Finite Group Databasebeta

← C2×#11736918 #14232393

Subgroups — C2×#11736918 #14232393

Order 1792.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90254C211yesmaximal, characteristic, complemented
2C2×#90256C211yesmaximal, characteristic, complemented
3C2×C7×#435C211yesmaximal, characteristic, complemented
4C2×#89907C211yesmaximal, characteristic, complemented
5C2×#89893C211yesmaximal, characteristic, complemented
6C2×#89887C211yesmaximal, characteristic, complemented
7C2×#89878C211yesmaximal, characteristic, complemented
8#11736918C2116yesmaximal, direct product factor
9C2×#89619C211yesmaximal, characteristic, complemented
10C2×#89618C211yesmaximal, characteristic, complemented
11C2×#89509C211yesmaximal, characteristic, complemented
12C2×#89509C211yesmaximal, characteristic, complemented
13C2×#89509C211yesmaximal, characteristic, complemented
14C2×#89508C211yesmaximal, characteristic, complemented
15C2×#89483C211yesmaximal, characteristic, complemented
16C2×#89474C211yesmaximal, characteristic, complemented
17C22×C7×M16C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×#6502—21no—
21C2×#6501—21no—
22C2×#6493C2211yescharacteristic
23C2×#6493C2211yescharacteristic
24C2×#6493C2211yescharacteristic
25C2×#6493C2211yescharacteristic
26C2×#6489C2211yescharacteristic
27C2×#6489C2211yescharacteristic
28C2×#6489C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×D56C2211yescharacteristic
31#90256—24no—
32#90256C2218yescomplemented
33#90254—24no—
34#90254C2218yescomplemented
35C2×#6461—21no—
36C2×#6455—21no—
37C2×#6448—21no—
38C2×#6448—21no—
39C2×#6446—21no—
40C2×(C22⋊D7)⋊C4—21no—
41C2×C4×D28C2211yescharacteristic
42C2×C4×D28C2211yescharacteristic
43C2×#6433C2211yescharacteristic
44C2×#6432C2211yescharacteristic
45C7×#435C2218yescomplemented
46C2×C7×C4⋊C8C2211yescharacteristic
47C2×C7×C22⋊C8C2211yescharacteristic
48C2×C7×C22⋊C8C2211yescharacteristic
49C2×C7×#97C2211yescharacteristic
50#89907C2218yescomplemented
51#89893C2218yescomplemented
52#89887C2218yescomplemented
53C2×#6395C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×#6395C2211yescharacteristic
56C2×#6395C2211yescharacteristic
57C2×#6395C2211yescharacteristic
58C2×#6395C2211yescharacteristic
59#89878C2218yescomplemented
60C2×#6392C2211yescharacteristic
61C2×#6392C2211yescharacteristic
62C2×#6392C2211yescharacteristic
63C2×#6392C2211yescharacteristic
64C2×#6392C2211yescharacteristic
65C2×#6391C2211yescharacteristic
66C2×#6391C2211yescharacteristic
67C2×#6391C2211yescharacteristic
68C2×#6391C2211yescharacteristic
69#89619C2218yescomplemented
70#89618C2218yescomplemented
71#89509C2218yescomplemented
72#89509C2218yescomplemented
73#89509C2218yescomplemented
74#89508C2218yescomplemented
75#89483C2218yescomplemented
76#89474C2218yescomplemented
77C2×#3347—71nomaximal, Sylow
78C22×C7×D4D411yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C23×Dic7—21no—
86C22×D28C2311yescharacteristic
87C22×D28C2311yescharacteristic
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×Dic14—21no—
91C2×C7×M16—24no—
92C2×C7×M16C2314yes—
93C22×C7×C8—24no—
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2314yes—
98C22×C7×C8C2311yescharacteristic
99C4×C7×D4D414yes—
100C4×C7×D4C2314yes—
101C2×C7×C4⋊C4D411yescharacteristic
102C2×C7×C22⋊C4D411yescharacteristic
103C2×C7×C22⋊C4D411yescharacteristic
104C2×C42×C7C2311yescharacteristic
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108#6502—28no—
109#6501—28no—
110#6493—22no—
111#6493—22no—
112#6493—22no—
113#6493—22no—
114#6493C2314yes—
115#6493C2314yes—
116#6493C2314yes—
117#6493C2314yes—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124#6489—22no—
125#6489—22no—
126#6489—22no—
127#6489C2314yes—
128#6489C2314yes—
129#6489C2314yes—
130C2×C4⋊Dic7—21no—
131C2×C4⋊Dic7—21no—
132C2×C4⋊Dic7—22no—
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2311yescharacteristic
135C2×C4⋊Dic7C2311yescharacteristic
136C2×C4⋊Dic7C2311yescharacteristic
137C2×C4⋊Dic7C2311yescharacteristic
138C2×C4⋊Dic7C2311yescharacteristic
139C2×C4⋊Dic7C2314yes—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×C4×Dic7—21no—
143C2×C4×Dic7—21no—
144C2×C4×Dic7—21no—
145C2×D56—24no—
146C2×D56C2314yes—
147#6461—28no—
148#6455—28no—
149#6448—28no—
150#6448—28no—
151#6446—28no—
152(C22⋊D7)⋊C4—28no—
153C4×D28—22no—
154C4×D28—22no—
155C4×D28C2314yes—
156C4×D28C2314yes—
157#6433—22no—
158#6433C2314yes—
159#6432—22no—
160#6432C2314yes—
161C7×C4⋊C8C2314yes—
162C7×C22⋊C8C2314yes—
163C7×C22⋊C8C2314yes—
164C7×#97C2314yes—
165#6395C2314yes—
166#6395C2314yes—
167#6395C2314yes—
168#6395C2314yes—
169#6395C2314yes—
170#6395C2314yes—
171#6392C2314yes—
172#6392C2314yes—
173#6392C2314yes—
174#6392C2314yes—
175#6392C2314yes—
176#6391C2314yes—
177#6391C2314yes—
178#6391C2314yes—
179#6391C2314yes—
180C2×#555—71no—
181C2×#553—71no—
182#3347—716no—
183C2×#501—71no—
184C2×#482—71no—
185C2×#482—71no—
186C2×#482—71no—
187C2×#480—71no—
188C2×#478—71no—
189C2×#474—71no—
190C2×#469—71no—
191C2×#466—71no—
192C2×#442—71no—
193C2×#435D711yescharacteristic, complemented
194C2×#428—71no—
195C2×#427—71no—
196C24×C7C2×D411yescharacteristic
197C24×C7C2×D411yescharacteristic
198C23×D7—21no—
199C23×D7—21no—
200C2×C7×D4—42no—
201C2×C7×D4C2×D414yes—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D412yes—
211C22×C4×C7C2×D412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2411yescharacteristic
215C2×C22⋊D7—24no—
216C2×C22⋊D7—24no—
217C2×C22⋊D7—24no—
218C2×C22⋊D7—24no—
219C2×C22⋊D7—44no—
220C2×C22⋊D7—82no—
221C2×C22⋊D7—82no—
222C2×C22⋊D7—82no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—24no—
230C22×Dic7—82no—
231C2×D28—22no—
232C2×D28—22no—
233C2×D28—22no—
234C2×D28—22no—
235C2×D28—21no—
236C2×D28—21no—
237C2×D28C2412yes—
238C2×D28C2412yes—
239C2×C4×D7—24no—
240C2×C4×D7—24no—
241C2×C4×D7—44no—
242C2×C4×D7—82no—
243C2×Dic14—24no—
244C2×Dic14—82no—
245C7×M16—28no—
246C2×C7×C8—22no—
247C2×C7×C8—22no—
248C2×C7×C8—22no—
249C2×C7×C8—28no—
250C2×C7×C8#4114yes—
251C2×C7×C8C2412yes—
252C2×C7×C8C2412yes—
253C2×C7×C8C2412yes—
254C2×C7×C8C2412yes—
255C7×C4⋊C4C2×D414yes—
256C7×C22⋊C4C2×D414yes—
257C7×C22⋊C4C2×D414yes—
258C42×C7C2×D412yes—
259C42×C7C2412yes—
260C22⋊Dic7—24no—
261C22⋊Dic7—24no—
262C22⋊Dic7—24no—
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—
268(C2×D7)⋊C4—24no—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7—24no—
272C4⋊Dic7—21no—
273C4⋊Dic7—21no—
274C4⋊Dic7—21no—
275C4⋊Dic7—21no—
276C4⋊Dic7—24no—
277C4⋊Dic7C2412yes—
278C4⋊Dic7C2412yes—
279C4⋊Dic7C2412yes—
280C4⋊Dic7C2412yes—
281C4⋊Dic7C2412yes—
282C4⋊Dic7C2412yes—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285C4×Dic7—24no—
286C4×Dic7—24no—
287C4×Dic7—24no—
288D56—28no—
289C22×D8—71no—
290C22×M16C2×D711yescharacteristic
291C23×C8C2×D711yescharacteristic
292#555—78no—
293#555—144no—
294#553—78no—
295#553—144no—
296C2×C4⋊Q8—71no—
297C2×#126—141no—
298C2×#125—71no—
299C2×#124—141no—
300C2×#124—141no—
301C2×#123—141no—
302C2×#121—71no—
303C2×#121—71no—
304C2×#121—71no—
305C2×#121—71no—
306C2×#121—141no—
307C2×#121—141no—
308C2×C4×D4—71no—
309C2×C4×D4—71no—
310C2×C4×D4—141no—
311C2×C4×D4C2×D711yescharacteristic
312C2×#117—71no—
313C2×#117—71no—
314C2×#117—71no—
315C2×#117—141no—
316C22×C4⋊C4—71no—
317#501—78no—
318#482—78no—
319#482—78no—
320#482—78no—
321#480—78no—
322#478—78no—
323#474—78no—
324#469—78no—
325#466—78no—
326#442—78no—
327#435C2×D718yescomplemented
328#428—78no—
329#427—78no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#107—71no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#106—71no—
336C2×#106—71no—
337C2×#106—71no—
338C2×#106—71no—
339C2×C4⋊C8C2×D711yescharacteristic
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×#102—71no—
344C2×#102—71no—
345C2×#102—71no—
346C2×C22⋊C8C2×D711yescharacteristic
347C2×C22⋊C8C2×D711yescharacteristic
348C2×#97C2×D711yescharacteristic
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7C22×D412yes—
356C23×C7C22×D412yes—
357C23×C7C22×D411yescharacteristic
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—42no—
361C22×D7—42no—
362C22×D7—42no—
363C22×D7—42no—
364C22×D7—42no—
365C22×D7—42no—
366C7×D4—44no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—24no—
372C2×C4×C7—24no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C2×#4112yes—
383C2×C4×C72−1+412yes—
384C2×C4×C7C2511yescharacteristic
385C22⋊D7—48no—
386C22⋊D7—84no—
387C22⋊D7—84no—
388C22⋊D7—84no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—42no—
396C2×Dic7—42no—
397C2×Dic7—42no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400C2×Dic7—42no—
401C2×Dic7—84no—
402D28—22no—
403D28—22no—
404D28—22no—
405D28—22no—
406D28—42no—
407D28—42no—
408C4×D7—48no—
409C4×D7—84no—
410Dic14—84no—
411C7×C8—22no—
412C7×C8—22no—
413C7×C8—22no—
414C7×C8C2×#4114yes—
415C22×Q8—141no—
416C22×D4—71no—
417C22×D4—71no—
418C22×D4—141no—
419C22×D4—141no—
420C22×D4—141no—
421C22×D4—141no—
422C22×D4D2811yescharacteristic
423C23×C4—141no—
424C23×C4—141no—
425C23×C4—141no—
426C23×C4C22×D711yescharacteristic
427C23×C4C22×D711yescharacteristic
428C2×D8—74no—
429C2×D8—144no—
430C2×M16—24no—
431C2×M16C22×D714yes—
432C22×C8—24no—
433C22×C8C22×D711yescharacteristic
434C22×C8C22×D714yes—
435C22×C8C22×D711yescharacteristic
436C22×C8C22×D711yescharacteristic
437C22×C8C22×D711yescharacteristic
438C4⋊Q8—74no—
439C4⋊Q8—142no—
440#126—148no—
441#125—74no—
442#125—142no—
443#124—148no—
444#124—148no—
445#123—148no—
446#121—74no—
447#121—74no—
448#121—74no—
449#121—74no—
450#121—148no—
451#121—148no—
452#121—142no—
453#121—142no—
454#121—142no—
455#121—142no—
456C4×D4—74no—
457C4×D4—74no—
458C4×D4—148no—
459C4×D4—142no—
460C4×D4—142no—
461C4×D4D2814yes—
462C4×D4C22×D714yes—
463#117—74no—
464#117—74no—
465#117—74no—
466#117—142no—
467#117—142no—
468#117—142no—
469#117—148no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—74no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—71no—
476C2×C4⋊C4—71no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—142no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4D2811yescharacteristic
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×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4D2811yescharacteristic
493C2×C22⋊C4D2811yescharacteristic
494C2×C42—141no—
495C2×C42—141no—
496C2×C42—141no—
497C2×C42C22×D711yescharacteristic
498#107—74no—
499#107—74no—
500#107—74no—
501#107—74no—
502#107—74no—
503#106—74no—
504#106—74no—
505#106—74no—
506#106—74no—
507C4⋊C8C22×D714yes—
508#102—74no—
509#102—74no—
510#102—74no—
511#102—74no—
512#102—74no—
513#102—74no—
514C22⋊C8C22×D714yes—
515C22⋊C8C22×D714yes—
516#97C22×D714yes—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—22no—
520C22×C7—22no—
521C22×C7—22no—
522C22×C7—22no—
523C22×C7—44no—
524C22×C7—44no—
525C22×C7#54712yes—
526C22×C7#57512yes—
527C22×C7#57612yes—
528C22×C7C23×D411yescharacteristic
529C2×D7—42no—
530C2×D7—42no—
531C2×D7—42no—
532C2×D7—42no—
533C2×D7—42no—
534C2×D7—42no—
535C2×D7—84no—
536C2×D7—84no—
537C4×C7—22no—
538C4×C7—22no—
539C4×C7—22no—
540C4×C7—22no—
541C4×C7#54712yes—
542C4×C7C22×#4111yescharacteristic
543C4×C7C2×2−1+411yescharacteristic
544Dic7—42no—
545Dic7—42no—
546Dic7—42no—
547Dic7—42no—
548Dic7—42no—
549Dic7—42no—
550C24—141no—
551C24—141no—
552C24C2×D2811yescharacteristic
553C24C2×D2811yescharacteristic
554C2×Q8—144no—
555C2×Q8—562no—
556C2×D4—42no—
557C2×D4—72no—
558C2×D4—72no—
559C2×D4—144no—
560C2×D4—144no—
561C2×D4—144no—
562C2×D4—144no—
563C2×D4—141no—
564C2×D4—141no—
565C2×D4—142no—
566C2×D4—142no—
567C2×D4—142no—
568C2×D4—142no—
569C2×D4—284no—
570C2×D4—562no—
571C2×D4—562no—
572C2×D4—562no—
573C2×D4C2×D2814yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—141no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—141no—
582C22×C4—141no—
583C22×C4—141no—
584C22×C4—144no—
585C22×C4—144no—
586C22×C4—144no—
587C22×C4—284no—
588C22×C4—562no—
589C22×C4—562no—
590C22×C4C2×D2812yes—
591C22×C4C2×D2812yes—
592C22×C4C2×D2811yescharacteristic
593C22×C4C2×D2811yescharacteristic
594C22×C4C2×D2811yescharacteristic
595C22×C4C2×D2811yescharacteristic
596C22×C4C23×D712yes—
597C22×C4C23×D712yes—
598C22×C4C23×D711yescharacteristic
599D8—148no—
600M16—28no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—28no—
605C2×C8#115914yes—
606C2×C8C23×D712yes—
607C2×C8C23×D712yes—
608C2×C8C23×D712yes—
609C2×C8C23×D712yes—
610C4⋊C4—72no—
611C4⋊C4—72no—
612C4⋊C4—72no—
613C4⋊C4—72no—
614C4⋊C4—72no—
615C4⋊C4—72no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—141no—
619C4⋊C4—141no—
620C4⋊C4—144no—
621C4⋊C4—141no—
622C4⋊C4—141no—
623C4⋊C4—141no—
624C4⋊C4—141no—
625C4⋊C4—144no—
626C4⋊C4C2×D2814yes—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4C2×D2814yes—
637C22⋊C4C2×D2814yes—
638C42—144no—
639C42—144no—
640C42—144no—
641C42C2×D2812yes—
642C42C23×D712yes—
643C2×C7—42no—
644C2×C7—42no—
645C2×C7#334714yescomplemented
646C2×C7C2×#54711yescharacteristic
647C2×C7C2×#57511yescharacteristic
648C2×C7C2×#57611yescharacteristic
649D7—82no—
650D7—82no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—142no—
658C23—142no—
659C23—282no—
660C23—282no—
661C23—282no—
662C23—282no—
663C23—282no—
664C23—282no—
665C23C22×D2812yes—
666C23C22×D2812yes—
667C23C22×D2811yescharacteristic
668Q8—564no—
669D4—44no—
670D4—142no—
671D4—142no—
672D4—142no—
673D4—142no—
674D4—288no—
675D4—282no—
676D4—282no—
677D4—564no—
678D4—564no—
679D4—564no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—288no—
697C2×C4—282no—
698C2×C4—282no—
699C2×C4—282no—
700C2×C4—282no—
701C2×C4—282no—
702C2×C4—282no—
703C2×C4—564no—
704C2×C4—564no—
705C2×C4C22×D2812yes—
706C2×C4C22×D2812yes—
707C2×C4C22×D2812yes—
708C2×C4C22×D2812yes—
709C2×C4C22×D2811yescharacteristic
710C2×C4C2×#115912yes—
711C2×C4#655412yes—
712C2×C4C24×D711yescharacteristic
713C8—22no—
714C8—22no—
715C8—22no—
716C8C2×#115914yes—
717C7C2×#334711yescharacteristic, complemented, Sylow
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—282no—
727C22—282no—
728C22—282no—
729C22—282no—
730C22—282no—
731C22—282no—
732C22—564no—
733C22—564no—
734C22#9024612yes—
735C22#9043912yes—
736C22#9044312yes—
737C22C23×D2811yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—282no—
743C4—282no—
744C4—282no—
745C4—282no—
746C4—282no—
747C4—282no—
748C4#9024612yes—
749C4C22×#115911yescharacteristic
750C4C2×#655411yescharacteristic
751C2—42no—
752C2—42no—
753C2—562no—
754C2—562no—
755C2#1173691814yesdirect product factor
756C2C2×#9024611yescharacteristic
757C2C2×#9043911yescharacteristic
758C2C2×#9044311yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#435C2
socleC23×C7C22×D4
hypercenterC2×#435D7
hypocenterC7C2×#3347
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
1. C2×#90254C2semidirect
2. C2×#90256C2semidirect
3. C2×C7×#435C2semidirect
4. C2×#89907C2semidirect
5. C2×#89893C2semidirect
6. C2×#89887C2semidirect
7. C2×#89878C2semidirect
8. #11736918C2direct (N × H)
9. C2×#89619C2semidirect
10. C2×#89618C2semidirect
11. C2×#89509C2semidirect
12. C2×#89509C2semidirect
13. C2×#89509C2semidirect
14. C2×#89508C2semidirect
15. C2×#89483C2semidirect
16. C2×#89474C2semidirect
32. #90256C22semidirect
34. #90254C22semidirect
45. C7×#435C22semidirect
50. #89907C22semidirect
51. #89893C22semidirect
52. #89887C22semidirect
59. #89878C22semidirect
69. #89619C22semidirect
70. #89618C22semidirect
71. #89509C22semidirect
72. #89509C22semidirect
73. #89509C22semidirect
74. #89508C22semidirect
75. #89483C22semidirect
76. #89474C22semidirect
193. C2×#435D7semidirect
327. #435C2×D7semidirect
645. C2×C7#3347semidirect
717. C7C2×#3347semidirect
755. C2#11736918direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902542
C2×#902562
C2×C7×#4352
C2×#899072
C2×#898932
C2×#898872
C2×#898782
#117369182
C2×#896192
C2×#896182
C2×#895092
C2×#895082
C2×#894832
C2×#894742
C2×#33477