Finite Group Databasebeta

← C2×#11741114 #14233555

Subgroups — C2×#11741114 #14233555

Order 1792.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#556C211yesmaximal, characteristic, complemented
2C2×#90270C211yesmaximal, characteristic, complemented
3#11741114C2116yesmaximal, direct product factor
4C2×#89855C211yesmaximal, characteristic, complemented
5C2×#89854C211yesmaximal, characteristic, complemented
6C2×#89829C211yesmaximal, characteristic
7C2×#89829C211yesmaximal, characteristic
8C2×#89827C211yesmaximal, characteristic, complemented
9C2×#89828C211yesmaximal, characteristic, complemented
10C2×#89798C211yesmaximal, characteristic, complemented
11C2×#89796C211yesmaximal, characteristic, complemented
12C2×#89794C211yesmaximal, characteristic, complemented
13C2×#89792C211yesmaximal, characteristic, complemented
14C2×C4×#1143C211yesmaximal, characteristic, complemented
15C2×#89781C211yesmaximal, characteristic, complemented
16C2×#89786C211yesmaximal, characteristic
17C7×#556—24no—
18C7×#556C2218yescomplemented
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#126—21no—
21C2×C7×#126—21no—
22C2×C7×#124C2211yescharacteristic
23C2×C7×#124C2211yescharacteristic
24C2×C7×C22⋊Q8—21no—
25C2×C4×C7×Q8C2211yescharacteristic
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×D4C2211yescharacteristic
29C2×C7×#117—21no—
30C2×#6509—21no—
31C22×#1143C2211yescharacteristic
32C22×#1143C2211yescharacteristic
33C22×#1141C2211yescharacteristic
34#90270—24no—
35#90270C2218yescomplemented
36C2×#6459—21no—
37C2×#6459—21no—
38C2×D7×C4⋊C4—21no—
39C2×C4×D28C2211yescharacteristic
40C2×C4×D28C2211yescharacteristic
41C2×C4×D28C2211yescharacteristic
42C2×#6433C2211yescharacteristic
43C2×#6433C2211yescharacteristic
44C2×#6432C2211yescharacteristic
45C2×#6409C2211yescharacteristic
46C2×#6409C2211yescharacteristic
47C2×#6409C2211yescharacteristic
48C2×#6409C2211yescharacteristic
49C2×#6409C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54#89855C2218yescomplemented
55#89854C2218yescomplemented
56#89829C2218yes—
57#89829C2218yes—
58#89828C2218yescomplemented
59#89827C2218yescomplemented
60#89798C2218yescomplemented
61C4×#1143C2218yescomplemented
62#89796C2218yescomplemented
63#89794C2218yescomplemented
64#89792C2218yescomplemented
65#89786C2218yes—
66#89781C2218yescomplemented
67C2×#6383C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71C2×C4⋊(C7⋊C8)C2211yescharacteristic
72C2×C4⋊(C7⋊C8)C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×#6377C2211yescharacteristic
75C2×#6377C2211yescharacteristic
76C2×C4×C7⋊C8C2211yescharacteristic
77C2×#3376—71nomaximal, Sylow
78C22×C7×Q8D411yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C22×D28C2311yescharacteristic
84C22×C4×D7—21no—
85C22×C4×D7—21no—
86C22×C4×D7—21no—
87C22×Dic14—21no—
88C7×C4⋊Q8—22no—
89C7×C4⋊Q8C2314yes—
90C7×#126—28no—
91C7×#126—28no—
92C7×#124—22no—
93C7×#124—22no—
94C7×#124C2314yes—
95C7×#124C2314yes—
96C7×C22⋊Q8—28no—
97C4×C7×Q8—22no—
98C4×C7×Q8—22no—
99C4×C7×Q8D414yes—
100C4×C7×Q8C2314yes—
101C4×C7×Q8C2314yes—
102C4×C7×Q8C2314yes—
103C4×C7×D4—22no—
104C4×C7×D4C2314yes—
105C7×#117—28no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4D411yescharacteristic
111C2×C7×C4⋊C4D411yescharacteristic
112C2×C7×C4⋊C4D411yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C42×C7—21no—
120C2×C42×C7—21no—
121C2×C42×C7C2311yescharacteristic
122C2×C42×C7C2311yescharacteristic
123C2×C42×C7C2311yescharacteristic
124#6509—28no—
125C2×#1143—24no—
126C2×#1143—24no—
127C2×#1143C2314yes—
128C2×#1143C2314yes—
129C2×#1141—24no—
130C2×#1141C2314yes—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134C2×C4⋊Dic7—21no—
135C2×C4⋊Dic7C2311yescharacteristic
136C2×C4⋊Dic7C2311yescharacteristic
137C2×C4⋊Dic7C2311yescharacteristic
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C22×C7⋊C8C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146#6459—28no—
147#6459—28no—
148D7×C4⋊C4—28no—
149C4×D28—22no—
150C4×D28—22no—
151C4×D28—22no—
152C4×D28C2314yes—
153C4×D28C2314yes—
154C4×D28C2314yes—
155#6433—22no—
156#6433—22no—
157#6433C2314yes—
158#6433C2314yes—
159#6432—22no—
160#6432C2314yes—
161#6409C2314yes—
162#6409C2314yes—
163#6409C2314yes—
164#6409C2314yes—
165#6409C2314yes—
166#6409C2314yes—
167#6406C2314yes—
168#6406C2314yes—
169#6406C2314yes—
170#6383C2314yes—
171#6382C2314yes—
172#6382C2314yes—
173#6381C2314yes—
174C4⋊(C7⋊C8)C2314yes—
175C4⋊(C7⋊C8)C2314yes—
176C4⋊(C7⋊C8)C2314yes—
177#6377C2314yes—
178#6377C2314yes—
179C4×C7⋊C8C2314yes—
180C2×#556D711yescharacteristic, complemented
181C2×#554—71no—
182#3376—716no—
183C2×#491—71no—
184C2×#489—71no—
185C2×#488—71no—
186C2×#479—71no—
187C2×#475—71no—
188C2×#478—71no—
189C2×#463—71no—
190C2×#463—71no—
191C2×#461—71no—
192C2×#446—71no—
193C2×#442—71no—
194C2×#440—71no—
195C2×C4×SD16—71no—
196C24×C7—21no—
197C23×D7—21no—
198C2×C7×Q8—21no—
199C2×C7×Q8—21no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8—22no—
203C2×C7×Q8—22no—
204C2×C7×Q8—42no—
205C2×C7×Q8C2×D414yes—
206C2×C7×Q8C2412yes—
207C2×C7×Q8C2412yes—
208C2×C7×D4—21no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4C2412yes—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—24no—
216C22×C4×C7—44no—
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2411yescharacteristic
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C2×D28—21no—
228C2×D28—22no—
229C2×D28#4114yes—
230C2×D28C2412yes—
231C2×C4×D7—24no—
232C2×C4×D7—24no—
233C2×C4×D7—24no—
234C2×C4×D7—44no—
235C2×C4×D7—82no—
236C2×C4×D7—82no—
237C2×Dic14—24no—
238C2×Dic14—82no—
239C7×C4⋊C4—24no—
240C7×C4⋊C4—24no—
241C7×C4⋊C4—24no—
242C7×C4⋊C4—24no—
243C7×C4⋊C4—21no—
244C7×C4⋊C4C2×D414yes—
245C7×C4⋊C4C2×D414yes—
246C7×C4⋊C4C2×D414yes—
247C7×C4⋊C4C2412yes—
248C7×C22⋊C4—24no—
249C7×C22⋊C4—24no—
250C7×C22⋊C4—24no—
251C7×C22⋊C4—24no—
252C7×C22⋊C4—24no—
253C42×C7—24no—
254C42×C7—24no—
255C42×C7C2×D412yes—
256C42×C7C2×D412yes—
257C42×C7C2×D412yes—
258C42×C7C2412yes—
259C42×C7C2412yes—
260C42×C7C2412yes—
261#1143—28no—
262#1143—28no—
263#1141—28no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—24no—
270C4⋊Dic7—21no—
271C4⋊Dic7C2412yes—
272C4⋊Dic7C2412yes—
273C4⋊Dic7C2412yes—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278C2×C7⋊C8—22no—
279C2×C7⋊C8—22no—
280C2×C7⋊C8—22no—
281C2×C7⋊C8—22no—
282C2×C7⋊C8C2412yes—
283C2×C7⋊C8C2412yes—
284C2×C7⋊C8C2412yes—
285C2×C7⋊C8C2412yes—
286C22×SD16—71no—
287C22×SD16—71no—
288C22×D8—71no—
289#556—24no—
290#556C2×D718yescomplemented
291#554—78no—
292#554—144no—
293C2×C4⋊Q8—71no—
294C2×C4⋊Q8C2×D711yescharacteristic
295C2×#126—21no—
296C2×#126—21no—
297C2×#125—71no—
298C2×#125—71no—
299C2×#124C2×D711yescharacteristic
300C2×#124C2×D711yescharacteristic
301C2×C22⋊Q8—21no—
302C2×C22⋊Q8—141no—
303C2×C22⋊Q8—141no—
304C2×C22⋊Q8—141no—
305C2×C4×Q8C2×D711yescharacteristic
306C2×C4×Q8C2×D711yescharacteristic
307C2×C4×Q8C2×D711yescharacteristic
308C2×C4×D4—71no—
309C2×C4×D4—71no—
310C2×C4×D4—71no—
311C2×C4×D4C2×D711yescharacteristic
312C2×#117—21no—
313C22×C4⋊C4—141no—
314#491—78no—
315#489—78no—
316#488—78no—
317#479—78no—
318#478—78no—
319#475—78no—
320#463—78no—
321#463—78no—
322#461—78no—
323#446—78no—
324#442—78no—
325#440—78no—
326C4×SD16—78no—
327C2×#107—71no—
328C2×#106—71no—
329C2×#106—71no—
330C2×C4⋊C8—71no—
331C2×C4⋊C8—71no—
332C2×C4⋊C8—71no—
333C2×#103—71no—
334C2×#103—71no—
335C2×#103—71no—
336C2×#103—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#102—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×#97—71no—
344C2×#97—71no—
345C2×C4×C8—71no—
346C23×C7—22no—
347C23×C7—42no—
348C23×C7—42no—
349C23×C7—42no—
350C23×C7C22×D411yescharacteristic
351C22×D7—24no—
352C22×D7—22no—
353C22×D7—42no—
354C22×D7—42no—
355C7×Q8—22no—
356C7×Q8—22no—
357C7×Q8—22no—
358C7×Q8—22no—
359C7×Q8—44no—
360C7×Q8—42no—
361C7×Q8—42no—
362C7×D4—22no—
363C7×D4—22no—
364C7×D4—42no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
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—48no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D412yes—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D411yescharacteristic
385C2×C4×C7C2×#4112yes—
386C2×C4×C72−1+412yes—
387C2×C4×C7C2511yescharacteristic
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394D28—24no—
395D28—22no—
396D28C2×#4114yes—
397C4×D7—48no—
398C4×D7—84no—
399C4×D7—84no—
400Dic14—84no—
401C7⋊C8—22no—
402C7⋊C8—22no—
403C7⋊C8—22no—
404C7⋊C8—22no—
405C22×Q8—141no—
406C22×Q8C22⋊D711yescharacteristic
407C22×Q8C22×D711yescharacteristic
408C22×Q8C22×D711yescharacteristic
409C22×D4—71no—
410C22×D4C22×D711yescharacteristic
411C23×C4—21no—
412C23×C4—141no—
413C23×C4—141no—
414C23×C4—141no—
415C2×SD16—74no—
416C2×SD16—74no—
417C2×SD16—144no—
418C2×SD16—144no—
419C2×D8—74no—
420C2×D8—144no—
421C22×C8—71no—
422C22×C8—71no—
423C22×C8—71no—
424C22×C8—71no—
425C4⋊Q8—22no—
426C4⋊Q8—74no—
427C4⋊Q8—142no—
428C4⋊Q8C22×D714yes—
429#126—28no—
430#126—28no—
431#125—74no—
432#125—74no—
433#125—142no—
434#125—142no—
435#124—22no—
436#124—22no—
437#124C22×D714yes—
438#124C22×D714yes—
439C22⋊Q8—28no—
440C22⋊Q8—148no—
441C22⋊Q8—148no—
442C22⋊Q8—148no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×Q8C22⋊D714yes—
446C4×Q8C22×D714yes—
447C4×Q8C22×D714yes—
448C4×Q8C22×D714yes—
449C4×D4—22no—
450C4×D4—74no—
451C4×D4—74no—
452C4×D4—74no—
453C4×D4—142no—
454C4×D4—142no—
455C4×D4—142no—
456C4×D4C22×D714yes—
457#117—28no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—71no—
463C2×C4⋊C4—71no—
464C2×C4⋊C4—71no—
465C2×C4⋊C4—141no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—148no—
471C2×C4⋊C4C22⋊D711yescharacteristic
472C2×C4⋊C4C22⋊D711yescharacteristic
473C2×C4⋊C4C22⋊D711yescharacteristic
474C2×C4⋊C4C22×D711yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—141no—
481C2×C22⋊C4—141no—
482C2×C22⋊C4—141no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42C22×D711yescharacteristic
486C2×C42C22×D711yescharacteristic
487C2×C42C22×D711yescharacteristic
488#107—74no—
489#106—74no—
490#106—74no—
491C4⋊C8—74no—
492C4⋊C8—74no—
493C4⋊C8—74no—
494#103—74no—
495#103—74no—
496#103—74no—
497#103—74no—
498#103—74no—
499#103—74no—
500#102—74no—
501#102—74no—
502#102—74no—
503#102—74no—
504#97—74no—
505#97—74no—
506C4×C8—74no—
507C22×C7—42no—
508C22×C7—42no—
509C22×C7—42no—
510C22×C7—84no—
511C22×C7#54812yes—
512C22×C7#57512yes—
513C22×C7#57712yes—
514C22×C7C23×D411yescharacteristic
515C2×D7—24no—
516C2×D7—48no—
517C2×D7—42no—
518C2×D7—42no—
519C4×C7—22no—
520C4×C7—22no—
521C4×C7—22no—
522C4×C7—22no—
523C4×C7—22no—
524C4×C7—22no—
525C4×C7—42no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7#54812yes—
529C4×C7C22×#4111yescharacteristic
530C4×C7C2×2−1+411yescharacteristic
531Dic7—42no—
532Dic7—42no—
533Dic7—42no—
534C24—21no—
535C24—141no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—42no—
543C2×Q8—144no—
544C2×Q8—562no—
545C2×Q8C2×C22⋊D714yes—
546C2×Q8C23×D712yes—
547C2×Q8C23×D712yes—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—74no—
552C2×D4—72no—
553C2×D4—142no—
554C2×D4—141no—
555C2×D4C23×D712yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—24no—
560C22×C4—44no—
561C22×C4—141no—
562C22×C4—141no—
563C22×C4—141no—
564C22×C4—144no—
565C22×C4—144no—
566C22×C4—144no—
567C22×C4—284no—
568C22×C4—562no—
569C22×C4—562no—
570C22×C4C2×C22⋊D711yescharacteristic
571C22×C4C2×C22⋊D711yescharacteristic
572C22×C4C2×C22⋊D711yescharacteristic
573C22×C4C2×C22⋊D711yescharacteristic
574C22×C4C2×C22⋊D711yescharacteristic
575C22×C4C2×C22⋊D711yescharacteristic
576C22×C4C23×D711yescharacteristic
577SD16—148no—
578SD16—148no—
579D8—148no—
580C2×C8—72no—
581C2×C8—72no—
582C2×C8—72no—
583C2×C8—72no—
584C2×C8—142no—
585C2×C8—142no—
586C2×C8—142no—
587C2×C8—142no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—72no—
594C4⋊C4—72no—
595C4⋊C4—72no—
596C4⋊C4—144no—
597C4⋊C4—144no—
598C4⋊C4—144no—
599C4⋊C4—144no—
600C4⋊C4—141no—
601C4⋊C4—141no—
602C4⋊C4—141no—
603C4⋊C4—144no—
604C4⋊C4C2×C22⋊D714yes—
605C4⋊C4C2×C22⋊D714yes—
606C4⋊C4C2×C22⋊D714yes—
607C4⋊C4C23×D712yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C22⋊C4—144no—
614C22⋊C4—144no—
615C22⋊C4—144no—
616C42—24no—
617C42—24no—
618C42C2×C22⋊D712yes—
619C42C2×C22⋊D712yes—
620C42C2×C22⋊D712yes—
621C42C23×D712yes—
622C42C23×D712yes—
623C42C23×D712yes—
624C2×C7—82no—
625C2×C7#337614yescomplemented
626C2×C7C2×#54811yescharacteristic
627C2×C7C2×#57511yescharacteristic
628C2×C7C2×#57711yescharacteristic
629D7—44no—
630C23—22no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—144no—
635C23—142no—
636C23—282no—
637C23—282no—
638C23C22×C22⋊D711yescharacteristic
639Q8—22no—
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—44no—
644Q8—42no—
645Q8—42no—
646Q8—564no—
647D4—22no—
648D4—22no—
649D4—42no—
650D4—74no—
651D4—144no—
652D4—142no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—48no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—288no—
670C2×C4—282no—
671C2×C4—282no—
672C2×C4—282no—
673C2×C4—564no—
674C2×C4—564no—
675C2×C4D7×#4112yes—
676C2×C4#655412yes—
677C2×C4C22×C22⋊D712yes—
678C2×C4C22×C22⋊D712yes—
679C2×C4C22×C22⋊D712yes—
680C2×C4C22×C22⋊D712yes—
681C2×C4C22×C22⋊D712yes—
682C2×C4C22×C22⋊D712yes—
683C2×C4C22×C22⋊D711yescharacteristic
684C2×C4C24×D711yescharacteristic
685C8—142no—
686C8—142no—
687C8—142no—
688C8—142no—
689C7C2×#337611yescharacteristic, complemented, Sylow
690C22—42no—
691C22—42no—
692C22—42no—
693C22—84no—
694C22—144no—
695C22—282no—
696C22—282no—
697C22—288no—
698C22#9051312yes—
699C22#9052212yes—
700C22#9052812yes—
701C22C23×C22⋊D711yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—282no—
712C4—282no—
713C4—282no—
714C4#9052212yes—
715C4C2×D7×#4111yescharacteristic
716C4C2×#655411yescharacteristic
717C2—82no—
718C2—284no—
719C2#1174111414yesdirect product factor
720C2C2×#9051311yescharacteristic
721C2C2×#9052211yescharacteristic
722C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#556C2
socleC23×C7C22×D4
prime radicalC22×#1141C22
hypercenterC2×#556D7
hypocenterC7C2×#3376
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×C7×#556C2semidirect
2. C2×#90270C2semidirect
3. #11741114C2direct (N × H)
4. C2×#89855C2semidirect
5. C2×#89854C2semidirect
8. C2×#89827C2semidirect
9. C2×#89828C2semidirect
10. C2×#89798C2semidirect
11. C2×#89796C2semidirect
12. C2×#89794C2semidirect
13. C2×#89792C2semidirect
14. C2×C4×#1143C2semidirect
15. C2×#89781C2semidirect
18. C7×#556C22semidirect
35. #90270C22semidirect
54. #89855C22semidirect
55. #89854C22semidirect
58. #89828C22semidirect
59. #89827C22semidirect
60. #89798C22semidirect
61. C4×#1143C22semidirect
62. #89796C22semidirect
63. #89794C22semidirect
64. #89792C22semidirect
66. #89781C22semidirect
180. C2×#556D7semidirect
290. #556C2×D7semidirect
625. C2×C7#3376semidirect
689. C7C2×#3376semidirect
719. C2#11741114direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5562
C2×#902702
#117411142
C2×#898552
C2×#898542
C2×#898292
C2×#898272
C2×#898282
C2×#897982
C2×#897962
C2×#897942
C2×#897922
C2×C4×#11432
C2×#897812
C2×#897862
C2×#33767