Finite Group Databasebeta

← C2×#11739111 #14223593

Subgroups — C2×#11739111 #14223593

Order 1792.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90424C211yesmaximal, characteristic, complemented
2C2×#90373C211yesmaximal, characteristic, complemented
3C2×C7×#489C211yesmaximal, characteristic, complemented
4C2×#89851C211yesmaximal, characteristic, complemented
5C2×#89831C211yesmaximal, characteristic, complemented
6#11739111C2116yesmaximal, direct product factor
7C2×#89588C211yesmaximal, characteristic, complemented
8C2×#89579C211yesmaximal, characteristic, complemented
9C2×#89561C211yesmaximal, characteristic, complemented
10C2×#89560C211yesmaximal, characteristic, complemented
11C2×#89554C211yesmaximal, characteristic
12C2×#89550C211yesmaximal, characteristic, complemented
13C2×#89557C211yesmaximal, characteristic, complemented
14C2×#89530C211yesmaximal, characteristic, complemented
15C2×#89486C211yesmaximal, characteristic, complemented
16C2×#89480C211yesmaximal, characteristic, complemented
17C2×C7×C4⋊Q8C2211yescharacteristic
18C2×C7×#124C2211yescharacteristic
19C2×#6510—21no—
20C2×#6509—21no—
21C2×#6509C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C22×#1144C2211yescharacteristic
24C22×#1143C2211yescharacteristic
25C2×#6501C2211yescharacteristic
26C2×D4×Dic7C2211yescharacteristic
27C22×#1142C2211yescharacteristic
28C22×#1141C2211yescharacteristic
29C22×#1131C2211yescharacteristic
30C22×C8×D7C2211yescharacteristic
31#90424—24no—
32#90424C2218yescomplemented
33#90373—24no—
34#90373C2218yescomplemented
35C2×#6461—21no—
36C2×#6460C2211yescharacteristic
37C2×#6458C2211yescharacteristic
38C2×#6457—21no—
39C2×#6456C2211yescharacteristic
40C2×#6450C2211yescharacteristic
41C2×#6449—21no—
42C2×#6448—21no—
43C2×#6442—21no—
44C2×#6441—21no—
45C2×#6438C2211yescharacteristic
46C2×#6435C2211yescharacteristic
47C2×#6432C2211yescharacteristic
48C7×#489C2218yescomplemented
49C2×C7×#103C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×C7×#102C2211yescharacteristic
53C2×C7×#97C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×#6395C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×#6390C2211yescharacteristic
58C2×#6389C2211yescharacteristic
59C2×C8×Dic7C2211yescharacteristic
60#89851C2218yescomplemented
61#89831C2218yescomplemented
62C2×#6382C2211yescharacteristic
63C2×#6382C2211yescharacteristic
64C2×#6382C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×C4×C7⋊C8C2211yescharacteristic
67#89588C2218yescomplemented
68#89579C2218yescomplemented
69#89561C2218yescomplemented
70#89560C2218yescomplemented
71#89557C2218yescomplemented
72#89554C2218yes—
73#89550C2218yescomplemented
74#89530C2218yescomplemented
75#89486C2218yescomplemented
76#89480C2218yescomplemented
77C2×#3173—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4C2311yescharacteristic
81C22×C22⋊D7—21no—
82C23×Dic7—21no—
83C22×D28—21no—
84C22×D28C2311yescharacteristic
85C22×C4×D7—21no—
86C22×C4×D7C2311yescharacteristic
87C22×Dic14—21no—
88C22×Dic14C2311yescharacteristic
89C22×C7×C8C2311yescharacteristic
90C22×C7×C8C2311yescharacteristic
91C7×C4⋊Q8—22no—
92C7×C4⋊Q8C2314yes—
93C7×#124—22no—
94C7×#124C2314yes—
95C2×C7×C4⋊C4—21no—
96C2×C7×C4⋊C4C2311yescharacteristic
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C22⋊C4—21no—
99C2×C7×C22⋊C4—21no—
100C2×C42×C7C2311yescharacteristic
101C2×C22⋊Dic7—21no—
102C2×C22⋊Dic7—21no—
103#6510—28no—
104#6509—22no—
105#6509—28no—
106#6509C2314yes—
107Q8×Dic7—22no—
108Q8×Dic7C2314yes—
109C2×#1144—24no—
110C2×#1144C2314yes—
111C2×#1143—24no—
112C2×#1143C2314yes—
113#6501—22no—
114#6501C2314yes—
115D4×Dic7—22no—
116D4×Dic7C2314yes—
117C2×#1142—24no—
118C2×#1142C2314yes—
119C2×#1141—24no—
120C2×#1141C2314yes—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4—21no—
125C2×(C2×D7)⋊C4—21no—
126C2×(C2×D7)⋊C4—21no—
127C2×(C2×D7)⋊C4D411yescharacteristic
128C2×(C2×D7)⋊C4D411yescharacteristic
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—21no—
131C2×C4⋊Dic7—21no—
132C2×C4⋊Dic7C2311yescharacteristic
133C2×C4⋊Dic7C2311yescharacteristic
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4D411yescharacteristic
137C2×Dic7⋊C4D411yescharacteristic
138C2×C4×Dic7—21no—
139C2×C4×Dic7—21no—
140C2×C4×Dic7C2311yescharacteristic
141C22×C7⋊C8C2311yescharacteristic
142C22×C7⋊C8C2311yescharacteristic
143C2×#1131—24no—
144C2×#1131C2314yes—
145C2×C8×D7—24no—
146C2×C8×D7C2314yes—
147#6461—28no—
148#6460—22no—
149#6460C2314yes—
150#6458—22no—
151#6458C2314yes—
152#6457—28no—
153#6456—22no—
154#6456C2314yes—
155#6450—22no—
156#6450C2314yes—
157#6449—28no—
158#6448—28no—
159#6442—28no—
160#6441—28no—
161#6438—22no—
162#6438C2314yes—
163#6435D414yes—
164#6435C2314yes—
165#6432—22no—
166#6432C2314yes—
167C7×#103C2314yes—
168C7×#103C2314yes—
169C7×#102C2314yes—
170C7×#102C2314yes—
171C7×#97C2314yes—
172#6395C2314yes—
173#6395C2314yes—
174#6390C2314yes—
175#6390C2314yes—
176#6389C2314yes—
177C8×Dic7C2314yes—
178#6382C2314yes—
179#6382C2314yes—
180#6382C2314yes—
181#6382C2314yes—
182C4×C7⋊C8C2314yes—
183C2×#542—71no—
184C2×#542—71no—
185#3173—716no—
186C2×#498—71no—
187C2×#495—71no—
188C2×#489—71no—
189C2×#489D711yescharacteristic, complemented
190C2×#470—71no—
191C2×#469—71no—
192C2×#465—71no—
193C2×#465—71no—
194C2×#442—71no—
195C2×#441—71no—
196C2×C4×SD16—71no—
197C2×C4×SD16—71no—
198C2×#405—71no—
199C24×C7—21no—
200C23×D7—21no—
201C23×D7C2×D411yescharacteristic
202C2×C7×Q8—21no—
203C2×C7×Q8—24no—
204C2×C7×Q8—22no—
205C2×C7×Q8—22no—
206C2×C7×Q8—82no—
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×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2411yescharacteristic
218C2×C22⋊D7—24no—
219C2×C22⋊D7—82no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—24no—
224C22×Dic7—82no—
225C22×Dic7C2×D411yescharacteristic
226C22×Dic7C2×D411yescharacteristic
227C22×Dic7C2×D411yescharacteristic
228C2×D28—22no—
229C2×D28—22no—
230C2×D28—21no—
231C2×D28—24no—
232C2×D28—82no—
233C2×D28C2412yes—
234C2×C4×D7—22no—
235C2×C4×D7—22no—
236C2×C4×D7—24no—
237C2×C4×D7—82no—
238C2×C4×D7C2×D412yes—
239C2×C4×D7C2412yes—
240C2×Dic14—22no—
241C2×Dic14—22no—
242C2×Dic14—21no—
243C2×Dic14—24no—
244C2×Dic14—82no—
245C2×Dic14C2412yes—
246C2×C7×C8—22no—
247C2×C7×C8—22no—
248C2×C7×C8C2412yes—
249C2×C7×C8C2412yes—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—24no—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C22⋊C4—24no—
256C7×C22⋊C4—24no—
257C42×C7C2×D412yes—
258C42×C7C2412yes—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261#1144—28no—
262#1143—28no—
263#1142—28no—
264#1141—28no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4C2×D414yes—
272(C2×D7)⋊C4C2×D414yes—
273C4⋊Dic7—21no—
274C4⋊Dic7—21no—
275C4⋊Dic7—24no—
276C4⋊Dic7—24no—
277C4⋊Dic7—24no—
278C4⋊Dic7C2412yes—
279C4⋊Dic7C2412yes—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4C2×D414yes—
283Dic7⋊C4C2×D414yes—
284C4×Dic7—24no—
285C4×Dic7—24no—
286C4×Dic7C2×D412yes—
287C4×Dic7C2412yes—
288C2×C7⋊C8#4114yes—
289C2×C7⋊C8#4114yes—
290C2×C7⋊C8C2412yes—
291C2×C7⋊C8C2412yes—
292#1131—28no—
293C8×D7—28no—
294C22×Q16—71no—
295C22×SD16—71no—
296C22×SD16—71no—
297C22×D8—71no—
298C22×M16—71no—
299C23×C8—71no—
300#542—78no—
301#542—78no—
302#542—144no—
303#542—144no—
304C2×C4⋊Q8—71no—
305C2×C4⋊Q8C2×D711yescharacteristic
306C2×#126—141no—
307C2×#126—141no—
308C2×#124—71no—
309C2×#124—141no—
310C2×#124—141no—
311C2×#124C2×D711yescharacteristic
312C2×#123—141no—
313C2×#123—141no—
314C2×C22⋊Q8—71no—
315C2×C22⋊Q8—71no—
316C2×C22⋊Q8—141no—
317C2×C22⋊Q8—141no—
318C2×#121—71no—
319C2×#121—71no—
320C2×C4×Q8—71no—
321C2×C4×Q8—71no—
322C2×C4×D4—71no—
323C2×C4×D4—71no—
324C2×#117—71no—
325#498—78no—
326#495—78no—
327#489—78no—
328#489C2×D718yescomplemented
329#470—78no—
330#469—78no—
331#465—78no—
332#465—78no—
333#442—78no—
334#441—78no—
335C4×SD16—78no—
336C4×SD16—78no—
337C2×#106—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×#106—71no—
341C2×#103—71no—
342C2×#103—71no—
343C2×#103C2×D711yescharacteristic
344C2×#103C2×D711yescharacteristic
345C2×#102—71no—
346C2×#102—71no—
347C2×#102C2×D711yescharacteristic
348C2×#102C2×D711yescharacteristic
349#405—78no—
350C2×#97—71no—
351C2×#97C2×D711yescharacteristic
352C2×C4×C8—71no—
353C2×C4×C8—71no—
354C23×C7—22no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7C22×D411yescharacteristic
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—42no—
364C22×D7—42no—
365C22×D7—42no—
366C22×D7C22×D412yes—
367C7×Q8—22no—
368C7×Q8—22no—
369C7×Q8—42no—
370C7×Q8—84no—
371C7×D4—22no—
372C7×D4—22no—
373C7×D4—42no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D411yescharacteristic
385C2×C4×C7C2×#4112yes—
386C2×C4×C7C2×#4112yes—
387C2×C4×C7C2511yescharacteristic
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—84no—
399C2×Dic7C22×D412yes—
400C2×Dic7C22×D412yes—
401C2×Dic7C22×D412yes—
402D28—22no—
403D28—22no—
404D28—42no—
405D28—84no—
406C4×D7—24no—
407C4×D7—22no—
408C4×D7—22no—
409C4×D7—84no—
410Dic14—22no—
411Dic14—22no—
412Dic14—42no—
413Dic14—84no—
414C7×C8—22no—
415C7×C8—22no—
416C7⋊C8C2×#4114yes—
417C7⋊C8C2×#4114yes—
418C22×Q8—21no—
419C22×Q8—71no—
420C22×Q8—141no—
421C22×Q8C22×D711yescharacteristic
422C22×D4—71no—
423C22×D4—141no—
424C22×D4—141no—
425C22×D4C22×D711yescharacteristic
426C23×C4—71no—
427C23×C4—141no—
428C23×C4—141no—
429C2×Q16—74no—
430C2×Q16—144no—
431C2×SD16—74no—
432C2×SD16—74no—
433C2×SD16—144no—
434C2×SD16—144no—
435C2×D8—74no—
436C2×D8—144no—
437C2×M16—74no—
438C2×M16—144no—
439C22×C8—71no—
440C22×C8—71no—
441C22×C8—74no—
442C22×C8—144no—
443C22×C8C22×D711yescharacteristic
444C22×C8C22×D711yescharacteristic
445C4⋊Q8—22no—
446C4⋊Q8—74no—
447C4⋊Q8—142no—
448C4⋊Q8C22×D714yes—
449#126—148no—
450#126—148no—
451#124—22no—
452#124—74no—
453#124—148no—
454#124—148no—
455#124—142no—
456#124C22×D714yes—
457#123—148no—
458#123—148no—
459C22⋊Q8—74no—
460C22⋊Q8—74no—
461C22⋊Q8—148no—
462C22⋊Q8—142no—
463C22⋊Q8—148no—
464C22⋊Q8—142no—
465#121—74no—
466#121—74no—
467#121—142no—
468#121—142no—
469C4×Q8—74no—
470C4×Q8—74no—
471C4×Q8—142no—
472C4×Q8—142no—
473C4×D4—74no—
474C4×D4—74no—
475C4×D4—142no—
476C4×D4—142no—
477#117—74no—
478#117—74no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—71no—
481C2×C4⋊C4—71no—
482C2×C4⋊C4—71no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4—141no—
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C4⋊C4C22×D711yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—71no—
494C2×C22⋊C4—71no—
495C2×C22⋊C4—141no—
496C2×C22⋊C4—141no—
497C2×C22⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C22⋊C4—141no—
500C2×C22⋊C4—141no—
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C42—71no—
504C2×C42—141no—
505C2×C42—141no—
506C2×C42C22×D711yescharacteristic
507#106—74no—
508#106—74no—
509#106—74no—
510#106—74no—
511#103—74no—
512#103—74no—
513#103C22×D714yes—
514#103C22×D714yes—
515#102—74no—
516#102—74no—
517#102C22×D714yes—
518#102C22×D714yes—
519#97—74no—
520#97C22×D714yes—
521C4×C8—74no—
522C4×C8—74no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—84no—
527C22×C7#53212yes—
528C22×C7#57712yes—
529C22×C7#57712yes—
530C22×C7C23×D411yescharacteristic
531C2×D7—22no—
532C2×D7—22no—
533C2×D7—22no—
534C2×D7—44no—
535C2×D7—42no—
536C2×D7—42no—
537C2×D7—42no—
538C2×D7—84no—
539C4×C7—22no—
540C4×C7—22no—
541C4×C7—42no—
542C4×C7—42no—
543C4×C7—42no—
544C4×C7#53212yes—
545C4×C7C22×#4111yescharacteristic
546C4×C7C22×#4111yescharacteristic
547Dic7—22no—
548Dic7—22no—
549Dic7—22no—
550Dic7—42no—
551Dic7—42no—
552Dic7—42no—
553C24—21no—
554C24—71no—
555C24—141no—
556C2×Q8—21no—
557C2×Q8—24no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—72no—
561C2×Q8—82no—
562C2×Q8—141no—
563C2×Q8—144no—
564C2×Q8—142no—
565C2×Q8—142no—
566C2×Q8—562no—
567C2×Q8C23×D712yes—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—72no—
572C2×D4—144no—
573C2×D4—144no—
574C2×D4—141no—
575C2×D4—142no—
576C2×D4—142no—
577C2×D4—562no—
578C2×D4—562no—
579C2×D4C23×D712yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—71no—
584C22×C4—71no—
585C22×C4—71no—
586C22×C4—72no—
587C22×C4—72no—
588C22×C4—144no—
589C22×C4—144no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—562no—
596C22×C4—562no—
597C22×C4D4×D711yescharacteristic
598C22×C4D4×D711yescharacteristic
599C22×C4C23×D711yescharacteristic
600Q16—148no—
601SD16—148no—
602SD16—148no—
603D8—148no—
604M16—148no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—74no—
608C2×C8—74no—
609C2×C8—72no—
610C2×C8—72no—
611C2×C8—148no—
612C2×C8C23×D712yes—
613C2×C8C23×D712yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—74no—
618C4⋊C4—74no—
619C4⋊C4—72no—
620C4⋊C4—72no—
621C4⋊C4—144no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4—144no—
625C4⋊C4—141no—
626C4⋊C4—141no—
627C4⋊C4—144no—
628C4⋊C4C23×D712yes—
629C4⋊C4C23×D712yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—74no—
633C22⋊C4—74no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4—144no—
637C22⋊C4—144no—
638C22⋊C4—144no—
639C22⋊C4—144no—
640C22⋊C4—144no—
641C22⋊C4—144no—
642C42—72no—
643C42—72no—
644C42—144no—
645C42—144no—
646C42D4×D712yes—
647C42C23×D712yes—
648C2×C7—82no—
649C2×C7#317314yescomplemented
650C2×C7C2×#53211yescharacteristic
651C2×C7C2×#57711yescharacteristic
652C2×C7C2×#57711yescharacteristic
653D7—42no—
654D7—82no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—72no—
660C23—142no—
661C23—142no—
662C23—142no—
663C23—142no—
664C23—282no—
665C23—282no—
666C23—282no—
667C23C2×D4×D711yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—84no—
672Q8—142no—
673Q8—142no—
674Q8—282no—
675Q8—564no—
676D4—22no—
677D4—22no—
678D4—42no—
679D4—142no—
680D4—142no—
681D4—282no—
682D4—564no—
683D4—564no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—72no—
693C2×C4—72no—
694C2×C4—72no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—144no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—282no—
705C2×C4—282no—
706C2×C4—282no—
707C2×C4—564no—
708C2×C4—564no—
709C2×C4C2×D4×D712yes—
710C2×C4C2×D4×D712yes—
711C2×C4C2×D4×D711yescharacteristic
712C2×C4D7×#4112yes—
713C2×C4D7×#4112yes—
714C2×C4C24×D711yescharacteristic
715C8—22no—
716C8—22no—
717C8—74no—
718C8—74no—
719C7C2×#317311yescharacteristic, complemented, Sylow
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—142no—
725C22—142no—
726C22—142no—
727C22—284no—
728C22—282no—
729C22—282no—
730C22—282no—
731C22—564no—
732C22#9035912yes—
733C22#9046612yes—
734C22#9046912yes—
735C22C22×D4×D711yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—142no—
742C4—142no—
743C4—142no—
744C4—282no—
745C4—282no—
746C4—282no—
747C4#9035912yes—
748C4C2×D7×#4111yescharacteristic
749C4C2×D7×#4111yescharacteristic
750C2—82no—
751C2—282no—
752C2—562no—
753C2#1173911114yesdirect product factor
754C2C2×#9035911yescharacteristic
755C2C2×#9046611yescharacteristic
756C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#489C2
socleC23×C7C22×D4
prime radicalC2×#89554C2
hypercenterC2×#489D7
hypocenterC7C2×#3173
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#90424C2semidirect
2. C2×#90373C2semidirect
3. C2×C7×#489C2semidirect
4. C2×#89851C2semidirect
5. C2×#89831C2semidirect
6. #11739111C2direct (N × H)
7. C2×#89588C2semidirect
8. C2×#89579C2semidirect
9. C2×#89561C2semidirect
10. C2×#89560C2semidirect
12. C2×#89550C2semidirect
13. C2×#89557C2semidirect
14. C2×#89530C2semidirect
15. C2×#89486C2semidirect
16. C2×#89480C2semidirect
32. #90424C22semidirect
34. #90373C22semidirect
48. C7×#489C22semidirect
60. #89851C22semidirect
61. #89831C22semidirect
67. #89588C22semidirect
68. #89579C22semidirect
69. #89561C22semidirect
70. #89560C22semidirect
71. #89557C22semidirect
73. #89550C22semidirect
74. #89530C22semidirect
75. #89486C22semidirect
76. #89480C22semidirect
189. C2×#489D7semidirect
328. #489C2×D7semidirect
649. C2×C7#3173semidirect
719. C7C2×#3173semidirect
753. C2#11739111direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904242
C2×#903732
C2×C7×#4892
C2×#898512
C2×#898312
#117391112
C2×#895882
C2×#895792
C2×#895612
C2×#895602
C2×#895542
C2×#895502
C2×#895572
C2×#895302
C2×#894862
C2×#894802
C2×#31737