Finite Group Databasebeta

← C2×#11741094 #14232407

Subgroups — C2×#11741094 #14232407

Order 1792.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#555C211yesmaximal, characteristic
2C2×#90232C211yesmaximal, characteristic, complemented
3#11741094C2116yesmaximal, direct product factor
4C2×#89866C211yesmaximal, characteristic, complemented
5C2×#89852C211yesmaximal, characteristic, complemented
6C2×#89814C211yesmaximal, characteristic, complemented
7C2×#89813C211yesmaximal, characteristic, complemented
8C2×#89806C211yesmaximal, characteristic, complemented
9C2×#89807C211yesmaximal, characteristic, complemented
10C2×#89783C211yesmaximal, characteristic, complemented
11C2×#89781C211yesmaximal, characteristic, complemented
12C2×#89790C211yesmaximal, characteristic, complemented
13C2×#89768C211yesmaximal, characteristic, complemented
14C2×#89768C211yesmaximal, characteristic, complemented
15C2×#89767C211yesmaximal, characteristic, complemented
16C2×#89770C211yesmaximal, characteristic, complemented
17C7×#555—24no—
18C7×#555C2218yes—
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#124—21no—
21C2×C7×#124—21no—
22C2×C7×#121—21no—
23C2×C7×#121C2211yescharacteristic
24C2×C7×#121C2211yescharacteristic
25C2×C4×C7×D4C2211yescharacteristic
26C2×C4×C7×D4C2211yescharacteristic
27C2×C7×#117—21no—
28C2×C7×#117C2211yescharacteristic
29C2×C7×#117C2211yescharacteristic
30C2×#6498—21no—
31C22×#1142C2211yescharacteristic
32C2×#6489C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C2×#6487C2211yescharacteristic
35C2×#6487C2211yescharacteristic
36C22×#1136C2211yescharacteristic
37C23×C7⋊C8C2211yescharacteristic
38#90232—24no—
39#90232C2218yescomplemented
40C2×#6452—21no—
41C2×#6442—21no—
42C2×#6440—21no—
43C2×#6433C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×#6406C2211yescharacteristic
46C2×#6406C2211yescharacteristic
47C2×#6406C2211yescharacteristic
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49C2×C22⋊(C7⋊C8)C2211yescharacteristic
50#89866C2218yescomplemented
51#89852C2218yescomplemented
52#89814C2218yescomplemented
53#89813C2218yescomplemented
54#89807C2218yescomplemented
55#89806C2218yescomplemented
56#89790C2218yescomplemented
57#89783C2218yescomplemented
58#89781C2218yescomplemented
59#89770C2218yescomplemented
60#89768C2218yescomplemented
61#89768C2218yescomplemented
62#89767C2218yescomplemented
63C2×#6384C2211yescharacteristic
64C2×#6384C2211yescharacteristic
65C2×#6384C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71C2×#6381C2211yescharacteristic
72C2×#6381C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3348—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×D4—21no—
80C22×C7×D4—21no—
81C22×C7×D4D411yescharacteristic
82C22×C7×D4C2311yescharacteristic
83C23×C4×C7—21no—
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×Dic7—21no—
87C22×Dic14C2311yescharacteristic
88C7×C4⋊Q8—22no—
89C7×C4⋊Q8C2314yes—
90C7×#124—28no—
91C7×#124—28no—
92C7×#121—28no—
93C7×#121—22no—
94C7×#121—22no—
95C7×#121C2314yes—
96C7×#121C2314yes—
97C4×C7×D4—22no—
98C4×C7×D4D414yes—
99C4×C7×D4C2314yes—
100C4×C7×D4C2314yes—
101C7×#117—22no—
102C7×#117—22no—
103C7×#117—28no—
104C7×#117C2314yes—
105C7×#117C2314yes—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4D411yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4D411yescharacteristic
117C2×C7×C22⋊C4D411yescharacteristic
118C2×C42×C7—21no—
119C2×C42×C7—21no—
120C2×C42×C7C2311yescharacteristic
121C2×C22⋊Dic7—21no—
122C2×C22⋊Dic7—21no—
123C2×C22⋊Dic7—21no—
124#6498—28no—
125C2×#1142—24no—
126C2×#1142C2314yes—
127#6489—22no—
128#6489C2314yes—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—22no—
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2314yes—
135#6487—22no—
136#6487—22no—
137#6487C2314yes—
138#6487C2314yes—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×C4×Dic7—21no—
145C2×C4×Dic7—21no—
146C2×#1136—24no—
147C2×#1136C2314yes—
148C22×C7⋊C8—24no—
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2314yes—
153C22×C7⋊C8C2311yescharacteristic
154#6452—28no—
155#6442—28no—
156#6440—28no—
157#6433—22no—
158#6433C2314yes—
159C4×Dic14—22no—
160C4×Dic14C2314yes—
161#6406C2314yes—
162#6406C2314yes—
163#6406C2314yes—
164C22⋊(C7⋊C8)C2314yes—
165C22⋊(C7⋊C8)C2314yes—
166#6384C2314yes—
167#6384C2314yes—
168#6384C2314yes—
169#6382C2314yes—
170#6382C2314yes—
171#6382C2314yes—
172#6382C2314yes—
173#6382C2314yes—
174#6381C2314yes—
175#6381C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178C4⋊(C7⋊C8)C2314yes—
179#6377C2314yes—
180C2×#555D711yescharacteristic
181C2×#552—71no—
182#3348—716no—
183C2×#501—71no—
184C2×#481—71no—
185C2×#485—71no—
186C2×#485—71no—
187C2×#482—71no—
188C2×#475—71no—
189C2×#478—71no—
190C2×#468—71no—
191C2×#465—71no—
192C2×#440—71no—
193C2×#435—71no—
194C2×#428—71no—
195C2×#427—71no—
196C24×C7—21no—
197C24×C7C2×D411yescharacteristic
198C24×C7C2×D411yescharacteristic
199C2×C7×Q8—24no—
200C2×C7×Q8—82no—
201C2×C7×D4—24no—
202C2×C7×D4—24no—
203C2×C7×D4—21no—
204C2×C7×D4—22no—
205C2×C7×D4—22no—
206C2×C7×D4—42no—
207C2×C7×D4—82no—
208C2×C7×D4—82no—
209C2×C7×D4C2×D414yes—
210C2×C7×D4C2412yes—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—24no—
219C22×C4×C7—44no—
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D412yes—
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2411yescharacteristic
229C22×Dic7—24no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—44no—
235C2×Dic14—22no—
236C2×Dic14—22no—
237C2×Dic14—21no—
238C2×Dic14C2412yes—
239C7×C4⋊C4—24no—
240C7×C4⋊C4—21no—
241C7×C4⋊C4—21no—
242C7×C4⋊C4—21no—
243C7×C4⋊C4C2×D414yes—
244C7×C4⋊C4C2412yes—
245C7×C4⋊C4C2412yes—
246C7×C4⋊C4C2412yes—
247C7×C22⋊C4—24no—
248C7×C22⋊C4—24no—
249C7×C22⋊C4—24no—
250C7×C22⋊C4—24no—
251C7×C22⋊C4—24no—
252C7×C22⋊C4C2×D414yes—
253C7×C22⋊C4C2×D414yes—
254C42×C7—24no—
255C42×C7—24no—
256C42×C7C2×D412yes—
257C42×C7C2412yes—
258C22⋊Dic7—24no—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261#1142—28no—
262C4⋊Dic7—21no—
263C4⋊Dic7—21no—
264C4⋊Dic7—21no—
265C4⋊Dic7—24no—
266C4⋊Dic7C2412yes—
267C4⋊Dic7C2412yes—
268C4⋊Dic7C2412yes—
269Dic7⋊C4—24no—
270Dic7⋊C4—24no—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274C4×Dic7—24no—
275C4×Dic7—24no—
276#1136—28no—
277C2×C7⋊C8—22no—
278C2×C7⋊C8—22no—
279C2×C7⋊C8—22no—
280C2×C7⋊C8—28no—
281C2×C7⋊C8#4114yes—
282C2×C7⋊C8C2412yes—
283C2×C7⋊C8C2412yes—
284C2×C7⋊C8C2412yes—
285C2×C7⋊C8C2412yes—
286C22×SD16—71no—
287C22×M16—71no—
288C23×C8—71no—
289#555—24no—
290#555C2×D718yes—
291#552—78no—
292#552—144no—
293C2×C4⋊Q8C2×D711yescharacteristic
294C2×#126—141no—
295C2×#125—71no—
296C2×#125—141no—
297C2×#124—21no—
298C2×#124—21no—
299C2×#123—141no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8—71no—
302C2×#121—21no—
303C2×#121C2×D711yescharacteristic
304C2×#121C2×D711yescharacteristic
305C2×C4×Q8—71no—
306C2×C4×D4C2×D711yescharacteristic
307C2×C4×D4C2×D711yescharacteristic
308C2×#117—21no—
309C2×#117—71no—
310C2×#117—141no—
311C2×#117C2×D711yescharacteristic
312C2×#117C2×D711yescharacteristic
313C22×C4⋊C4—71no—
314#501—78no—
315#485—78no—
316#485—78no—
317#482—78no—
318#481—78no—
319#478—78no—
320#475—78no—
321#468—78no—
322#465—78no—
323#440—78no—
324#435—78no—
325#428—78no—
326#427—78no—
327C2×#107—71no—
328C2×#107—71no—
329C2×#107—71no—
330C2×#107—71no—
331C2×#106—71no—
332C2×#106—71no—
333C2×#106—71no—
334C2×#106—71no—
335C2×#106—71no—
336C2×C4⋊C8—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#103—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×C22⋊C8—71no—
344C2×C22⋊C8—71no—
345C2×#97—71no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7C22×D412yes—
357C23×C7C22×D412yes—
358C23×C7C22×D411yescharacteristic
359C7×Q8—84no—
360C7×D4—22no—
361C7×D4—22no—
362C7×D4—44no—
363C7×D4—42no—
364C7×D4—84no—
365C7×D4—84no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—24no—
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—22no—
378C2×C4×C7—22no—
379C2×C4×C7—48no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D412yes—
386C2×C4×C7C22×D412yes—
387C2×C4×C7C22×D411yescharacteristic
388C2×C4×C7C2×#4112yes—
389C2×C4×C72−1+412yes—
390C2×C4×C7C2511yescharacteristic
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—48no—
396C2×Dic7—42no—
397C2×Dic7—42no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400Dic14—22no—
401Dic14—22no—
402Dic14—42no—
403C7⋊C8—22no—
404C7⋊C8—22no—
405C7⋊C8—22no—
406C7⋊C8C2×#4114yes—
407C22×Q8—21no—
408C22×Q8—71no—
409C22×D4—21no—
410C22×D4—21no—
411C22×D4C22⋊D711yescharacteristic
412C22×D4C22×D711yescharacteristic
413C23×C4—21no—
414C23×C4—141no—
415C23×C4C22×D711yescharacteristic
416C23×C4C22×D711yescharacteristic
417C2×SD16—74no—
418C2×SD16—144no—
419C2×M16—74no—
420C2×M16—144no—
421C22×C8—71no—
422C22×C8—71no—
423C22×C8—74no—
424C22×C8—71no—
425C22×C8—71no—
426C22×C8—144no—
427C4⋊Q8—22no—
428C4⋊Q8C22×D714yes—
429#126—148no—
430#125—74no—
431#125—148no—
432#125—142no—
433#124—28no—
434#124—28no—
435#123—148no—
436C22⋊Q8—74no—
437C22⋊Q8—74no—
438C22⋊Q8—142no—
439C22⋊Q8—142no—
440#121—28no—
441#121—22no—
442#121—22no—
443#121C22×D714yes—
444#121C22×D714yes—
445C4×Q8—74no—
446C4×Q8—142no—
447C4×D4—22no—
448C4×D4C22⋊D714yes—
449C4×D4C22×D714yes—
450C4×D4C22×D714yes—
451#117—22no—
452#117—22no—
453#117—28no—
454#117—74no—
455#117—142no—
456#117—148no—
457#117C22×D714yes—
458#117C22×D714yes—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—71no—
461C2×C4⋊C4—71no—
462C2×C4⋊C4—74no—
463C2×C4⋊C4—71no—
464C2×C4⋊C4—141no—
465C2×C4⋊C4—142no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4C22⋊D711yescharacteristic
472C2×C4⋊C4C22×D711yescharacteristic
473C2×C4⋊C4C22×D711yescharacteristic
474C2×C4⋊C4C22×D711yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—141no—
481C2×C22⋊C4—141no—
482C2×C22⋊C4—141no—
483C2×C22⋊C4C22⋊D711yescharacteristic
484C2×C22⋊C4C22⋊D711yescharacteristic
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—141no—
488C2×C42—141no—
489C2×C42C22×D711yescharacteristic
490#107—74no—
491#107—74no—
492#107—74no—
493#107—74no—
494#106—74no—
495#106—74no—
496#106—74no—
497#106—74no—
498#106—74no—
499C4⋊C8—74no—
500#103—74no—
501#103—74no—
502#103—74no—
503#102—74no—
504#102—74no—
505#102—74no—
506C22⋊C8—74no—
507C22⋊C8—74no—
508#97—74no—
509C22×C7—22no—
510C22×C7—22no—
511C22×C7—22no—
512C22×C7—22no—
513C22×C7—22no—
514C22×C7—22no—
515C22×C7—44no—
516C22×C7—44no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7—84no—
521C22×C7#54712yes—
522C22×C7#57512yes—
523C22×C7#57712yes—
524C22×C7C23×D411yescharacteristic
525C4×C7—22no—
526C4×C7—22no—
527C4×C7—22no—
528C4×C7—22no—
529C4×C7—42no—
530C4×C7—42no—
531C4×C7—42no—
532C4×C7#54712yes—
533C4×C7C22×#4111yescharacteristic
534C4×C7C2×2−1+411yescharacteristic
535Dic7—42no—
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539C24—21no—
540C24C2×C22⋊D711yescharacteristic
541C24C2×C22⋊D711yescharacteristic
542C2×Q8—24no—
543C2×Q8—72no—
544C2×Q8—82no—
545C2×Q8—141no—
546C2×Q8—142no—
547C2×Q8—142no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4C2×C22⋊D714yes—
557C2×D4C23×D712yes—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—44no—
567C22×C4—144no—
568C22×C4—141no—
569C22×C4—141no—
570C22×C4—141no—
571C22×C4—141no—
572C22×C4—284no—
573C22×C4C2×C22⋊D712yes—
574C22×C4C2×C22⋊D712yes—
575C22×C4C2×C22⋊D711yescharacteristic
576C22×C4C2×C22⋊D711yescharacteristic
577C22×C4C2×C22⋊D711yescharacteristic
578C22×C4C2×C22⋊D711yescharacteristic
579C22×C4C23×D712yes—
580C22×C4C23×D712yes—
581C22×C4C23×D711yescharacteristic
582SD16—148no—
583M16—148no—
584C2×C8—74no—
585C2×C8—72no—
586C2×C8—72no—
587C2×C8—72no—
588C2×C8—72no—
589C2×C8—148no—
590C2×C8—142no—
591C2×C8—142no—
592C2×C8—142no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—72no—
598C4⋊C4—72no—
599C4⋊C4—72no—
600C4⋊C4—144no—
601C4⋊C4—144no—
602C4⋊C4—144no—
603C4⋊C4—144no—
604C4⋊C4—144no—
605C4⋊C4—141no—
606C4⋊C4—141no—
607C4⋊C4—144no—
608C4⋊C4—141no—
609C4⋊C4C2×C22⋊D714yes—
610C4⋊C4C23×D712yes—
611C4⋊C4C23×D712yes—
612C4⋊C4C23×D712yes—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—144no—
619C22⋊C4—144no—
620C22⋊C4—144no—
621C22⋊C4C2×C22⋊D714yes—
622C22⋊C4C2×C22⋊D714yes—
623C42—24no—
624C42—24no—
625C42—144no—
626C42—144no—
627C42C2×C22⋊D712yes—
628C42C23×D712yes—
629C2×C7—42no—
630C2×C7—42no—
631C2×C7—82no—
632C2×C7#334814yescomplemented
633C2×C7C2×#54711yescharacteristic
634C2×C7C2×#57511yescharacteristic
635C2×C7C2×#57711yescharacteristic
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23C22×C22⋊D712yes—
647C23C22×C22⋊D712yes—
648C23C22×C22⋊D711yescharacteristic
649Q8—84no—
650Q8—142no—
651Q8—142no—
652Q8—282no—
653D4—22no—
654D4—22no—
655D4—44no—
656D4—42no—
657D4—84no—
658D4—84no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—48no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—142no—
677C2×C4—142no—
678C2×C4—142no—
679C2×C4—142no—
680C2×C4—288no—
681C2×C4—282no—
682C2×C4—282no—
683C2×C4—282no—
684C2×C4—282no—
685C2×C4D7×#4112yes—
686C2×C4#655412yes—
687C2×C4C22×C22⋊D712yes—
688C2×C4C22×C22⋊D712yes—
689C2×C4C22×C22⋊D712yes—
690C2×C4C22×C22⋊D712yes—
691C2×C4C22×C22⋊D711yescharacteristic
692C2×C4C24×D711yescharacteristic
693C8—74no—
694C8—142no—
695C8—142no—
696C8—142no—
697C7C2×#334811yescharacteristic, complemented, Sylow
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22#9051312yes—
711C22#9051512yes—
712C22#9052712yes—
713C22C23×C22⋊D711yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—282no—
722C4—282no—
723C4—282no—
724C4—282no—
725C4#9051512yes—
726C4C2×D7×#4111yescharacteristic
727C4C2×#655411yescharacteristic
728C2—42no—
729C2—42no—
730C2—82no—
731C2#1174109414yesdirect product factor
732C2C2×#9051311yescharacteristic
733C2C2×#9051511yescharacteristic
734C2C2×#9052711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
Fitting, prime radicalC2×C7×#555C2
socleC23×C7C22×D4
hypercenterC2×#555D7
hypocenterC7C2×#3348
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
2. C2×#90232C2semidirect
3. #11741094C2direct (N × H)
4. C2×#89866C2semidirect
5. C2×#89852C2semidirect
6. C2×#89814C2semidirect
7. C2×#89813C2semidirect
8. C2×#89806C2semidirect
9. C2×#89807C2semidirect
10. C2×#89783C2semidirect
11. C2×#89781C2semidirect
12. C2×#89790C2semidirect
13. C2×#89768C2semidirect
14. C2×#89768C2semidirect
15. C2×#89767C2semidirect
16. C2×#89770C2semidirect
39. #90232C22semidirect
50. #89866C22semidirect
51. #89852C22semidirect
52. #89814C22semidirect
53. #89813C22semidirect
54. #89807C22semidirect
55. #89806C22semidirect
56. #89790C22semidirect
57. #89783C22semidirect
58. #89781C22semidirect
59. #89770C22semidirect
60. #89768C22semidirect
61. #89768C22semidirect
62. #89767C22semidirect
632. C2×C7#3348semidirect
697. C7C2×#3348semidirect
731. C2#11741094direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5552
C2×#902322
#117410942
C2×#898662
C2×#898522
C2×#898142
C2×#898132
C2×#898062
C2×#898072
C2×#897832
C2×#897812
C2×#897902
C2×#897682
C2×#897672
C2×#897702
C2×#33487