Finite Group Databasebeta

← C2×#11737621 #14222076

Subgroups — C2×#11737621 #14222076

Order 1792.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90503C211yesmaximal, characteristic, complemented
2C2×#90334C211yesmaximal, characteristic
3C2×C7×#451C211yesmaximal, characteristic, complemented
4C2×#89999C211yesmaximal, characteristic
5C2×#89957C211yesmaximal, characteristic, complemented
6C2×#89957C211yesmaximal, characteristic, complemented
7C2×#89956C211yesmaximal, characteristic, complemented
8C2×Q16×Dic7C211yesmaximal, characteristic, complemented
9C2×#89817C211yesmaximal, characteristic, complemented
10#11737621C2116yesmaximal, direct product factor
11C2×#89566C211yesmaximal, characteristic, complemented
12C2×#89563C211yesmaximal, characteristic, complemented
13C2×#89589C211yesmaximal, characteristic, complemented
14C2×#89560C211yesmaximal, characteristic, complemented
15C2×#89509C211yesmaximal, characteristic
16C2×#89492C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C22×C7×Q16C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×#6510C2211yescharacteristic
22#90503—24no—
23#90503C2218yescomplemented
24C2×Q8×Dic7—21no—
25C2×Q8×Dic7—21no—
26C2×Q8×Dic7C2211yescharacteristic
27C2×Q8×Dic7C2211yescharacteristic
28C2×Q8×Dic7C2211yescharacteristic
29C2×Q8×Dic7C2211yescharacteristic
30C2×Q8×Dic7C2211yescharacteristic
31C22×#1143C2211yescharacteristic
32C22×#1143C2211yescharacteristic
33C2×#6493C2211yescharacteristic
34C2×#6489—21no—
35C2×#6489—21no—
36C2×#6489C2211yescharacteristic
37C2×#6489C2211yescharacteristic
38#90334—24no—
39#90334C2218yes—
40C2×#6461—21no—
41C2×#6460—21no—
42C2×#6456C2211yescharacteristic
43C2×#6451C2211yescharacteristic
44C2×#6448—21no—
45C2×#6446—21no—
46C7×#451C2218yescomplemented
47C2×C7×#103C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50#89999C2218yes—
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×C22⋊(C7⋊C8)C2211yescharacteristic
56#89957C2218yescomplemented
57#89957C2218yescomplemented
58#89956C2218yescomplemented
59Q16×Dic7C2218yescomplemented
60C2×#6395C2211yescharacteristic
61C2×#6395C2211yescharacteristic
62C2×#6392C2211yescharacteristic
63C2×#6391C2211yescharacteristic
64C2×#6389C2211yescharacteristic
65C2×Dic7⋊C8C2211yescharacteristic
66C2×Dic7⋊C8C2211yescharacteristic
67C2×C8×Dic7C2211yescharacteristic
68#89817C2218yescomplemented
69C2×#6382C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71#89589C2218yescomplemented
72#89566C2218yescomplemented
73#89563C2218yescomplemented
74#89560C2218yescomplemented
75#89509C2218yes—
76#89492C2218yescomplemented
77C2×#3121—71nomaximal, Sylow
78C22×C7×Q8—24no—
79C22×C7×Q8—24no—
80C22×C7×Q8—21no—
81C22×C7×Q8—22no—
82C22×C7×Q8C2314yes—
83C22×C7×Q8C2311yescharacteristic
84C22×C7×Q8C2311yescharacteristic
85C22×C7×Q8C2311yescharacteristic
86C23×C4×C7—21no—
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—21no—
89C22×D28C2311yescharacteristic
90C22×C4×D7—21no—
91C22×Dic14—21no—
92C2×C7×Q16—24no—
93C2×C7×Q16—24no—
94C2×C7×Q16C2314yes—
95C2×C7×Q16C2314yes—
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2311yescharacteristic
98C7×C22⋊Q8—22no—
99C7×C22⋊Q8C2314yes—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C22⋊C4—21no—
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7D411yescharacteristic
105C2×C22⋊Dic7D411yescharacteristic
106#6510—22no—
107#6510C2314yes—
108Q8×Dic7—28no—
109Q8×Dic7—28no—
110Q8×Dic7—22no—
111Q8×Dic7—22no—
112Q8×Dic7—22no—
113Q8×Dic7—22no—
114Q8×Dic7—22no—
115Q8×Dic7C2314yes—
116Q8×Dic7C2314yes—
117Q8×Dic7C2314yes—
118Q8×Dic7C2314yes—
119Q8×Dic7C2314yes—
120C2×#1143—24no—
121C2×#1143—24no—
122C2×#1143C2314yes—
123C2×#1143C2314yes—
124#6493—22no—
125#6493C2314yes—
126C2×(C2×D7)⋊C4—21no—
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4—21no—
129C2×(C2×D7)⋊C4—21no—
130#6489—22no—
131#6489—28no—
132#6489—28no—
133#6489D414yes—
134#6489C2314yes—
135#6489C2314yes—
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7—21no—
138C2×C4⋊Dic7—21no—
139C2×C4⋊Dic7—21no—
140C2×C4⋊Dic7—21no—
141C2×C4⋊Dic7D411yescharacteristic
142C2×C4⋊Dic7D411yescharacteristic
143C2×C4⋊Dic7C2311yescharacteristic
144C2×C4⋊Dic7C2311yescharacteristic
145C2×C4⋊Dic7C2311yescharacteristic
146C2×Dic7⋊C4—21no—
147C2×C4×Dic7—21no—
148C2×C4×Dic7—21no—
149C2×C4×Dic7—21no—
150C2×C4×Dic7—21no—
151C2×C4×Dic7—21no—
152C2×C4×Dic7—21no—
153C2×C4×Dic7C2311yescharacteristic
154C2×C4×Dic7C2311yescharacteristic
155C22×C7⋊C8C2311yescharacteristic
156C22×C7⋊C8C2311yescharacteristic
157#6461—28no—
158#6460—28no—
159#6456—22no—
160#6456C2314yes—
161#6451—22no—
162#6451C2314yes—
163#6448—28no—
164#6446—28no—
165C7×#103C2314yes—
166C7×#103C2314yes—
167C7×C22⋊C8C2314yes—
168#6409C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171#6409C2314yes—
172C22⋊(C7⋊C8)C2314yes—
173#6395C2314yes—
174#6395C2314yes—
175#6392C2314yes—
176#6391C2314yes—
177#6389C2314yes—
178Dic7⋊C8C2314yes—
179Dic7⋊C8C2314yes—
180C8×Dic7C2314yes—
181#6382C2314yes—
182#6381C2314yes—
183C2×#542—71no—
184C2×#519—71no—
185#3121—716no—
186C2×#485—71no—
187C2×#482—71no—
188C2×#477—71no—
189C2×#475—71no—
190C2×#464—71no—
191C2×#464—71no—
192C2×#451D711yescharacteristic, complemented
193C2×#448—71no—
194C2×#441—71no—
195C2×#440—71no—
196C2×C4×Q16—71no—
197C2×C4×SD16—71no—
198C2×#433—71no—
199C24×C7C2×D411yescharacteristic
200C23×D7—21no—
201C2×C7×Q8—216no—
202C2×C7×Q8—28no—
203C2×C7×Q8—28no—
204C2×C7×Q8—28no—
205C2×C7×Q8—24no—
206C2×C7×Q8—21no—
207C2×C7×Q8—21no—
208C2×C7×Q8—21no—
209C2×C7×Q8—22no—
210C2×C7×Q8—22no—
211C2×C7×Q8—22no—
212C2×C7×Q8—22no—
213C2×C7×Q8#4114yes—
214C2×C7×Q8#4114yes—
215C2×C7×Q8C2412yes—
216C2×C7×Q8C2412yes—
217C2×C7×Q8C2412yes—
218C22×C4×C7—28no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—24no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2411yescharacteristic
230C2×C22⋊D7—24no—
231C2×C22⋊D7—82no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7C2×D411yescharacteristic
236C22×Dic7C2×D411yescharacteristic
237C22×Dic7C2×D411yescharacteristic
238C22×Dic7C2×D411yescharacteristic
239C2×D28—22no—
240C2×D28—22no—
241C2×D28—21no—
242C2×D28C2412yes—
243C2×C4×D7—24no—
244C2×C4×D7—82no—
245C2×Dic14—24no—
246C2×Dic14—82no—
247C7×Q16—28no—
248C7×Q16—28no—
249C2×C7×C8—22no—
250C2×C7×C8—22no—
251C2×C7×C8C2412yes—
252C2×C7×C8C2412yes—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4C2412yes—
256C7×C22⋊C4—24no—
257C22⋊Dic7—24no—
258C22⋊Dic7C2×D414yes—
259C22⋊Dic7C2×D414yes—
260#1143—28no—
261#1143—28no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—24no—
270C4⋊Dic7—24no—
271C4⋊Dic7—24no—
272C4⋊Dic7—24no—
273C4⋊Dic7—24no—
274C4⋊Dic7C2×D414yes—
275C4⋊Dic7C2×D414yes—
276C4⋊Dic7C2412yes—
277C4⋊Dic7C2412yes—
278C4⋊Dic7C2412yes—
279Dic7⋊C4—24no—
280C4×Dic7—24no—
281C4×Dic7—24no—
282C4×Dic7—24no—
283C4×Dic7—24no—
284C4×Dic7—24no—
285C4×Dic7—24no—
286C4×Dic7C2×D412yes—
287C4×Dic7C2×D412yes—
288C4×Dic7C2412yes—
289C4×Dic7C2412yes—
290C2×C7⋊C8—22no—
291C2×C7⋊C8—22no—
292C2×C7⋊C8C2412yes—
293C2×C7⋊C8C2412yes—
294C23×Q8C2×D711yescharacteristic
295C22×Q16C2×D711yescharacteristic
296C22×Q16C2×D711yescharacteristic
297C22×SD16—71no—
298C22×SD16—71no—
299#542—78no—
300#542—144no—
301C2×C4⋊Q8—71no—
302C2×#126—141no—
303C2×#124—71no—
304C2×#124—141no—
305C2×#123—141no—
306C2×C22⋊Q8—141no—
307C2×C22⋊Q8C2×D711yescharacteristic
308C2×#121—71no—
309#519—78no—
310#519—144no—
311C2×C4×Q8—71no—
312C2×C4×Q8—71no—
313C2×C4×Q8—71no—
314C2×C4×Q8—71no—
315C2×C4×Q8—71no—
316C2×C4×Q8—141no—
317C2×C4×Q8—141no—
318C2×C4×D4—71no—
319C2×#117—71no—
320C2×#117—71no—
321C2×#117—141no—
322C2×#117—141no—
323#485—78no—
324#482—78no—
325#477—78no—
326#475—78no—
327#464—78no—
328#464—78no—
329#451C2×D718yescomplemented
330#448—78no—
331#441—78no—
332#440—78no—
333C4×Q16—78no—
334C4×SD16—78no—
335#433—78no—
336C2×#107—71no—
337C2×#107—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×C4⋊C8—71no—
341C2×C4⋊C8—71no—
342C2×#103—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#103C2×D711yescharacteristic
347C2×#103C2×D711yescharacteristic
348C2×#102—71no—
349C2×#102—71no—
350C2×C22⋊C8—71no—
351C2×C22⋊C8C2×D711yescharacteristic
352C2×#97—71no—
353C2×C4×C8—71no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7C22×D412yes—
358C23×C7C22×D411yescharacteristic
359C22×D7—22no—
360C22×D7—42no—
361C22×D7—42no—
362C22×D7—42no—
363C7×Q8—216no—
364C7×Q8—24no—
365C7×Q8—24no—
366C7×Q8—22no—
367C7×Q8—22no—
368C7×Q8—22no—
369C7×Q8—22no—
370C7×Q8—42no—
371C7×Q8C2×#4114yes—
372C7×Q8C2×#4114yes—
373C2×C4×C7—216no—
374C2×C4×C7—24no—
375C2×C4×C7—24no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—24no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—42no—
385C2×C4×C7—42no—
386C2×C4×C7C22×D412yes—
387C2×C4×C7C22×D411yescharacteristic
388C2×C4×C7C2×#4112yes—
389C2×C4×C7C2×#4112yes—
390C2×C4×C7C2511yescharacteristic
391C22⋊D7—84no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—42no—
400C2×Dic7—42no—
401C2×Dic7—42no—
402C2×Dic7C22×D412yes—
403C2×Dic7C22×D412yes—
404C2×Dic7C22×D412yes—
405C2×Dic7C22×D412yes—
406D28—22no—
407D28—22no—
408D28—42no—
409C4×D7—84no—
410Dic14—84no—
411C7×C8—22no—
412C7×C8—22no—
413C7⋊C8—22no—
414C7⋊C8—22no—
415C22×Q8—24no—
416C22×Q8—24no—
417C22×Q8—21no—
418C22×Q8—22no—
419C22×Q8—141no—
420C22×Q8C22×D711yescharacteristic
421C22×Q8C22×D714yes—
422C22×Q8C22×D711yescharacteristic
423C22×Q8C22×D711yescharacteristic
424C22×D4—71no—
425C22×D4—141no—
426C23×C4—21no—
427C23×C4—141no—
428C23×C4C22×D711yescharacteristic
429C2×Q16—24no—
430C2×Q16—24no—
431C2×Q16C22×D714yes—
432C2×Q16C22×D714yes—
433C2×SD16—74no—
434C2×SD16—74no—
435C2×SD16—144no—
436C2×SD16—144no—
437C22×C8—71no—
438C22×C8—71no—
439C22×C8C22×D711yescharacteristic
440C22×C8C22×D711yescharacteristic
441C4⋊Q8—74no—
442C4⋊Q8—142no—
443#126—148no—
444#124—74no—
445#124—142no—
446#124—148no—
447#123—148no—
448C22⋊Q8—22no—
449C22⋊Q8—148no—
450C22⋊Q8C22×D714yes—
451#121—74no—
452#121—142no—
453C4×Q8—74no—
454C4×Q8—74no—
455C4×Q8—74no—
456C4×Q8—74no—
457C4×Q8—74no—
458C4×Q8—142no—
459C4×Q8—142no—
460C4×Q8—142no—
461C4×Q8—142no—
462C4×Q8—142no—
463C4×Q8—148no—
464C4×Q8—148no—
465C4×D4—74no—
466C4×D4—142no—
467#117—74no—
468#117—74no—
469#117—74no—
470#117—148no—
471#117—148no—
472#117—142no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—71no—
476C2×C4⋊C4—71no—
477C2×C4⋊C4—71no—
478C2×C4⋊C4—71no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4C22×D711yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—71no—
488C2×C22⋊C4—71no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C42—71no—
495C2×C42—71no—
496C2×C42—141no—
497C2×C42—141no—
498C2×C42—141no—
499C2×C42—141no—
500C2×C42—141no—
501C2×C42—141no—
502#107—74no—
503#107—74no—
504#106—74no—
505#106—74no—
506C4⋊C8—74no—
507C4⋊C8—74no—
508#103—74no—
509#103—74no—
510#103—74no—
511#103—74no—
512#103C22×D714yes—
513#103C22×D714yes—
514#102—74no—
515#102—74no—
516C22⋊C8—74no—
517C22⋊C8C22×D714yes—
518#97—74no—
519C4×C8—74no—
520C22×C7—22no—
521C22×C7—22no—
522C22×C7—22no—
523C22×C7—44no—
524C22×C7#52512yes—
525C22×C7#57712yes—
526C22×C7#57812yes—
527C22×C7C23×D411yescharacteristic
528C2×D7—42no—
529C2×D7—42no—
530C2×D7—42no—
531C2×D7—84no—
532C4×C7—24no—
533C4×C7—24no—
534C4×C7—22no—
535C4×C7—42no—
536C4×C7—42no—
537C4×C7#52512yes—
538C4×C7C22×#4111yescharacteristic
539C4×C7C22×#4111yescharacteristic
540Dic7—22no—
541Dic7—22no—
542Dic7—22no—
543Dic7—22no—
544Dic7—42no—
545Dic7—42no—
546Dic7—42no—
547C24—141no—
548C24D4×D711yescharacteristic
549C2×Q8—216no—
550C2×Q8—28no—
551C2×Q8—28no—
552C2×Q8—28no—
553C2×Q8—24no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—144no—
562C2×Q8—562no—
563C2×Q8#115914yes—
564C2×Q8#115914yes—
565C2×Q8C23×D712yes—
566C2×Q8C23×D712yes—
567C2×Q8C23×D712yes—
568C2×D4—72no—
569C2×D4—144no—
570C2×D4—141no—
571C2×D4—142no—
572C2×D4—142no—
573C2×D4—562no—
574C22×C4—28no—
575C22×C4—24no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—71no—
583C22×C4—71no—
584C22×C4—71no—
585C22×C4—71no—
586C22×C4—144no—
587C22×C4—141no—
588C22×C4—141no—
589C22×C4—141no—
590C22×C4—562no—
591C22×C4D4×D712yes—
592C22×C4D4×D711yescharacteristic
593C22×C4C23×D712yes—
594C22×C4C23×D711yescharacteristic
595Q16—28no—
596Q16—28no—
597SD16—148no—
598SD16—148no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—72no—
602C2×C8—72no—
603C2×C8—142no—
604C2×C8—142no—
605C2×C8C23×D712yes—
606C2×C8C23×D712yes—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—74no—
610C4⋊C4—74no—
611C4⋊C4—72no—
612C4⋊C4—72no—
613C4⋊C4—72no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—141no—
621C4⋊C4—141no—
622C4⋊C4—141no—
623C4⋊C4C23×D712yes—
624C22⋊C4—24no—
625C22⋊C4—74no—
626C22⋊C4—74no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C22⋊C4—144no—
632C42—72no—
633C42—72no—
634C42—72no—
635C42—72no—
636C42—144no—
637C42—144no—
638C42—144no—
639C42—144no—
640C42—144no—
641C42—144no—
642C2×C7—42no—
643C2×C7#312114yescomplemented
644C2×C7C2×#52511yescharacteristic
645C2×C7C2×#57711yescharacteristic
646C2×C7C2×#57811yescharacteristic
647D7—82no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—142no—
652C23—282no—
653C23—282no—
654C23—282no—
655C23C2×D4×D712yes—
656C23C2×D4×D711yescharacteristic
657Q8—216no—
658Q8—24no—
659Q8—24no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—22no—
664Q8—42no—
665Q8—564no—
666Q8C2×#115914yes—
667Q8C2×#115914yes—
668D4—142no—
669D4—142no—
670D4—282no—
671D4—564no—
672C2×C4—216no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—72no—
686C2×C4—72no—
687C2×C4—72no—
688C2×C4—72no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—282no—
697C2×C4—282no—
698C2×C4—282no—
699C2×C4—564no—
700C2×C4C2×D4×D712yes—
701C2×C4C2×D4×D711yescharacteristic
702C2×C4C2×#115912yes—
703C2×C4C2×#115912yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—22no—
707C8—142no—
708C8—142no—
709C7C2×#312111yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—282no—
715C22—282no—
716C22—282no—
717C22—564no—
718C22#9027712yes—
719C22#9045712yes—
720C22#9046912yes—
721C22C22×D4×D711yescharacteristic
722C4—24no—
723C4—24no—
724C4—22no—
725C4—42no—
726C4—42no—
727C4—142no—
728C4—142no—
729C4—142no—
730C4—142no—
731C4—282no—
732C4—282no—
733C4—282no—
734C4#9027712yes—
735C4C22×#115911yescharacteristic
736C4C22×#115911yescharacteristic
737C2—42no—
738C2—562no—
739C2#1173762114yesdirect product factor
740C2C2×#9027711yescharacteristic
741C2C2×#9045711yescharacteristic
742C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#451C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
hypercenterC2×#451D7
hypocenterC7C2×#3121
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×#90503C2semidirect
3. C2×C7×#451C2semidirect
5. C2×#89957C2semidirect
6. C2×#89957C2semidirect
7. C2×#89956C2semidirect
8. C2×Q16×Dic7C2semidirect
9. C2×#89817C2semidirect
10. #11737621C2direct (N × H)
11. C2×#89566C2semidirect
12. C2×#89563C2semidirect
13. C2×#89589C2semidirect
14. C2×#89560C2semidirect
16. C2×#89492C2semidirect
23. #90503C22semidirect
46. C7×#451C22semidirect
56. #89957C22semidirect
57. #89957C22semidirect
58. #89956C22semidirect
59. Q16×Dic7C22semidirect
68. #89817C22semidirect
71. #89589C22semidirect
72. #89566C22semidirect
73. #89563C22semidirect
74. #89560C22semidirect
76. #89492C22semidirect
192. C2×#451D7semidirect
329. #451C2×D7semidirect
643. C2×C7#3121semidirect
709. C7C2×#3121semidirect
739. C2#11737621direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#905032
C2×#903342
C2×C7×#4512
C2×#899992
C2×#899572
C2×#899562
C2×Q16×Dic72
C2×#898172
#117376212
C2×#895662
C2×#895632
C2×#895892
C2×#895602
C2×#895092
C2×#894922
C2×#31217