Finite Group Databasebeta

← C2×#11738812 #14232498

Subgroups — C2×#11738812 #14232498

Order 1792.

2082 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90302C211yesmaximal, characteristic
2C2×#90224C211yesmaximal, characteristic, complemented
3C2×C7×#482C211yesmaximal, characteristic, complemented
4C2×#89814C211yesmaximal, characteristic, complemented
5C2×#89767C211yesmaximal, characteristic, complemented
6#11738812C2116yesmaximal, direct product factor
7C2×#89656C211yesmaximal, characteristic, complemented
8C2×#89646C211yesmaximal, characteristic, complemented
9C2×#89626C211yesmaximal, characteristic, complemented
10C2×#89633C211yesmaximal, characteristic, complemented
11C2×#89556C211yesmaximal, characteristic, complemented
12C2×#89552C211yesmaximal, characteristic, complemented
13C2×#89531C211yesmaximal, characteristic, complemented
14C2×#89530C211yesmaximal, characteristic, complemented
15C2×#89501C211yesmaximal, characteristic, complemented
16C2×#89494C211yesmaximal, characteristic, complemented
17C22×#1159—21no—
18C2×C7×#121C2211yescharacteristic
19C2×C7×#117C2211yescharacteristic
20C2×#6501C2211yescharacteristic
21C2×#6498—21no—
22C2×D4×Dic7C2211yescharacteristic
23C22×#1142C2211yescharacteristic
24C2×C4×C22⋊D7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C2×#6487C2211yescharacteristic
27C22×#1136C2211yescharacteristic
28C22×#1131C2211yescharacteristic
29#90302—24no—
30#90302C2218yes—
31#90224—24no—
32#90224C2218yescomplemented
33C2×#6460C2211yescharacteristic
34C2×#6455C2211yescharacteristic
35C2×D7×C4⋊C4C2211yescharacteristic
36C2×#6451C2211yescharacteristic
37C2×#6451C2211yescharacteristic
38C2×#6450C2211yescharacteristic
39C2×#6448—21no—
40C2×#6446—21no—
41C2×#6442—21no—
42C2×#6441—21no—
43C2×#6439—21no—
44C2×C4×Dic14—21no—
45C7×#482C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#106C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×(C2×D7)⋊C8C2211yescharacteristic
53C2×#6392C2211yescharacteristic
54C2×#6392C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89814C2218yescomplemented
60#89767C2218yescomplemented
61C2×#6384C2211yescharacteristic
62C2×#6382C2211yescharacteristic
63C2×#6382C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67#89656C2218yescomplemented
68#89646C2218yescomplemented
69#89633C2218yescomplemented
70#89626C2218yescomplemented
71#89556C2218yescomplemented
72#89552C2218yescomplemented
73#89531C2218yescomplemented
74#89530C2218yescomplemented
75#89501C2218yescomplemented
76#89494C2218yescomplemented
77C2×#3353—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7D411yescharacteristic
83C23×Dic7—21no—
84C23×Dic7—21no—
85C2×#1159—28no—
86C2×#1159—48no—
87C22×C4×D7—21no—
88C22×C4×D7C2311yescharacteristic
89C22×Dic14—21no—
90C22×Dic14—21no—
91C22×Dic14C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C7×#121—22no—
95C7×#121C2314yes—
96C7×#117—22no—
97C7×#117C2314yes—
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C22⋊C4—21no—
102C2×C7×C22⋊C4—21no—
103C2×C42×C7—21no—
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7D411yescharacteristic
108#6501—22no—
109#6501C2314yes—
110#6498—28no—
111D4×Dic7—22no—
112D4×Dic7C2314yes—
113C2×#1142—24no—
114C2×#1142C2314yes—
115C4×C22⋊D7D414yes—
116C4×C22⋊D7C2314yes—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4D411yescharacteristic
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7—22no—
122C2×C4⋊Dic7—21no—
123C2×C4⋊Dic7C2311yescharacteristic
124C2×C4⋊Dic7C2311yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2314yes—
127#6487—22no—
128#6487C2314yes—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4D411yescharacteristic
135C2×C4×Dic7—21no—
136C2×C4×Dic7—21no—
137C2×C4×Dic7C2311yescharacteristic
138C2×#1136—24no—
139C2×#1136C2314yes—
140C22×C7⋊C8C2311yescharacteristic
141C22×C7⋊C8C2311yescharacteristic
142C2×#1131—24no—
143C2×#1131C2314yes—
144#6460—22no—
145#6460C2314yes—
146#6455—22no—
147#6455C2314yes—
148D7×C4⋊C4—22no—
149D7×C4⋊C4C2314yes—
150#6451—22no—
151#6451—22no—
152#6451C2314yes—
153#6451C2314yes—
154#6450—22no—
155#6450C2314yes—
156#6448—28no—
157#6446—28no—
158#6442—28no—
159#6441—28no—
160#6439—28no—
161C4×Dic14—28no—
162C7×#107C2314yes—
163C7×#106C2314yes—
164C7×#102C2314yes—
165C7×#102C2314yes—
166C7×C22⋊C8C2314yes—
167#6406C2314yes—
168(C2×D7)⋊C8C2314yes—
169#6392C2314yes—
170#6392C2314yes—
171#6390C2314yes—
172#6390C2314yes—
173Dic7⋊C8C2314yes—
174C8×Dic7C2314yes—
175#6384C2314yes—
176#6382C2314yes—
177#6382C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180#6381C2314yes—
181C2×#556—71no—
182C2×#547—71no—
183#3353—716no—
184C2×#500—71no—
185C2×#484—71no—
186C2×#484—71no—
187C2×#482—71no—
188C2×#482D711yescharacteristic, complemented
189C2×#475—71no—
190C2×#474—71no—
191C2×#468—71no—
192C2×#468—71no—
193C2×C4×SD16—71no—
194C2×#436—71no—
195C2×#428—71no—
196C2×#428—71no—
197C24×C7—21no—
198C24×C7C2×D411yescharacteristic
199C23×D7C2×D411yescharacteristic
200C2×C7×D4—24no—
201C2×C7×D4—21no—
202C2×C7×D4—22no—
203C2×C7×D4—22no—
204C2×C7×D4—44no—
205C2×C7×D4C2412yes—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2411yescharacteristic
215C2×C22⋊D7—24no—
216C2×C22⋊D7—24no—
217C2×C22⋊D7—44no—
218C2×C22⋊D7C2×D414yes—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—24no—
224C22×Dic7—24no—
225C22×Dic7—44no—
226C22×Dic7—44no—
227C22×Dic7C2×D411yescharacteristic
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230#1159—432no—
231C2×C4×D7—22no—
232C2×C4×D7—22no—
233C2×C4×D7—24no—
234C2×C4×D7—44no—
235C2×C4×D7C2×D412yes—
236C2×C4×D7C2412yes—
237C2×Dic14—22no—
238C2×Dic14—22no—
239C2×Dic14—21no—
240C2×Dic14—24no—
241C2×Dic14—24no—
242C2×Dic14—44no—
243C2×Dic14—44no—
244C2×Dic14C2412yes—
245C2×C7×C8—22no—
246C2×C7×C8—22no—
247C2×C7×C8C2412yes—
248C2×C7×C8C2412yes—
249C7×C4⋊C4—21no—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4C2412yes—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C22⋊C4—24no—
256C7×C22⋊C4—24no—
257C42×C7—24no—
258C22⋊Dic7—24no—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261C22⋊Dic7C2×D414yes—
262#1142—28no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4C2×D414yes—
266C4⋊Dic7—24no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—21no—
270C4⋊Dic7—24no—
271C4⋊Dic7C2412yes—
272C4⋊Dic7C2412yes—
273C4⋊Dic7C2412yes—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4C2×D414yes—
280C4×Dic7—24no—
281C4×Dic7—24no—
282C4×Dic7C2×D412yes—
283C4×Dic7C2412yes—
284#1136—28no—
285C2×C7⋊C8—22no—
286C2×C7⋊C8#4114yescomplemented
287C2×C7⋊C8C2412yes—
288C2×C7⋊C8C2412yes—
289#1131—28no—
290C22×#41—141no—
291C22×SD16—71no—
292C22×M16—71no—
293C22×M16—71no—
294#556—78no—
295#556—144no—
296#547—78no—
297#547—144no—
298C2×C4⋊Q8—71no—
299C2×C4⋊Q8—71no—
300C2×#126—141no—
301C2×#126—141no—
302C2×#124—141no—
303C2×#123—141no—
304C2×#123—141no—
305C2×C22⋊Q8—71no—
306C2×C22⋊Q8—71no—
307C2×C22⋊Q8—141no—
308C2×#121—71no—
309C2×#121C2×D711yescharacteristic
310C2×C4×Q8—71no—
311C2×C4×Q8—141no—
312C2×C4×D4—71no—
313C2×C4×D4—71no—
314C2×#117—71no—
315C2×#117C2×D711yescharacteristic
316C22×C4⋊C4—71no—
317C22×C4⋊C4—71no—
318#500—78no—
319#484—78no—
320#484—78no—
321#482—78no—
322#482C2×D718yescomplemented
323#475—78no—
324#474—78no—
325#468—78no—
326#468—78no—
327C4×SD16—78no—
328#436—78no—
329#428—78no—
330#428—78no—
331C2×#107—71no—
332C2×#107—71no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#107—71no—
336C2×#107C2×D711yescharacteristic
337C2×#106—71no—
338C2×#106—71no—
339C2×#106C2×D711yescharacteristic
340C2×C4⋊C8—71no—
341C2×#103—71no—
342C2×#103—71no—
343C2×#103—71no—
344C2×#102—71no—
345C2×#102C2×D711yescharacteristic
346C2×#102C2×D711yescharacteristic
347C2×C22⋊C8—71no—
348C2×C22⋊C8C2×D711yescharacteristic
349C2×C4×C8—71no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7C22×D412yes—
358C23×C7C22×D411yescharacteristic
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7C22×D412yes—
363C7×D4—22no—
364C7×D4—22no—
365C7×D4—48no—
366C7×D4—42no—
367C2×C4×C7—22no—
368C2×C4×C7—24no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D411yescharacteristic
379C2×C4×C7C2×#4112yes—
380C2×C4×C72−1+412yes—
381C2×C4×C7C2511yescharacteristic
382C22⋊D7—28no—
383C22⋊D7—48no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—48no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—48no—
396C2×Dic7AGL(1,ℤ/8)14yes—
397C2×Dic7C22×D412yes—
398C2×Dic7C22×D412yes—
399C2×Dic7C22×D412yes—
400C4×D7—24no—
401C4×D7—22no—
402C4×D7—22no—
403C4×D7—48no—
404Dic14—22no—
405Dic14—22no—
406Dic14—42no—
407Dic14—48no—
408Dic14—48no—
409C7×C8—22no—
410C7×C8—22no—
411C7⋊C8—22no—
412C7⋊C8C2×#4114yescomplemented
413C2×#41—148no—
414C2×#41—288no—
415C22×Q8—71no—
416C22×Q8—141no—
417C22×Q8—141no—
418C22×D4—21no—
419C22×D4—71no—
420C22×D4—141no—
421C22×D4C22×D711yescharacteristic
422C23×C4—71no—
423C23×C4—141no—
424C23×C4—141no—
425C23×C4—141no—
426C23×C4C22×D711yescharacteristic
427C2×SD16—74no—
428C2×SD16—144no—
429C2×M16—74no—
430C2×M16—74no—
431C2×M16—144no—
432C2×M16—144no—
433C22×C8—71no—
434C22×C8—71no—
435C22×C8C22×D711yescharacteristic
436C22×C8C22×D711yescharacteristic
437C4⋊Q8—74no—
438C4⋊Q8—74no—
439C4⋊Q8—142no—
440C4⋊Q8—142no—
441#126—148no—
442#126—148no—
443#124—148no—
444#123—148no—
445#123—148no—
446C22⋊Q8—74no—
447C22⋊Q8—74no—
448C22⋊Q8—148no—
449C22⋊Q8—142no—
450C22⋊Q8—142no—
451#121—22no—
452#121—74no—
453#121—142no—
454#121C22×D714yes—
455C4×Q8—74no—
456C4×Q8—148no—
457C4×Q8—142no—
458C4×D4—74no—
459C4×D4—74no—
460C4×D4—74no—
461C4×D4—142no—
462#117—22no—
463#117—74no—
464#117—142no—
465#117C22×D714yes—
466C2×C4⋊C4—71no—
467C2×C4⋊C4—71no—
468C2×C4⋊C4—71no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—74no—
472C2×C4⋊C4—142no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4—141no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—142no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4C22×D711yescharacteristic
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C4⋊C4C22×D711yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—71no—
487C2×C22⋊C4—71no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C42—21no—
494C2×C42—71no—
495C2×C42—141no—
496C2×C42—141no—
497#107—74no—
498#107—74no—
499#107—74no—
500#107—74no—
501#107—74no—
502#107C22×D714yes—
503#106—74no—
504#106—74no—
505#106C22×D714yes—
506C4⋊C8—74no—
507#103—74no—
508#103—74no—
509#103—74no—
510#102—74no—
511#102C22×D714yes—
512#102C22×D714yes—
513C22⋊C8—74no—
514C22⋊C8C22×D714yes—
515C4×C8—74no—
516C22×C7—22no—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—44no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—84no—
524C22×C7#54712yes—
525C22×C7C2×AGL(1,ℤ/8)12yes—
526C22×C7#57812yes—
527C22×C7C23×D411yescharacteristic
528C2×D7—22no—
529C2×D7—22no—
530C2×D7—22no—
531C2×D7—44no—
532C4×C7—22no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7#54712yes—
537C4×C7C22×#4111yescharacteristic
538C4×C7C2×2−1+411yescharacteristic
539Dic7—22no—
540Dic7—22no—
541Dic7—42no—
542Dic7—42no—
543Dic7—42no—
544Dic7—42no—
545Dic7C2×AGL(1,ℤ/8)14yes—
546C24—21no—
547C24—71no—
548C24D4×D711yescharacteristic
549#41—2832no—
550C2×Q8—72no—
551C2×Q8—144no—
552C2×Q8—144no—
553C2×Q8—141no—
554C2×Q8—142no—
555C2×Q8—142no—
556C2×Q8—284no—
557C2×Q8—284no—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—44no—
563C2×D4—74no—
564C2×D4—144no—
565C2×D4—144no—
566C2×D4—284no—
567C2×D4C23×D712yes—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—71no—
574C22×C4—71no—
575C22×C4—71no—
576C22×C4—72no—
577C22×C4—72no—
578C22×C4—144no—
579C22×C4—144no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—144no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—284no—
588C22×C4—284no—
589C22×C4—284no—
590C22×C4D4×D712yes—
591C22×C4D4×D711yescharacteristic
592C22×C4C23×D712yes—
593C22×C4C23×D711yescharacteristic
594SD16—148no—
595M16—148no—
596M16—148no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—74no—
600C2×C8—72no—
601C2×C8—72no—
602C2×C8—142no—
603C2×C8C23×D712yes—
604C2×C8C23×D712yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—74no—
609C4⋊C4—72no—
610C4⋊C4—72no—
611C4⋊C4—72no—
612C4⋊C4—144no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—141no—
619C4⋊C4—141no—
620C4⋊C4—144no—
621C4⋊C4—141no—
622C4⋊C4C23×D712yes—
623C4⋊C4C23×D712yes—
624C4⋊C4C23×D712yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—74no—
628C22⋊C4—74no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C42—24no—
635C42—72no—
636C42—72no—
637C42—144no—
638C42—144no—
639C2×C7—42no—
640C2×C7—82no—
641C2×C7#335314yescomplemented
642C2×C7C2×#54711yescharacteristic
643C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
644C2×C7C2×#57811yescharacteristic
645D7—42no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—72no—
654C23—142no—
655C23—142no—
656C23—142no—
657C23C2×D4×D712yes—
658C23C2×D4×D711yescharacteristic
659Q8—142no—
660Q8—142no—
661Q8—288no—
662Q8—288no—
663Q8—282no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—42no—
668D4—148no—
669D4—288no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—74no—
681C2×C4—72no—
682C2×C4—72no—
683C2×C4—72no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—144no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—288no—
694C2×C4—288no—
695C2×C4—288no—
696C2×C4—282no—
697C2×C4—282no—
698C2×C4—282no—
699C2×C4—282no—
700C2×C4C2×D4×D712yes—
701C2×C4C2×D4×D711yescharacteristic
702C2×C4D7×#4112yes—
703C2×C4#655412yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—22no—
707C8—74no—
708C8—142no—
709C7C2×#335311yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—142no—
719C22—142no—
720C22—142no—
721C22—284no—
722C22#9034612yes—
723C22#9046212yes—
724C22D7×AGL(1,ℤ/8)12yes—
725C22C22×D4×D711yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—74no—
731C4—142no—
732C4—142no—
733C4—282no—
734C4—282no—
735C4—282no—
736C4—282no—
737C4#9034612yes—
738C4C2×D7×#4111yescharacteristic
739C4C2×#655411yescharacteristic
740C2—42no—
741C2—82no—
742C2—282no—
743C2#1173881214yesdirect product factor
744C2C2×#9034611yescharacteristic
745C2C2×#9046211yescharacteristic
746C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#482C2
socleC23×C7C22×D4
prime radicalC2×#90302C2
hypercenterC2×#482D7
hypocenterC7C2×#3353
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#90224C2semidirect
3. C2×C7×#482C2semidirect
4. C2×#89814C2semidirect
5. C2×#89767C2semidirect
6. #11738812C2direct (N × H)
7. C2×#89656C2semidirect
8. C2×#89646C2semidirect
9. C2×#89626C2semidirect
10. C2×#89633C2semidirect
11. C2×#89556C2semidirect
12. C2×#89552C2semidirect
13. C2×#89531C2semidirect
14. C2×#89530C2semidirect
15. C2×#89501C2semidirect
16. C2×#89494C2semidirect
32. #90224C22semidirect
45. C7×#482C22semidirect
59. #89814C22semidirect
60. #89767C22semidirect
67. #89656C22semidirect
68. #89646C22semidirect
69. #89633C22semidirect
70. #89626C22semidirect
71. #89556C22semidirect
72. #89552C22semidirect
73. #89531C22semidirect
74. #89530C22semidirect
75. #89501C22semidirect
76. #89494C22semidirect
188. C2×#482D7semidirect
286. C2×C7⋊C8#41semidirect
322. #482C2×D7semidirect
412. C7⋊C8C2×#41semidirect
641. C2×C7#3353semidirect
709. C7C2×#3353semidirect
743. C2#11738812direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903022
C2×#902242
C2×C7×#4822
C2×#898142
C2×#897672
#117388122
C2×#896562
C2×#896462
C2×#896262
C2×#896332
C2×#895562
C2×#895522
C2×#895312
C2×#895302
C2×#895012
C2×#894942
C2×#33537