Finite Group Databasebeta

← C2×#11741136 #14233577

Subgroups — C2×#11741136 #14233577

Order 1792.

1874 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×#557C211yesmaximal, characteristic, complemented
2C2×#90276C211yesmaximal, characteristic
3#11741136C2116yesmaximal, direct product factor
4C2×#89856C211yesmaximal, characteristic, complemented
5C2×#89861C211yesmaximal, characteristic, complemented
6C2×#89835C211yesmaximal, characteristic, complemented
7C2×#89838C211yesmaximal, characteristic, complemented
8C2×#89839C211yesmaximal, characteristic
9C2×#89840C211yesmaximal, characteristic, complemented
10C2×#89800C211yesmaximal, characteristic, complemented
11C2×#89800C211yesmaximal, characteristic, complemented
12C2×#89799C211yesmaximal, characteristic
13C2×#89798C211yesmaximal, characteristic, complemented
14C2×#89796C211yesmaximal, characteristic, complemented
15C2×#89802C211yesmaximal, characteristic, complemented
16C2×C4×#1143C211yesmaximal, characteristic, complemented
17C7×#557—24no—
18C7×#557C2218yescomplemented
19C2×C7×C4⋊Q8—21no—
20C2×C7×C4⋊Q8C2211yescharacteristic
21C2×C7×#125—21no—
22C2×C7×#125—21no—
23C2×C7×#125C2211yescharacteristic
24C2×C7×#125C2211yescharacteristic
25C2×C4×C7×Q8—21no—
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×Q8C2211yescharacteristic
29C2×C4×C7×Q8C2211yescharacteristic
30C2×#6510—21no—
31C22×#1144C2211yescharacteristic
32C22×#1143C2211yescharacteristic
33C22×#1143C2211yescharacteristic
34#90276—24no—
35#90276C2218yes—
36C2×#6457—21no—
37C2×#6457—21no—
38C2×#6456—21no—
39C2×#6438C2211yescharacteristic
40C2×#6438C2211yescharacteristic
41C2×#6437C2211yescharacteristic
42C2×C4×D28C2211yescharacteristic
43C2×C4×D28C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×#6409C2211yescharacteristic
46#89861C2218yescomplemented
47#89856C2218yescomplemented
48#89840C2218yescomplemented
49#89839C2218yes—
50#89838C2218yescomplemented
51#89835C2218yescomplemented
52#89802C2218yescomplemented
53#89800C2218yescomplemented
54#89800C2218yescomplemented
55#89799C2218yes—
56#89798C2218yescomplemented
57C4×#1143C2218yescomplemented
58#89796C2218yescomplemented
59C2×#6384C2211yescharacteristic
60C2×#6384C2211yescharacteristic
61C2×#6384C2211yescharacteristic
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6383C2211yescharacteristic
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×#3371—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8D411yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×D28—21no—
82C22×D28—21no—
83C22×D28C2311yescharacteristic
84C22×D28C2311yescharacteristic
85C22×C4×D7—21no—
86C22×C4×D7—21no—
87C22×Dic14C2311yescharacteristic
88C7×C4⋊Q8—28no—
89C7×C4⋊Q8—22no—
90C7×C4⋊Q8C2314yes—
91C7×#125—28no—
92C7×#125—28no—
93C7×#125—22no—
94C7×#125—22no—
95C7×#125C2314yes—
96C7×#125C2314yes—
97C4×C7×Q8—28no—
98C4×C7×Q8—22no—
99C4×C7×Q8—22no—
100C4×C7×Q8—22no—
101C4×C7×Q8D414yes—
102C4×C7×Q8C2314yes—
103C4×C7×Q8C2314yes—
104C4×C7×Q8C2314yes—
105C4×C7×Q8C2314yes—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4D411yescharacteristic
115C2×C7×C4⋊C4D411yescharacteristic
116C2×C7×C4⋊C4D411yescharacteristic
117C2×C7×C4⋊C4C2311yescharacteristic
118C2×C7×C4⋊C4C2311yescharacteristic
119C2×C7×C4⋊C4C2311yescharacteristic
120C2×C42×C7—21no—
121C2×C42×C7—21no—
122C2×C42×C7—21no—
123C2×C42×C7C2311yescharacteristic
124C2×C42×C7C2311yescharacteristic
125C2×C42×C7C2311yescharacteristic
126#6510—28no—
127C2×#1144—24no—
128C2×#1144C2314yes—
129C2×#1143—24no—
130C2×#1143—24no—
131C2×#1143C2314yes—
132C2×#1143C2314yes—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135C2×(C2×D7)⋊C4—21no—
136C2×(C2×D7)⋊C4—21no—
137C2×(C2×D7)⋊C4—21no—
138C2×(C2×D7)⋊C4—21no—
139C2×C4⋊Dic7C2311yescharacteristic
140C2×Dic7⋊C4—21no—
141C2×C4×Dic7—21no—
142C22×C7⋊C8C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146#6457—28no—
147#6457—28no—
148#6456—28no—
149#6438—22no—
150#6438—22no—
151#6438C2314yes—
152#6438C2314yes—
153#6437—22no—
154#6437C2314yes—
155C4×D28—22no—
156C4×D28—22no—
157C4×D28C2314yes—
158C4×D28C2314yes—
159C4×Dic14—22no—
160C4×Dic14C2314yes—
161#6409C2314yes—
162#6384C2314yes—
163#6384C2314yes—
164#6384C2314yes—
165#6383C2314yes—
166#6383C2314yes—
167#6383C2314yes—
168#6383C2314yes—
169#6383C2314yes—
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×#559—71no—
181C2×#557D711yescharacteristic, complemented
182#3371—716no—
183C2×#490—71no—
184C2×#489—71no—
185C2×#488—71no—
186C2×#479—71no—
187C2×#478—71no—
188C2×#476—71no—
189C2×#464—71no—
190C2×#464—71no—
191C2×#460—71no—
192C2×#446—71no—
193C2×#441—71no—
194C2×#440—71no—
195C2×C4×SD16—71no—
196C23×D7—21no—
197C23×D7—21no—
198C2×C7×Q8—21no—
199C2×C7×Q8—24no—
200C2×C7×Q8—22no—
201C2×C7×Q8—42no—
202C2×C7×Q8—44no—
203C2×C7×Q8C2×D414yes—
204C2×C7×Q8#4114yes—
205C2×C7×Q8C2412yes—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2411yescharacteristic
217C22×Dic7—21no—
218C22×Dic7—21no—
219C2×D28—22no—
220C2×D28—22no—
221C2×D28—22no—
222C2×D28—22no—
223C2×D28—21no—
224C2×D28—21no—
225C2×D28—24no—
226C2×D28—24no—
227C2×D28—44no—
228C2×D28—82no—
229C2×D28C2412yes—
230C2×D28C2412yes—
231C2×C4×D7—24no—
232C2×C4×D7—24no—
233C2×C4×D7—82no—
234C2×C4×D7—82no—
235C2×Dic14—22no—
236C2×Dic14—22no—
237C2×Dic14—21no—
238C2×Dic14C2412yes—
239C7×C4⋊C4—24no—
240C7×C4⋊C4—24no—
241C7×C4⋊C4—24no—
242C7×C4⋊C4—24no—
243C7×C4⋊C4—24no—
244C7×C4⋊C4—24no—
245C7×C4⋊C4—24no—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—21no—
249C7×C4⋊C4—21no—
250C7×C4⋊C4C2×D414yes—
251C7×C4⋊C4C2×D414yes—
252C7×C4⋊C4C2×D414yes—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C4⋊C4C2412yes—
256C42×C7—24no—
257C42×C7—24no—
258C42×C7—24no—
259C42×C7C2×D412yes—
260C42×C7C2×D412yes—
261C42×C7C2×D412yes—
262C42×C7C2412yes—
263C42×C7C2412yes—
264C42×C7C2412yes—
265#1144—28no—
266#1143—28no—
267#1143—28no—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4—24no—
274C4⋊Dic7—21no—
275C4⋊Dic7C2412yes—
276Dic7⋊C4—24no—
277C4×Dic7—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×Q16—71no—
287C22×SD16—71no—
288C22×SD16—71no—
289#559—78no—
290#559—144no—
291#557—24no—
292#557C2×D718yescomplemented
293C2×C4⋊Q8—21no—
294C2×C4⋊Q8C2×D711yescharacteristic
295C2×#127—71no—
296C2×#125—21no—
297C2×#125—21no—
298C2×#125C2×D711yescharacteristic
299C2×#125C2×D711yescharacteristic
300C2×#124—71no—
301C2×#124—71no—
302C2×#124—141no—
303C2×#123—141no—
304C2×#123—141no—
305C2×C4×Q8—21no—
306C2×C4×Q8—71no—
307C2×C4×Q8C2×D711yescharacteristic
308C2×C4×Q8C2×D711yescharacteristic
309C2×C4×Q8C2×D711yescharacteristic
310C2×C4×Q8C2×D711yescharacteristic
311C2×C4×D4—71no—
312C2×C4×D4—71no—
313C2×C4×D4—141no—
314#490—78no—
315#489—78no—
316#488—78no—
317#479—78no—
318#478—78no—
319#476—78no—
320#464—78no—
321#464—78no—
322#460—78no—
323#446—78no—
324#441—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×#102—71no—
338C2×#102—71no—
339C2×#102—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×#97—71no—
344C2×#97—71no—
345C2×C4×C8—71no—
346C23×C7C22×D411yescharacteristic
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—42no—
350C22×D7—42no—
351C22×D7—42no—
352C22×D7—42no—
353C22×D7—42no—
354C22×D7—42no—
355C7×Q8—24no—
356C7×Q8—22no—
357C7×Q8—44no—
358C7×Q8—48no—
359C7×Q8C2×#4114yes—
360C2×C4×C7—24no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
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—22no—
370C2×C4×C7—22no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—42no—
374C2×C4×C7C22×D412yes—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D412yes—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7C2×#4112yes—
382C2×C4×C72−1+412yes—
383C2×C4×C7C2511yescharacteristic
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388D28—22no—
389D28—22no—
390D28—22no—
391D28—22no—
392D28—48no—
393D28—42no—
394D28—42no—
395D28—84no—
396C4×D7—84no—
397C4×D7—84no—
398Dic14—22no—
399Dic14—22no—
400Dic14—42no—
401C7⋊C8—22no—
402C7⋊C8—22no—
403C7⋊C8—22no—
404C7⋊C8—22no—
405C22×Q8—21no—
406C22×Q8—71no—
407C22×Q8C22⋊D711yescharacteristic
408C22×Q8C22×D711yescharacteristic
409C22×D4—71no—
410C22×D4—71no—
411C22×D4—141no—
412C22×D4—141no—
413C23×C4—141no—
414C23×C4—141no—
415C2×Q16—74no—
416C2×Q16—144no—
417C2×SD16—74no—
418C2×SD16—74no—
419C2×SD16—144no—
420C2×SD16—144no—
421C22×C8—71no—
422C22×C8—71no—
423C22×C8—71no—
424C22×C8—71no—
425C4⋊Q8—28no—
426C4⋊Q8—22no—
427C4⋊Q8C22×D714yes—
428#127—74no—
429#127—142no—
430#125—28no—
431#125—28no—
432#125—22no—
433#125—22no—
434#125C22×D714yes—
435#125C22×D714yes—
436#124—74no—
437#124—74no—
438#124—148no—
439#124—142no—
440#124—142no—
441#123—148no—
442#123—148no—
443C4×Q8—28no—
444C4×Q8—22no—
445C4×Q8—22no—
446C4×Q8—22no—
447C4×Q8—74no—
448C4×Q8—142no—
449C4×Q8C22⋊D714yes—
450C4×Q8C22×D714yes—
451C4×Q8C22×D714yes—
452C4×Q8C22×D714yes—
453C4×Q8C22×D714yes—
454C4×D4—74no—
455C4×D4—74no—
456C4×D4—148no—
457C4×D4—142no—
458C4×D4—142no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—71no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4C22⋊D711yescharacteristic
470C2×C4⋊C4C22⋊D711yescharacteristic
471C2×C4⋊C4C22⋊D711yescharacteristic
472C2×C4⋊C4C22×D711yescharacteristic
473C2×C4⋊C4C22×D711yescharacteristic
474C2×C4⋊C4C22×D711yescharacteristic
475C2×C22⋊C4—141no—
476C2×C22⋊C4—141no—
477C2×C22⋊C4—141no—
478C2×C22⋊C4—141no—
479C2×C22⋊C4—141no—
480C2×C22⋊C4—141no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—141no—
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#102—74no—
499#102—74no—
500#102—74no—
501#102—74no—
502#102—74no—
503#102—74no—
504#97—74no—
505#97—74no—
506C4×C8—74no—
507C22×C7#54812yes—
508C22×C7#57512yes—
509C22×C7#57712yes—
510C22×C7C23×D411yescharacteristic
511C2×D7—42no—
512C2×D7—42no—
513C2×D7—42no—
514C2×D7—42no—
515C2×D7—42no—
516C2×D7—42no—
517C2×D7—84no—
518C2×D7—84no—
519C4×C7—24no—
520C4×C7—22no—
521C4×C7—22no—
522C4×C7—22no—
523C4×C7—22no—
524C4×C7—22no—
525C4×C7—22no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7—42no—
529C4×C7#54812yes—
530C4×C7C22×#4111yescharacteristic
531C4×C7C2×2−1+411yescharacteristic
532Dic7—42no—
533Dic7—42no—
534C24—141no—
535C24—141no—
536C2×Q8—22no—
537C2×Q8—21no—
538C2×Q8—24no—
539C2×Q8—42no—
540C2×Q8—44no—
541C2×Q8—72no—
542C2×Q8—141no—
543C2×Q8—142no—
544C2×Q8—142no—
545C2×Q8#116114yes—
546C2×Q8C2×C22⋊D714yes—
547C2×Q8C23×D712yes—
548C2×D4—72no—
549C2×D4—72no—
550C2×D4—142no—
551C2×D4—142no—
552C2×D4—142no—
553C2×D4—142no—
554C2×D4—144no—
555C2×D4—141no—
556C2×D4—141no—
557C2×D4—144no—
558C2×D4—284no—
559C2×D4—562no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—141no—
565C22×C4—141no—
566C22×C4—144no—
567C22×C4—144no—
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
577Q16—148no—
578SD16—148no—
579SD16—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—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—72no—
600C4⋊C4—144no—
601C4⋊C4—141no—
602C4⋊C4C2×C22⋊D714yes—
603C4⋊C4C2×C22⋊D714yes—
604C4⋊C4C2×C22⋊D714yes—
605C4⋊C4C23×D712yes—
606C4⋊C4C23×D712yes—
607C4⋊C4C23×D712yes—
608C22⋊C4—144no—
609C22⋊C4—144no—
610C22⋊C4—144no—
611C22⋊C4—144no—
612C22⋊C4—144no—
613C22⋊C4—144no—
614C42—24no—
615C42—24no—
616C42—24no—
617C42—144no—
618C42C2×C22⋊D712yes—
619C42C2×C22⋊D712yes—
620C42C2×C22⋊D712yes—
621C42C23×D712yes—
622C42C23×D712yes—
623C42C23×D712yes—
624C2×C7#337114yescomplemented
625C2×C7C2×#54811yescharacteristic
626C2×C7C2×#57511yescharacteristic
627C2×C7C2×#57711yescharacteristic
628D7—82no—
629D7—82no—
630C23—142no—
631C23—142no—
632C23—282no—
633C23—282no—
634C23—282no—
635C23—282no—
636C23—282no—
637C23—282no—
638C23C22×C22⋊D711yescharacteristic
639Q8—24no—
640Q8—22no—
641Q8—44no—
642Q8—48no—
643Q8—142no—
644Q8—142no—
645Q8—282no—
646Q8C2×#116114yes—
647D4—142no—
648D4—142no—
649D4—142no—
650D4—142no—
651D4—288no—
652D4—282no—
653D4—282no—
654D4—564no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—142no—
670C2×C4—142no—
671C2×C4—282no—
672C2×C4—282no—
673C2×C4—564no—
674C2×C4—564no—
675C2×C4C2×#116112yes—
676C2×C4#655112yes—
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×#337111yescharacteristic, complemented, Sylow
690C22—282no—
691C22—282no—
692C22—282no—
693C22—282no—
694C22—282no—
695C22—282no—
696C22—564no—
697C22—564no—
698C22#9050812yes—
699C22#9051312yes—
700C22#9052812yes—
701C22C23×C22⋊D711yescharacteristic
702C4—24no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—282no—
713C4—282no—
714C4#9050812yes—
715C4C22×#116111yescharacteristic
716C4C2×#655111yescharacteristic
717C2—562no—
718C2—562no—
719C2#1174113614yesdirect product factor
720C2C2×#9050811yescharacteristic
721C2C2×#9051311yescharacteristic
722C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#557C2
socleC23×C7C22×D4
prime radicalC2×#6437C22
hypercenterC2×#557D7
hypocenterC7C2×#3371
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. C2×C7×#557C2semidirect
3. #11741136C2direct (N × H)
4. C2×#89856C2semidirect
5. C2×#89861C2semidirect
6. C2×#89835C2semidirect
7. C2×#89838C2semidirect
9. C2×#89840C2semidirect
10. C2×#89800C2semidirect
11. C2×#89800C2semidirect
13. C2×#89798C2semidirect
14. C2×#89796C2semidirect
15. C2×#89802C2semidirect
16. C2×C4×#1143C2semidirect
18. C7×#557C22semidirect
46. #89861C22semidirect
47. #89856C22semidirect
48. #89840C22semidirect
50. #89838C22semidirect
51. #89835C22semidirect
52. #89802C22semidirect
53. #89800C22semidirect
54. #89800C22semidirect
56. #89798C22semidirect
57. C4×#1143C22semidirect
58. #89796C22semidirect
181. C2×#557D7semidirect
292. #557C2×D7semidirect
624. C2×C7#3371semidirect
689. C7C2×#3371semidirect
719. C2#11741136direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5572
C2×#902762
#117411362
C2×#898562
C2×#898612
C2×#898352
C2×#898382
C2×#898392
C2×#898402
C2×#898002
C2×#897992
C2×#897982
C2×#897962
C2×#898022
C2×C4×#11432
C2×#33717