Finite Group Databasebeta

← C2×#11738779 #14232266

Subgroups — C2×#11738779 #14232266

Order 1792.

1994 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×#90309C211yesmaximal, characteristic, complemented
2C2×#90205C211yesmaximal, characteristic, complemented
3C2×C7×#481C211yesmaximal, characteristic, complemented
4C2×#89810C211yesmaximal, characteristic, complemented
5C22×#6381C211yesmaximal, characteristic, complemented
6#11738779C2116yesmaximal, direct product factor
7C2×#89643C211yesmaximal, characteristic, complemented
8C2×#89638C211yesmaximal, characteristic, complemented
9C2×#89632C211yesmaximal, characteristic, complemented
10C2×#89630C211yesmaximal, characteristic, complemented
11C2×#89547C211yesmaximal, characteristic, complemented
12C2×#89551C211yesmaximal, characteristic, complemented
13C2×#89535C211yesmaximal, characteristic, complemented
14C2×#89528C211yesmaximal, characteristic, complemented
15C2×(C22⋊D7)⋊C8C211yesmaximal, characteristic, complemented
16C2×#89507C211yesmaximal, characteristic, complemented
17C2×C7×#121C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C2×#6502—21no—
20C2×#6501C2211yescharacteristic
21C2×D4×Dic7—21no—
22C2×D4×Dic7C2211yescharacteristic
23C22×#1141C2211yescharacteristic
24C2×#6493—21no—
25C2×#6493C2211yescharacteristic
26C2×C4×C22⋊D7—21no—
27C2×C4×C22⋊D7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C23×C7⋊C8C2211yescharacteristic
30C22×C8×D7C2211yescharacteristic
31#90309—24no—
32#90309C2218yescomplemented
33#90205—24no—
34#90205C2218yescomplemented
35C2×#6461—21no—
36C2×#6458C2211yescharacteristic
37C2×#6457—21no—
38C2×#6456C2211yescharacteristic
39C2×#6455C2211yescharacteristic
40C2×#6455C2211yescharacteristic
41C2×#6453C2211yescharacteristic
42C2×#6453C2211yescharacteristic
43C2×#6449—21no—
44C2×#6442—21no—
45C7×#481C2218yescomplemented
46C2×C7×#106C2211yescharacteristic
47C2×C7×#106C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6391C2211yescharacteristic
56C2×#6391C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89810C2218yescomplemented
60C2×#6383C2211yescharacteristic
61C2×#6381C2211yescharacteristic
62C2×#6381C2211yescharacteristic
63C2×#6381C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6381C2218yescomplemented
67#89643C2218yescomplemented
68#89638C2218yescomplemented
69#89632C2218yescomplemented
70#89630C2218yescomplemented
71#89551C2218yescomplemented
72#89547C2218yescomplemented
73#89535C2218yescomplemented
74#89528C2218yescomplemented
75#89507C2218yescomplemented
76(C22⋊D7)⋊C8C2218yescomplemented
77C2×#3339—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×C22⋊D7D411yescharacteristic
85C23×Dic7—21no—
86C23×Dic7—21no—
87C22×D28—21no—
88C22×D28C2311yescharacteristic
89C22×C4×D7—21no—
90C22×C4×D7C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C7×#121—22no—
94C7×#121C2314yes—
95C2×C7×C4⋊C4—21no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4C2314yes—
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C22⋊C4—21no—
102C2×C22⋊Dic7—21no—
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7D411yescharacteristic
105#6502—28no—
106#6501—22no—
107#6501C2314yes—
108D4×Dic7—28no—
109D4×Dic7—22no—
110D4×Dic7C2314yes—
111C2×#1141—24no—
112C2×#1141C2314yes—
113#6493—22no—
114#6493—28no—
115#6493C2314yes—
116C4×C22⋊D7—28no—
117C4×C22⋊D7D414yes—
118C4×C22⋊D7C2314yes—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4D411yescharacteristic
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7—22no—
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7C2311yescharacteristic
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2314yes—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4D411yescharacteristic
136C2×C4×Dic7—21no—
137C2×C4×Dic7—21no—
138C2×C4×Dic7C2311yescharacteristic
139C22×C7⋊C8—24no—
140C22×C7⋊C8C2311yescharacteristic
141C22×C7⋊C8C2314yes—
142C22×C7⋊C8C2311yescharacteristic
143C2×C8×D7—24no—
144C2×C8×D7C2314yes—
145#6461—28no—
146#6458—22no—
147#6458C2314yes—
148#6457—28no—
149#6456—22no—
150#6456C2314yes—
151#6455—22no—
152#6455—22no—
153#6455C2314yes—
154#6455C2314yes—
155#6453—22no—
156#6453—22no—
157#6453C2314yes—
158#6453C2314yes—
159#6449—28no—
160#6442—28no—
161C7×#106C2314yes—
162C7×#106C2314yes—
163C7×#102C2314yes—
164C7×#102C2314yes—
165C7×C22⋊C8C2314yes—
166#6406C2314yes—
167#6395C2314yes—
168#6395C2314yes—
169(C2×D7)⋊C8C2314yes—
170#6391C2314yes—
171#6391C2314yes—
172Dic7⋊C8C2314yes—
173C8×Dic7C2314yes—
174#6383C2314yes—
175#6381C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180C2×#553—71no—
181C2×#553—71no—
182#3339—716no—
183C2×#499—71no—
184C2×#481—71no—
185C2×#481D711yescharacteristic, complemented
186C2×#482—71no—
187C2×#482—71no—
188C2×#478—71no—
189C2×#478—71no—
190C2×#466—71no—
191C2×#466—71no—
192C2×C4×D8—71no—
193C2×C8×D4—71no—
194C2×#427—71no—
195C22×#107—71no—
196C24×C7—21no—
197C24×C7C2×D411yescharacteristic
198C23×D7—21no—
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×C7—24no—
212C22×C4×C7—82no—
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2411yescharacteristic
217C2×C22⋊D7—24no—
218C2×C22⋊D7—24no—
219C2×C22⋊D7—24no—
220C2×C22⋊D7—44no—
221C2×C22⋊D7—82no—
222C2×C22⋊D7C2×D414yes—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—24no—
227C22×Dic7—24no—
228C22×Dic7—82no—
229C22×Dic7—82no—
230C22×Dic7C2×D411yescharacteristic
231C22×Dic7C2×D411yescharacteristic
232C22×Dic7C2×D411yescharacteristic
233C2×D28—22no—
234C2×D28—22no—
235C2×D28—21no—
236C2×D28—24no—
237C2×D28—82no—
238C2×D28C2412yes—
239C2×C4×D7—22no—
240C2×C4×D7—22no—
241C2×C4×D7—24no—
242C2×C4×D7—82no—
243C2×C4×D7C2×D412yes—
244C2×C4×D7C2412yes—
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⋊C4—24no—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C4⋊C4C2412yes—
256C7×C22⋊C4—24no—
257C22⋊Dic7—24no—
258C22⋊Dic7—24no—
259C22⋊Dic7C2×D414yes—
260#1141—28no—
261(C2×D7)⋊C4—24no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4C2×D414yes—
267C4⋊Dic7—24no—
268C4⋊Dic7—21no—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7—24no—
272C4⋊Dic7—24no—
273C4⋊Dic7C2412yes—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4C2×D414yes—
279C4×Dic7—24no—
280C4×Dic7—24no—
281C4×Dic7C2×D412yes—
282C4×Dic7C2412yes—
283C2×C7⋊C8—22no—
284C2×C7⋊C8—28no—
285C2×C7⋊C8#4114yes—
286C2×C7⋊C8C2412yes—
287C2×C7⋊C8C2412yes—
288C8×D7—28no—
289C22×D8—71no—
290C23×C8—71no—
291C23×C8—71no—
292#553—78no—
293#553—78no—
294#553—144no—
295#553—144no—
296C2×#126—141no—
297C2×#126—141no—
298C2×#125—71no—
299C2×#125—71no—
300C2×#123—141no—
301C2×#123—141no—
302C2×#121—71no—
303C2×#121—71no—
304C2×#121—71no—
305C2×#121—141no—
306C2×#121—141no—
307C2×#121C2×D711yescharacteristic
308C2×C4×D4—71no—
309C2×C4×D4—71no—
310C2×C4×D4—71no—
311C2×C4×D4—141no—
312C2×C4×D4—141no—
313C2×#117—71no—
314C2×#117—71no—
315C22×C4⋊C4—71no—
316C22×C4⋊C4C2×D711yescharacteristic
317#499—78no—
318#482—78no—
319#482—78no—
320#481—78no—
321#481C2×D718yescomplemented
322#478—78no—
323#478—78no—
324#466—78no—
325#466—78no—
326C4×D8—78no—
327C8×D4—78no—
328#427—78no—
329C2×#107—71no—
330C2×#107—71no—
331C2×#107—78no—
332C2×#107—71no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#106—71no—
336C2×#106—71no—
337C2×#106C2×D711yescharacteristic
338C2×#106C2×D711yescharacteristic
339C2×C4⋊C8—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×#102—71no—
344C2×#102C2×D711yescharacteristic
345C2×#102C2×D711yescharacteristic
346C2×C22⋊C8—71no—
347C2×C22⋊C8C2×D711yescharacteristic
348C2×C4×C8—71no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7#13514yes—
356C23×C7C22×D412yes—
357C23×C7C22×D411yescharacteristic
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—42no—
363C22×D7—42no—
364C22×D7—42no—
365C22×D7C22×D412yes—
366C7×D4—22no—
367C7×D4—22no—
368C7×D4—48no—
369C7×D4—42no—
370C2×C4×C7—22no—
371C2×C4×C7—24no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—84no—
381C2×C4×C7C22×D412yes—
382C2×C4×C7C22×D411yescharacteristic
383C2×C4×C7C2×#4112yes—
384C2×C4×C72−1+412yes—
385C2×C4×C7C2511yescharacteristic
386C22⋊D7—28no—
387C22⋊D7—48no—
388C22⋊D7—84no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—42no—
396C2×Dic7—42no—
397C2×Dic7—42no—
398C2×Dic7—84no—
399C2×Dic7—84no—
400C2×Dic7C22×D412yes—
401C2×Dic7C22×D412yes—
402C2×Dic7C22×D412yes—
403D28—22no—
404D28—22no—
405D28—42no—
406D28—84no—
407C4×D7—24no—
408C4×D7—22no—
409C4×D7—22no—
410C4×D7—84no—
411C7×C8—22no—
412C7×C8—22no—
413C7⋊C8—22no—
414C7⋊C8C2×#4114yes—
415C22×D4—21no—
416C22×D4—71no—
417C22×D4—71no—
418C22×D4—141no—
419C22×D4—141no—
420C22×D4—141no—
421C22×D4C22×D711yescharacteristic
422C23×C4—21no—
423C23×C4—71no—
424C23×C4—141no—
425C23×C4—141no—
426C23×C4—141no—
427C23×C4C22×D711yescharacteristic
428C2×D8—74no—
429C2×D8—144no—
430C22×C8—71no—
431C22×C8—71no—
432C22×C8—74no—
433C22×C8—74no—
434C22×C8—144no—
435C22×C8—144no—
436C22×C8C22×D711yescharacteristic
437C22×C8C22×D711yescharacteristic
438#126—148no—
439#126—148no—
440#125—74no—
441#125—74no—
442#125—142no—
443#125—142no—
444#123—148no—
445#123—148no—
446#121—22no—
447#121—74no—
448#121—74no—
449#121—74no—
450#121—142no—
451#121—148no—
452#121—142no—
453#121—148no—
454#121—142no—
455#121C22×D714yes—
456C4×D4—74no—
457C4×D4—74no—
458C4×D4—74no—
459C4×D4—74no—
460C4×D4—142no—
461C4×D4—142no—
462C4×D4—148no—
463C4×D4—148no—
464#117—74no—
465#117—74no—
466#117—142no—
467#117—142no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—74no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—142no—
481C2×C4⋊C4C22×D711yescharacteristic
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C4⋊C4C22×D714yes—
484C2×C4⋊C4C22×D711yescharacteristic
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×C22⋊C4—141no—
494C2×C22⋊C4—141no—
495C2×C42—71no—
496C2×C42—141no—
497C2×C42—141no—
498#107—74no—
499#107—74no—
500#107—74no—
501#107—74no—
502#107—74no—
503#106—74no—
504#106—74no—
505#106C22×D714yes—
506#106C22×D714yes—
507C4⋊C8—74no—
508#102—74no—
509#102—74no—
510#102—74no—
511#102—74no—
512#102C22×D714yes—
513#102C22×D714yes—
514C22⋊C8—74no—
515C22⋊C8C22×D714yes—
516C4×C8—74no—
517C22×C7—28no—
518C22×C7—22no—
519C22×C7—22no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—84no—
524C22×C7#54712yes—
525C22×C7C2×#13514yes—
526C22×C7C2×#13512yes—
527C22×C7#57612yes—
528C22×C7C23×D411yescharacteristic
529C2×D7—22no—
530C2×D7—22no—
531C2×D7—22no—
532C2×D7—44no—
533C2×D7—42no—
534C2×D7—42no—
535C2×D7—42no—
536C2×D7—84no—
537C4×C7—22no—
538C4×C7—42no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7#54712yes—
542C4×C7C22×#4111yescharacteristic
543C4×C7C2×2−1+411yescharacteristic
544Dic7—22no—
545Dic7—22no—
546Dic7—22no—
547Dic7—42no—
548Dic7—42no—
549Dic7—42no—
550C24—21no—
551C24—71no—
552C24—141no—
553C24D4×D711yescharacteristic
554C2×D4—24no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—44no—
559C2×D4—74no—
560C2×D4—72no—
561C2×D4—144no—
562C2×D4—144no—
563C2×D4—144no—
564C2×D4—144no—
565C2×D4—141no—
566C2×D4—142no—
567C2×D4—142no—
568C2×D4—284no—
569C2×D4—562no—
570C2×D4—562no—
571C2×D4C23×D712yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—71no—
579C22×C4—71no—
580C22×C4—71no—
581C22×C4—72no—
582C22×C4—72no—
583C22×C4—82no—
584C22×C4—144no—
585C22×C4—144no—
586C22×C4—142no—
587C22×C4—142no—
588C22×C4—141no—
589C22×C4—141no—
590C22×C4—141no—
591C22×C4—144no—
592C22×C4—562no—
593C22×C4—562no—
594C22×C4—562no—
595C22×C4D4×D712yes—
596C22×C4D4×D711yescharacteristic
597C22×C4C23×D712yes—
598C22×C4C23×D711yescharacteristic
599D8—148no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—74no—
603C2×C8—72no—
604C2×C8—72no—
605C2×C8—148no—
606C2×C8—148no—
607C2×C8—142no—
608C2×C8C23×D712yes—
609C2×C8C23×D712yes—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—74no—
615C4⋊C4—72no—
616C4⋊C4—72no—
617C4⋊C4—72no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—144no—
621C4⋊C4—144no—
622C4⋊C4—141no—
623C4⋊C4—141no—
624C4⋊C4—144no—
625C4⋊C4—141no—
626C4⋊C4C23×D712yes—
627C4⋊C4C23×D712yes—
628C4⋊C4C23×D712yes—
629C22⋊C4—24no—
630C22⋊C4—74no—
631C22⋊C4—74no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4—144no—
637C22⋊C4—144no—
638C22⋊C4—144no—
639C42—72no—
640C42—72no—
641C42—144no—
642C42—144no—
643C2×C7—24no—
644C2×C7—82no—
645C2×C7#333914yescomplemented
646C2×C7C2×#54711yescharacteristic
647C2×C7C22×#13511yescharacteristic
648C2×C7C2×#57611yescharacteristic
649D7—42no—
650D7—82no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—72no—
658C23—142no—
659C23—142no—
660C23—142no—
661C23—142no—
662C23—282no—
663C23—282no—
664C23—282no—
665C23#647914yes—
666C23C2×D4×D712yes—
667C23C2×D4×D711yescharacteristic
668D4—22no—
669D4—22no—
670D4—48no—
671D4—42no—
672D4—148no—
673D4—142no—
674D4—142no—
675D4—288no—
676D4—282no—
677D4—564no—
678D4—564no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—72no—
690C2×C4—72no—
691C2×C4—72no—
692C2×C4—84no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—144no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—282no—
703C2×C4—282no—
704C2×C4—282no—
705C2×C4—564no—
706C2×C4—564no—
707C2×C4—564no—
708C2×C4C2×D4×D712yes—
709C2×C4C2×D4×D711yescharacteristic
710C2×C4D7×#4112yes—
711C2×C4#655412yes—
712C2×C4C24×D711yescharacteristic
713C8—22no—
714C8—22no—
715C8—74no—
716C8—142no—
717C7C2×#333911yescharacteristic, complemented, Sylow
718C22—22no—
719C22—22no—
720C22—28no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—142no—
726C22—142no—
727C22—142no—
728C22—284no—
729C22—282no—
730C22—282no—
731C22—282no—
732C22—564no—
733C22#9034612yes—
734C22C2×#647914yes—
735C22C2×#647912yes—
736C22#9046512yes—
737C22C22×D4×D711yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—142no—
743C4—142no—
744C4—142no—
745C4—282no—
746C4—282no—
747C4—282no—
748C4#9034612yes—
749C4C2×D7×#4111yescharacteristic
750C4C2×#655411yescharacteristic
751C2—24no—
752C2—82no—
753C2—282no—
754C2—562no—
755C2#1173877914yesdirect product factor
756C2C2×#9034611yescharacteristic
757C2C22×#647911yescharacteristic
758C2C2×#9046511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#481C2
socleC23×C7C22×D4
hypercenterC2×#481D7
hypocenterC7C2×#3339
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#90309C2semidirect
2. C2×#90205C2semidirect
3. C2×C7×#481C2semidirect
4. C2×#89810C2semidirect
5. C22×#6381C2semidirect
6. #11738779C2direct (N × H)
7. C2×#89643C2semidirect
8. C2×#89638C2semidirect
9. C2×#89632C2semidirect
10. C2×#89630C2semidirect
11. C2×#89547C2semidirect
12. C2×#89551C2semidirect
13. C2×#89535C2semidirect
14. C2×#89528C2semidirect
15. C2×(C22⋊D7)⋊C8C2semidirect
16. C2×#89507C2semidirect
32. #90309C22semidirect
34. #90205C22semidirect
45. C7×#481C22semidirect
59. #89810C22semidirect
66. C2×#6381C22semidirect
67. #89643C22semidirect
68. #89638C22semidirect
69. #89632C22semidirect
70. #89630C22semidirect
71. #89551C22semidirect
72. #89547C22semidirect
73. #89535C22semidirect
74. #89528C22semidirect
75. #89507C22semidirect
76. (C22⋊D7)⋊C8C22semidirect
185. C2×#481D7semidirect
321. #481C2×D7semidirect
645. C2×C7#3339semidirect
717. C7C2×#3339semidirect
755. C2#11738779direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903092
C2×#902052
C2×C7×#4812
C2×#898102
C22×#63812
#117387792
C2×#896432
C2×#896382
C2×#896322
C2×#896302
C2×#895472
C2×#895512
C2×#895352
C2×#895282
C2×(C22⋊D7)⋊C82
C2×#895072
C2×#33397