Finite Group Databasebeta

← C2×#11737306 #14223686

Subgroups — C2×#11737306 #14223686

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×#90252C211yesmaximal, characteristic, complemented
2C2×#90253C211yesmaximal, characteristic, complemented
3C2×C7×#442C211yesmaximal, characteristic, complemented
4C2×#89929C211yesmaximal, characteristic, complemented
5C2×#89926C211yesmaximal, characteristic, complemented
6C2×C4×#1142C211yesmaximal, characteristic, complemented
7C2×C4×#1141C211yesmaximal, characteristic, complemented
8#11737306C2116yesmaximal, direct product factor
9C2×#89636C211yesmaximal, characteristic, complemented
10C2×#89628C211yesmaximal, characteristic, complemented
11C2×#89554C211yesmaximal, characteristic, complemented
12C2×#89552C211yesmaximal, characteristic, complemented
13C2×#89540C211yesmaximal, characteristic, complemented
14C2×#89532C211yesmaximal, characteristic, complemented
15C2×#89482C211yesmaximal, characteristic, complemented
16C2×#89480C211yesmaximal, characteristic, complemented
17C22×C7×D8C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×#6503C2211yescharacteristic
21C2×#6501C2211yescharacteristic
22C2×#6501C2211yescharacteristic
23C2×#6499C2211yescharacteristic
24C22×#1142C2211yescharacteristic
25C22×#1141C2211yescharacteristic
26C2×#6493—21no—
27C2×#6492—21no—
28C2×#6492—21no—
29C2×#6487—21no—
30C22×#1132C2211yescharacteristic
31C22×#1131C2211yescharacteristic
32C22×C8×D7C2211yescharacteristic
33#90253—24no—
34#90253C2218yescomplemented
35#90252—24no—
36#90252C2218yescomplemented
37C2×#6460C2211yescharacteristic
38C2×#6458C2211yescharacteristic
39C2×#6453C2211yescharacteristic
40C2×#6451C2211yescharacteristic
41C2×#6448—21no—
42C2×#6447—21no—
43C2×#6446—21no—
44C2×#6442—21no—
45C2×C4×D28C2211yescharacteristic
46C2×#6435C2211yescharacteristic
47C2×C4×Dic14C2211yescharacteristic
48C7×#442C2218yescomplemented
49C2×C7×#106C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×C7×#97C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55#89929C2218yescomplemented
56#89926C2218yescomplemented
57C2×#6395C2211yescharacteristic
58C2×#6392C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×#6389C2211yescharacteristic
61C2×C8×Dic7C2211yescharacteristic
62C4×#1142C2218yescomplemented
63C4×#1141C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×C4×C7⋊C8C2211yescharacteristic
69#89636C2218yescomplemented
70#89628C2218yescomplemented
71#89554C2218yescomplemented
72#89552C2218yescomplemented
73#89540C2218yescomplemented
74#89532C2218yescomplemented
75#89482C2218yescomplemented
76#89480C2218yescomplemented
77C2×#3179—71nomaximal, Sylow
78C22×C7×D4C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C23×C4×C7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C22×C22⋊D7—21no—
86C22×D28—21no—
87C22×D28C2311yescharacteristic
88C22×C4×D7—21no—
89C22×C4×D7C2311yescharacteristic
90C22×Dic14—21no—
91C22×Dic14C2311yescharacteristic
92C2×C7×D8—24no—
93C2×C7×D8C2314yes—
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C4×C7×D4—22no—
97C4×C7×D4—22no—
98C4×C7×D4C2314yes—
99C4×C7×D4C2314yes—
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C22⋊C4—21no—
103C2×C7×C22⋊C4—21no—
104C2×C42×C7C2311yescharacteristic
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109#6503—22no—
110#6503C2314yes—
111#6501—22no—
112#6501—22no—
113#6501C2314yes—
114#6501C2314yes—
115#6499—22no—
116#6499C2314yes—
117C2×#1142—24no—
118C2×#1142C2314yes—
119C2×#1141—24no—
120C2×#1141C2314yes—
121#6493—28no—
122#6492—28no—
123#6492—28no—
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⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133#6487—28no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4D411yescharacteristic
138C2×Dic7⋊C4D411yescharacteristic
139C2×C4×Dic7—21no—
140C2×C4×Dic7C2311yescharacteristic
141C22×C7⋊C8C2311yescharacteristic
142C22×C7⋊C8C2311yescharacteristic
143C2×#1132—24no—
144C2×#1132C2314yes—
145C2×#1131—24no—
146C2×#1131C2314yes—
147C2×C8×D7—24no—
148C2×C8×D7C2314yes—
149#6460—22no—
150#6460C2314yes—
151#6458—22no—
152#6458C2314yes—
153#6453—22no—
154#6453C2314yes—
155#6451—22no—
156#6451C2314yes—
157#6448—28no—
158#6447—28no—
159#6446—28no—
160#6442—28no—
161C4×D28—22no—
162C4×D28C2314yes—
163#6435D414yes—
164#6435C2314yes—
165C4×Dic14—22no—
166C4×Dic14C2314yes—
167C7×#106C2314yes—
168C7×#102C2314yes—
169C7×#102C2314yes—
170C7×#97C2314yes—
171#6406C2314yes—
172#6406C2314yes—
173#6395C2314yes—
174#6392C2314yes—
175#6390C2314yes—
176#6389C2314yes—
177C8×Dic7C2314yes—
178#6384C2314yes—
179#6383C2314yes—
180#6382C2314yes—
181#6381C2314yes—
182C4×C7⋊C8C2314yes—
183C2×#542—71no—
184C2×#540—71no—
185#3179—716no—
186C2×#501—71no—
187C2×#496—71no—
188C2×#488—71no—
189C2×#486—71no—
190C2×#469—71no—
191C2×#468—71no—
192C2×#466—71no—
193C2×#465—71no—
194C2×#442D711yescharacteristic, complemented
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×D4—21no—
204C2×C7×D4—21no—
205C2×C7×D4—22no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4—22no—
209C2×C7×D4C2412yes—
210C2×C7×D4C2412yes—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—24no—
214C22×C4×C7—24no—
215C22×C4×C7—82no—
216C22×C4×C7—82no—
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2411yescharacteristic
220C2×C22⋊D7—24no—
221C2×C22⋊D7—24no—
222C2×C22⋊D7—24no—
223C2×C22⋊D7—24no—
224C2×C22⋊D7—82no—
225C2×C22⋊D7—82no—
226C2×C22⋊D7—82no—
227C2×C22⋊D7—82no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7C2×D411yescharacteristic
232C22×Dic7C2×D411yescharacteristic
233C22×Dic7C2×D411yescharacteristic
234C2×D28—22no—
235C2×D28—22no—
236C2×D28—21no—
237C2×D28—24no—
238C2×D28—82no—
239C2×D28C2412yes—
240C2×C4×D7—22no—
241C2×C4×D7—22no—
242C2×C4×D7—24no—
243C2×C4×D7—82no—
244C2×C4×D7C2×D412yes—
245C2×C4×D7C2412yes—
246C2×Dic14—22no—
247C2×Dic14—22no—
248C2×Dic14—21no—
249C2×Dic14—24no—
250C2×Dic14—82no—
251C2×Dic14C2412yes—
252C7×D8—28no—
253C2×C7×C8—22no—
254C2×C7×C8#4114yes—
255C2×C7×C8C2412yes—
256C2×C7×C8C2412yes—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4C2412yes—
260C7×C4⋊C4C2412yes—
261C7×C22⋊C4—24no—
262C7×C22⋊C4—24no—
263C42×C7C2×D412yes—
264C42×C7C2412yes—
265C22⋊Dic7—24no—
266C22⋊Dic7—24no—
267C22⋊Dic7—24no—
268C22⋊Dic7—24no—
269#1142—28no—
270#1141—28no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4—24no—
274(C2×D7)⋊C4C2×D414yes—
275(C2×D7)⋊C4C2×D414yes—
276C4⋊Dic7—21no—
277C4⋊Dic7—21no—
278C4⋊Dic7—24no—
279C4⋊Dic7—24no—
280C4⋊Dic7C2412yes—
281C4⋊Dic7C2412yes—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285Dic7⋊C4C2×D414yes—
286Dic7⋊C4C2×D414yes—
287C4×Dic7—24no—
288C4×Dic7C2×D412yes—
289C4×Dic7C2412yes—
290C2×C7⋊C8—22no—
291C2×C7⋊C8#4114yes—
292C2×C7⋊C8C2412yes—
293C2×C7⋊C8C2412yes—
294#1132—28no—
295#1131—28no—
296C8×D7—28no—
297C22×SD16—71no—
298C22×SD16—71no—
299C22×D8—71no—
300C22×D8C2×D711yescharacteristic
301C22×M16—71no—
302C23×C8—71no—
303#542—78no—
304#542—144no—
305#540—78no—
306#540—144no—
307C2×C4⋊Q8—71no—
308C2×#127—71no—
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×D4C2×D711yescharacteristic
326C2×C4×D4C2×D711yescharacteristic
327C2×#117—71no—
328#501—78no—
329#496—78no—
330#488—78no—
331#486—78no—
332#469—78no—
333#468—78no—
334#466—78no—
335#465—78no—
336#442C2×D718yescomplemented
337#440—78no—
338C4×SD16—78no—
339C4×D8—78no—
340C2×#107—71no—
341C2×#107—71no—
342C2×#106—71no—
343C2×#106C2×D711yescharacteristic
344C2×#103—71no—
345C2×#103—71no—
346C2×#102—71no—
347C2×#102—71no—
348C2×#102—71no—
349C2×#102—71no—
350C2×#102C2×D711yescharacteristic
351C2×#102C2×D711yescharacteristic
352#405—78no—
353C2×#97—71no—
354C2×#97C2×D711yescharacteristic
355C2×C4×C8—71no—
356C2×C4×C8—71no—
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×D4—22no—
375C7×D4—22no—
376C7×D4—22no—
377C7×D4—22no—
378C7×D4—42no—
379C7×D4—42no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—42no—
385C2×C4×C7—42no—
386C2×C4×C7—84no—
387C2×C4×C7—84no—
388C2×C4×C7C22×D412yes—
389C2×C4×C7C22×D412yes—
390C2×C4×C7C22×D411yescharacteristic
391C2×C4×C7C2×#4112yes—
392C2×C4×C7C2×#4112yes—
393C2×C4×C7C2511yescharacteristic
394C22⋊D7—84no—
395C22⋊D7—84no—
396C22⋊D7—84no—
397C22⋊D7—84no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—42no—
405C2×Dic7—42no—
406C2×Dic7—42no—
407C2×Dic7C22×D412yes—
408C2×Dic7C22×D412yes—
409C2×Dic7C22×D412yes—
410D28—22no—
411D28—22no—
412D28—42no—
413D28—84no—
414C4×D7—24no—
415C4×D7—22no—
416C4×D7—22no—
417C4×D7—84no—
418Dic14—22no—
419Dic14—22no—
420Dic14—42no—
421Dic14—84no—
422C7×C8—22no—
423C7×C8C2×#4114yes—
424C7⋊C8—22no—
425C7⋊C8C2×#4114yes—
426C22×Q8—71no—
427C22×Q8—141no—
428C22×D4—71no—
429C22×D4—141no—
430C22×D4—141no—
431C22×D4—141no—
432C22×D4—141no—
433C22×D4—141no—
434C22×D4C22×D711yescharacteristic
435C22×D4C22×D711yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—71no—
439C23×C4—141no—
440C2×SD16—74no—
441C2×SD16—74no—
442C2×SD16—144no—
443C2×SD16—144no—
444C2×D8—24no—
445C2×D8—74no—
446C2×D8—144no—
447C2×D8C22×D714yes—
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—74no—
457C4⋊Q8—142no—
458#127—74no—
459#127—142no—
460#126—148no—
461#125—74no—
462#125—142no—
463#124—74no—
464#124—142no—
465#124—148no—
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—22no—
483C4×D4—22no—
484C4×D4—74no—
485C4×D4—142no—
486C4×D4C22×D714yes—
487C4×D4C22×D714yes—
488#117—74no—
489#117—74no—
490C2×C4⋊C4—71no—
491C2×C4⋊C4—71no—
492C2×C4⋊C4—71no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—141no—
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—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—71no—
504C2×C22⋊C4—71no—
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#106C22×D714yes—
519#103—74no—
520#103—74no—
521#102—74no—
522#102—74no—
523#102—74no—
524#102—74no—
525#102C22×D714yes—
526#102C22×D714yes—
527#97—74no—
528#97C22×D714yes—
529C4×C8—74no—
530C4×C8—74no—
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—72no—
569C2×Q8—144no—
570C2×Q8—141no—
571C2×Q8—142no—
572C2×Q8—142no—
573C2×Q8—562no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—72no—
581C2×D4—144no—
582C2×D4—144no—
583C2×D4—144no—
584C2×D4—144no—
585C2×D4—144no—
586C2×D4—142no—
587C2×D4—141no—
588C2×D4—142no—
589C2×D4—562no—
590C2×D4—562no—
591C2×D4—562no—
592C2×D4—562no—
593C2×D4—562no—
594C2×D4C23×D712yes—
595C2×D4C23×D712yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—71no—
601C22×C4—71no—
602C22×C4—71no—
603C22×C4—72no—
604C22×C4—72no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4—141no—
610C22×C4—141no—
611C22×C4—141no—
612C22×C4—144no—
613C22×C4—562no—
614C22×C4D4×D711yescharacteristic
615C22×C4D4×D711yescharacteristic
616C22×C4C23×D711yescharacteristic
617SD16—148no—
618SD16—148no—
619D8—28no—
620D8—148no—
621M16—148no—
622C2×C8—22no—
623C2×C8—74no—
624C2×C8—72no—
625C2×C8—72no—
626C2×C8—142no—
627C2×C8—148no—
628C2×C8#115714yes—
629C2×C8C23×D712yes—
630C2×C8C23×D712yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—74no—
634C4⋊C4—74no—
635C4⋊C4—72no—
636C4⋊C4—72no—
637C4⋊C4—144no—
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—24no—
647C22⋊C4—24no—
648C22⋊C4—74no—
649C22⋊C4—74no—
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—142no—
688Q8—142no—
689Q8—282no—
690Q8—564no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—42no—
697D4—142no—
698D4—142no—
699D4—282no—
700D4—564no—
701D4—564no—
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—84no—
715C2×C4—84no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—144no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—282no—
726C2×C4—282no—
727C2×C4—282no—
728C2×C4—564no—
729C2×C4C2×#115712yes—
730C2×C4C2×D4×D712yes—
731C2×C4C2×D4×D712yes—
732C2×C4C2×D4×D711yescharacteristic
733C2×C4D7×#4112yes—
734C2×C4C24×D711yescharacteristic
735C8—22no—
736C8—74no—
737C8—142no—
738C8C2×#115714yes—
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#9023912yes—
757C22#9046512yes—
758C22#9046612yes—
759C22C22×D4×D711yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—142no—
765C4—142no—
766C4—142no—
767C4—282no—
768C4—282no—
769C4—282no—
770C4#9023912yes—
771C4C22×#115711yescharacteristic
772C4C2×D7×#4111yescharacteristic
773C2—82no—
774C2—82no—
775C2—282no—
776C2—562no—
777C2#1173730614yesdirect product factor
778C2C2×#9023911yescharacteristic
779C2C2×#9046511yescharacteristic
780C2C2×#9046611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#442C2
socleC23×C7C22×D4
hypercenterC2×#442D7
hypocenterC7C2×#3179
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#90252C2semidirect
2. C2×#90253C2semidirect
3. C2×C7×#442C2semidirect
4. C2×#89929C2semidirect
5. C2×#89926C2semidirect
6. C2×C4×#1142C2semidirect
7. C2×C4×#1141C2semidirect
8. #11737306C2direct (N × H)
9. C2×#89636C2semidirect
10. C2×#89628C2semidirect
11. C2×#89554C2semidirect
12. C2×#89552C2semidirect
13. C2×#89540C2semidirect
14. C2×#89532C2semidirect
15. C2×#89482C2semidirect
16. C2×#89480C2semidirect
34. #90253C22semidirect
36. #90252C22semidirect
48. C7×#442C22semidirect
55. #89929C22semidirect
56. #89926C22semidirect
62. C4×#1142C22semidirect
63. C4×#1141C22semidirect
69. #89636C22semidirect
70. #89628C22semidirect
71. #89554C22semidirect
72. #89552C22semidirect
73. #89540C22semidirect
74. #89532C22semidirect
75. #89482C22semidirect
76. #89480C22semidirect
194. C2×#442D7semidirect
336. #442C2×D7semidirect
664. C2×C7#3179semidirect
739. C7C2×#3179semidirect
777. C2#11737306direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902522
C2×#902532
C2×C7×#4422
C2×#899292
C2×#899262
C2×C4×#11422
C2×C4×#11412
#117373062
C2×#896362
C2×#896282
C2×#895542
C2×#895522
C2×#895402
C2×#895322
C2×#894822
C2×#894802
C2×#31797