Finite Group Databasebeta

← C2×#11737234 #14222141

Subgroups — C2×#11737234 #14222141

Order 1792.

2122 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90263C211yesmaximal, characteristic, complemented
2C2×#90253C211yesmaximal, characteristic
3C2×C7×#440C211yesmaximal, characteristic, complemented
4C2×#89942C211yesmaximal, characteristic, complemented
5C2×#89935C211yesmaximal, characteristic, complemented
6C2×C4×#1143C211yesmaximal, characteristic, complemented
7C2×C4×#1142C211yesmaximal, characteristic, complemented
8#11737234C2116yesmaximal, direct product factor
9C2×#89649C211yesmaximal, characteristic, complemented
10C2×#89657C211yesmaximal, characteristic, complemented
11C2×#89578C211yesmaximal, characteristic, complemented
12C2×#89568C211yesmaximal, characteristic, complemented
13C2×#89534C211yesmaximal, characteristic, complemented
14C2×#89556C211yesmaximal, characteristic, complemented
15C2×#89482C211yesmaximal, characteristic, complemented
16C2×#89481C211yesmaximal, characteristic, complemented
17C22×Q8×D7C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×Q8×Dic7C2211yescharacteristic
22C22×#1143C2211yescharacteristic
23C2×#6503C2211yescharacteristic
24C2×#6501C2211yescharacteristic
25C22×#1142C2211yescharacteristic
26C2×#6493—21no—
27C2×#6492—21no—
28C22×#1132C2211yescharacteristic
29#90263—24no—
30#90263C2218yescomplemented
31#90253—24no—
32#90253C2218yes—
33C2×#6458C2211yescharacteristic
34C2×#6455—21no—
35C2×#6455C2211yescharacteristic
36C2×#6453C2211yescharacteristic
37C2×#6450—21no—
38C2×#6450C2211yescharacteristic
39C2×#6447—21no—
40C2×#6446—21no—
41C2×C4×D28C2211yescharacteristic
42C2×#6435—21no—
43C2×#6435C2211yescharacteristic
44C2×C4×Dic14—21no—
45C2×C4×Dic14C2211yescharacteristic
46C7×#440C2218yescomplemented
47C2×C7×#107C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×#97C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53#89942C2218yescomplemented
54#89935C2218yescomplemented
55C2×#6395C2211yescharacteristic
56C2×(C2×D7)⋊C8C2211yescharacteristic
57C2×(C2×D7)⋊C8C2211yescharacteristic
58C2×#6392C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×Dic7⋊C8C2211yescharacteristic
62C4×#1143C2218yescomplemented
63C4×#1142C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×C4×C7⋊C8C2211yescharacteristic
69#89657C2218yescomplemented
70#89649C2218yescomplemented
71#89578C2218yescomplemented
72#89568C2218yescomplemented
73#89556C2218yescomplemented
74#89534C2218yescomplemented
75#89482C2218yescomplemented
76#89481C2218yescomplemented
77C2×#3126—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C2×Q8×D7—24no—
85C2×Q8×D7—22no—
86C2×Q8×D7—24no—
87C2×Q8×D7C2314yes—
88C22×D28—21no—
89C22×D28C2311yescharacteristic
90C22×C4×D7—21no—
91C22×C4×D7—21no—
92C22×C4×D7C2311yescharacteristic
93C22×Dic14—21no—
94C22×Dic14C2311yescharacteristic
95C2×C7×SD16—24no—
96C2×C7×SD16C2314yes—
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C4×C7×Q8—22no—
100C4×C7×Q8C2314yes—
101C4×C7×D4—22no—
102C4×C7×D4C2314yes—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C22⋊C4—21no—
107C2×C42×C7—21no—
108C2×C42×C7C2311yescharacteristic
109C2×C22⋊Dic7—21no—
110Q8×Dic7—22no—
111Q8×Dic7C2314yes—
112C2×#1143—24no—
113C2×#1143C2314yes—
114#6503—22no—
115#6503C2314yes—
116#6501—22no—
117#6501C2314yes—
118C2×#1142—24no—
119C2×#1142C2314yes—
120#6493—28no—
121#6492—28no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4—21no—
125C2×(C2×D7)⋊C4D411yescharacteristic
126C2×(C2×D7)⋊C4D411yescharacteristic
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7C2311yescharacteristic
130C2×C4⋊Dic7C2311yescharacteristic
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4D411yescharacteristic
135C2×Dic7⋊C4D411yescharacteristic
136C2×C4×Dic7—21no—
137C2×C4×Dic7—21no—
138C2×C4×Dic7—21no—
139C2×C4×Dic7—21no—
140C2×C4×Dic7C2311yescharacteristic
141C22×C7⋊C8C2311yescharacteristic
142C22×C7⋊C8C2311yescharacteristic
143C2×#1132—24no—
144C2×#1132C2314yes—
145#6458—22no—
146#6458C2314yes—
147#6455—22no—
148#6455—28no—
149#6455C2314yes—
150#6453—22no—
151#6453C2314yes—
152#6450—28no—
153#6450—22no—
154#6450C2314yes—
155#6447—28no—
156#6446—28no—
157C4×D28—22no—
158C4×D28C2314yes—
159#6435—28no—
160#6435D414yes—
161#6435C2314yes—
162C4×Dic14—22no—
163C4×Dic14—28no—
164C4×Dic14C2314yes—
165C7×#107C2314yes—
166C7×#103C2314yes—
167C7×#102C2314yes—
168C7×#97C2314yes—
169#6409C2314yes—
170#6406C2314yes—
171#6395C2314yes—
172(C2×D7)⋊C8C2314yes—
173(C2×D7)⋊C8C2314yes—
174#6392C2314yes—
175#6390C2314yes—
176Dic7⋊C8C2314yes—
177Dic7⋊C8C2314yes—
178#6384C2314yes—
179#6383C2314yes—
180#6382C2314yes—
181#6382C2314yes—
182C4×C7⋊C8C2314yes—
183C2×#540—71no—
184C2×#519—71no—
185#3126—716no—
186C2×#482—71no—
187C2×#482—71no—
188C2×#479—71no—
189C2×#479—71no—
190C2×#460—71no—
191C2×#460—71no—
192C2×#448—71no—
193C2×#448—71no—
194C2×#440—71no—
195C2×#440D711yescharacteristic, complemented
196C2×C4×SD16—71no—
197C2×C4×SD16—71no—
198C2×#433—71no—
199C24×C7—21no—
200C23×D7—21no—
201C23×D7C2×D411yescharacteristic
202C2×C7×Q8—21no—
203C2×C7×Q8—22no—
204C2×C7×Q8#4114yes—
205C2×C7×Q8C2412yes—
206C2×C7×D4—21no—
207C2×C7×D4—22no—
208C2×C7×D4—22no—
209C2×C7×D4C2412yes—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—24no—
214C22×C4×C7—82no—
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2411yescharacteristic
218C2×C22⋊D7—24no—
219C2×C22⋊D7—24no—
220C2×C22⋊D7—24no—
221C2×C22⋊D7—82no—
222C2×C22⋊D7—82no—
223C2×C22⋊D7—82no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7C2×D411yescharacteristic
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230Q8×D7—216no—
231Q8×D7—28no—
232Q8×D7—28no—
233C2×D28—22no—
234C2×D28—22no—
235C2×D28—21no—
236C2×D28—24no—
237C2×D28—82no—
238C2×D28C2412yes—
239C2×C4×D7—28no—
240C2×C4×D7—24no—
241C2×C4×D7—22no—
242C2×C4×D7—22no—
243C2×C4×D7—24no—
244C2×C4×D7—82no—
245C2×C4×D7C2×D412yes—
246C2×C4×D7C2412yes—
247C2×Dic14—28no—
248C2×Dic14—21no—
249C2×Dic14—22no—
250C2×Dic14—24no—
251C2×Dic14#4114yes—
252C2×Dic14C2412yes—
253C7×SD16—28no—
254C2×C7×C8—22no—
255C2×C7×C8—22no—
256C2×C7×C8C2412yes—
257C2×C7×C8C2412yes—
258C7×C4⋊C4—24no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—21no—
261C7×C4⋊C4C2412yes—
262C7×C4⋊C4C2412yes—
263C7×C22⋊C4—24no—
264C42×C7—24no—
265C42×C7C2×D412yes—
266C42×C7C2412yes—
267C22⋊Dic7—24no—
268#1143—28no—
269#1142—28no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4C2×D414yes—
274(C2×D7)⋊C4C2×D414yes—
275C4⋊Dic7—21no—
276C4⋊Dic7—21no—
277C4⋊Dic7—24no—
278C4⋊Dic7—24no—
279C4⋊Dic7C2412yes—
280C4⋊Dic7C2412yes—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4C2×D414yes—
285Dic7⋊C4C2×D414yes—
286C4×Dic7—24no—
287C4×Dic7—24no—
288C4×Dic7—24no—
289C4×Dic7—24no—
290C4×Dic7C2×D412yes—
291C4×Dic7C2412yes—
292C2×C7⋊C8—22no—
293C2×C7⋊C8—22no—
294C2×C7⋊C8C2412yes—
295C2×C7⋊C8C2412yes—
296#1132—28no—
297C23×Q8—71no—
298C22×SD16—71no—
299C22×SD16—71no—
300C22×SD16—71no—
301C22×SD16C2×D711yescharacteristic
302#540—78no—
303#540—144no—
304C2×#127—71no—
305C2×#125—71no—
306C2×#123—141no—
307C2×#123—141no—
308C2×#121—71no—
309C2×#121—71no—
310C2×#121—141no—
311C2×#121—141no—
312#519—78no—
313#519—144no—
314C2×C4×Q8—71no—
315C2×C4×Q8—71no—
316C2×C4×Q8—71no—
317C2×C4×Q8—141no—
318C2×C4×Q8—141no—
319C2×C4×Q8C2×D711yescharacteristic
320C2×C4×D4—71no—
321C2×C4×D4C2×D711yescharacteristic
322C2×#117—71no—
323C2×#117—71no—
324C2×#117—141no—
325C2×#117—141no—
326#482—78no—
327#482—78no—
328#479—78no—
329#479—78no—
330#460—78no—
331#460—78no—
332#448—78no—
333#448—78no—
334#440—78no—
335#440C2×D718yescomplemented
336C4×SD16—78no—
337C4×SD16—78no—
338#433—78no—
339C2×#107—71no—
340C2×#107C2×D711yescharacteristic
341C2×#106—71no—
342C2×#106—71no—
343C2×C4⋊C8—71no—
344C2×C4⋊C8—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103C2×D711yescharacteristic
349C2×#102—71no—
350C2×#102—71no—
351C2×#102—71no—
352C2×#102C2×D711yescharacteristic
353C2×C22⋊C8—71no—
354C2×C22⋊C8—71no—
355C2×#97C2×D711yescharacteristic
356C2×C4×C8—71no—
357C23×C7—22no—
358C23×C7—42no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7C22×D411yescharacteristic
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—42no—
367C22×D7—42no—
368C22×D7—42no—
369C22×D7C22×D412yes—
370C7×Q8—24no—
371C7×Q8—22no—
372C7×Q8C2×#4114yes—
373C7×D4—22no—
374C7×D4—22no—
375C7×D4—42no—
376C2×C4×C7—24no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7—84no—
385C2×C4×C7C22×D412yes—
386C2×C4×C7C22×D412yes—
387C2×C4×C7C22×D411yescharacteristic
388C2×C4×C7C2×#4112yes—
389C2×C4×C7C2×#4112yes—
390C2×C4×C7C2511yescharacteristic
391C22⋊D7—84no—
392C22⋊D7—84no—
393C22⋊D7—84no—
394C2×Dic7—22no—
395C2×Dic7—24no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—42no—
402C2×Dic7—42no—
403C2×Dic7C22×D412yes—
404C2×Dic7C22×D412yes—
405C2×Dic7C22×D412yes—
406D28—22no—
407D28—22no—
408D28—42no—
409D28—84no—
410C4×D7—216no—
411C4×D7—24no—
412C4×D7—22no—
413C4×D7—22no—
414C4×D7—84no—
415Dic14—216no—
416Dic14—24no—
417Dic14—22no—
418Dic14C2×#4114yes—
419C7×C8—22no—
420C7×C8—22no—
421C7⋊C8—22no—
422C7⋊C8—22no—
423C22×Q8—74no—
424C22×Q8—71no—
425C22×Q8—141no—
426C22×Q8—142no—
427C22×Q8—144no—
428C22×Q8—144no—
429C22×Q8C22×D711yescharacteristic
430C22×D4—71no—
431C22×D4—141no—
432C22×D4—141no—
433C22×D4—141no—
434C22×D4—141no—
435C22×D4C22×D711yescharacteristic
436C23×C4—21no—
437C23×C4—71no—
438C23×C4—141no—
439C23×C4—141no—
440C2×SD16—24no—
441C2×SD16—74no—
442C2×SD16—74no—
443C2×SD16—74no—
444C2×SD16—144no—
445C2×SD16—144no—
446C2×SD16—144no—
447C2×SD16C22×D714yes—
448C22×C8—71no—
449C22×C8—71no—
450C22×C8C22×D711yescharacteristic
451C22×C8C22×D711yescharacteristic
452#127—74no—
453#127—142no—
454#125—74no—
455#125—142no—
456#123—148no—
457#123—148no—
458#121—74no—
459#121—74no—
460#121—148no—
461#121—148no—
462#121—142no—
463#121—142no—
464C4×Q8—22no—
465C4×Q8—74no—
466C4×Q8—74no—
467C4×Q8—74no—
468C4×Q8—148no—
469C4×Q8—142no—
470C4×Q8—142no—
471C4×Q8—148no—
472C4×Q8—142no—
473C4×Q8C22×D714yes—
474C4×D4—22no—
475C4×D4—74no—
476C4×D4—142no—
477C4×D4C22×D714yes—
478#117—74no—
479#117—74no—
480#117—74no—
481#117—148no—
482#117—148no—
483#117—142no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—71no—
486C2×C4⋊C4—71no—
487C2×C4⋊C4—71no—
488C2×C4⋊C4—71no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4—141no—
494C2×C4⋊C4C22×D711yescharacteristic
495C2×C4⋊C4C22×D711yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—71no—
498C2×C22⋊C4—71no—
499C2×C22⋊C4—141no—
500C2×C22⋊C4—141no—
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C42—21no—
504C2×C42—71no—
505C2×C42—141no—
506C2×C42—141no—
507C2×C42—141no—
508C2×C42—141no—
509C2×C42C22×D711yescharacteristic
510#107—74no—
511#107C22×D714yes—
512#106—74no—
513#106—74no—
514C4⋊C8—74no—
515C4⋊C8—74no—
516#103—74no—
517#103—74no—
518#103—74no—
519#103C22×D714yes—
520#102—74no—
521#102—74no—
522#102—74no—
523#102C22×D714yes—
524C22⋊C8—74no—
525C22⋊C8—74no—
526#97C22×D714yes—
527C4×C8—74no—
528C22×C7—42no—
529C22×C7—42no—
530C22×C7—42no—
531C22×C7—84no—
532C22×C7#52512yes—
533C22×C7#57712yes—
534C22×C7#57712yes—
535C22×C7C23×D411yescharacteristic
536C2×D7—22no—
537C2×D7—22no—
538C2×D7—22no—
539C2×D7—44no—
540C2×D7—42no—
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—84no—
544C4×C7—24no—
545C4×C7—22no—
546C4×C7—22no—
547C4×C7—42no—
548C4×C7—42no—
549C4×C7#52512yes—
550C4×C7C22×#4111yescharacteristic
551C4×C7C22×#4111yescharacteristic
552Dic7—22no—
553Dic7—24no—
554Dic7—22no—
555Dic7—22no—
556Dic7—42no—
557Dic7—42no—
558C24—21no—
559C24—71no—
560C24—141no—
561C2×Q8—21no—
562C2×Q8—22no—
563C2×Q8—74no—
564C2×Q8—72no—
565C2×Q8—144no—
566C2×Q8—148no—
567C2×Q8—148no—
568C2×Q8—1416no—
569C2×Q8—148no—
570C2×Q8—142no—
571C2×Q8—141no—
572C2×Q8#115714yes—
573C2×Q8C23×D712yes—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—72no—
578C2×D4—144no—
579C2×D4—144no—
580C2×D4—144no—
581C2×D4—144no—
582C2×D4—142no—
583C2×D4—141no—
584C2×D4—142no—
585C2×D4—562no—
586C2×D4—562no—
587C2×D4—562no—
588C2×D4—562no—
589C2×D4C23×D712yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—71no—
595C22×C4—71no—
596C22×C4—71no—
597C22×C4—72no—
598C22×C4—72no—
599C22×C4—82no—
600C22×C4—144no—
601C22×C4—148no—
602C22×C4—141no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—141no—
606C22×C4—141no—
607C22×C4—144no—
608C22×C4—562no—
609C22×C4D4×D711yescharacteristic
610C22×C4D4×D711yescharacteristic
611C22×C4C23×D711yescharacteristic
612SD16—28no—
613SD16—148no—
614SD16—148no—
615SD16—148no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—72no—
619C2×C8—72no—
620C2×C8—142no—
621C2×C8—142no—
622C2×C8C23×D712yes—
623C2×C8C23×D712yes—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—74no—
628C4⋊C4—74no—
629C4⋊C4—72no—
630C4⋊C4—72no—
631C4⋊C4—144no—
632C4⋊C4—144no—
633C4⋊C4—144no—
634C4⋊C4—144no—
635C4⋊C4—144no—
636C4⋊C4—141no—
637C4⋊C4—141no—
638C4⋊C4C23×D712yes—
639C4⋊C4C23×D712yes—
640C22⋊C4—24no—
641C22⋊C4—74no—
642C22⋊C4—74no—
643C22⋊C4—144no—
644C22⋊C4—144no—
645C22⋊C4—144no—
646C22⋊C4—144no—
647C42—24no—
648C42—72no—
649C42—72no—
650C42—144no—
651C42—144no—
652C42—144no—
653C42—144no—
654C42D4×D712yes—
655C42C23×D712yes—
656C2×C7—82no—
657C2×C7#312614yescomplemented
658C2×C7C2×#52511yescharacteristic
659C2×C7C2×#57711yescharacteristic
660C2×C7C2×#57711yescharacteristic
661D7—42no—
662D7—82no—
663C23—22no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—72no—
668C23—142no—
669C23—142no—
670C23—142no—
671C23—142no—
672C23—282no—
673C23—282no—
674C23—282no—
675C23C2×D4×D711yescharacteristic
676Q8—24no—
677Q8—22no—
678Q8—74no—
679Q8—1416no—
680Q8—144no—
681Q8—142no—
682Q8C2×#115714yes—
683D4—22no—
684D4—22no—
685D4—42no—
686D4—142no—
687D4—142no—
688D4—282no—
689D4—564no—
690D4—564no—
691D4—564no—
692D4—564no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—72no—
702C2×C4—72no—
703C2×C4—72no—
704C2×C4—84no—
705C2×C4—1416no—
706C2×C4—142no—
707C2×C4—142no—
708C2×C4—142no—
709C2×C4—144no—
710C2×C4—142no—
711C2×C4—144no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—282no—
717C2×C4—282no—
718C2×C4—564no—
719C2×C4C2×#115712yes—
720C2×C4C2×D4×D712yes—
721C2×C4C2×D4×D712yes—
722C2×C4C2×D4×D711yescharacteristic
723C2×C4D7×#4112yes—
724C2×C4C24×D711yescharacteristic
725C8—22no—
726C8—22no—
727C8—142no—
728C8—142no—
729C7C2×#312611yescharacteristic, complemented, Sylow
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—142no—
735C22—142no—
736C22—142no—
737C22—284no—
738C22—282no—
739C22—282no—
740C22—282no—
741C22—564no—
742C22#9023812yes—
743C22#9046612yes—
744C22#9046912yes—
745C22C22×D4×D711yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—142no—
752C4—142no—
753C4—142no—
754C4—144no—
755C4—282no—
756C4—282no—
757C4#9023812yes—
758C4C22×#115711yescharacteristic
759C4C2×D7×#4111yescharacteristic
760C2—82no—
761C2—282no—
762C2—562no—
763C2#1173723414yesdirect product factor
764C2C2×#9023811yescharacteristic
765C2C2×#9046611yescharacteristic
766C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#440C2
socleC23×C7C22×D4
prime radicalC2×#90253C2
hypercenterC2×#440D7
hypocenterC7C2×#3126
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#90263C2semidirect
3. C2×C7×#440C2semidirect
4. C2×#89942C2semidirect
5. C2×#89935C2semidirect
6. C2×C4×#1143C2semidirect
7. C2×C4×#1142C2semidirect
8. #11737234C2direct (N × H)
9. C2×#89649C2semidirect
10. C2×#89657C2semidirect
11. C2×#89578C2semidirect
12. C2×#89568C2semidirect
13. C2×#89534C2semidirect
14. C2×#89556C2semidirect
15. C2×#89482C2semidirect
16. C2×#89481C2semidirect
30. #90263C22semidirect
46. C7×#440C22semidirect
53. #89942C22semidirect
54. #89935C22semidirect
62. C4×#1143C22semidirect
63. C4×#1142C22semidirect
69. #89657C22semidirect
70. #89649C22semidirect
71. #89578C22semidirect
72. #89568C22semidirect
73. #89556C22semidirect
74. #89534C22semidirect
75. #89482C22semidirect
76. #89481C22semidirect
195. C2×#440D7semidirect
335. #440C2×D7semidirect
657. C2×C7#3126semidirect
729. C7C2×#3126semidirect
763. C2#11737234direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902632
C2×#902532
C2×C7×#4402
C2×#899422
C2×#899352
C2×C4×#11432
C2×C4×#11422
#117372342
C2×#896492
C2×#896572
C2×#895782
C2×#895682
C2×#895342
C2×#895562
C2×#894822
C2×#894812
C2×#31267