect
7. C22×#6391C2semidirect
8. #11736915C2direct (N × H)
9. C2×#89601C2semidirect
10. C2×#89623C2semidirect
11. C2×#89494C2semidirect
12. C2×#89495C2semidirect
13. C2×#89493C2semidirect
14. C2×#89493C2semidirect
15. C2×#89488C2semidirect
16. C2×#89474C2semidirect
50. #89909C22semidirect
51. #89893C22semidirect
52. #89888C22semidirect
62. C2×#6391C22semidirect
69. #89623C22semidirect
70. #89601C22semidirect
71. #89495C22semidirect
72. #89494C22semidirect
73. #89493C22semidirect
74. #89493C22semidirect
75. #89488C22semidirect
76. #89474C22semidirect
623. C2×C7#3344semidirect
685. C7C2×#3344semidirect
715. C2#11736915direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902342
C2×#902322
C2×C7×#4352
C2×#899092
C2×#898932
C2×#898882
C22×#63912
#117369152
C2×#896012
C2×#896232
C2×#894942
C2×#894952
C2×#894932
C2×#894882
C2×#894742
C2×#33447