Finite Group Databasebeta

← C2×#11729776 #13355653

Subgroups — C2×#11729776 #13355653

Order 1792.

1654 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#568C211yesmaximal, characteristic
2C22×#6514C211yesmaximal, characteristic
3C2×#90008C211yesmaximal, characteristic
4C2×#89892C211yesmaximal, characteristic, complemented
5C22×#6398C211yesmaximal, characteristic, complemented
6#11729776C218yesmaximal, direct product factor
7C2×#89354C211yesmaximal, characteristic, complemented
8C2×C7⋊#338C211yesmaximal, characteristic, complemented
9C22×C7×#41C2211yescharacteristic
10C23×Dic14C2211yescharacteristic
11C7×#568—22no—
12C7×#568—22no—
13C7×#568—22no—
14C7×#568C2214yes—
15C2×C7×#131—22no—
16C2×C7×#131—22no—
17C22×C7×M16—22no—
18C22×C7×M16C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C2×#6514—22no—
21C2×#6514—22no—
22C2×#6514—22no—
23C2×#6514—22no—
24C2×#6514C414yescomplemented
25C2×#6514C2214yes—
26C22×#1144C412yescomplemented
27C22×#1142C412yescomplemented
28C2×#6489C2211yescharacteristic
29C22×#1136C2211yescharacteristic
30C22×#1136C2211yescharacteristic
31#90008—22no—
32#90008C2214yes—
33C2×#6411—22no—
34C2×#6398—22no—
35C2×#6398—22no—
36C2×#6398C2214yescomplemented
37#89892—22no—
38#89892C2214yescomplemented
39C2×#6390—22no—
40C7⋊#338C2214yescomplemented
41#89354C2214yescomplemented
42C2×#1902—71nomaximal, Sylow
43C2×C7×#41—21no—
44C2×C7×#41—21no—
45C2×C7×#41—21no—
46C2×C7×#41—21no—
47C2×C7×#41—21no—
48C2×C7×#41—21no—
49C2×C7×#41C2×C412yes—
50C2×C7×#41D412yes—
51C2×C7×#41D412yes—
52C2×C7×#41D412yes—
53C2×C7×#41D412yes—
54C2×C7×#41C2312yes—
55C22×C7×Q8C2×C411yescharacteristic
56C22×C7×D4—21no—
57C22×C7×D4C2×C411yescharacteristic
58C23×C4×C7—21no—
59C23×C4×C7C2311yescharacteristic
60C23×Dic7—21no—
61C22×Dic14—21no—
62C22×Dic14—21no—
63C22×Dic14—21no—
64C22×Dic14—21no—
65C22×Dic14—21no—
66C22×Dic14—21no—
67C22×Dic14—21no—
68C22×Dic14—21no—
69C22×Dic14—21no—
70C22×Dic14—21no—
71C22×Dic14—21no—
72C22×Dic14C2×C412yes—
73C22×Dic14C2×C412yes—
74C22×Dic14C2312yes—
75C7×#131—28no—
76C7×#131—28no—
77C7×#131—28no—
78C7×#131—28no—
79C2×C7×M16—24no—
80C2×C7×M16—28no—
81C2×C7×M16—21no—
82C2×C7×M16—21no—
83C2×C7×M16—21no—
84C2×C7×M16—21no—
85C2×C7×M16—21no—
86C2×C7×M16—21no—
87C2×C7×M16—21no—
88C2×C7×M16—28no—
89C2×C7×M16D412yes—
90C2×C7×M16D412yes—
91C2×C7×M16D412yes—
92C2×C7×M16C2312yes—
93C2×C7×M16C2312yes—
94C22×C7×C8—24no—
95C22×C7×C8—21no—
96C22×C7×C8D412yes—
97C2×C22⋊Dic7—21no—
98#6514—28no—
99#6514—28no—
100#6514—28no—
101#6514—28no—
102C2×#1144—24no—
103C2×#1144—24no—
104C2×#1144C2×C418yescomplemented
105C2×#1142—24no—
106C2×#1142—24no—
107C2×#1142C2×C418yescomplemented
108#6489—21no—
109#6489—21no—
110#6489—21no—
111#6489C2312yes—
112C2×C4⋊Dic7—21no—
113C2×C4×Dic7—21no—
114C2×#1136—21no—
115C2×#1136—21no—
116C2×#1136—21no—
117C2×#1136—21no—
118C2×#1136—21no—
119C2×#1136—21no—
120C2×#1136—21no—
121C2×#1136—21no—
122C2×#1136—21no—
123C2×#1136C2×C412yes—
124C2×#1136C2312yes—
125C2×#1136C2312yes—
126C22×C7⋊C8—21no—
127C22×C7⋊C8C2×C412yes—
128#6411—28no—
129#6398—28no—
130#6390—28no—
131C22×#137—71no—
132C2×#568D711yescharacteristic
133C2×#421—71no—
134C2×#419—71no—
135C22×#101—71no—
136#1902—78no—
137C2×#344—71no—
138C2×#338—71no—
139C24×C7—21no—
140C24×C7#4111yescharacteristic
141C7×#41—22no—
142C7×#41—22no—
143C7×#41—22no—
144C7×#41—22no—
145C7×#41—22no—
146C7×#41—22no—
147C7×#41—22no—
148C7×#41—22no—
149C7×#41—22no—
150C7×#41—22no—
151C7×#41—22no—
152C7×#41—22no—
153C7×#41C22⋊C414yes—
154C7×#41C22⋊C414yes—
155C7×#41C2×D414yes—
156C7×#41C2×D414yes—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8C22⋊C412yes—
161C2×C7×Q8C22⋊C412yes—
162C2×C7×Q8C22×C412yes—
163C2×C7×D4—22no—
164C2×C7×D4—22no—
165C2×C7×D4—22no—
166C2×C7×D4—22no—
167C2×C7×D4—22no—
168C2×C7×D4—22no—
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
172C2×C7×D4C22⋊C412yes—
173C2×C7×D4C22⋊C412yes—
174C2×C7×D4C22×C412yes—
175C22×C4×C7—21no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7C22×C411yescharacteristic
183C22×C4×C7C22×C411yescharacteristic
184C22×C4×C7C2×D411yescharacteristic
185C22×C4×C7C2×D411yescharacteristic
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7C2×D411yescharacteristic
188C22×C4×C7C2×D411yescharacteristic
189C22×C4×C7C2×D411yescharacteristic
190C22×C4×C7C2×D411yescharacteristic
191C22×C4×C7C2×D411yescharacteristic
192C22×C4×C7#4111yescharacteristic
193C22×C4×C7#4111yescharacteristic
194C22×C4×C7#4111yescharacteristic
195C22×C4×C7C2411yescharacteristic
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—41no—
200C22×Dic7—41no—
201C22×Dic7—41no—
202C22×Dic7—41no—
203C22×Dic7—41no—
204C2×Dic14—22no—
205C2×Dic14—22no—
206C2×Dic14—22no—
207C2×Dic14—22no—
208C2×Dic14—22no—
209C2×Dic14—22no—
210C2×Dic14—22no—
211C2×Dic14—22no—
212C2×Dic14—22no—
213C2×Dic14—22no—
214C2×Dic14—22no—
215C2×Dic14—22no—
216C2×Dic14—22no—
217C2×Dic14—22no—
218C2×Dic14—22no—
219C2×Dic14—41no—
220C2×Dic14—41no—
221C2×Dic14—41no—
222C2×Dic14—41no—
223C2×Dic14—41no—
224C2×Dic14—41no—
225C2×Dic14—41no—
226C2×Dic14—41no—
227C2×Dic14—41no—
228C2×Dic14—41no—
229C2×Dic14—41no—
230C2×Dic14—41no—
231C2×Dic14C22×C414yes—
232C7×M16—216no—
233C7×M16—22no—
234C7×M16—22no—
235C7×M16—22no—
236C7×M16—22no—
237C7×M16—22no—
238C7×M16—22no—
239C7×M16—22no—
240C7×M16C2×D414yes—
241C2×C7×C8—216no—
242C2×C7×C8—22no—
243C2×C7×C8—22no—
244C2×C7×C8—22no—
245C2×C7×C8—22no—
246C2×C7×C8—22no—
247C2×C7×C8C2×D414yes—
248C22⋊Dic7—22no—
249C22⋊Dic7—41no—
250#1144—216no—
251#1142—216no—
252C4⋊Dic7—22no—
253C4⋊Dic7—41no—
254C4×Dic7—22no—
255C4×Dic7—41no—
256#1136—22no—
257#1136—22no—
258#1136—22no—
259#1136—22no—
260#1136—22no—
261#1136—22no—
262#1136—41no—
263#1136—41no—
264C2×C7⋊C8—22no—
265C2×C7⋊C8—22no—
266C2×C7⋊C8—22no—
267C2×C7⋊C8—41no—
268C2×C7⋊C8—41no—
269C2×C7⋊C8C22×C414yes—
270C22×#41C2×D711yescharacteristic
271C23×Q8—71no—
272C2×#137—74no—
273C2×#137—74no—
274C2×#137—142no—
275C2×#137—142no—
276C2×#137—142no—
277C2×#137—142no—
278C22×Q16—72no—
279C22×SD16—72no—
280#568—22no—
281#568—22no—
282#568—22no—
283#568C2×D714yes—
284C2×#131—22no—
285C2×#131—22no—
286C22×M16—22no—
287C22×M16—71no—
288C22×M16—71no—
289C22×M16C2×D711yescharacteristic
290C22×M16C2×D711yescharacteristic
291C2×#117—71no—
292#421—74no—
293#421—142no—
294C2×#104—142no—
295#419—74no—
296#419—142no—
297C2×#103—142no—
298C2×#101—74no—
299C2×#101—142no—
300C2×#101—142no—
301#344—74no—
302#338—74no—
303C23×C7—22no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—42no—
307C23×C7—82no—
308C23×C7C4×D411yescharacteristic
309C23×C7C4×D411yescharacteristic
310C23×C7#12111yescharacteristic
311C23×C7#12111yescharacteristic
312C23×C7#12311yescharacteristic
313C23×C7#12311yescharacteristic
314C23×C7C2×#4111yescharacteristic
315C7×Q8—22no—
316C7×Q8—22no—
317C7×Q8—22no—
318C7×Q8C2×C22⋊C414yes—
319C7×D4—24no—
320C7×D4—24no—
321C7×D4—24no—
322C7×D4—24no—
323C7×D4—22no—
324C7×D4—22no—
325C7×D4—22no—
326C7×D4C2×C22⋊C414yes—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—24no—
331C2×C4×C7—24no—
332C2×C4×C7—24no—
333C2×C4×C7—24no—
334C2×C4×C7C2×C22⋊C411yescharacteristic
335C2×C4×C7C2×C22⋊C411yescharacteristic
336C2×C4×C7C2×C22⋊C411yescharacteristic
337C2×C4×C7C2×C22⋊C411yescharacteristic
338C2×C4×C7C4×D411yescharacteristic
339C2×C4×C7C4×D411yescharacteristic
340C2×C4×C7C4×D411yescharacteristic
341C2×C4×C7C4×D411yescharacteristic
342C2×C4×C7C4×D411yescharacteristic
343C2×C4×C7C4×D411yescharacteristic
344C2×C4×C7#12011yescharacteristic
345C2×C4×C7#12011yescharacteristic
346C2×C4×C7#12011yescharacteristic
347C2×C4×C7#12011yescharacteristic
348C2×C4×C7#12111yescharacteristic
349C2×C4×C7#12111yescharacteristic
350C2×C4×C7#12111yescharacteristic
351C2×C4×C7#12111yescharacteristic
352C2×C4×C7#12111yescharacteristic
353C2×C4×C7#12111yescharacteristic
354C2×C4×C7#12311yescharacteristic
355C2×C4×C7#12311yescharacteristic
356C2×C4×C7C23×C411yescharacteristic
357C2×C4×C7C22×D411yescharacteristic
358C2×C4×C7C22×D411yescharacteristic
359C2×C4×C7C22×D411yescharacteristic
360C2×C4×C7C22×D411yescharacteristic
361C2×C4×C7C2×#4111yescharacteristic
362C2×Dic7—24no—
363C2×Dic7—42no—
364C2×Dic7—42no—
365C2×Dic7—42no—
366C2×Dic7—42no—
367C2×Dic7—42no—
368C2×Dic7—42no—
369C2×Dic7—42no—
370C2×Dic7—82no—
371Dic14—24no—
372Dic14—24no—
373Dic14—42no—
374Dic14—42no—
375Dic14—42no—
376Dic14—42no—
377Dic14—42no—
378Dic14—42no—
379C7×C8—24no—
380C7×C8—24no—
381C7⋊C8—24no—
382C7⋊C8—42no—
383C2×#41—21no—
384C2×#41—21no—
385C2×#41—21no—
386C2×#41—21no—
387C2×#41—21no—
388C2×#41—21no—
389C2×#41C4×D712yes—
390C2×#41D2812yes—
391C2×#41D2812yes—
392C2×#41C22⋊D712yes—
393C2×#41C22⋊D712yes—
394C2×#41C22×D712yes—
395C22×Q8—72no—
396C22×Q8—72no—
397C22×Q8—72no—
398C22×Q8—141no—
399C22×Q8—141no—
400C22×Q8—141no—
401C22×Q8—141no—
402C22×Q8—141no—
403C22×Q8—141no—
404C22×Q8—141no—
405C22×Q8—141no—
406C22×Q8—141no—
407C22×Q8—141no—
408C22×Q8—141no—
409C22×Q8C4×D711yescharacteristic
410C22×D4—21no—
411C22×D4C4×D711yescharacteristic
412C23×C4—21no—
413C23×C4—141no—
414C23×C4C22×D711yescharacteristic
415#137—148no—
416#137—148no—
417#137—148no—
418#137—148no—
419C2×Q16—78no—
420C2×Q16—144no—
421C2×Q16—144no—
422C2×SD16—78no—
423C2×SD16—144no—
424C2×SD16—144no—
425#131—28no—
426#131—28no—
427#131—28no—
428#131—28no—
429C2×M16—24no—
430C2×M16—28no—
431C2×M16—21no—
432C2×M16—21no—
433C2×M16—21no—
434C2×M16—21no—
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—28no—
439C2×M16—72no—
440C2×M16—72no—
441C2×M16—72no—
442C2×M16—141no—
443C2×M16—141no—
444C2×M16—141no—
445C2×M16—141no—
446C2×M16—141no—
447C2×M16—141no—
448C2×M16—141no—
449C2×M16—141no—
450C2×M16—141no—
451C2×M16C22⋊D712yes—
452C2×M16C22⋊D712yes—
453C2×M16C22⋊D712yes—
454C2×M16C22×D712yes—
455C2×M16C22×D712yes—
456C22×C8—24no—
457C22×C8—21no—
458C22×C8—72no—
459C22×C8—141no—
460C22×C8C22⋊D712yes—
461#117—72no—
462#117—141no—
463#117—141no—
464#117—141no—
465C2×C4⋊C4—141no—
466C2×C22⋊C4—141no—
467C2×C42—141no—
468#104—148no—
469#103—148no—
470#101—148no—
471C22×C7—22no—
472C22×C7—22no—
473C22×C7—22no—
474C22×C7—24no—
475C22×C7—41no—
476C22×C7—41no—
477C22×C7—41no—
478C22×C7—41no—
479C22×C7—44no—
480C22×C7—82no—
481C22×C7—82no—
482C22×C7#38611yescharacteristic
483C22×C7#38611yescharacteristic
484C22×C7#38611yescharacteristic
485C22×C7#38611yescharacteristic
486C22×C7C2×C4×D411yescharacteristic
487C22×C7C2×#12111yescharacteristic
488C22×C7C2×#12311yescharacteristic
489C4×C7—24no—
490C4×C7#38611yescharacteristic
491C4×C7#38611yescharacteristic
492C4×C7#38611yescharacteristic
493C4×C7#38611yescharacteristic
494C4×C7C22×C22⋊C411yescharacteristic
495C4×C7C2×C4×D411yescharacteristic
496C4×C7C2×#12011yescharacteristic
497C4×C7C2×#12111yescharacteristic
498Dic7—44no—
499Dic7—82no—
500C24—21no—
501C24#115711yescharacteristic
502#41—22no—
503#41—22no—
504#41—22no—
505#41—22no—
506#41—22no—
507#41—22no—
508#41—22no—
509#41—22no—
510#41—22no—
511#41—22no—
512#41—22no—
513#41—22no—
514#41(C2×D7)⋊C414yes—
515#41(C2×D7)⋊C414yes—
516#41C2×D2814yes—
517#41C2×C22⋊D714yes—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—74no—
522C2×Q8—142no—
523C2×Q8—142no—
524C2×Q8—142no—
525C2×Q8—142no—
526C2×Q8—142no—
527C2×Q8—142no—
528C2×Q8—142no—
529C2×Q8—142no—
530C2×Q8—142no—
531C2×Q8—142no—
532C2×Q8—142no—
533C2×Q8—142no—
534C2×Q8—142no—
535C2×Q8—142no—
536C2×Q8—142no—
537C2×Q8—281no—
538C2×Q8—281no—
539C2×Q8—281no—
540C2×Q8—281no—
541C2×Q8—281no—
542C2×Q8—281no—
543C2×Q8—281no—
544C2×Q8—281no—
545C2×Q8—281no—
546C2×Q8—281no—
547C2×Q8—281no—
548C2×Q8—281no—
549C2×Q8(C2×D7)⋊C412yes—
550C2×Q8(C2×D7)⋊C412yes—
551C2×Q8C2×C4×D712yes—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4(C2×D7)⋊C412yes—
562C2×D4(C2×D7)⋊C412yes—
563C2×D4C2×C4×D712yes—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—281no—
575C22×C4—281no—
576C22×C4—281no—
577C22×C4—281no—
578C22×C4—281no—
579C22×C4C2×C4×D711yescharacteristic
580C22×C4C2×C4×D711yescharacteristic
581C22×C4C2×D2811yescharacteristic
582C22×C4C2×D2811yescharacteristic
583C22×C4#115711yescharacteristic
584C22×C4#115711yescharacteristic
585C22×C4#115711yescharacteristic
586C22×C4C2×C22⋊D711yescharacteristic
587C22×C4C2×C22⋊D711yescharacteristic
588C22×C4C2×C22⋊D711yescharacteristic
589C22×C4C2×C22⋊D711yescharacteristic
590C22×C4C2×C22⋊D711yescharacteristic
591C22×C4C2×C22⋊D711yescharacteristic
592C22×C4C23×D711yescharacteristic
593Q16—1416no—
594SD16—1416no—
595M16—216no—
596M16—22no—
597M16—22no—
598M16—22no—
599M16—22no—
600M16—22no—
601M16—22no—
602M16—22no—
603M16—142no—
604M16—142no—
605M16—142no—
606M16—142no—
607M16—142no—
608M16—142no—
609M16—281no—
610M16—281no—
611M16C2×C22⋊D714yes—
612C2×C8—216no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—74no—
619C2×C8—142no—
620C2×C8—142no—
621C2×C8—142no—
622C2×C8—281no—
623C2×C8—281no—
624C2×C8C2×C22⋊D714yes—
625C4⋊C4—142no—
626C4⋊C4—281no—
627C22⋊C4—142no—
628C22⋊C4—281no—
629C42—142no—
630C42—281no—
631C2×C7—21no—
632C2×C7—21no—
633C2×C7—21no—
634C2×C7—21no—
635C2×C7—21no—
636C2×C7—21no—
637C2×C7—44no—
638C2×C7#190212yescomplemented
639C2×C7C2×#38611yescharacteristic
640C23—22no—
641C23—22no—
642C23—22no—
643C23—42no—
644C23—82no—
645C23C4×C22⋊D711yescharacteristic
646C23C4×C22⋊D711yescharacteristic
647C23#649211yescharacteristic
648C23#649211yescharacteristic
649C23#649311yescharacteristic
650C23#649311yescharacteristic
651C23C2×#115711yescharacteristic
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—144no—
656Q8—144no—
657Q8—282no—
658Q8—282no—
659Q8—282no—
660Q8—282no—
661Q8—282no—
662Q8—282no—
663Q8C2×(C2×D7)⋊C414yes—
664D4—24no—
665D4—24no—
666D4—24no—
667D4—24no—
668D4—22no—
669D4—22no—
670D4—22no—
671D4C2×(C2×D7)⋊C414yes—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—144no—
680C2×C4—282no—
681C2×C4—282no—
682C2×C4—282no—
683C2×C4—282no—
684C2×C4—282no—
685C2×C4—282no—
686C2×C4—282no—
687C2×C4—562no—
688C2×C4C2×(C2×D7)⋊C411yescharacteristic
689C2×C4C2×(C2×D7)⋊C411yescharacteristic
690C2×C4C2×(C2×D7)⋊C411yescharacteristic
691C2×C4C2×(C2×D7)⋊C411yescharacteristic
692C2×C4C4×C22⋊D711yescharacteristic
693C2×C4C4×C22⋊D711yescharacteristic
694C2×C4C4×C22⋊D711yescharacteristic
695C2×C4C4×C22⋊D711yescharacteristic
696C2×C4C4×C22⋊D711yescharacteristic
697C2×C4C4×C22⋊D711yescharacteristic
698C2×C4#649211yescharacteristic
699C2×C4#649211yescharacteristic
700C2×C4#649311yescharacteristic
701C2×C4#649311yescharacteristic
702C2×C4#649311yescharacteristic
703C2×C4#649311yescharacteristic
704C2×C4#649311yescharacteristic
705C2×C4#649311yescharacteristic
706C2×C4#651611yescharacteristic
707C2×C4#651611yescharacteristic
708C2×C4#651611yescharacteristic
709C2×C4#651611yescharacteristic
710C2×C4C22×C4×D711yescharacteristic
711C2×C4C22×D2811yescharacteristic
712C2×C4C2×#115711yescharacteristic
713C2×C4C22×C22⋊D711yescharacteristic
714C2×C4C22×C22⋊D711yescharacteristic
715C2×C4C22×C22⋊D711yescharacteristic
716C8—24no—
717C8—24no—
718C8—144no—
719C8—282no—
720C7C2×#190211yescharacteristic, complemented, Sylow
721C22—22no—
722C22—22no—
723C22—22no—
724C22—24no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—44no—
730C22—82no—
731C22—82no—
732C22#8998511yescharacteristic
733C22#8998511yescharacteristic
734C22#8998511yescharacteristic
735C22#8998511yescharacteristic
736C22C2×C4×C22⋊D711yescharacteristic
737C22C2×#649211yescharacteristic
738C22C2×#649311yescharacteristic
739C4—24no—
740C4—284no—
741C4—562no—
742C4#8998511yescharacteristic
743C4#8998511yescharacteristic
744C4#8998511yescharacteristic
745C4#8998511yescharacteristic
746C4C22×(C2×D7)⋊C411yescharacteristic
747C4C2×C4×C22⋊D711yescharacteristic
748C4C2×#649311yescharacteristic
749C4C2×#651611yescharacteristic
750C2—21no—
751C2—21no—
752C2—21no—
753C2—21no—
754C2—21no—
755C2—21no—
756C2—44no—
757C2#1172977612yesdirect product factor
758C2C2×#8998511yescharacteristic
subgroupG/H
centerC22#89985
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#568C2
socleC22×C7#386
prime radicalC22×C7×#41C22
cosocleC22×C4×C7C24
hypercenterC2×#568D7
hypocenterC7C2×#1902
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
4. C2×#89892C2semidirect
5. C22×#6398C2semidirect
6. #11729776C2direct (N × H)
7. C2×#89354C2semidirect
8. C2×C7⋊#338C2semidirect
24. C2×#6514C4semidirect
26. C22×#1144C4semidirect
27. C22×#1142C4semidirect
36. C2×#6398C22semidirect
38. #89892C22semidirect
40. C7⋊#338C22semidirect
41. #89354C22semidirect
104. C2×#1144C2×C4semidirect
107. C2×#1142C2×C4semidirect
638. C2×C7#1902semidirect
720. C7C2×#1902semidirect
757. C2#11729776direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5682
C22×#65142
C2×#900082
C2×#898922
C22×#63982
#117297762
C2×#893542
C2×C7⋊#3382
C2×#19027