Finite Group Databasebeta

← C2×#11738861 #14222062

Subgroups — C2×#11738861 #14222062

Order 1792.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90316C211yesmaximal, characteristic, complemented
2C2×#90195C211yesmaximal, characteristic
3C2×C7×#483C211yesmaximal, characteristic, complemented
4C2×#89819C211yesmaximal, characteristic
5C2×#89742C211yesmaximal, characteristic, complemented
6#11738861C2116yesmaximal, direct product factor
7C2×#89629C211yesmaximal, characteristic, complemented
8C2×#89643C211yesmaximal, characteristic, complemented
9C2×#89625C211yesmaximal, characteristic, complemented
10C2×#89624C211yesmaximal, characteristic, complemented
11C2×#89565C211yesmaximal, characteristic, complemented
12C2×#89590C211yesmaximal, characteristic, complemented
13C2×#89589C211yesmaximal, characteristic, complemented
14C2×#89562C211yesmaximal, characteristic, complemented
15C2×#89505C211yesmaximal, characteristic
16C2×#89492C211yesmaximal, characteristic, complemented
17C22×#1157C2211yescharacteristic
18C2×C7×C22⋊Q8C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C2×Q8×Dic7C2211yescharacteristic
21C2×#6507C2211yescharacteristic
22C22×#1144C2211yescharacteristic
23C22×#1143C2211yescharacteristic
24C2×C4×C22⋊D7—21no—
25C2×C4×C22⋊D7—21no—
26C2×#6489C2211yescharacteristic
27C2×#6487C2211yescharacteristic
28C22×Dic28C2211yescharacteristic
29C22×#1132C2211yescharacteristic
30#90316—24no—
31#90316C2218yescomplemented
32#90195—24no—
33#90195C2218yes—
34C2×#6456C2211yescharacteristic
35C2×#6456C2211yescharacteristic
36C2×#6455—21no—
37C2×D7×C4⋊C4—21no—
38C2×#6453—21no—
39C2×#6453C2211yescharacteristic
40C2×#6452—21no—
41C2×#6450C2211yescharacteristic
42C2×#6450C2211yescharacteristic
43C2×#6450C2211yescharacteristic
44C2×#6442—21no—
45C2×#6442—21no—
46C7×#483C2218yescomplemented
47C2×C7×#106C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×C22⋊C8C2211yescharacteristic
52C2×C22⋊(C7⋊C8)C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×#6390C2211yescharacteristic
55C2×#6389C2211yescharacteristic
56C2×Dic7⋊C8C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89819C2218yes—
60#89742C2218yescomplemented
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67#89643C2218yescomplemented
68#89629C2218yescomplemented
69#89625C2218yescomplemented
70#89624C2218yescomplemented
71#89590C2218yescomplemented
72#89589C2218yescomplemented
73#89565C2218yescomplemented
74#89562C2218yescomplemented
75#89505C2218yes—
76#89492C2218yescomplemented
77C2×#3120—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C23×C4×C7—21no—
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C2×#1157—22no—
83C2×#1157—24no—
84C2×#1157—24no—
85C2×#1157C2314yes—
86C22×D28C2311yescharacteristic
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×Dic14C2311yescharacteristic
91C22×Dic14C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C7×C22⋊Q8—22no—
95C7×C22⋊Q8C2314yes—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4C2314yes—
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C22⋊C4—21no—
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7D411yescharacteristic
106C2×C22⋊Dic7D411yescharacteristic
107Q8×Dic7—22no—
108Q8×Dic7C2314yes—
109#6507—22no—
110#6507C2314yes—
111C2×#1144—24no—
112C2×#1144C2314yes—
113C2×#1143—24no—
114C2×#1143C2314yes—
115C4×C22⋊D7—28no—
116C4×C22⋊D7—28no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119#6489D414yes—
120#6489C2314yes—
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7—21no—
123C2×C4⋊Dic7D411yescharacteristic
124C2×C4⋊Dic7D411yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126#6487—22no—
127#6487C2314yes—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×C4×Dic7—21no—
136C2×C4×Dic7—21no—
137C2×C4×Dic7—21no—
138C2×C4×Dic7—21no—
139C2×C4×Dic7C2311yescharacteristic
140C2×C4×Dic7C2311yescharacteristic
141C22×C7⋊C8C2311yescharacteristic
142C22×C7⋊C8C2311yescharacteristic
143C2×Dic28—24no—
144C2×Dic28C2314yes—
145C2×#1132—24no—
146C2×#1132C2314yes—
147#6456—22no—
148#6456—22no—
149#6456C2314yes—
150#6456C2314yes—
151#6455—28no—
152D7×C4⋊C4—28no—
153#6453—28no—
154#6453—22no—
155#6453C2314yes—
156#6452—28no—
157#6450—22no—
158#6450—22no—
159#6450—22no—
160#6450C2314yes—
161#6450C2314yes—
162#6450C2314yes—
163#6442—28no—
164#6442—28no—
165C7×#106C2314yes—
166C7×#106C2314yes—
167C7×#103C2314yes—
168C7×#103C2314yes—
169C7×C22⋊C8C2314yes—
170C22⋊(C7⋊C8)C2314yes—
171#6395C2314yes—
172#6390C2314yes—
173#6389C2314yes—
174Dic7⋊C8C2314yes—
175Dic7⋊C8C2314yes—
176C8×Dic7C2314yes—
177#6384C2314yes—
178#6384C2314yes—
179#6384C2314yes—
180#6383C2314yes—
181#6381C2314yes—
182#6381C2314yes—
183C2×#541—71no—
184C2×#520—71no—
185#3120—716no—
186C2×#484—71no—
187C2×#483D711yescharacteristic, complemented
188C2×#479—71no—
189C2×#478—71no—
190C2×#462—71no—
191C2×#461—71no—
192C2×#452—71no—
193C2×#452—71no—
194C2×#441—71no—
195C2×#440—71no—
196C2×C4×Q16—71no—
197C2×C4×SD16—71no—
198C2×#433—71no—
199C24×C7C2×D411yescharacteristic
200C23×D7—21no—
201C2×C7×Q8—21no—
202C2×C7×Q8—22no—
203C2×C7×Q8—22no—
204C2×C7×Q8C2412yes—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—24no—
212C22×C4×C7—82no—
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2411yescharacteristic
217C2×C22⋊D7—28no—
218C2×C22⋊D7—24no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7C2×D411yescharacteristic
223C22×Dic7C2×D411yescharacteristic
224C22×Dic7C2×D411yescharacteristic
225C22×Dic7C2×D411yescharacteristic
226#1157—216no—
227#1157—28no—
228#1157—28no—
229C2×D28—21no—
230C2×D28—22no—
231C2×D28#4114yes—
232C2×D28C2412yes—
233C2×C4×D7—28no—
234C2×C4×D7—24no—
235C2×C4×D7—24no—
236C2×C4×D7—24no—
237C2×C4×D7—82no—
238C2×C4×D7—82no—
239C2×Dic14—21no—
240C2×Dic14—22no—
241C2×Dic14—22no—
242C2×Dic14—22no—
243C2×Dic14—21no—
244C2×Dic14#4114yes—
245C2×Dic14C2412yes—
246C2×Dic14C2412yes—
247C2×C7×C8—22no—
248C2×C7×C8—22no—
249C2×C7×C8C2412yes—
250C2×C7×C8C2412yes—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—24no—
256C7×C4⋊C4C2412yes—
257C7×C4⋊C4C2412yes—
258C7×C4⋊C4C2412yes—
259C7×C22⋊C4—24no—
260C22⋊Dic7—24no—
261C22⋊Dic7C2×D414yes—
262C22⋊Dic7C2×D414yes—
263#1144—28no—
264#1143—28no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267C4⋊Dic7—21no—
268C4⋊Dic7—24no—
269C4⋊Dic7—24no—
270C4⋊Dic7C2×D414yes—
271C4⋊Dic7C2×D414yes—
272C4⋊Dic7C2412yes—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280C4×Dic7—24no—
281C4×Dic7—24no—
282C4×Dic7—24no—
283C4×Dic7—24no—
284C4×Dic7C2×D412yes—
285C4×Dic7C2×D412yes—
286C4×Dic7C2412yes—
287C4×Dic7C2412yes—
288C2×C7⋊C8—22no—
289C2×C7⋊C8—22no—
290C2×C7⋊C8C2412yes—
291C2×C7⋊C8C2412yes—
292Dic28—28no—
293#1132—28no—
294C22×#41—71no—
295C22×Q16—71no—
296C22×Q16—71no—
297C22×SD16—71no—
298C22×SD16—71no—
299#541—78no—
300#541—144no—
301C2×C4⋊Q8—71no—
302C2×#126—141no—
303C2×#126—141no—
304C2×#125—71no—
305C2×#125—141no—
306C2×#125—141no—
307C2×C22⋊Q8—71no—
308C2×C22⋊Q8C2×D711yescharacteristic
309#520—78no—
310#520—144no—
311C2×C4×Q8—71no—
312C2×C4×Q8—71no—
313C2×C4×Q8—71no—
314C2×C4×Q8—71no—
315C2×C4×D4—71no—
316C2×C4×D4—71no—
317C2×C4×D4—141no—
318C2×C4×D4—141no—
319C2×#117—71no—
320C2×#117—141no—
321C22×C4⋊C4—141no—
322C22×C4⋊C4C2×D711yescharacteristic
323#484—78no—
324#483C2×D718yescomplemented
325#479—78no—
326#478—78no—
327#462—78no—
328#461—78no—
329#452—78no—
330#452—78no—
331#441—78no—
332#440—78no—
333C4×Q16—78no—
334C4×SD16—78no—
335#433—78no—
336C2×#107—71no—
337C2×#107—71no—
338C2×#106C2×D711yescharacteristic
339C2×#106C2×D711yescharacteristic
340C2×C4⋊C8—71no—
341C2×C4⋊C8—71no—
342C2×#103—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#103C2×D711yescharacteristic
347C2×#103C2×D711yescharacteristic
348C2×#102—71no—
349C2×#102—71no—
350C2×C22⋊C8—71no—
351C2×C22⋊C8C2×D711yescharacteristic
352C2×#97—71no—
353C2×C4×C8—71no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7C22×D412yes—
358C23×C7C22×D411yescharacteristic
359C22×D7—24no—
360C22×D7—22no—
361C22×D7—42no—
362C22×D7—42no—
363C7×Q8—22no—
364C7×Q8—22no—
365C7×Q8—42no—
366C2×C4×C7—22no—
367C2×C4×C7—24no—
368C2×C4×C7—22no—
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×C7—42no—
378C2×C4×C7—84no—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7C2×#4112yes—
382C2×C4×C7C2×#4112yes—
383C2×C4×C7C2511yescharacteristic
384C22⋊D7—216no—
385C2×Dic7—24no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7C22×D412yes—
396C2×Dic7C22×D412yes—
397C2×Dic7C22×D412yes—
398C2×Dic7C22×D412yes—
399D28—24no—
400D28—22no—
401D28C2×#4114yes—
402C4×D7—216no—
403C4×D7—84no—
404C4×D7—84no—
405Dic14—24no—
406Dic14—22no—
407Dic14—22no—
408Dic14—22no—
409Dic14—42no—
410Dic14C2×#4114yes—
411C7×C8—22no—
412C7×C8—22no—
413C7⋊C8—22no—
414C7⋊C8—22no—
415C2×#41—74no—
416C2×#41—144no—
417C2×#41—144no—
418C2×#41—142no—
419C22×Q8—71no—
420C22×Q8—71no—
421C22×Q8C22×D711yescharacteristic
422C22×D4—71no—
423C22×D4—141no—
424C23×C4—21no—
425C23×C4—141no—
426C23×C4—141no—
427C23×C4—141no—
428C23×C4C22×D711yescharacteristic
429C2×Q16—74no—
430C2×Q16—74no—
431C2×Q16—144no—
432C2×Q16—144no—
433C2×SD16—74no—
434C2×SD16—74no—
435C2×SD16—144no—
436C2×SD16—144no—
437C22×C8—71no—
438C22×C8—71no—
439C22×C8C22×D711yescharacteristic
440C22×C8C22×D711yescharacteristic
441C4⋊Q8—74no—
442C4⋊Q8—142no—
443#126—148no—
444#126—148no—
445#125—74no—
446#125—142no—
447#125—148no—
448#125—148no—
449C22⋊Q8—22no—
450C22⋊Q8—74no—
451C22⋊Q8—142no—
452C22⋊Q8C22×D714yes—
453C4×Q8—74no—
454C4×Q8—74no—
455C4×Q8—74no—
456C4×Q8—74no—
457C4×Q8—142no—
458C4×Q8—142no—
459C4×Q8—142no—
460C4×Q8—142no—
461C4×D4—74no—
462C4×D4—74no—
463C4×D4—142no—
464C4×D4—142no—
465C4×D4—148no—
466C4×D4—148no—
467#117—74no—
468#117—74no—
469#117—148no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—71no—
476C2×C4⋊C4—148no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4C22×D711yescharacteristic
487C2×C4⋊C4C22×D711yescharacteristic
488C2×C4⋊C4C22×D714yes—
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—71no—
492C2×C22⋊C4—71no—
493C2×C22⋊C4—141no—
494C2×C22⋊C4—141no—
495C2×C22⋊C4—141no—
496C2×C42—71no—
497C2×C42—71no—
498C2×C42—141no—
499C2×C42—141no—
500C2×C42—141no—
501C2×C42—141no—
502#107—74no—
503#107—74no—
504#106C22×D714yes—
505#106C22×D714yes—
506C4⋊C8—74no—
507C4⋊C8—74no—
508#103—74no—
509#103—74no—
510#103—74no—
511#103—74no—
512#103C22×D714yes—
513#103C22×D714yes—
514#102—74no—
515#102—74no—
516C22⋊C8—74no—
517C22⋊C8C22×D714yes—
518#97—74no—
519C4×C8—74no—
520C22×C7—22no—
521C22×C7—22no—
522C22×C7—22no—
523C22×C7—44no—
524C22×C7#52512yes—
525C22×C7#57712yes—
526C22×C7#57812yes—
527C22×C7C23×D411yescharacteristic
528C2×D7—24no—
529C2×D7—48no—
530C2×D7—42no—
531C2×D7—42no—
532C4×C7—22no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7—42no—
537C4×C7#52512yes—
538C4×C7C22×#4111yescharacteristic
539C4×C7C22×#4111yescharacteristic
540Dic7—24no—
541Dic7—22no—
542Dic7—22no—
543Dic7—22no—
544Dic7—22no—
545Dic7—42no—
546Dic7—42no—
547C24—141no—
548C24D4×D711yescharacteristic
549#41—148no—
550#41—148no—
551#41—1416no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—74no—
556C2×Q8—72no—
557C2×Q8—72no—
558C2×Q8—141no—
559C2×Q8—141no—
560C2×Q8—142no—
561C2×Q8—142no—
562C2×Q8—142no—
563C2×Q8C23×D712yes—
564C2×D4—74no—
565C2×D4—72no—
566C2×D4—148no—
567C2×D4—144no—
568C2×D4—141no—
569C2×D4—142no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—71no—
578C22×C4—71no—
579C22×C4—71no—
580C22×C4—71no—
581C22×C4—82no—
582C22×C4—144no—
583C22×C4—144no—
584C22×C4—148no—
585C22×C4—141no—
586C22×C4—144no—
587C22×C4—141no—
588C22×C4—141no—
589C22×C4—562no—
590C22×C4—562no—
591C22×C4D4×D712yes—
592C22×C4D4×D711yescharacteristic
593C22×C4C23×D712yes—
594C22×C4C23×D711yescharacteristic
595Q16—148no—
596Q16—148no—
597SD16—148no—
598SD16—148no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—72no—
602C2×C8—72no—
603C2×C8—142no—
604C2×C8—142no—
605C2×C8C23×D712yes—
606C2×C8C23×D712yes—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—74no—
613C4⋊C4—74no—
614C4⋊C4—72no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—144no—
621C4⋊C4—144no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4—141no—
625C4⋊C4C23×D712yes—
626C4⋊C4C23×D712yes—
627C4⋊C4C23×D712yes—
628C22⋊C4—24no—
629C22⋊C4—74no—
630C22⋊C4—74no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C42—72no—
635C42—72no—
636C42—72no—
637C42—72no—
638C42—144no—
639C42—144no—
640C42—144no—
641C42—144no—
642C2×C7—42no—
643C2×C7#312014yescomplemented
644C2×C7C2×#52511yescharacteristic
645C2×C7C2×#57711yescharacteristic
646C2×C7C2×#57811yescharacteristic
647D7—44no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—144no—
652C23—142no—
653C23—282no—
654C23—282no—
655C23C2×D4×D712yes—
656C23C2×D4×D711yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—42no—
660Q8—74no—
661Q8—144no—
662Q8—142no—
663Q8—142no—
664Q8—142no—
665Q8—282no—
666D4—74no—
667D4—1416no—
668D4—144no—
669D4—142no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—72no—
683C2×C4—72no—
684C2×C4—72no—
685C2×C4—72no—
686C2×C4—84no—
687C2×C4—1416no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—144no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—282no—
697C2×C4—282no—
698C2×C4—564no—
699C2×C4—564no—
700C2×C4C2×D4×D712yes—
701C2×C4C2×D4×D711yescharacteristic
702C2×C4D7×#4112yes—
703C2×C4D7×#4112yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—22no—
707C8—142no—
708C8—142no—
709C7C2×#312011yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—144no—
715C22—282no—
716C22—288no—
717C22—282no—
718C22#9034712yes—
719C22#9045312yes—
720C22#9047012yes—
721C22C22×D4×D711yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—142no—
728C4—142no—
729C4—144no—
730C4—142no—
731C4—142no—
732C4—282no—
733C4—282no—
734C4#9034712yes—
735C4C2×D7×#4111yescharacteristic
736C4C2×D7×#4111yescharacteristic
737C2—42no—
738C2—284no—
739C2#1173886114yesdirect product factor
740C2C2×#9034711yescharacteristic
741C2C2×#9045311yescharacteristic
742C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#483C2
socleC23×C7C22×D4
prime radicalC22×#1157C22
hypercenterC2×#483D7
hypocenterC7C2×#3120
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#90316C2semidirect
3. C2×C7×#483C2semidirect
5. C2×#89742C2semidirect
6. #11738861C2direct (N × H)
7. C2×#89629C2semidirect
8. C2×#89643C2semidirect
9. C2×#89625C2semidirect
10. C2×#89624C2semidirect
11. C2×#89565C2semidirect
12. C2×#89590C2semidirect
13. C2×#89589C2semidirect
14. C2×#89562C2semidirect
16. C2×#89492C2semidirect
31. #90316C22semidirect
46. C7×#483C22semidirect
60. #89742C22semidirect
67. #89643C22semidirect
68. #89629C22semidirect
69. #89625C22semidirect
70. #89624C22semidirect
71. #89590C22semidirect
72. #89589C22semidirect
73. #89565C22semidirect
74. #89562C22semidirect
76. #89492C22semidirect
187. C2×#483D7semidirect
324. #483C2×D7semidirect
643. C2×C7#3120semidirect
709. C7C2×#3120semidirect
739. C2#11738861direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903162
C2×#901952
C2×C7×#4832
C2×#898192
C2×#897422
#117388612
C2×#896292
C2×#896432
C2×#896252
C2×#896242
C2×#895652
C2×#895902
C2×#895892
C2×#895622
C2×#895052
C2×#894922
C2×#31207