Finite Group Databasebeta

← C2×#11736671 #14232376

Subgroups — C2×#11736671 #14232376

Order 1792.

1942 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×#90221C211yesmaximal, characteristic
2C2×#90202C211yesmaximal, characteristic, complemented
3C2×C7×#428C211yesmaximal, characteristic, complemented
4C2×#89906C211yesmaximal, characteristic, complemented
5C2×#89899C211yesmaximal, characteristic, complemented
6C2×#89768C211yesmaximal, characteristic, complemented
7C2×#89739C211yesmaximal, characteristic, complemented
8#11736671C2116yesmaximal, direct product factor
9C2×#89662C211yesmaximal, characteristic, complemented
10C2×#89656C211yesmaximal, characteristic, complemented
11C2×D7×#107C211yesmaximal, characteristic, complemented
12C2×#89661C211yesmaximal, characteristic, complemented
13C2×#89629C211yesmaximal, characteristic, complemented
14C2×#89635C211yesmaximal, characteristic, complemented
15C2×#89636C211yesmaximal, characteristic, complemented
16C2×#89628C211yesmaximal, characteristic, complemented
17C22×C7×M16C2211yescharacteristic
18C2×C7×#117C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C2×#6493C2211yescharacteristic
21C2×C4×C22⋊D7—21no—
22C2×C4×C22⋊D7C2211yescharacteristic
23C2×#6487—21no—
24C2×#6487C2211yescharacteristic
25C22×#1132C2211yescharacteristic
26C22×C8×D7C2211yescharacteristic
27#90221—24no—
28#90221C2218yes—
29#90202—24no—
30#90202C2218yescomplemented
31C2×#6460C2211yescharacteristic
32C2×#6459—21no—
33C2×#6458C2211yescharacteristic
34C2×#6456C2211yescharacteristic
35C2×D7×C4⋊C4C2211yescharacteristic
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×#6453C2211yescharacteristic
38C2×#6452—21no—
39C2×#6451C2211yescharacteristic
40C2×#6450C2211yescharacteristic
41C2×#6447—21no—
42C2×#6446—21no—
43C2×#6439—21no—
44C2×C4×D28—21no—
45C7×#428C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#107C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×#106C2211yescharacteristic
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51#89906C2218yescomplemented
52#89899C2218yescomplemented
53C2×#6395C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6392C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×#6389C2211yescharacteristic
58C2×Dic7⋊C8C2211yescharacteristic
59#89768C2218yescomplemented
60C2×#6384C2211yescharacteristic
61C2×#6384C2211yescharacteristic
62#89739C2218yescomplemented
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69#89662C2218yescomplemented
70#89661C2218yescomplemented
71#89656C2218yescomplemented
72D7×#107C2218yescomplemented
73#89636C2218yescomplemented
74#89635C2218yescomplemented
75#89629C2218yescomplemented
76#89628C2218yescomplemented
77C2×#3346—71nomaximal, Sylow
78C23×C4×C7—21no—
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7—21no—
81C22×C22⋊D7D411yescharacteristic
82C22×D28—21no—
83C22×D28C2311yescharacteristic
84C22×C4×D7—21no—
85C22×C4×D7—21no—
86C22×C4×D7—21no—
87C22×C4×D7C2311yescharacteristic
88C22×Dic14—21no—
89C22×Dic14C2311yescharacteristic
90C2×C7×M16—24no—
91C2×C7×M16C2314yes—
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C7×#117—22no—
95C7×#117C2314yes—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2314yes—
103C2×C7×C22⋊C4—21no—
104C2×C42×C7—21no—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7D411yescharacteristic
107#6493—22no—
108#6493C2314yes—
109C4×C22⋊D7—28no—
110C4×C22⋊D7D414yes—
111C4×C22⋊D7C2314yes—
112C2×(C2×D7)⋊C4—21no—
113C2×(C2×D7)⋊C4—21no—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4D411yescharacteristic
117C2×C4⋊Dic7—21no—
118C2×C4⋊Dic7—21no—
119C2×C4⋊Dic7C2311yescharacteristic
120C2×C4⋊Dic7C2311yescharacteristic
121#6487—22no—
122#6487—28no—
123#6487C2314yes—
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4D411yescharacteristic
131C2×C4×Dic7—21no—
132C2×C4×Dic7C2311yescharacteristic
133C22×C7⋊C8C2311yescharacteristic
134C22×C7⋊C8C2311yescharacteristic
135C2×#1132—24no—
136C2×#1132C2314yes—
137C2×C8×D7—24no—
138C2×C8×D7C2314yes—
139#6460—22no—
140#6460C2314yes—
141#6459—28no—
142#6458—22no—
143#6458C2314yes—
144#6456—22no—
145#6456C2314yes—
146D7×C4⋊C4—22no—
147D7×C4⋊C4—22no—
148D7×C4⋊C4C2314yes—
149D7×C4⋊C4C2314yes—
150#6453—22no—
151#6453C2314yes—
152#6452—28no—
153#6451—22no—
154#6451C2314yes—
155#6450—22no—
156#6450C2314yes—
157#6447—28no—
158#6446—28no—
159#6439—28no—
160C4×D28—28no—
161C7×#107C2314yes—
162C7×#107C2314yes—
163C7×#106C2314yes—
164C7×#106C2314yes—
165C22⋊(C7⋊C8)C2314yes—
166#6395C2314yes—
167(C2×D7)⋊C8C2314yes—
168#6392C2314yes—
169#6390C2314yes—
170#6389C2314yes—
171Dic7⋊C8C2314yes—
172#6384C2314yes—
173#6384C2314yes—
174#6383C2314yes—
175#6383C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180C2×#554—71no—
181C2×#553—71no—
182#3346—716no—
183C2×#501—71no—
184C2×#484—71no—
185C2×#481—71no—
186C2×#485—71no—
187C2×#480—71no—
188C2×#479—71no—
189C2×#474—71no—
190C2×#468—71no—
191C2×#465—71no—
192C2×#440—71no—
193C2×#435—71no—
194C2×#428D711yescharacteristic, complemented
195C22×#107—71no—
196C24×C7C2×D411yescharacteristic
197C23×D7—21no—
198C23×D7C2×D411yescharacteristic
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—24no—
206C22×C4×C7—82no—
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2411yescharacteristic
211C2×C22⋊D7—24no—
212C2×C22⋊D7—24no—
213C2×C22⋊D7—82no—
214C2×C22⋊D7C2×D414yes—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7C2×D411yescharacteristic
219C22×Dic7C2×D411yescharacteristic
220C22×Dic7C2×D411yescharacteristic
221C2×D28—22no—
222C2×D28—22no—
223C2×D28—24no—
224C2×D28—21no—
225C2×D28—44no—
226C2×D28C2412yes—
227C2×C4×D7—22no—
228C2×C4×D7—22no—
229C2×C4×D7—24no—
230C2×C4×D7—24no—
231C2×C4×D7—24no—
232C2×C4×D7—82no—
233C2×C4×D7—82no—
234C2×C4×D7—82no—
235C2×C4×D7C2×D412yes—
236C2×C4×D7C2412yes—
237C2×Dic14—22no—
238C2×Dic14—22no—
239C2×Dic14—21no—
240C2×Dic14—24no—
241C2×Dic14—82no—
242C2×Dic14C2412yes—
243C7×M16—28no—
244C2×C7×C8—22no—
245C2×C7×C8#4114yes—
246C2×C7×C8C2412yes—
247C2×C7×C8C2412yes—
248C7×C4⋊C4—21no—
249C7×C4⋊C4—21no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C4⋊C4C2412yes—
256C7×C4⋊C4C2412yes—
257C7×C22⋊C4—24no—
258C42×C7—24no—
259C22⋊Dic7—24no—
260C22⋊Dic7C2×D414yes—
261(C2×D7)⋊C4—24no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4C2×D414yes—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—24no—
269C4⋊Dic7—24no—
270C4⋊Dic7C2412yes—
271C4⋊Dic7C2412yes—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4C2×D414yes—
279C4×Dic7—24no—
280C4×Dic7C2×D412yes—
281C4×Dic7C2412yes—
282C2×C7⋊C8—22no—
283C2×C7⋊C8—22no—
284C2×C7⋊C8C2412yes—
285C2×C7⋊C8C2412yes—
286#1132—28no—
287C8×D7—28no—
288C22×SD16—71no—
289C22×M16C2×D711yescharacteristic
290C23×C8—71no—
291#554—78no—
292#554—144no—
293#553—78no—
294#553—144no—
295C2×C4⋊Q8—71no—
296C2×#126—141no—
297C2×#125—71no—
298C2×#125—141no—
299C2×#123—141no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8—71no—
302C2×C22⋊Q8—141no—
303C2×C22⋊Q8—141no—
304C2×#121—71no—
305C2×#121—71no—
306C2×#121—141no—
307C2×C4×Q8—71no—
308C2×C4×D4—71no—
309C2×C4×D4—71no—
310C2×C4×D4—141no—
311C2×C4×D4—141no—
312C2×#117C2×D711yescharacteristic
313C22×C4⋊C4—71no—
314C22×C4⋊C4—71no—
315C22×C4⋊C4C2×D711yescharacteristic
316#501—78no—
317#485—78no—
318#484—78no—
319#481—78no—
320#480—78no—
321#479—78no—
322#474—78no—
323#468—78no—
324#465—78no—
325#440—78no—
326#435—78no—
327#428C2×D718yescomplemented
328C2×#107—71no—
329C2×#107—71no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#107—78no—
333C2×#107C2×D711yescharacteristic
334C2×#107C2×D711yescharacteristic
335C2×#106—71no—
336C2×#106C2×D711yescharacteristic
337C2×#106C2×D711yescharacteristic
338C2×C4⋊C8—71no—
339C2×#103—71no—
340C2×#103—71no—
341C2×#103—71no—
342C2×#102—71no—
343C2×#102—71no—
344C2×#102—71no—
345C2×C22⋊C8—71no—
346C2×C22⋊C8—71no—
347C2×#97—71no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7C22×D412yes—
352C23×C7C22×D411yescharacteristic
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—42no—
357C22×D7—42no—
358C22×D7—42no—
359C22×D7#13714yes—
360C22×D7C22×D412yes—
361C2×C4×C7—22no—
362C2×C4×C7—24no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—84no—
374C2×C4×C7C22×D412yes—
375C2×C4×C7C22×D411yescharacteristic
376C2×C4×C7C2×#4112yes—
377C2×C4×C72−1+412yes—
378C2×C4×C7C2511yescharacteristic
379C22⋊D7—28no—
380C22⋊D7—84no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7C22×D412yes—
391C2×Dic7C22×D412yes—
392C2×Dic7C22×D412yes—
393D28—22no—
394D28—22no—
395D28—48no—
396D28—42no—
397C4×D7—24no—
398C4×D7—22no—
399C4×D7—22no—
400C4×D7—84no—
401C4×D7—84no—
402C4×D7—84no—
403Dic14—22no—
404Dic14—22no—
405Dic14—42no—
406Dic14—84no—
407C7×C8—22no—
408C7×C8C2×#4114yes—
409C7⋊C8—22no—
410C7⋊C8—22no—
411C22×Q8—71no—
412C22×Q8—141no—
413C22×D4—71no—
414C22×D4—71no—
415C22×D4—141no—
416C22×D4—141no—
417C23×C4—21no—
418C23×C4—71no—
419C23×C4—141no—
420C23×C4—141no—
421C23×C4—141no—
422C23×C4C22×D711yescharacteristic
423C2×SD16—74no—
424C2×SD16—144no—
425C2×M16—24no—
426C2×M16C22×D714yes—
427C22×C8—71no—
428C22×C8—71no—
429C22×C8—74no—
430C22×C8—144no—
431C22×C8C22×D711yescharacteristic
432C22×C8C22×D711yescharacteristic
433C4⋊Q8—74no—
434C4⋊Q8—142no—
435#126—148no—
436#125—74no—
437#125—142no—
438#125—148no—
439#123—148no—
440C22⋊Q8—74no—
441C22⋊Q8—74no—
442C22⋊Q8—148no—
443C22⋊Q8—148no—
444C22⋊Q8—142no—
445C22⋊Q8—142no—
446#121—74no—
447#121—74no—
448#121—148no—
449#121—142no—
450#121—142no—
451C4×Q8—74no—
452C4×Q8—142no—
453C4×D4—74no—
454C4×D4—74no—
455C4×D4—74no—
456C4×D4—148no—
457C4×D4—142no—
458C4×D4—148no—
459#117—22no—
460#117C22×D714yes—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—71no—
464C2×C4⋊C4—71no—
465C2×C4⋊C4—71no—
466C2×C4⋊C4—74no—
467C2×C4⋊C4—74no—
468C2×C4⋊C4—142no—
469C2×C4⋊C4—142no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4—141no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4—141no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4C22×D711yescharacteristic
479C2×C4⋊C4C22×D711yescharacteristic
480C2×C4⋊C4C22×D711yescharacteristic
481C2×C4⋊C4C22×D714yes—
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—71no—
485C2×C22⋊C4—71no—
486C2×C22⋊C4—141no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C42—21no—
492C2×C42—71no—
493C2×C42—141no—
494#107—74no—
495#107—74no—
496#107—74no—
497#107—74no—
498#107C22×D714yes—
499#107C22×D714yes—
500#106—74no—
501#106C22×D714yes—
502#106C22×D714yes—
503C4⋊C8—74no—
504#103—74no—
505#103—74no—
506#103—74no—
507#102—74no—
508#102—74no—
509#102—74no—
510C22⋊C8—74no—
511C22⋊C8—74no—
512#97—74no—
513C22×C7—22no—
514C22×C7—22no—
515C22×C7—22no—
516C22×C7—44no—
517C22×C7#54712yes—
518C22×C7C2×#13712yes—
519C22×C7#57612yes—
520C22×C7C23×D411yescharacteristic
521C2×D7—28no—
522C2×D7—22no—
523C2×D7—22no—
524C2×D7—42no—
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—84no—
528C2×D7C2×#13714yes—
529C4×C7—22no—
530C4×C7—42no—
531C4×C7—42no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7#54712yes—
535C4×C7C22×#4111yescharacteristic
536C4×C7C2×2−1+411yescharacteristic
537Dic7—22no—
538Dic7—22no—
539Dic7—22no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543C24—71no—
544C24—141no—
545C24D4×D711yescharacteristic
546C2×Q8—72no—
547C2×Q8—144no—
548C2×Q8—141no—
549C2×Q8—142no—
550C2×Q8—142no—
551C2×Q8—562no—
552C2×D4—74no—
553C2×D4—72no—
554C2×D4—144no—
555C2×D4—144no—
556C2×D4—144no—
557C2×D4—142no—
558C2×D4—141no—
559C2×D4—142no—
560C2×D4—284no—
561C2×D4—562no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—71no—
570C22×C4—71no—
571C22×C4—71no—
572C22×C4—72no—
573C22×C4—72no—
574C22×C4—82no—
575C22×C4—144no—
576C22×C4—144no—
577C22×C4—144no—
578C22×C4—142no—
579C22×C4—142no—
580C22×C4—141no—
581C22×C4—141no—
582C22×C4—141no—
583C22×C4—562no—
584C22×C4—562no—
585C22×C4—562no—
586C22×C4D4×D712yes—
587C22×C4D4×D711yescharacteristic
588C22×C4C23×D712yes—
589C22×C4C23×D711yescharacteristic
590SD16—148no—
591M16—28no—
592C2×C8—22no—
593C2×C8—72no—
594C2×C8—72no—
595C2×C8—142no—
596C2×C8—142no—
597C2×C8—148no—
598C2×C8#115714yes—
599C2×C8C23×D712yes—
600C2×C8C23×D712yes—
601C4⋊C4—21no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—74no—
607C4⋊C4—72no—
608C4⋊C4—72no—
609C4⋊C4—144no—
610C4⋊C4—144no—
611C4⋊C4—144no—
612C4⋊C4—144no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—141no—
618C4⋊C4—141no—
619C4⋊C4C23×D712yes—
620C4⋊C4C23×D712yes—
621C4⋊C4C23×D712yes—
622C4⋊C4C23×D712yes—
623C22⋊C4—24no—
624C22⋊C4—74no—
625C22⋊C4—74no—
626C22⋊C4—144no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C42—24no—
632C42—72no—
633C42—72no—
634C42—144no—
635C2×C7—42no—
636C2×C7#334614yescomplemented
637C2×C7C2×#54711yescharacteristic
638C2×C7C22×#13711yescharacteristic
639C2×C7C2×#57611yescharacteristic
640D7—24no—
641D7—82no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—74no—
646C23—72no—
647C23—142no—
648C23—142no—
649C23—142no—
650C23—282no—
651C23—282no—
652C23—282no—
653C23C2×D4×D712yes—
654C23C2×D4×D711yescharacteristic
655Q8—142no—
656Q8—142no—
657Q8—282no—
658Q8—564no—
659D4—148no—
660D4—142no—
661D4—142no—
662D4—288no—
663D4—282no—
664D4—564no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—72no—
678C2×C4—72no—
679C2×C4—72no—
680C2×C4—84no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—144no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—282no—
691C2×C4—282no—
692C2×C4—282no—
693C2×C4—564no—
694C2×C4—564no—
695C2×C4—564no—
696C2×C4C2×#115712yes—
697C2×C4C2×D4×D712yes—
698C2×C4C2×D4×D711yescharacteristic
699C2×C4#655112yes—
700C2×C4C24×D711yescharacteristic
701C8—22no—
702C8—142no—
703C8—142no—
704C8C2×#115714yes—
705C7C2×#334611yescharacteristic, complemented, Sylow
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—74no—
711C22—142no—
712C22—142no—
713C22—148no—
714C22—282no—
715C22—282no—
716C22—282no—
717C22—564no—
718C22#9019812yes—
719C22#9046512yes—
720C22D7×#13712yes—
721C22C22×D4×D711yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—142no—
728C4—142no—
729C4—142no—
730C4—282no—
731C4—282no—
732C4—282no—
733C4#9019812yes—
734C4C22×#115711yescharacteristic
735C4C2×#655111yescharacteristic
736C2—42no—
737C2—144no—
738C2—562no—
739C2#1173667114yesdirect product factor
740C2C2×#9019811yescharacteristic
741C2C2×#9046511yescharacteristic
742C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#428C2
socleC23×C7C22×D4
prime radicalC2×#90221C2
hypercenterC2×#428D7
hypocenterC7C2×#3346
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C2×#90202C2semidirect
3. C2×C7×#428C2semidirect
4. C2×#89906C2semidirect
5. C2×#89899C2semidirect
6. C2×#89768C2semidirect
7. C2×#89739C2semidirect
8. #11736671C2direct (N × H)
9. C2×#89662C2semidirect
10. C2×#89656C2semidirect
11. C2×D7×#107C2semidirect
12. C2×#89661C2semidirect
13. C2×#89629C2semidirect
14. C2×#89635C2semidirect
15. C2×#89636C2semidirect
16. C2×#89628C2semidirect
30. #90202C22semidirect
45. C7×#428C22semidirect
51. #89906C22semidirect
52. #89899C22semidirect
59. #89768C22semidirect
62. #89739C22semidirect
69. #89662C22semidirect
70. #89661C22semidirect
71. #89656C22semidirect
72. D7×#107C22semidirect
73. #89636C22semidirect
74. #89635C22semidirect
75. #89629C22semidirect
76. #89628C22semidirect
194. C2×#428D7semidirect
327. #428C2×D7semidirect
636. C2×C7#3346semidirect
705. C7C2×#3346semidirect
739. C2#11736671direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902212
C2×#902022
C2×C7×#4282
C2×#899062
C2×#898992
C2×#897682
C2×#897392
#117366712
C2×#896622
C2×#896562
C2×D7×#1072
C2×#896612
C2×#896292
C2×#896352
C2×#896362
C2×#896282
C2×#33467