Finite Group Databasebeta

← C2×#11738092 #14226765

Subgroups — C2×#11738092 #14226765

Order 1792.

1882 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×#90334C211yesmaximal, characteristic, complemented
2C2×#90294C211yesmaximal, characteristic, complemented
3C2×C7×#465C211yesmaximal, characteristic, complemented
4C2×#89938C211yesmaximal, characteristic, complemented
5C2×#89937C211yesmaximal, characteristic, complemented
6C2×#89886C211yesmaximal, characteristic, complemented
7C2×#89874C211yesmaximal, characteristic, complemented
8C2×#89824C211yesmaximal, characteristic, complemented
9C2×#89811C211yesmaximal, characteristic
10#11738092C2116yesmaximal, direct product factor
11C2×#89626C211yesmaximal, characteristic, complemented
12C2×#89642C211yesmaximal, characteristic, complemented
13C2×#89570C211yesmaximal, characteristic, complemented
14C2×#89563C211yesmaximal, characteristic, complemented
15C2×#89559C211yesmaximal, characteristic, complemented
16C2×#89533C211yesmaximal, characteristic, complemented
17C22×C7×SD16C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×#121C2211yescharacteristic
21C2×#6510C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C22×#1144C2211yescharacteristic
24C2×#6499—21no—
25C2×#6499C2211yescharacteristic
26C2×#6498—21no—
27C2×D4×Dic7C2211yescharacteristic
28C22×#1141C2211yescharacteristic
29C2×#6493C2211yescharacteristic
30C2×#6489C2211yescharacteristic
31C2×#6487C2211yescharacteristic
32C22×#1136C2211yescharacteristic
33C22×#1132C2211yescharacteristic
34#90334—24no—
35#90334C2218yescomplemented
36#90294—24no—
37#90294C2218yescomplemented
38C2×#6461—21no—
39C2×#6460—21no—
40C2×#6456C2211yescharacteristic
41C2×#6451C2211yescharacteristic
42C2×#6451C2211yescharacteristic
43C2×#6450C2211yescharacteristic
44C2×#6448—21no—
45C2×#6446—21no—
46C2×#6442—21no—
47C2×#6441—21no—
48C7×#465C2218yescomplemented
49C2×C7×#106C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54#89938C2218yescomplemented
55#89937C2218yescomplemented
56#89886C2218yescomplemented
57C2×#6395C2211yescharacteristic
58C2×#6391C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60#89874C2218yescomplemented
61C2×Dic7⋊C8C2211yescharacteristic
62C2×Dic7⋊C8C2211yescharacteristic
63C2×Dic7⋊C8C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65#89824C2218yescomplemented
66#89811C2218yes—
67C2×#6384C2211yescharacteristic
68C2×#6383C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71#89642C2218yescomplemented
72#89626C2218yescomplemented
73#89570C2218yescomplemented
74#89563C2218yescomplemented
75#89559C2218yescomplemented
76#89533C2218yescomplemented
77C2×#3263—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4—21no—
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—21no—
83C23×Dic7—21no—
84C22×D28C2311yescharacteristic
85C22×C4×D7—21no—
86C22×Dic14—21no—
87C22×Dic14—21no—
88C22×Dic14C2311yescharacteristic
89C2×C7×SD16—42no—
90C2×C7×SD16C2314yes—
91C22×C7×C8—42no—
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2314yes—
95C7×C22⋊Q8—22no—
96C7×C22⋊Q8C2314yes—
97C7×#121—22no—
98C7×#121C2314yes—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C22⋊C4—21no—
103C2×C7×C22⋊C4—21no—
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7D411yescharacteristic
109C2×C22⋊Dic7D411yescharacteristic
110#6510—22no—
111#6510C2314yes—
112Q8×Dic7—22no—
113Q8×Dic7C2314yes—
114C2×#1144—42no—
115C2×#1144C2314yes—
116#6499—28no—
117#6499—22no—
118#6499C2314yes—
119#6498—28no—
120D4×Dic7—22no—
121D4×Dic7C2314yes—
122C2×#1141—42no—
123C2×#1141C2314yes—
124#6493—22no—
125#6493C2314yes—
126C2×(C2×D7)⋊C4—21no—
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4—21no—
129C2×(C2×D7)⋊C4—21no—
130#6489D414yes—
131#6489C2314yes—
132C2×C4⋊Dic7—21no—
133C2×C4⋊Dic7D411yescharacteristic
134C2×C4⋊Dic7D411yescharacteristic
135C2×C4⋊Dic7C2311yescharacteristic
136C2×C4⋊Dic7C2311yescharacteristic
137#6487—22no—
138#6487C2314yes—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×C4×Dic7—21no—
144C2×C4×Dic7—21no—
145C2×C4×Dic7C2311yescharacteristic
146C2×C4×Dic7C2311yescharacteristic
147C2×#1136—42no—
148C2×#1136C2314yes—
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C2×#1132—42no—
152C2×#1132C2314yes—
153#6461—28no—
154#6460—28no—
155#6456—22no—
156#6456C2314yes—
157#6451—22no—
158#6451—22no—
159#6451C2314yes—
160#6451C2314yes—
161#6450—22no—
162#6450C2314yes—
163#6448—28no—
164#6446—28no—
165#6442—28no—
166#6441—28no—
167C7×#106C2314yes—
168C7×#103C2314yes—
169C7×#102C2314yes—
170#6409C2314yes—
171#6406C2314yes—
172#6395C2314yes—
173#6391C2314yes—
174#6390C2314yes—
175Dic7⋊C8C2314yes—
176Dic7⋊C8C2314yes—
177Dic7⋊C8C2314yes—
178Dic7⋊C8C2314yes—
179#6384C2314yes—
180#6383C2314yes—
181#6382C2314yes—
182#6382C2314yes—
183C2×#542—71no—
184C2×#542—71no—
185#3263—716no—
186C2×#475—71no—
187C2×#475—71no—
188C2×#476—71no—
189C2×#476—71no—
190C2×#470—71no—
191C2×#469—71no—
192C2×#465—71no—
193C2×#465D711yescharacteristic, complemented
194C2×#464—71no—
195C2×#464—71no—
196C2×#463—71no—
197C2×#463—71no—
198C2×#424—71no—
199C24×C7—21no—
200C24×C7C2×D411yescharacteristic
201C23×D7—21no—
202C2×C7×Q8—21no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8C2412yes—
206C2×C7×D4—24no—
207C2×C7×D4—21no—
208C2×C7×D4—22no—
209C2×C7×D4—22no—
210C2×C7×D4—82no—
211C2×C7×D4C2412yes—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2412yes—
220C22×C4×C7C2411yescharacteristic
221C2×C22⋊D7—24no—
222C2×C22⋊D7—82no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—24no—
227C22×Dic7—82no—
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230C22×Dic7C2×D411yescharacteristic
231C22×Dic7C2×D411yescharacteristic
232C2×D28—22no—
233C2×D28—22no—
234C2×D28—21no—
235C2×D28C2412yes—
236C2×C4×D7—24no—
237C2×C4×D7—82no—
238C2×Dic14—22no—
239C2×Dic14—22no—
240C2×Dic14—21no—
241C2×Dic14—24no—
242C2×Dic14—24no—
243C2×Dic14—82no—
244C2×Dic14—82no—
245C2×Dic14C2412yes—
246C7×SD16—44no—
247C2×C7×C8—22no—
248C2×C7×C8—22no—
249C2×C7×C8—44no—
250C2×C7×C8C2412yes—
251C2×C7×C8C2412yes—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4C2412yes—
256C7×C4⋊C4C2412yes—
257C7×C22⋊C4—24no—
258C7×C22⋊C4—24no—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261C22⋊Dic7—24no—
262C22⋊Dic7—24no—
263C22⋊Dic7C2×D414yes—
264C22⋊Dic7C2×D414yes—
265#1144—44no—
266#1141—44no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4—24no—
271C4⋊Dic7—21no—
272C4⋊Dic7—21no—
273C4⋊Dic7—24no—
274C4⋊Dic7C2×D414yes—
275C4⋊Dic7C2×D414yes—
276C4⋊Dic7C2412yes—
277C4⋊Dic7C2412yes—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282C4×Dic7—24no—
283C4×Dic7—24no—
284C4×Dic7C2×D412yes—
285C4×Dic7C2×D412yes—
286C4×Dic7C2412yes—
287C4×Dic7C2412yes—
288#1136—44no—
289C2×C7⋊C8—22no—
290C2×C7⋊C8—22no—
291C2×C7⋊C8C2412yes—
292C2×C7⋊C8C2412yes—
293#1132—44no—
294C22×Q16—71no—
295C22×SD16—71no—
296C22×SD16C2×D711yescharacteristic
297C22×D8—71no—
298C22×M16—71no—
299C23×C8C2×D711yescharacteristic
300#542—78no—
301#542—78no—
302#542—144no—
303#542—144no—
304C2×C4⋊Q8—71no—
305C2×C4⋊Q8—71no—
306C2×#126—141no—
307C2×#126—141no—
308C2×#124—71no—
309C2×#124—71no—
310C2×#124—141no—
311C2×#124—141no—
312C2×#123—141no—
313C2×#123—141no—
314C2×C22⋊Q8—71no—
315C2×C22⋊Q8—141no—
316C2×C22⋊Q8—141no—
317C2×C22⋊Q8C2×D711yescharacteristic
318C2×#121—71no—
319C2×#121C2×D711yescharacteristic
320C2×C4×Q8—71no—
321C2×C4×Q8—71no—
322C2×C4×D4—71no—
323C2×C4×D4—71no—
324C2×#117—71no—
325#476—78no—
326#476—78no—
327#475—78no—
328#475—78no—
329#470—78no—
330#469—78no—
331#465—78no—
332#465C2×D718yescomplemented
333#464—78no—
334#464—78no—
335#463—78no—
336#463—78no—
337C2×#106—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×#106C2×D711yescharacteristic
341#424—78no—
342C2×C4⋊C8—71no—
343C2×C4⋊C8—71no—
344C2×C4⋊C8—71no—
345C2×C4⋊C8—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103—71no—
349C2×#103C2×D711yescharacteristic
350C2×#102—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×#102C2×D711yescharacteristic
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—42no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7C22×D412yes—
362C23×C7C22×D411yescharacteristic
363C22×D7—22no—
364C22×D7—42no—
365C22×D7—42no—
366C22×D7—42no—
367C7×Q8—22no—
368C7×Q8—22no—
369C7×Q8—42no—
370C7×D4—22no—
371C7×D4—22no—
372C7×D4—42no—
373C7×D4—84no—
374C2×C4×C7—22no—
375C2×C4×C7—24no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D411yescharacteristic
386C2×C4×C7H(5,𝔽2)12yes—
387C2×C4×C72−1+412yes—
388C2×C4×C7C2511yescharacteristic
389C22⋊D7—84no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—42no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400C2×Dic7—84no—
401C2×Dic7C22×D412yes—
402C2×Dic7C22×D412yes—
403C2×Dic7C22×D412yes—
404C2×Dic7C22×D412yes—
405D28—22no—
406D28—22no—
407D28—42no—
408C4×D7—84no—
409Dic14—22no—
410Dic14—22no—
411Dic14—42no—
412Dic14—84no—
413Dic14—84no—
414C7×C8—22no—
415C7×C8—22no—
416C7⋊C8—22no—
417C7⋊C8—22no—
418C22×Q8—71no—
419C22×Q8—141no—
420C22×Q8—141no—
421C22×Q8C22×D711yescharacteristic
422C22×D4—21no—
423C22×D4—71no—
424C22×D4—141no—
425C22×D4C22×D711yescharacteristic
426C23×C4—141no—
427C23×C4—141no—
428C23×C4C22×D711yescharacteristic
429C2×Q16—74no—
430C2×Q16—282no—
431C2×SD16—42no—
432C2×SD16—74no—
433C2×SD16—282no—
434C2×SD16C22×D714yes—
435C2×D8—74no—
436C2×D8—282no—
437C2×M16—74no—
438C2×M16—282no—
439C22×C8—42no—
440C22×C8—71no—
441C22×C8—71no—
442C22×C8C22×D711yescharacteristic
443C22×C8C22×D711yescharacteristic
444C22×C8C22×D714yes—
445C4⋊Q8—74no—
446C4⋊Q8—74no—
447C4⋊Q8—142no—
448C4⋊Q8—142no—
449#126—148no—
450#126—148no—
451#124—74no—
452#124—74no—
453#124—142no—
454#124—142no—
455#124—148no—
456#124—148no—
457#123—148no—
458#123—148no—
459C22⋊Q8—22no—
460C22⋊Q8—74no—
461C22⋊Q8—148no—
462C22⋊Q8—148no—
463C22⋊Q8—142no—
464C22⋊Q8C22×D714yes—
465#121—22no—
466#121—74no—
467#121—142no—
468#121C22×D714yes—
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—71no—
505C2×C42—141no—
506C2×C42—141no—
507#106—74no—
508#106—74no—
509#106—74no—
510#106C22×D714yes—
511C4⋊C8—74no—
512C4⋊C8—74no—
513C4⋊C8—74no—
514C4⋊C8—74no—
515#103—74no—
516#103—74no—
517#103—74no—
518#103C22×D714yes—
519#102—74no—
520#102—74no—
521#102—74no—
522#102C22×D714yes—
523C22×C7—22no—
524C22×C7—22no—
525C22×C7—22no—
526C22×C7—44no—
527C22×C7—42no—
528C22×C7—42no—
529C22×C7—42no—
530C22×C7—84no—
531C22×C7#53712yes—
532C22×C7#57712yes—
533C22×C7#57712yes—
534C22×C7C23×D411yescharacteristic
535C2×D7—42no—
536C2×D7—42no—
537C2×D7—42no—
538C2×D7—84no—
539C4×C7—22no—
540C4×C7—42no—
541C4×C7—42no—
542C4×C7—42no—
543C4×C7#53712yes—
544C4×C7C2×H(5,𝔽2)11yescharacteristic
545C4×C7C2×2−1+411yescharacteristic
546Dic7—22no—
547Dic7—22no—
548Dic7—22no—
549Dic7—22no—
550Dic7—42no—
551Dic7—42no—
552Dic7—42no—
553C24—21no—
554C24—141no—
555C24D4×D711yescharacteristic
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—72no—
560C2×Q8—144no—
561C2×Q8—144no—
562C2×Q8—141no—
563C2×Q8—142no—
564C2×Q8—142no—
565C2×Q8—562no—
566C2×Q8—562no—
567C2×Q8C23×D712yes—
568C2×D4—24no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—72no—
573C2×D4—82no—
574C2×D4—144no—
575C2×D4—141no—
576C2×D4—142no—
577C2×D4—142no—
578C2×D4—562no—
579C2×D4C23×D712yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—71no—
586C22×C4—71no—
587C22×C4—71no—
588C22×C4—71no—
589C22×C4—144no—
590C22×C4—144no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—562no—
595C22×C4—562no—
596C22×C4D4×D712yes—
597C22×C4D4×D711yescharacteristic
598C22×C4C23×D712yes—
599C22×C4C23×D711yescharacteristic
600Q16—284no—
601SD16—44no—
602SD16—284no—
603D8—284no—
604M16—284no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—44no—
608C2×C8—72no—
609C2×C8—72no—
610C2×C8—142no—
611C2×C8—142no—
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—144no—
626C4⋊C4—141no—
627C4⋊C4—141no—
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—72no—
645C42—72no—
646C42—144no—
647C42—144no—
648C2×C7—42no—
649C2×C7—82no—
650C2×C7#326314yescomplemented
651C2×C7C2×#53711yescharacteristic
652C2×C7C2×#57711yescharacteristic
653C2×C7C2×#57711yescharacteristic
654D7—82no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—142no—
663C23—282no—
664C23—282no—
665C23—282no—
666C23C2×D4×D712yes—
667C23C2×D4×D711yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—142no—
672Q8—142no—
673Q8—282no—
674Q8—564no—
675Q8—564no—
676D4—22no—
677D4—22no—
678D4—42no—
679D4—84no—
680D4—142no—
681D4—142no—
682D4—282no—
683D4—564no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—72no—
695C2×C4—72no—
696C2×C4—72no—
697C2×C4—72no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—282no—
706C2×C4—282no—
707C2×C4—282no—
708C2×C4—564no—
709C2×C4—564no—
710C2×C4C2×D4×D712yes—
711C2×C4C2×D4×D711yescharacteristic
712C2×C4#654812yes—
713C2×C4#655412yes—
714C2×C4C24×D711yescharacteristic
715C8—22no—
716C8—22no—
717C8—142no—
718C8—142no—
719C7C2×#326311yescharacteristic, complemented, Sylow
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—282no—
729C22—282no—
730C22—282no—
731C22—564no—
732C22#9028812yes—
733C22#9045312yes—
734C22#9046112yes—
735C22C22×D4×D711yescharacteristic
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—142no—
741C4—142no—
742C4—142no—
743C4—142no—
744C4—282no—
745C4—282no—
746C4—282no—
747C4#9028812yes—
748C4C2×#654811yescharacteristic
749C4C2×#655411yescharacteristic
750C2—42no—
751C2—82no—
752C2—562no—
753C2#1173809214yesdirect product factor
754C2C2×#9028811yescharacteristic
755C2C2×#9045311yescharacteristic
756C2C2×#9046111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#465C2
socleC23×C7C22×D4
prime radicalC2×#89811C2
hypercenterC2×#465D7
hypocenterC7C2×#3263
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#90334C2semidirect
2. C2×#90294C2semidirect
3. C2×C7×#465C2semidirect
4. C2×#89938C2semidirect
5. C2×#89937C2semidirect
6. C2×#89886C2semidirect
7. C2×#89874C2semidirect
8. C2×#89824C2semidirect
10. #11738092C2direct (N × H)
11. C2×#89626C2semidirect
12. C2×#89642C2semidirect
13. C2×#89570C2semidirect
14. C2×#89563C2semidirect
15. C2×#89559C2semidirect
16. C2×#89533C2semidirect
35. #90334C22semidirect
37. #90294C22semidirect
48. C7×#465C22semidirect
54. #89938C22semidirect
55. #89937C22semidirect
56. #89886C22semidirect
60. #89874C22semidirect
65. #89824C22semidirect
71. #89642C22semidirect
72. #89626C22semidirect
73. #89570C22semidirect
74. #89563C22semidirect
75. #89559C22semidirect
76. #89533C22semidirect
193. C2×#465D7semidirect
332. #465C2×D7semidirect
650. C2×C7#3263semidirect
719. C7C2×#3263semidirect
753. C2#11738092direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903342
C2×#902942
C2×C7×#4652
C2×#899382
C2×#899372
C2×#898862
C2×#898742
C2×#898242
C2×#898112
#117380922
C2×#896262
C2×#896422
C2×#895702
C2×#895632
C2×#895592
C2×#895332
C2×#32637