Finite Group Databasebeta

← C2×#11738556 #14221374

Subgroups — C2×#11738556 #14221374

Order 1792.

2094 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90420C211yesmaximal, characteristic, complemented
2C2×#90265C211yesmaximal, characteristic
3C2×C7×#477C211yesmaximal, characteristic, complemented
4C2×#89859C211yesmaximal, characteristic, complemented
5C2×#89794C211yesmaximal, characteristic, complemented
6#11738556C2116yesmaximal, direct product factor
7C2×#89663C211yesmaximal, characteristic, complemented
8C2×#89662C211yesmaximal, characteristic, complemented
9C2×#89653C211yesmaximal, characteristic, complemented
10C2×D7×#107C211yesmaximal, characteristic, complemented
11C2×#89619C211yesmaximal, characteristic, complemented
12C2×#89611C211yesmaximal, characteristic, complemented
13C2×#89575C211yesmaximal, characteristic
14C2×#89576C211yesmaximal, characteristic
15C2×#89571C211yesmaximal, characteristic, complemented
16C2×#89566C211yesmaximal, characteristic, complemented
17C22×#1161C2211yescharacteristic
18C2×C7×C4⋊Q8C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×#6509—21no—
21C2×Q8×Dic7C2211yescharacteristic
22C2×#6507—21no—
23C22×#1131C2211yescharacteristic
24C22×C8×D7C2211yescharacteristic
25#90420—24no—
26#90420C2218yescomplemented
27#90265—24no—
28#90265C2218yes—
29C2×#6459—21no—
30C2×#6456—21no—
31C2×#6456C2211yescharacteristic
32C2×#6455C2211yescharacteristic
33C2×D7×C4⋊C4—21no—
34C2×D7×C4⋊C4C2211yescharacteristic
35C2×D7×C4⋊C4C2211yescharacteristic
36C2×#6453C2211yescharacteristic
37C2×#6452—21no—
38C2×#6451C2211yescharacteristic
39C2×C4×D28—21no—
40C2×C4×D28C2211yescharacteristic
41C2×#6435—21no—
42C2×#6435C2211yescharacteristic
43C2×#6433C2211yescharacteristic
44C7×#477C2218yescomplemented
45C2×C7×#107C2211yescharacteristic
46C2×C7×#107C2211yescharacteristic
47C2×C7×C4⋊C8C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×#6392C2211yescharacteristic
55C2×#6391C2211yescharacteristic
56C2×Dic7⋊C8C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58#89859C2218yescomplemented
59#89794C2218yescomplemented
60C2×#6383C2211yescharacteristic
61C2×#6383C2211yescharacteristic
62C2×#6382C2211yescharacteristic
63C2×#6381C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×C4⋊(C7⋊C8)C2211yescharacteristic
67#89663C2218yescomplemented
68#89662C2218yescomplemented
69#89653C2218yescomplemented
70D7×#107C2218yescomplemented
71#89619C2218yescomplemented
72#89611C2218yescomplemented
73#89576C2218yes—
74#89575C2218yes—
75#89571C2218yescomplemented
76#89566C2218yescomplemented
77C2×#3083—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C2×#1161—22no—
81C2×#1161—24no—
82C2×#1161Q818yescomplemented
83C2×#1161C2314yes—
84C22×D28—21no—
85C22×D28C2311yescharacteristic
86C22×C4×D7—21no—
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×C4×D7—21no—
91C22×C4×D7C2311yescharacteristic
92C22×Dic14—21no—
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C7×C4⋊Q8—22no—
96C7×C4⋊Q8C2314yes—
97C4×C7×Q8—22no—
98C4×C7×Q8C2314yes—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C42×C7—21no—
105C2×C42×C7C2311yescharacteristic
106#6509—28no—
107Q8×Dic7—22no—
108Q8×Dic7C2314yes—
109#6507—28no—
110C2×(C2×D7)⋊C4—21no—
111C2×(C2×D7)⋊C4—21no—
112C2×(C2×D7)⋊C4—21no—
113C2×(C2×D7)⋊C4D411yescharacteristic
114C2×(C2×D7)⋊C4D411yescharacteristic
115C2×C4⋊Dic7—21no—
116C2×C4⋊Dic7—21no—
117C2×C4⋊Dic7C2311yescharacteristic
118C2×C4⋊Dic7C2311yescharacteristic
119C2×C4⋊Dic7C2311yescharacteristic
120C2×Dic7⋊C4—21no—
121C2×Dic7⋊C4—21no—
122C2×Dic7⋊C4—21no—
123C2×Dic7⋊C4—21no—
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4D411yescharacteristic
127C2×Dic7⋊C4D411yescharacteristic
128C2×C4×Dic7—21no—
129C2×C4×Dic7—21no—
130C2×C4×Dic7C2311yescharacteristic
131C22×C7⋊C8C2311yescharacteristic
132C22×C7⋊C8C2311yescharacteristic
133C2×#1131—24no—
134C2×#1131C2314yes—
135C2×C8×D7—24no—
136C2×C8×D7C2314yes—
137#6459—28no—
138#6456—28no—
139#6456—22no—
140#6456C2314yes—
141#6455—22no—
142#6455C2314yes—
143D7×C4⋊C4—22no—
144D7×C4⋊C4—22no—
145D7×C4⋊C4—28no—
146D7×C4⋊C4C2314yes—
147D7×C4⋊C4C2314yes—
148#6453—22no—
149#6453C2314yes—
150#6452—28no—
151#6451—22no—
152#6451C2314yes—
153C4×D28—22no—
154C4×D28—28no—
155C4×D28C2314yes—
156#6435—28no—
157#6435D414yes—
158#6435C2314yes—
159#6433—22no—
160#6433C2314yes—
161C7×#107C2314yes—
162C7×#107C2314yes—
163C7×C4⋊C8C2314yes—
164C7×#103C2314yes—
165C7×#103C2314yes—
166#6409C2314yes—
167#6409C2314yes—
168#6395C2314yes—
169#6395C2314yes—
170#6392C2314yes—
171#6391C2314yes—
172Dic7⋊C8C2314yes—
173Dic7⋊C8C2314yes—
174#6383C2314yes—
175#6383C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180C4⋊(C7⋊C8)C2314yes—
181C2×#544—71no—
182C2×#520—71no—
183#3083—716no—
184C2×#479—71no—
185C2×#479—71no—
186C2×#477—71no—
187C2×#477D711yescharacteristic, complemented
188C2×#478—71no—
189C2×#478—71no—
190C2×#474—71no—
191C2×#474—71no—
192C2×#428—71no—
193C22×#107—71no—
194C2×#424—71no—
195C2×#417—71no—
196C2×#416—71no—
197C23×D7—21no—
198C23×D7C2×D411yescharacteristic
199C2×C7×Q8—21no—
200C2×C7×Q8—24no—
201C2×C7×Q8—22no—
202C2×C7×Q8—82no—
203C2×C7×Q8C2×Q814yes—
204C2×C7×Q8C2412yes—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2411yescharacteristic
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7C2×D411yescharacteristic
216C22×Dic7C2×D411yescharacteristic
217C22×Dic7C2×D411yescharacteristic
218#1161—216no—
219#1161—28no—
220#1161C2×Q8116yescomplemented
221C2×D28—28no—
222C2×D28—24no—
223C2×D28—21no—
224C2×D28—22no—
225C2×D28C2×Q814yes—
226C2×D28C2412yes—
227C2×C4×D7—28no—
228C2×C4×D7—24no—
229C2×C4×D7—24no—
230C2×C4×D7—24no—
231C2×C4×D7—24no—
232C2×C4×D7—24no—
233C2×C4×D7—82no—
234C2×C4×D7—82no—
235C2×C4×D7—82no—
236C2×C4×D7—82no—
237C2×C4×D7C2×D412yes—
238C2×C4×D7C2×Q814yes—
239C2×C4×D7#4114yes—
240C2×C4×D7C2412yes—
241C2×Dic14—24no—
242C2×Dic14—82no—
243C2×C7×C8—22no—
244C2×C7×C8—22no—
245C2×C7×C8C2412yes—
246C2×C7×C8C2412yes—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—21no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4C2412yes—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C42×C7—24no—
256C42×C7C2×D412yes—
257C42×C7C2412yes—
258(C2×D7)⋊C4—24no—
259(C2×D7)⋊C4—24no—
260(C2×D7)⋊C4—24no—
261(C2×D7)⋊C4C2×D414yes—
262(C2×D7)⋊C4C2×D414yes—
263C4⋊Dic7—21no—
264C4⋊Dic7—21no—
265C4⋊Dic7—21no—
266C4⋊Dic7—24no—
267C4⋊Dic7—24no—
268C4⋊Dic7C2412yes—
269C4⋊Dic7C2412yes—
270C4⋊Dic7C2412yes—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4C2×D414yes—
278Dic7⋊C4C2×D414yes—
279C4×Dic7—24no—
280C4×Dic7—24no—
281C4×Dic7C2×D412yes—
282C4×Dic7C2412yes—
283C2×C7⋊C8—22no—
284C2×C7⋊C8—22no—
285C2×C7⋊C8C2412yes—
286C2×C7⋊C8C2412yes—
287#1131—28no—
288C8×D7—28no—
289C22×#41—71no—
290C22×M16—71no—
291C23×C8—71no—
292#544—78no—
293#544—144no—
294C2×C4⋊Q8—71no—
295C2×C4⋊Q8—141no—
296C2×C4⋊Q8C2×D711yescharacteristic
297C2×#125—71no—
298C2×#125—71no—
299C2×#125—141no—
300C2×C22⋊Q8—141no—
301C2×C22⋊Q8—141no—
302#520—78no—
303#520—144no—
304C2×C4×Q8—71no—
305C2×C4×Q8C2×D711yescharacteristic
306C2×C4×D4—71no—
307C2×C4×D4—71no—
308C2×C4×D4—141no—
309C2×C4×D4—141no—
310C2×#117—71no—
311C2×#117—71no—
312C2×#117—141no—
313C22×C4⋊C4—71no—
314C22×C4⋊C4—71no—
315C22×C4⋊C4—141no—
316#479—78no—
317#479—78no—
318#478—78no—
319#478—78no—
320#477—78no—
321#477C2×D718yescomplemented
322#474—78no—
323#474—78no—
324#428—78no—
325C2×#107—71no—
326C2×#107—71no—
327C2×#107—71no—
328C2×#107—71no—
329C2×#107—78no—
330C2×#107C2×D711yescharacteristic
331C2×#107C2×D711yescharacteristic
332C2×#106—71no—
333C2×#106—71no—
334#424—78no—
335C2×C4⋊C8—71no—
336C2×C4⋊C8—71no—
337C2×C4⋊C8—71no—
338C2×C4⋊C8C2×D711yescharacteristic
339#417—78no—
340#416—78no—
341C2×#103—71no—
342C2×#103—71no—
343C2×#103C2×D711yescharacteristic
344C2×#103C2×D711yescharacteristic
345C2×#102—71no—
346C2×#102—71no—
347C2×#102—71no—
348C2×#102—71no—
349C23×C7C22×D411yescharacteristic
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—24no—
353C22×D7—22no—
354C22×D7—42no—
355C22×D7—42no—
356C22×D7C22⋊Q814yes—
357C22×D7C22×D412yes—
358C7×Q8—24no—
359C7×Q8—22no—
360C7×Q8—84no—
361C7×Q8C22×Q814yes—
362C2×C4×C7—24no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7C22×D412yes—
373C2×C4×C7C22×D412yes—
374C2×C4×C7C22×D411yescharacteristic
375C2×C4×C7C22×Q812yes—
376C2×C4×C7C2×#4112yes—
377C2×C4×C7C2511yescharacteristic
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—42no—
384C2×Dic7—42no—
385C2×Dic7—42no—
386C2×Dic7C22⋊Q814yes—
387C2×Dic7C22×D412yes—
388C2×Dic7C22×D412yes—
389C2×Dic7C22×D412yes—
390D28—216no—
391D28—24no—
392D28—22no—
393D28C22×Q814yes—
394C4×D7—216no—
395C4×D7—84no—
396C4×D7—84no—
397C4×D7—84no—
398C4×D7—84no—
399C4×D7C22⋊Q818yes—
400C4×D7C22×Q814yes—
401C4×D7C2×#4114yes—
402Dic14—84no—
403C7×C8—22no—
404C7×C8—22no—
405C7⋊C8—22no—
406C7⋊C8—22no—
407C2×#41—78no—
408C2×#41—74no—
409C2×#41—142no—
410C2×#41—144no—
411C22×Q8—21no—
412C22×Q8—141no—
413C22×Q8C22×D711yescharacteristic
414C22×D4—71no—
415C22×D4—141no—
416C23×C4—71no—
417C23×C4—141no—
418C23×C4—141no—
419C23×C4—141no—
420C23×C4—141no—
421C23×C4—141no—
422C2×M16—74no—
423C2×M16—144no—
424C22×C8—71no—
425C22×C8—71no—
426C22×C8—74no—
427C22×C8—144no—
428C22×C8C22×D711yescharacteristic
429C22×C8C22×D711yescharacteristic
430C4⋊Q8—22no—
431C4⋊Q8—74no—
432C4⋊Q8—142no—
433C4⋊Q8—148no—
434C4⋊Q8C22×D714yes—
435#125—74no—
436#125—74no—
437#125—142no—
438#125—148no—
439#125—142no—
440C22⋊Q8—148no—
441C22⋊Q8—148no—
442C4×Q8—22no—
443C4×Q8—74no—
444C4×Q8—142no—
445C4×Q8C22×D714yes—
446C4×D4—74no—
447C4×D4—74no—
448C4×D4—148no—
449C4×D4—142no—
450C4×D4—148no—
451C4×D4—142no—
452#117—74no—
453#117—74no—
454#117—74no—
455#117—148no—
456#117—142no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—71no—
460C2×C4⋊C4—71no—
461C2×C4⋊C4—71no—
462C2×C4⋊C4—71no—
463C2×C4⋊C4—71no—
464C2×C4⋊C4—74no—
465C2×C4⋊C4—74no—
466C2×C4⋊C4—148no—
467C2×C4⋊C4—142no—
468C2×C4⋊C4—142no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4—141no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4—141no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4C22×D711yescharacteristic
478C2×C4⋊C4C22×D711yescharacteristic
479C2×C4⋊C4C22×D711yescharacteristic
480C2×C22⋊C4—71no—
481C2×C22⋊C4—71no—
482C2×C22⋊C4—141no—
483C2×C22⋊C4—141no—
484C2×C22⋊C4—141no—
485C2×C42—21no—
486C2×C42—71no—
487C2×C42—141no—
488C2×C42—141no—
489C2×C42C22×D711yescharacteristic
490#107—74no—
491#107—74no—
492#107—74no—
493#107—74no—
494#107C22×D714yes—
495#107C22×D714yes—
496#106—74no—
497#106—74no—
498C4⋊C8—74no—
499C4⋊C8—74no—
500C4⋊C8—74no—
501C4⋊C8C22×D714yes—
502#103—74no—
503#103—74no—
504#103C22×D714yes—
505#103C22×D714yes—
506#102—74no—
507#102—74no—
508#102—74no—
509#102—74no—
510C22×C7C2×C22⋊Q812yes—
511C22×C7#57612yes—
512C22×C7#57812yes—
513C22×C7C23×D411yescharacteristic
514C2×D7—28no—
515C2×D7—22no—
516C2×D7—22no—
517C2×D7—24no—
518C2×D7—48no—
519C2×D7—42no—
520C2×D7—42no—
521C2×D7C2×C22⋊Q814yes—
522C4×C7—24no—
523C4×C7—22no—
524C4×C7—22no—
525C4×C7—42no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7C2×C22⋊Q812yes—
529C4×C7C23×Q811yescharacteristic
530C4×C7C22×#4111yescharacteristic
531Dic7—22no—
532Dic7—22no—
533Dic7—42no—
534Dic7—42no—
535Dic7—42no—
536Dic7C2×C22⋊Q814yes—
537C24—71no—
538C24—141no—
539#41—716no—
540#41—1416no—
541#41—148no—
542C2×Q8—21no—
543C2×Q8—24no—
544C2×Q8—22no—
545C2×Q8—82no—
546C2×Q8—144no—
547C2×Q8—562no—
548C2×Q8Q8×D714yes—
549C2×Q8C23×D712yes—
550C2×D4—74no—
551C2×D4—72no—
552C2×D4—144no—
553C2×D4—148no—
554C2×D4—141no—
555C2×D4—142no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—71no—
561C22×C4—72no—
562C22×C4—74no—
563C22×C4—74no—
564C22×C4—72no—
565C22×C4—71no—
566C22×C4—71no—
567C22×C4—144no—
568C22×C4—148no—
569C22×C4—144no—
570C22×C4—144no—
571C22×C4—144no—
572C22×C4—141no—
573C22×C4—141no—
574C22×C4—141no—
575C22×C4—144no—
576C22×C4—562no—
577C22×C4—562no—
578C22×C4—562no—
579C22×C4—562no—
580C22×C4D4×D711yescharacteristic
581C22×C4D4×D711yescharacteristic
582C22×C4C23×D711yescharacteristic
583M16—148no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—72no—
587C2×C8—72no—
588C2×C8—148no—
589C2×C8—142no—
590C2×C8—142no—
591C2×C8C23×D712yes—
592C2×C8C23×D712yes—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—74no—
599C4⋊C4—74no—
600C4⋊C4—72no—
601C4⋊C4—72no—
602C4⋊C4—72no—
603C4⋊C4—144no—
604C4⋊C4—144no—
605C4⋊C4—144no—
606C4⋊C4—144no—
607C4⋊C4—144no—
608C4⋊C4—144no—
609C4⋊C4—144no—
610C4⋊C4—144no—
611C4⋊C4—141no—
612C4⋊C4—141no—
613C4⋊C4—141no—
614C4⋊C4C23×D712yes—
615C4⋊C4C23×D712yes—
616C4⋊C4C23×D712yes—
617C22⋊C4—74no—
618C22⋊C4—74no—
619C22⋊C4—144no—
620C22⋊C4—144no—
621C22⋊C4—144no—
622C42—24no—
623C42—72no—
624C42—72no—
625C42—144no—
626C42—144no—
627C42D4×D712yes—
628C42C23×D712yes—
629C2×C7#308314yescomplemented
630C2×C7C22×C22⋊Q811yescharacteristic
631C2×C7C2×#57611yescharacteristic
632C2×C7C2×#57811yescharacteristic
633D7—24no—
634D7—44no—
635C23—74no—
636C23—72no—
637C23—142no—
638C23—142no—
639C23—144no—
640C23—142no—
641C23—282no—
642C23—282no—
643C23C2×D4×D711yescharacteristic
644Q8—24no—
645Q8—22no—
646Q8—84no—
647Q8—564no—
648Q8C2×Q8×D714yes—
649D4—74no—
650D4—1416no—
651D4—144no—
652D4—142no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—74no—
664C2×C4—72no—
665C2×C4—78no—
666C2×C4—74no—
667C2×C4—74no—
668C2×C4—72no—
669C2×C4—72no—
670C2×C4—1416no—
671C2×C4—142no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—142no—
675C2×C4—142no—
676C2×C4—282no—
677C2×C4—282no—
678C2×C4—282no—
679C2×C4—564no—
680C2×C4—564no—
681C2×C4—564no—
682C2×C4—564no—
683C2×C4C2×D4×D712yes—
684C2×C4C2×D4×D712yes—
685C2×C4C2×D4×D711yescharacteristic
686C2×C4C2×Q8×D712yes—
687C2×C4D7×#4112yes—
688C2×C4C24×D711yescharacteristic
689C8—22no—
690C8—22no—
691C8—142no—
692C8—142no—
693C7C2×#308311yescharacteristic, complemented, Sylow
694C22—74no—
695C22—142no—
696C22—148no—
697C22—142no—
698C22—144no—
699C22—282no—
700C22—288no—
701C22—282no—
702C22D7×C22⋊Q812yes—
703C22#9045712yes—
704C22#9046512yes—
705C22C22×D4×D711yescharacteristic
706C4—22no—
707C4—24no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—74no—
713C4—142no—
714C4—142no—
715C4—282no—
716C4—282no—
717C4—282no—
718C4D7×C22⋊Q812yes—
719C4C22×Q8×D711yescharacteristic
720C4C2×D7×#4111yescharacteristic
721C2—144no—
722C2—284no—
723C2#1173855614yesdirect product factor
724C2C2×D7×C22⋊Q811yescharacteristic
725C2C2×#9045711yescharacteristic
726C2C2×#9046511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#477C2
socleC23×C7C22×D4
prime radicalC22×#1161C22
hypercenterC2×#477D7
hypocenterC7C2×#3083
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#90420C2semidirect
3. C2×C7×#477C2semidirect
4. C2×#89859C2semidirect
5. C2×#89794C2semidirect
6. #11738556C2direct (N × H)
7. C2×#89663C2semidirect
8. C2×#89662C2semidirect
9. C2×#89653C2semidirect
10. C2×D7×#107C2semidirect
11. C2×#89619C2semidirect
12. C2×#89611C2semidirect
15. C2×#89571C2semidirect
16. C2×#89566C2semidirect
26. #90420C22semidirect
44. C7×#477C22semidirect
58. #89859C22semidirect
59. #89794C22semidirect
67. #89663C22semidirect
68. #89662C22semidirect
69. #89653C22semidirect
70. D7×#107C22semidirect
71. #89619C22semidirect
72. #89611C22semidirect
75. #89571C22semidirect
76. #89566C22semidirect
82. C2×#1161Q8semidirect
187. C2×#477D7semidirect
220. #1161C2×Q8semidirect
321. #477C2×D7semidirect
629. C2×C7#3083semidirect
693. C7C2×#3083semidirect
723. C2#11738556direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904202
C2×#902652
C2×C7×#4772
C2×#898592
C2×#897942
#117385562
C2×#896632
C2×#896622
C2×#896532
C2×D7×#1072
C2×#896192
C2×#896112
C2×#895752
C2×#895762
C2×#895712
C2×#895662
C2×#30837