Finite Group Databasebeta

← C2×#11737330 #14232396

Subgroups — C2×#11737330 #14232396

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×#90249C211yesmaximal, characteristic, complemented
2C2×#90254C211yesmaximal, characteristic, complemented
3C2×C7×#442C211yesmaximal, characteristic, complemented
4C2×#89931C211yesmaximal, characteristic, complemented
5C2×#89929C211yesmaximal, characteristic, complemented
6C2×#89781C211yesmaximal, characteristic, complemented
7C2×#89779C211yesmaximal, characteristic, complemented
8#11737330C2116yesmaximal, direct product factor
9C2×#89633C211yesmaximal, characteristic, complemented
10C2×#89632C211yesmaximal, characteristic, complemented
11C2×#89556C211yesmaximal, characteristic, complemented
12C2×#89546C211yesmaximal, characteristic, complemented
13C2×#89551C211yesmaximal, characteristic, complemented
14C2×#89551C211yesmaximal, characteristic, complemented
15C2×#89478C211yesmaximal, characteristic, complemented
16C2×#89474C211yesmaximal, characteristic, complemented
17C22×C7×D8C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×#6501C2211yescharacteristic
21C2×#6501C2211yescharacteristic
22C2×#6501C2211yescharacteristic
23C2×#6501C2211yescharacteristic
24C2×#6493—21no—
25C2×#6492—21no—
26C2×C4×C22⋊D7—21no—
27C2×#6489—21no—
28C22×#1131C2211yescharacteristic
29C22×C8×D7C2211yescharacteristic
30#90254—24no—
31#90254C2218yescomplemented
32#90249—24no—
33#90249C2218yescomplemented
34C2×#6455C2211yescharacteristic
35C2×#6455C2211yescharacteristic
36C2×#6455C2211yescharacteristic
37C2×D7×C4⋊C4C2211yescharacteristic
38C2×#6448—21no—
39C2×#6448—21no—
40C2×#6447—21no—
41C2×#6442—21no—
42C2×C4×D28C2211yescharacteristic
43C2×#6433C2211yescharacteristic
44C2×#6432C2211yescharacteristic
45C7×#442C2218yescomplemented
46C2×C7×#106C2211yescharacteristic
47C2×C7×#102C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#97C2211yescharacteristic
50C2×#6406C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54#89931C2218yescomplemented
55#89929C2218yescomplemented
56C2×(C2×D7)⋊C8C2211yescharacteristic
57C2×(C2×D7)⋊C8C2211yescharacteristic
58C2×#6392C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6391C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62#89781C2218yescomplemented
63#89779C2218yescomplemented
64C2×#6382C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×C4⋊(C7⋊C8)C2211yescharacteristic
69#89633C2218yescomplemented
70#89632C2218yescomplemented
71#89556C2218yescomplemented
72#89551C2218yescomplemented
73#89551C2218yescomplemented
74#89546C2218yescomplemented
75#89478C2218yescomplemented
76#89474C2218yescomplemented
77C2×#3347—71nomaximal, Sylow
78C22×C7×D4C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C23×C4×C7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C22×C22⋊D7—21no—
86C22×D28D411yescharacteristic
87C22×C4×D7—21no—
88C22×C4×D7C2311yescharacteristic
89C22×C4×D7C2311yescharacteristic
90C22×Dic14—21no—
91C2×C7×D8—24no—
92C2×C7×D8C2314yes—
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C4×C7×D4—22no—
96C4×C7×D4—22no—
97C4×C7×D4C2314yes—
98C4×C7×D4C2314yes—
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C22⋊C4—21no—
102C2×C7×C22⋊C4—21no—
103C2×C42×C7C2311yescharacteristic
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108#6501—22no—
109#6501—22no—
110#6501—22no—
111#6501—22no—
112#6501C2314yes—
113#6501C2314yes—
114#6501C2314yes—
115#6501C2314yes—
116#6493—28no—
117#6492—28no—
118C4×C22⋊D7—28no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4D411yescharacteristic
123C2×(C2×D7)⋊C4D411yescharacteristic
124#6489—28no—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7D411yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129C2×C4⋊Dic7C2311yescharacteristic
130C2×C4⋊Dic7C2311yescharacteristic
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×C4×Dic7—21no—
135C2×C4×Dic7—21no—
136C2×C4×Dic7—21no—
137C22×C7⋊C8C2311yescharacteristic
138C22×C7⋊C8C2311yescharacteristic
139C2×#1131—24no—
140C2×#1131C2314yes—
141C2×C8×D7—24no—
142C2×C8×D7C2314yes—
143#6455—22no—
144#6455—22no—
145#6455—22no—
146#6455C2314yes—
147#6455C2314yes—
148#6455C2314yes—
149D7×C4⋊C4—22no—
150D7×C4⋊C4C2314yes—
151#6448—28no—
152#6448—28no—
153#6447—28no—
154#6442—28no—
155C4×D28D414yes—
156C4×D28C2314yes—
157#6433—22no—
158#6433C2314yes—
159#6432—22no—
160#6432C2314yes—
161C7×#106C2314yes—
162C7×#102C2314yes—
163C7×#102C2314yes—
164C7×#97C2314yes—
165#6406C2314yes—
166#6406C2314yes—
167#6406C2314yes—
168#6406C2314yes—
169(C2×D7)⋊C8C2314yes—
170(C2×D7)⋊C8C2314yes—
171#6392C2314yes—
172#6392C2314yes—
173#6391C2314yes—
174#6391C2314yes—
175#6382C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179C4⋊(C7⋊C8)C2314yes—
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×#442D711yescharacteristic, complemented
193C2×#435—71no—
194C2×#428—71no—
195C2×#427—71no—
196C24×C7—21no—
197C24×C7—21no—
198C23×D7C2×D411yescharacteristic
199C23×D7C2×D411yescharacteristic
200C2×C7×D4—21no—
201C2×C7×D4—21no—
202C2×C7×D4—22no—
203C2×C7×D4—22no—
204C2×C7×D4—22no—
205C2×C7×D4—22no—
206C2×C7×D4C2412yes—
207C2×C7×D4C2412yes—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—24no—
211C22×C4×C7—24no—
212C22×C4×C7—44no—
213C22×C4×C7—82no—
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2411yescharacteristic
217C2×C22⋊D7—24no—
218C2×C22⋊D7—24no—
219C2×C22⋊D7—24no—
220C2×C22⋊D7—24no—
221C2×C22⋊D7—44no—
222C2×C22⋊D7—82no—
223C2×C22⋊D7—82no—
224C2×C22⋊D7—82no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7C2×D411yescharacteristic
230C22×Dic7C2×D411yescharacteristic
231C2×D28—42no—
232C2×D28C2×D414yes—
233C2×C4×D7—22no—
234C2×C4×D7—22no—
235C2×C4×D7—22no—
236C2×C4×D7—22no—
237C2×C4×D7—24no—
238C2×C4×D7—82no—
239C2×C4×D7C2×D412yes—
240C2×C4×D7C2×D412yes—
241C2×C4×D7C2412yes—
242C2×C4×D7C2412yes—
243C2×Dic14—24no—
244C2×Dic14—82no—
245C7×D8—28no—
246C2×C7×C8—22no—
247C2×C7×C8#4114yes—
248C2×C7×C8C2412yes—
249C2×C7×C8C2412yes—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4C2412yes—
253C7×C4⋊C4C2412yes—
254C7×C22⋊C4—24no—
255C7×C22⋊C4—24no—
256C42×C7C2×D412yes—
257C42×C7C2412yes—
258C22⋊Dic7—24no—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261C22⋊Dic7—24no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4C2×D414yes—
266(C2×D7)⋊C4C2×D414yes—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—24no—
270C4⋊Dic7—21no—
271C4⋊Dic7—21no—
272C4⋊Dic7C2×D414yes—
273C4⋊Dic7C2412yes—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276C4⋊Dic7C2412yes—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280C4×Dic7—24no—
281C4×Dic7—24no—
282C4×Dic7—24no—
283C2×C7⋊C8—22no—
284C2×C7⋊C8—22no—
285C2×C7⋊C8C2412yes—
286C2×C7⋊C8C2412yes—
287#1131—28no—
288C8×D7—28no—
289C22×D8C2×D711yescharacteristic
290C22×M16—71no—
291C23×C8—71no—
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—141no—
310C2×C4×D4C2×D711yescharacteristic
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#442C2×D718yescomplemented
327#435—78no—
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×#106C2×D711yescharacteristic
339C2×C4⋊C8—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×#102—71no—
344C2×#102C2×D711yescharacteristic
345C2×#102C2×D711yescharacteristic
346C2×C22⋊C8—71no—
347C2×C22⋊C8—71no—
348C2×#97C2×D711yescharacteristic
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7C22×D411yescharacteristic
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7C22×D412yes—
365C22×D7C22×D412yes—
366C7×D4—22no—
367C7×D4—22no—
368C7×D4—22no—
369C7×D4—22no—
370C7×D4—42no—
371C7×D4—42no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—48no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—84no—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D412yes—
382C2×C4×C7C22×D411yescharacteristic
383C2×C4×C7C2×#4112yes—
384C2×C4×C72−1+412yes—
385C2×C4×C7C2511yescharacteristic
386C22⋊D7—48no—
387C22⋊D7—84no—
388C22⋊D7—84no—
389C22⋊D7—84no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—42no—
397C2×Dic7—42no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400C2×Dic7C22×D412yes—
401C2×Dic7C22×D412yes—
402D28—44no—
403C4×D7—24no—
404C4×D7—24no—
405C4×D7—22no—
406C4×D7—22no—
407C4×D7—22no—
408C4×D7—22no—
409C4×D7—84no—
410Dic14—84no—
411C7×C8—22no—
412C7×C8C2×#4114yes—
413C7⋊C8—22no—
414C7⋊C8—22no—
415C22×Q8—141no—
416C22×D4—71no—
417C22×D4—141no—
418C22×D4—141no—
419C22×D4—141no—
420C22×D4—141no—
421C22×D4C22×D711yescharacteristic
422C22×D4C22×D711yescharacteristic
423C23×C4—21no—
424C23×C4—21no—
425C23×C4—71no—
426C23×C4—71no—
427C23×C4—141no—
428C2×D8—24no—
429C2×D8C22×D714yes—
430C2×M16—74no—
431C2×M16—144no—
432C22×C8—71no—
433C22×C8—71no—
434C22×C8—74no—
435C22×C8—144no—
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—22no—
457C4×D4—22no—
458C4×D4—74no—
459C4×D4—74no—
460C4×D4—148no—
461C4×D4C22×D714yes—
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—71no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—142no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4C22×D711yescharacteristic
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—71no—
486C2×C22⋊C4—71no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
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#106C22×D714yes—
507C4⋊C8—74no—
508#102—74no—
509#102—74no—
510#102—74no—
511#102—74no—
512#102C22×D714yes—
513#102C22×D714yes—
514C22⋊C8—74no—
515C22⋊C8—74no—
516#97C22×D714yes—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—84no—
524C22×C7—84no—
525C22×C7#54712yes—
526C22×C7#57512yes—
527C22×C7#57612yes—
528C22×C7C23×D411yescharacteristic
529C2×D7—22no—
530C2×D7—22no—
531C2×D7—22no—
532C2×D7—22no—
533C2×D7—22no—
534C2×D7—22no—
535C2×D7—44no—
536C2×D7—44no—
537C4×C7—22no—
538C4×C7—22no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7#54712yes—
542C4×C7C22×#4111yescharacteristic
543C4×C7C2×2−1+411yescharacteristic
544Dic7—22no—
545Dic7—22no—
546Dic7—42no—
547Dic7—42no—
548Dic7—42no—
549Dic7—42no—
550C24—21no—
551C24—21no—
552C24—71no—
553C24—71no—
554C2×Q8—144no—
555C2×Q8—562no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—74no—
563C2×D4—144no—
564C2×D4—144no—
565C2×D4—144no—
566C2×D4—144no—
567C2×D4—282no—
568C2×D4—284no—
569C2×D4—562no—
570C2×D4—562no—
571C2×D4—562no—
572C2×D4C23×D712yes—
573C2×D4C23×D712yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—44no—
579C22×C4—71no—
580C22×C4—71no—
581C22×C4—72no—
582C22×C4—72no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—82no—
586C22×C4—144no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—562no—
596C22×C4D4×D711yescharacteristic
597C22×C4D4×D711yescharacteristic
598C22×C4C23×D711yescharacteristic
599D8—28no—
600M16—148no—
601C2×C8—22no—
602C2×C8—72no—
603C2×C8—72no—
604C2×C8—142no—
605C2×C8—142no—
606C2×C8—148no—
607C2×C8#115714yes—
608C2×C8C23×D712yes—
609C2×C8C23×D712yes—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—74no—
613C4⋊C4—72no—
614C4⋊C4—72no—
615C4⋊C4—72no—
616C4⋊C4—72no—
617C4⋊C4—144no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—141no—
621C4⋊C4—141no—
622C4⋊C4—141no—
623C4⋊C4—141no—
624C4⋊C4—144no—
625C4⋊C4C23×D712yes—
626C4⋊C4C23×D712yes—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—74no—
630C22⋊C4—74no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4—144no—
637C22⋊C4—144no—
638C42—144no—
639C42—144no—
640C42—144no—
641C42D4×D712yes—
642C42C23×D712yes—
643C2×C7—82no—
644C2×C7—82no—
645C2×C7#334714yescomplemented
646C2×C7C2×#54711yescharacteristic
647C2×C7C2×#57511yescharacteristic
648C2×C7C2×#57611yescharacteristic
649D7—42no—
650D7—42no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—72no—
660C23—72no—
661C23—142no—
662C23—142no—
663C23—142no—
664C23—142no—
665C23—142no—
666C23—142no—
667C23C2×D4×D711yescharacteristic
668Q8—564no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4—22no—
673D4—42no—
674D4—42no—
675D4—284no—
676D4—288no—
677D4—564no—
678D4—564no—
679D4—564no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—72no—
688C2×C4—72no—
689C2×C4—84no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—144no—
693C2×C4—144no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—282no—
703C2×C4—282no—
704C2×C4—282no—
705C2×C4—282no—
706C2×C4—564no—
707C2×C4C2×#115712yes—
708C2×C4C2×D4×D712yes—
709C2×C4C2×D4×D712yes—
710C2×C4C2×D4×D711yescharacteristic
711C2×C4#655412yes—
712C2×C4C24×D711yescharacteristic
713C8—22no—
714C8—142no—
715C8—142no—
716C8C2×#115714yes—
717C7C2×#334711yescharacteristic, complemented, Sylow
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—84no—
726C22—142no—
727C22—142no—
728C22—142no—
729C22—142no—
730C22—142no—
731C22—142no—
732C22—284no—
733C22—284no—
734C22#9024212yes—
735C22#9046412yes—
736C22#9046512yes—
737C22C22×D4×D711yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—142no—
743C4—142no—
744C4—282no—
745C4—282no—
746C4—282no—
747C4—282no—
748C4#9024212yes—
749C4C22×#115711yescharacteristic
750C4C2×#655411yescharacteristic
751C2—82no—
752C2—82no—
753C2—282no—
754C2—282no—
755C2#1173733014yesdirect product factor
756C2C2×#9024211yescharacteristic
757C2C2×#9046411yescharacteristic
758C2C2×#9046511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#442C2
socleC23×C7C22×D4
hypercenterC2×#442D7
hypocenterC7C2×#3347
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×#90249C2semidirect
2. C2×#90254C2semidirect
3. C2×C7×#442C2semidirect
4. C2×#89931C2semidirect
5. C2×#89929C2semidirect
6. C2×#89781C2semidirect
7. C2×#89779C2semidirect
8. #11737330C2direct (N × H)
9. C2×#89633C2semidirect
10. C2×#89632C2semidirect
11. C2×#89556C2semidirect
12. C2×#89546C2semidirect
13. C2×#89551C2semidirect
14. C2×#89551C2semidirect
15. C2×#89478C2semidirect
16. C2×#89474C2semidirect
31. #90254C22semidirect
33. #90249C22semidirect
45. C7×#442C22semidirect
54. #89931C22semidirect
55. #89929C22semidirect
62. #89781C22semidirect
63. #89779C22semidirect
69. #89633C22semidirect
70. #89632C22semidirect
71. #89556C22semidirect
72. #89551C22semidirect
73. #89551C22semidirect
74. #89546C22semidirect
75. #89478C22semidirect
76. #89474C22semidirect
192. C2×#442D7semidirect
326. #442C2×D7semidirect
645. C2×C7#3347semidirect
717. C7C2×#3347semidirect
755. C2#11737330direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902492
C2×#902542
C2×C7×#4422
C2×#899312
C2×#899292
C2×#897812
C2×#897792
#117373302
C2×#896332
C2×#896322
C2×#895562
C2×#895462
C2×#895512
C2×#894782
C2×#894742
C2×#33477