Finite Group Databasebeta

← C2×#11739003 #14223687

Subgroups — C2×#11739003 #14223687

Order 1792.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90424C211yesmaximal, characteristic, complemented
2C2×#90410C211yesmaximal, characteristic, complemented
3C2×C7×#486C211yesmaximal, characteristic, complemented
4C2×#89852C211yesmaximal, characteristic, complemented
5C2×#89846C211yesmaximal, characteristic, complemented
6#11739003C2116yesmaximal, direct product factor
7C2×#89554C211yesmaximal, characteristic, complemented
8C2×#89552C211yesmaximal, characteristic, complemented
9C2×#89547C211yesmaximal, characteristic, complemented
10C2×#89550C211yesmaximal, characteristic, complemented
11C2×#89557C211yesmaximal, characteristic, complemented
12C2×#89529C211yesmaximal, characteristic, complemented
13C2×#89530C211yesmaximal, characteristic, complemented
14C2×#89528C211yesmaximal, characteristic, complemented
15C2×#89469C211yesmaximal, characteristic, complemented
16C2×#89461C211yesmaximal, characteristic, complemented
17C2×C7×C4⋊Q8C2211yescharacteristic
18C2×C7×#127C2211yescharacteristic
19C2×#6510—21no—
20C2×#6509—21no—
21C2×#6502—21no—
22C2×#6502—21no—
23C2×#6501C2211yescharacteristic
24C2×#6501C2211yescharacteristic
25C2×#6498—21no—
26C2×#6498—21no—
27C2×D4×Dic7C2211yescharacteristic
28C2×D4×Dic7C2211yescharacteristic
29C22×#1142C2211yescharacteristic
30C22×#1142C2211yescharacteristic
31C22×#1141C2211yescharacteristic
32C22×#1141C2211yescharacteristic
33C22×#1131C2211yescharacteristic
34C22×C8×D7C2211yescharacteristic
35#90424—24no—
36#90424C2218yescomplemented
37#90410—24no—
38#90410C2218yescomplemented
39C2×#6461—21no—
40C2×#6460C2211yescharacteristic
41C2×#6458C2211yescharacteristic
42C2×#6457—21no—
43C2×#6456C2211yescharacteristic
44C2×#6450C2211yescharacteristic
45C2×#6438C2211yescharacteristic
46C2×#6435C2211yescharacteristic
47C2×#6433C2211yescharacteristic
48C7×#486C2218yescomplemented
49C2×C7×#102C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×C7×#102C2211yescharacteristic
53C2×C4×C7×C8C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×#6395C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×#6390C2211yescharacteristic
58C2×#6389C2211yescharacteristic
59C2×C8×Dic7C2211yescharacteristic
60#89852C2218yescomplemented
61#89846C2218yescomplemented
62C2×#6382C2211yescharacteristic
63C2×#6382C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6377C2211yescharacteristic
67#89557C2218yescomplemented
68#89554C2218yescomplemented
69#89552C2218yescomplemented
70#89550C2218yescomplemented
71#89547C2218yescomplemented
72#89530C2218yescomplemented
73#89529C2218yescomplemented
74#89528C2218yescomplemented
75#89469C2218yescomplemented
76#89461C2218yescomplemented
77C2×#3179—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×D4—21no—
80C22×C7×D4—21no—
81C22×C7×D4C2311yescharacteristic
82C22×C7×D4C2311yescharacteristic
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C23×Dic7—21no—
86C23×Dic7—21no—
87C22×D28—21no—
88C22×D28C2311yescharacteristic
89C22×C4×D7—21no—
90C22×C4×D7C2311yescharacteristic
91C22×Dic14C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C7×C4⋊Q8—22no—
95C7×C4⋊Q8C2314yes—
96C7×#127—22no—
97C7×#127C2314yes—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C42×C7C2311yescharacteristic
102C2×C22⋊Dic7—21no—
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106#6510—28no—
107#6509—28no—
108#6502—28no—
109#6502—28no—
110#6501—22no—
111#6501—22no—
112#6501C2314yes—
113#6501C2314yes—
114#6498—28no—
115#6498—28no—
116D4×Dic7—22no—
117D4×Dic7—22no—
118D4×Dic7C2314yes—
119D4×Dic7C2314yes—
120C2×#1142—24no—
121C2×#1142—24no—
122C2×#1142C2314yes—
123C2×#1142C2314yes—
124C2×#1141—24no—
125C2×#1141—24no—
126C2×#1141C2314yes—
127C2×#1141C2314yes—
128C2×(C2×D7)⋊C4—21no—
129C2×(C2×D7)⋊C4—21no—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4D411yescharacteristic
134C2×(C2×D7)⋊C4D411yescharacteristic
135C2×C4⋊Dic7—21no—
136C2×C4⋊Dic7C2311yescharacteristic
137C2×C4⋊Dic7C2311yescharacteristic
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4D411yescharacteristic
142C2×Dic7⋊C4D411yescharacteristic
143C2×C4×Dic7—21no—
144C2×C4×Dic7C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146C22×C7⋊C8C2311yescharacteristic
147C2×#1131—24no—
148C2×#1131C2314yes—
149C2×C8×D7—24no—
150C2×C8×D7C2314yes—
151#6461—28no—
152#6460—22no—
153#6460C2314yes—
154#6458—22no—
155#6458C2314yes—
156#6457—28no—
157#6456—22no—
158#6456C2314yes—
159#6450—22no—
160#6450C2314yes—
161#6438—22no—
162#6438C2314yes—
163#6435D414yes—
164#6435C2314yes—
165#6433—22no—
166#6433C2314yes—
167C7×#102C2314yes—
168C7×#102C2314yes—
169C7×#102C2314yes—
170C7×#102C2314yes—
171C4×C7×C8C2314yes—
172#6395C2314yes—
173#6395C2314yes—
174#6390C2314yes—
175#6390C2314yes—
176#6389C2314yes—
177C8×Dic7C2314yes—
178#6382C2314yes—
179#6382C2314yes—
180#6381C2314yes—
181#6381C2314yes—
182#6377C2314yes—
183C2×#542—71no—
184C2×#540—71no—
185#3179—716no—
186C2×#501—71no—
187C2×#496—71no—
188C2×#488—71no—
189C2×#486D711yescharacteristic, complemented
190C2×#469—71no—
191C2×#468—71no—
192C2×#466—71no—
193C2×#465—71no—
194C2×#442—71no—
195C2×#440—71no—
196C2×C4×SD16—71no—
197C2×C4×D8—71no—
198C2×#405—71no—
199C24×C7—21no—
200C24×C7—21no—
201C23×D7—21no—
202C23×D7C2×D411yescharacteristic
203C2×C7×Q8—24no—
204C2×C7×Q8—82no—
205C2×C7×D4—21no—
206C2×C7×D4—21no—
207C2×C7×D4—24no—
208C2×C7×D4—24no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4—22no—
212C2×C7×D4—22no—
213C2×C7×D4—82no—
214C2×C7×D4—82no—
215C2×C7×D4C2412yes—
216C2×C7×D4C2412yes—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2411yescharacteristic
222C2×C22⋊D7—24no—
223C2×C22⋊D7—24no—
224C2×C22⋊D7—82no—
225C2×C22⋊D7—82no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—24no—
230C22×Dic7—24no—
231C22×Dic7—82no—
232C22×Dic7—82no—
233C22×Dic7C2×D411yescharacteristic
234C22×Dic7C2×D411yescharacteristic
235C22×Dic7C2×D411yescharacteristic
236C2×D28—22no—
237C2×D28—22no—
238C2×D28—21no—
239C2×D28—24no—
240C2×D28—82no—
241C2×D28C2412yes—
242C2×C4×D7—22no—
243C2×C4×D7—22no—
244C2×C4×D7—24no—
245C2×C4×D7—82no—
246C2×C4×D7C2×D412yes—
247C2×C4×D7C2412yes—
248C2×Dic14—22no—
249C2×Dic14—22no—
250C2×Dic14—21no—
251C2×Dic14C2412yes—
252C2×C7×C8—22no—
253C2×C7×C8—22no—
254C2×C7×C8C2412yes—
255C2×C7×C8C2412yes—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—24no—
259C7×C4⋊C4C2412yes—
260C7×C4⋊C4C2412yes—
261C42×C7C2×D412yes—
262C42×C7C2412yes—
263C22⋊Dic7—24no—
264C22⋊Dic7—24no—
265C22⋊Dic7—24no—
266C22⋊Dic7—24no—
267#1142—28no—
268#1142—28no—
269#1141—28no—
270#1141—28no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4—24no—
274(C2×D7)⋊C4—24no—
275(C2×D7)⋊C4—24no—
276(C2×D7)⋊C4C2×D414yes—
277(C2×D7)⋊C4C2×D414yes—
278C4⋊Dic7—21no—
279C4⋊Dic7—21no—
280C4⋊Dic7—24no—
281C4⋊Dic7C2412yes—
282C4⋊Dic7C2412yes—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285Dic7⋊C4—24no—
286Dic7⋊C4C2×D414yes—
287Dic7⋊C4C2×D414yes—
288C4×Dic7—24no—
289C4×Dic7C2×D412yes—
290C4×Dic7C2412yes—
291C2×C7⋊C8#4114yes—
292C2×C7⋊C8#4114yes—
293C2×C7⋊C8C2412yes—
294C2×C7⋊C8C2412yes—
295#1131—28no—
296C8×D7—28no—
297C22×SD16—71no—
298C22×SD16—71no—
299C22×D8—71no—
300C22×D8—71no—
301C22×M16—71no—
302C23×C8—71no—
303#542—78no—
304#542—144no—
305#540—78no—
306#540—144no—
307C2×C4⋊Q8C2×D711yescharacteristic
308C2×#127C2×D711yescharacteristic
309C2×#126—141no—
310C2×#125—71no—
311C2×#124—71no—
312C2×#124—141no—
313C2×#123—141no—
314C2×#123—141no—
315C2×#123—141no—
316C2×C22⋊Q8—71no—
317C2×C22⋊Q8—141no—
318C2×#121—71no—
319C2×#121—71no—
320C2×#121—71no—
321C2×#121—141no—
322C2×#121—141no—
323C2×C4×Q8—71no—
324C2×C4×D4—71no—
325C2×C4×D4—71no—
326C2×C4×D4—71no—
327C2×#117—71no—
328#501—78no—
329#496—78no—
330#488—78no—
331#486C2×D718yescomplemented
332#469—78no—
333#468—78no—
334#466—78no—
335#465—78no—
336#442—78no—
337#440—78no—
338C4×SD16—78no—
339C4×D8—78no—
340C2×#107—71no—
341C2×#107—71no—
342C2×#106—71no—
343C2×#106—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#102—71no—
347C2×#102—71no—
348C2×#102C2×D711yescharacteristic
349C2×#102C2×D711yescharacteristic
350C2×#102C2×D711yescharacteristic
351C2×#102C2×D711yescharacteristic
352#405—78no—
353C2×#97—71no—
354C2×#97—71no—
355C2×C4×C8—71no—
356C2×C4×C8C2×D711yescharacteristic
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7C22×D411yescharacteristic
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—42no—
371C22×D7—42no—
372C22×D7—42no—
373C22×D7C22×D412yes—
374C7×Q8—84no—
375C7×D4—22no—
376C7×D4—22no—
377C7×D4—22no—
378C7×D4—22no—
379C7×D4—42no—
380C7×D4—42no—
381C7×D4—84no—
382C7×D4—84no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—42no—
388C2×C4×C7—42no—
389C2×C4×C7C22×D412yes—
390C2×C4×C7C22×D412yes—
391C2×C4×C7C22×D411yescharacteristic
392C2×C4×C7C2×#4112yes—
393C2×C4×C7C2×#4112yes—
394C2×C4×C7C2511yescharacteristic
395C22⋊D7—84no—
396C22⋊D7—84no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—42no—
404C2×Dic7—42no—
405C2×Dic7—42no—
406C2×Dic7—84no—
407C2×Dic7—84no—
408C2×Dic7C22×D412yes—
409C2×Dic7C22×D412yes—
410C2×Dic7C22×D412yes—
411D28—22no—
412D28—22no—
413D28—42no—
414D28—84no—
415C4×D7—24no—
416C4×D7—22no—
417C4×D7—22no—
418C4×D7—84no—
419Dic14—22no—
420Dic14—22no—
421Dic14—42no—
422C7×C8—22no—
423C7×C8—22no—
424C7⋊C8C2×#4114yes—
425C7⋊C8C2×#4114yes—
426C22×Q8—21no—
427C22×Q8—71no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4—71no—
431C22×D4—141no—
432C22×D4—141no—
433C22×D4—141no—
434C22×D4C22×D711yescharacteristic
435C22×D4C22×D711yescharacteristic
436C23×C4—71no—
437C23×C4—141no—
438C23×C4—141no—
439C23×C4—141no—
440C2×SD16—74no—
441C2×SD16—74no—
442C2×SD16—144no—
443C2×SD16—144no—
444C2×D8—74no—
445C2×D8—74no—
446C2×D8—144no—
447C2×D8—144no—
448C2×M16—74no—
449C2×M16—144no—
450C22×C8—71no—
451C22×C8—71no—
452C22×C8—74no—
453C22×C8—144no—
454C22×C8C22×D711yescharacteristic
455C22×C8C22×D711yescharacteristic
456C4⋊Q8—22no—
457C4⋊Q8C22×D714yes—
458#127—22no—
459#127C22×D714yes—
460#126—148no—
461#125—74no—
462#125—142no—
463#124—74no—
464#124—148no—
465#124—142no—
466#123—148no—
467#123—148no—
468#123—148no—
469C22⋊Q8—74no—
470C22⋊Q8—142no—
471C22⋊Q8—148no—
472#121—74no—
473#121—74no—
474#121—74no—
475#121—148no—
476#121—148no—
477#121—142no—
478#121—142no—
479#121—142no—
480C4×Q8—74no—
481C4×Q8—142no—
482C4×D4—74no—
483C4×D4—74no—
484C4×D4—74no—
485C4×D4—142no—
486C4×D4—142no—
487C4×D4—142no—
488#117—74no—
489#117—74no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—71no—
492C2×C4⋊C4—71no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—71no—
495C2×C4⋊C4—141no—
496C2×C4⋊C4—141no—
497C2×C4⋊C4—141no—
498C2×C4⋊C4—141no—
499C2×C4⋊C4C22×D711yescharacteristic
500C2×C4⋊C4C22×D711yescharacteristic
501C2×C22⋊C4—71no—
502C2×C22⋊C4—71no—
503C2×C22⋊C4—141no—
504C2×C22⋊C4—141no—
505C2×C22⋊C4—141no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4—141no—
508C2×C22⋊C4—141no—
509C2×C22⋊C4—141no—
510C2×C22⋊C4—141no—
511C2×C22⋊C4—141no—
512C2×C42—71no—
513C2×C42—141no—
514C2×C42C22×D711yescharacteristic
515#107—74no—
516#107—74no—
517#106—74no—
518#106—74no—
519#103—74no—
520#103—74no—
521#102—74no—
522#102—74no—
523#102C22×D714yes—
524#102C22×D714yes—
525#102C22×D714yes—
526#102C22×D714yes—
527#97—74no—
528#97—74no—
529C4×C8—74no—
530C4×C8C22×D714yes—
531C22×C7—42no—
532C22×C7—42no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—84no—
538C22×C7—84no—
539C22×C7#53212yes—
540C22×C7#57612yes—
541C22×C7#57712yes—
542C22×C7C23×D411yescharacteristic
543C2×D7—22no—
544C2×D7—22no—
545C2×D7—22no—
546C2×D7—44no—
547C2×D7—42no—
548C2×D7—42no—
549C2×D7—42no—
550C2×D7—84no—
551C4×C7—22no—
552C4×C7—22no—
553C4×C7—42no—
554C4×C7—42no—
555C4×C7#53212yes—
556C4×C7C22×#4111yescharacteristic
557C4×C7C22×#4111yescharacteristic
558Dic7—22no—
559Dic7—22no—
560Dic7—22no—
561Dic7—42no—
562Dic7—42no—
563Dic7—42no—
564C24—21no—
565C24—21no—
566C24—71no—
567C24—141no—
568C2×Q8—24no—
569C2×Q8—72no—
570C2×Q8—82no—
571C2×Q8—141no—
572C2×Q8—142no—
573C2×Q8—142no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—24no—
577C2×D4—24no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—72no—
583C2×D4—82no—
584C2×D4—82no—
585C2×D4—144no—
586C2×D4—144no—
587C2×D4—144no—
588C2×D4—141no—
589C2×D4—142no—
590C2×D4—142no—
591C2×D4—562no—
592C2×D4—562no—
593C2×D4—562no—
594C2×D4C23×D712yes—
595C2×D4C23×D712yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—71no—
599C22×C4—71no—
600C22×C4—71no—
601C22×C4—72no—
602C22×C4—72no—
603C22×C4—144no—
604C22×C4—144no—
605C22×C4—144no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—141no—
609C22×C4—141no—
610C22×C4—141no—
611C22×C4—562no—
612C22×C4—562no—
613C22×C4—562no—
614C22×C4D4×D711yescharacteristic
615C22×C4D4×D711yescharacteristic
616C22×C4C23×D711yescharacteristic
617SD16—148no—
618SD16—148no—
619D8—148no—
620D8—148no—
621M16—148no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—74no—
625C2×C8—74no—
626C2×C8—72no—
627C2×C8—72no—
628C2×C8—148no—
629C2×C8C23×D712yes—
630C2×C8C23×D712yes—
631C4⋊C4—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—74no—
635C4⋊C4—74no—
636C4⋊C4—72no—
637C4⋊C4—72no—
638C4⋊C4—144no—
639C4⋊C4—144no—
640C4⋊C4—144no—
641C4⋊C4—144no—
642C4⋊C4—141no—
643C4⋊C4—141no—
644C4⋊C4C23×D712yes—
645C4⋊C4C23×D712yes—
646C22⋊C4—74no—
647C22⋊C4—74no—
648C22⋊C4—144no—
649C22⋊C4—144no—
650C22⋊C4—144no—
651C22⋊C4—144no—
652C22⋊C4—144no—
653C22⋊C4—144no—
654C22⋊C4—144no—
655C22⋊C4—144no—
656C22⋊C4—144no—
657C42—72no—
658C42—72no—
659C42—144no—
660C42D4×D712yes—
661C42C23×D712yes—
662C2×C7—82no—
663C2×C7—82no—
664C2×C7#317914yescomplemented
665C2×C7C2×#53211yescharacteristic
666C2×C7C2×#57611yescharacteristic
667C2×C7C2×#57711yescharacteristic
668D7—42no—
669D7—82no—
670C23—22no—
671C23—22no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—72no—
679C23—142no—
680C23—142no—
681C23—142no—
682C23—142no—
683C23—282no—
684C23—282no—
685C23—282no—
686C23C2×D4×D711yescharacteristic
687Q8—84no—
688Q8—142no—
689Q8—142no—
690Q8—282no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—42no—
697D4—84no—
698D4—84no—
699D4—142no—
700D4—142no—
701D4—282no—
702D4—564no—
703D4—564no—
704D4—564no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—72no—
712C2×C4—72no—
713C2×C4—72no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—144no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—282no—
724C2×C4—282no—
725C2×C4—282no—
726C2×C4—564no—
727C2×C4—564no—
728C2×C4—564no—
729C2×C4C2×D4×D712yes—
730C2×C4C2×D4×D712yes—
731C2×C4C2×D4×D711yescharacteristic
732C2×C4D7×#4112yes—
733C2×C4D7×#4112yes—
734C2×C4C24×D711yescharacteristic
735C8—22no—
736C8—22no—
737C8—74no—
738C8—74no—
739C7C2×#317911yescharacteristic, complemented, Sylow
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—84no—
747C22—84no—
748C22—142no—
749C22—142no—
750C22—142no—
751C22—284no—
752C22—282no—
753C22—282no—
754C22—282no—
755C22—564no—
756C22#9035912yes—
757C22#9044812yes—
758C22#9045312yes—
759C22C22×D4×D711yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—142no—
765C4—142no—
766C4—142no—
767C4—282no—
768C4—282no—
769C4—282no—
770C4#9035912yes—
771C4C2×D7×#4111yescharacteristic
772C4C2×D7×#4111yescharacteristic
773C2—82no—
774C2—82no—
775C2—282no—
776C2—562no—
777C2#1173900314yesdirect product factor
778C2C2×#9035911yescharacteristic
779C2C2×#9044811yescharacteristic
780C2C2×#9045311yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#486C2
socleC23×C7C22×D4
hypercenterC2×#486D7
hypocenterC7C2×#3179
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#90424C2semidirect
2. C2×#90410C2semidirect
3. C2×C7×#486C2semidirect
4. C2×#89852C2semidirect
5. C2×#89846C2semidirect
6. #11739003C2direct (N × H)
7. C2×#89554C2semidirect
8. C2×#89552C2semidirect
9. C2×#89547C2semidirect
10. C2×#89550C2semidirect
11. C2×#89557C2semidirect
12. C2×#89529C2semidirect
13. C2×#89530C2semidirect
14. C2×#89528C2semidirect
15. C2×#89469C2semidirect
16. C2×#89461C2semidirect
36. #90424C22semidirect
38. #90410C22semidirect
48. C7×#486C22semidirect
60. #89852C22semidirect
61. #89846C22semidirect
67. #89557C22semidirect
68. #89554C22semidirect
69. #89552C22semidirect
70. #89550C22semidirect
71. #89547C22semidirect
72. #89530C22semidirect
73. #89529C22semidirect
74. #89528C22semidirect
75. #89469C22semidirect
76. #89461C22semidirect
189. C2×#486D7semidirect
331. #486C2×D7semidirect
664. C2×C7#3179semidirect
739. C7C2×#3179semidirect
777. C2#11739003direct (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×#904102
C2×C7×#4862
C2×#898522
C2×#898462
#117390032
C2×#895542
C2×#895522
C2×#895472
C2×#895502
C2×#895572
C2×#895292
C2×#895302
C2×#895282
C2×#894692
C2×#894612
C2×#31797