Finite Group Databasebeta

← C2×#11737663 #14222112

Subgroups — C2×#11737663 #14222112

Order 1792.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90518C211yesmaximal, characteristic, complemented
2C2×#90334C211yesmaximal, characteristic, complemented
3C2×C7×#452C211yesmaximal, characteristic, complemented
4C2×#90010C211yesmaximal, characteristic
5C2×#89957C211yesmaximal, characteristic, complemented
6C2×Q16×Dic7C211yesmaximal, characteristic, complemented
7C2×#89937C211yesmaximal, characteristic, complemented
8C2×#89936C211yesmaximal, characteristic, complemented
9C2×#89816C211yesmaximal, characteristic, complemented
10#11737663C2116yesmaximal, direct product factor
11C2×#89566C211yesmaximal, characteristic, complemented
12C2×#89589C211yesmaximal, characteristic, complemented
13C2×#89531C211yesmaximal, characteristic, complemented
14C2×#89528C211yesmaximal, characteristic, complemented
15C2×#89508C211yesmaximal, characteristic, complemented
16C2×#89492C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21#90518—24no—
22#90518C2218yescomplemented
23C2×#6510C2211yescharacteristic
24C2×Q8×Dic7C2211yescharacteristic
25C2×Q8×Dic7C2211yescharacteristic
26C2×Q8×Dic7C2211yescharacteristic
27C22×#1143C2211yescharacteristic
28C2×D4×Dic7—21no—
29C2×D4×Dic7—21no—
30C2×D4×Dic7C2211yescharacteristic
31C2×D4×Dic7C2211yescharacteristic
32C22×#1141C2211yescharacteristic
33C2×#6493C2211yescharacteristic
34C2×#6489—21no—
35C2×#6489C2211yescharacteristic
36C22×C4⋊Dic7—21no—
37C22×C4⋊Dic7C2211yescharacteristic
38#90334—24no—
39#90334C2218yescomplemented
40C2×#6461—21no—
41C2×#6460—21no—
42C2×#6456C2211yescharacteristic
43C2×#6451C2211yescharacteristic
44C2×#6448—21no—
45C2×#6446—21no—
46C7×#452C2218yescomplemented
47C2×C7×#103C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50#90010C2218yes—
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×C22⋊(C7⋊C8)C2211yescharacteristic
56#89957C2218yescomplemented
57Q16×Dic7C2218yescomplemented
58#89937C2218yescomplemented
59#89936C2218yescomplemented
60C2×#6395C2211yescharacteristic
61C2×#6395C2211yescharacteristic
62C2×#6392C2211yescharacteristic
63C2×#6392C2211yescharacteristic
64C2×#6389C2211yescharacteristic
65C2×Dic7⋊C8C2211yescharacteristic
66C2×Dic7⋊C8C2211yescharacteristic
67C2×C8×Dic7C2211yescharacteristic
68#89816C2218yescomplemented
69C2×#6381C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71#89589C2218yescomplemented
72#89566C2218yescomplemented
73#89531C2218yescomplemented
74#89528C2218yescomplemented
75#89508C2218yescomplemented
76#89492C2218yescomplemented
77C2×#3124—71nomaximal, Sylow
78C2×C7×#41—24no—
79C2×C7×#41—24no—
80C2×C7×#41—22no—
81C2×C7×#41C2314yes—
82C22×C7×Q8C2311yescharacteristic
83C22×C7×Q8C2311yescharacteristic
84C22×C7×D4—21no—
85C22×C7×D4C2311yescharacteristic
86C23×C4×C7—21no—
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—21no—
89C23×Dic7—21no—
90C23×Dic7—21no—
91C23×Dic7—21no—
92C22×D28C2311yescharacteristic
93C22×C4×D7—21no—
94C22×Dic14—21no—
95C2×C7×Q16—24no—
96C2×C7×Q16C2314yes—
97C2×C7×SD16—24no—
98C2×C7×SD16C2314yes—
99C22×C7×C8C2311yescharacteristic
100C22×C7×C8C2311yescharacteristic
101C7×C22⋊Q8—22no—
102C7×C22⋊Q8C2314yes—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C22⋊C4—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7D411yescharacteristic
109C2×C22⋊Dic7D411yescharacteristic
110#6510—22no—
111#6510C2314yes—
112Q8×Dic7—22no—
113Q8×Dic7—22no—
114Q8×Dic7—22no—
115Q8×Dic7C2314yes—
116Q8×Dic7C2314yes—
117Q8×Dic7C2314yes—
118C2×#1143—24no—
119C2×#1143C2314yes—
120D4×Dic7—28no—
121D4×Dic7—28no—
122D4×Dic7—22no—
123D4×Dic7—22no—
124D4×Dic7C2314yes—
125D4×Dic7C2314yes—
126C2×#1141—24no—
127C2×#1141C2314yes—
128#6493—22no—
129#6493C2314yes—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134#6489—28no—
135#6489D414yes—
136#6489C2314yes—
137C2×C4⋊Dic7—21no—
138C2×C4⋊Dic7—22no—
139C2×C4⋊Dic7—21no—
140C2×C4⋊Dic7—21no—
141C2×C4⋊Dic7—21no—
142C2×C4⋊Dic7—28no—
143C2×C4⋊Dic7D411yescharacteristic
144C2×C4⋊Dic7D411yescharacteristic
145C2×C4⋊Dic7C2311yescharacteristic
146C2×C4⋊Dic7C2311yescharacteristic
147C2×C4⋊Dic7C2311yescharacteristic
148C2×C4⋊Dic7C2314yes—
149C2×Dic7⋊C4—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×#102C2314yes—
167C7×C22⋊C8C2314yes—
168#6409C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171#6406C2314yes—
172C22⋊(C7⋊C8)C2314yes—
173#6395C2314yes—
174#6395C2314yes—
175#6392C2314yes—
176#6392C2314yes—
177#6389C2314yes—
178Dic7⋊C8C2314yes—
179Dic7⋊C8C2314yes—
180C8×Dic7C2314yes—
181#6381C2314yes—
182#6381C2314yes—
183C2×#542—71no—
184C2×#520—71no—
185#3124—716no—
186C2×#484—71no—
187C2×#480—71no—
188C2×#477—71no—
189C2×#474—71no—
190C2×#464—71no—
191C2×#463—71no—
192C2×#452D711yescharacteristic, complemented
193C2×#449—71no—
194C2×#440—71no—
195C2×#440—71no—
196C2×C4×Q16—71no—
197C2×C4×D8—71no—
198C2×#433—71no—
199C24×C7—21no—
200C24×C7C2×D411yescharacteristic
201C23×D7—21no—
202C7×#41—216no—
203C7×#41—28no—
204C7×#41—28no—
205C2×C7×Q8—21no—
206C2×C7×Q8—21no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8—22no—
210C2×C7×Q8#4114yes—
211C2×C7×Q8C2412yes—
212C2×C7×Q8C2412yes—
213C2×C7×D4—28no—
214C2×C7×D4—24no—
215C2×C7×D4—21no—
216C2×C7×D4—22no—
217C2×C7×D4#4114yes—
218C2×C7×D4C2412yes—
219C22×C4×C7—28no—
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×Dic7—24no—
236C22×Dic7—24no—
237C22×Dic7—24no—
238C22×Dic7—82no—
239C22×Dic7—82no—
240C22×Dic7—82no—
241C22×Dic7C2×D411yescharacteristic
242C22×Dic7C2×D411yescharacteristic
243C22×Dic7C2×D411yescharacteristic
244C22×Dic7C2×D411yescharacteristic
245C2×D28—22no—
246C2×D28—22no—
247C2×D28—21no—
248C2×D28C2412yes—
249C2×C4×D7—24no—
250C2×C4×D7—82no—
251C2×Dic14—24no—
252C2×Dic14—82no—
253C7×Q16—28no—
254C7×SD16—28no—
255C2×C7×C8—22no—
256C2×C7×C8—22no—
257C2×C7×C8C2412yes—
258C2×C7×C8C2412yes—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—24no—
261C7×C4⋊C4C2412yes—
262C7×C22⋊C4—24no—
263C22⋊Dic7—24no—
264C22⋊Dic7—24no—
265C22⋊Dic7C2×D414yes—
266C22⋊Dic7C2×D414yes—
267#1143—28no—
268#1141—28no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273C4⋊Dic7—21no—
274C4⋊Dic7—24no—
275C4⋊Dic7—21no—
276C4⋊Dic7—21no—
277C4⋊Dic7—24no—
278C4⋊Dic7—24no—
279C4⋊Dic7—24no—
280C4⋊Dic7C2×D414yes—
281C4⋊Dic7C2×D414yes—
282C4⋊Dic7C2412yes—
283C4⋊Dic7C2412yes—
284C4⋊Dic7C2412yes—
285Dic7⋊C4—24no—
286C4×Dic7—24no—
287C4×Dic7—24no—
288C4×Dic7—24no—
289C4×Dic7C2×D412yes—
290C4×Dic7C2×D412yes—
291C4×Dic7C2412yes—
292C4×Dic7C2412yes—
293C2×C7⋊C8—22no—
294C2×C7⋊C8—22no—
295C2×C7⋊C8C2412yes—
296C2×C7⋊C8C2412yes—
297C22×#41C2×D711yescharacteristic
298C22×Q16C2×D711yescharacteristic
299C22×SD16—71no—
300C22×SD16C2×D711yescharacteristic
301C22×D8—71no—
302#542—78no—
303#542—144no—
304C2×C4⋊Q8—71no—
305C2×#126—141no—
306C2×#124—71no—
307C2×#124—141no—
308C2×#123—141no—
309C2×C22⋊Q8—141no—
310C2×C22⋊Q8C2×D711yescharacteristic
311C2×#121—71no—
312#520—78no—
313#520—144no—
314C2×C4×Q8—71no—
315C2×C4×Q8—71no—
316C2×C4×Q8—71no—
317C2×C4×D4—71no—
318C2×C4×D4—71no—
319C2×C4×D4—71no—
320C2×C4×D4—141no—
321C2×C4×D4—141no—
322C2×#117—71no—
323C2×#117—141no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4—141no—
326#484—78no—
327#480—78no—
328#477—78no—
329#474—78no—
330#464—78no—
331#463—78no—
332#452C2×D718yescomplemented
333#449—78no—
334#440—78no—
335#440—78no—
336C4×Q16—78no—
337C4×D8—78no—
338#433—78no—
339C2×#107—71no—
340C2×#107—71no—
341C2×#107—71no—
342C2×#107—71no—
343C2×C4⋊C8—71no—
344C2×C4⋊C8—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103C2×D711yescharacteristic
349C2×#102—71no—
350C2×#102—71no—
351C2×#102—71no—
352C2×#102C2×D711yescharacteristic
353C2×C22⋊C8—71no—
354C2×C22⋊C8C2×D711yescharacteristic
355C2×#97—71no—
356C2×C4×C8—71no—
357C23×C7—22no—
358C23×C7—24no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7C22×D412yes—
365C23×C7C22×D411yescharacteristic
366C22×D7—22no—
367C22×D7—42no—
368C22×D7—42no—
369C22×D7—42no—
370C7×Q8—24no—
371C7×Q8—22no—
372C7×Q8—22no—
373C7×Q8—22no—
374C7×Q8—42no—
375C7×Q8C2×#4114yes—
376C7×D4—216no—
377C7×D4—24no—
378C7×D4—22no—
379C7×D4C2×#4114yes—
380C2×C4×C7—216no—
381C2×C4×C7—22no—
382C2×C4×C7—24no—
383C2×C4×C7—22no—
384C2×C4×C7—24no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D411yescharacteristic
393C2×C4×C7C2×#4112yes—
394C2×C4×C7C2×#4112yes—
395C2×C4×C7C2511yescharacteristic
396C22⋊D7—84no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—42no—
405C2×Dic7—42no—
406C2×Dic7—42no—
407C2×Dic7—84no—
408C2×Dic7—84no—
409C2×Dic7—84no—
410C2×Dic7C22×D412yes—
411C2×Dic7C22×D412yes—
412C2×Dic7C22×D412yes—
413C2×Dic7C22×D412yes—
414D28—22no—
415D28—22no—
416D28—42no—
417C4×D7—84no—
418Dic14—84no—
419C7×C8—22no—
420C7×C8—22no—
421C7⋊C8—22no—
422C7⋊C8—22no—
423C2×#41—24no—
424C2×#41—24no—
425C2×#41—22no—
426C2×#41C22×D714yes—
427C22×Q8—141no—
428C22×Q8C22×D711yescharacteristic
429C22×Q8C22×D711yescharacteristic
430C22×D4—21no—
431C22×D4—71no—
432C22×D4—141no—
433C22×D4C22×D711yescharacteristic
434C23×C4—21no—
435C23×C4—141no—
436C23×C4—141no—
437C23×C4—141no—
438C23×C4—141no—
439C23×C4C22×D711yescharacteristic
440C2×Q16—24no—
441C2×Q16C22×D714yes—
442C2×SD16—24no—
443C2×SD16—74no—
444C2×SD16—144no—
445C2×SD16C22×D714yes—
446C2×D8—74no—
447C2×D8—144no—
448C22×C8—71no—
449C22×C8—71no—
450C22×C8C22×D711yescharacteristic
451C22×C8C22×D711yescharacteristic
452C4⋊Q8—74no—
453C4⋊Q8—142no—
454#126—148no—
455#124—74no—
456#124—142no—
457#124—148no—
458#123—148no—
459C22⋊Q8—22no—
460C22⋊Q8—148no—
461C22⋊Q8C22×D714yes—
462#121—74no—
463#121—142no—
464C4×Q8—74no—
465C4×Q8—74no—
466C4×Q8—74no—
467C4×Q8—142no—
468C4×Q8—142no—
469C4×Q8—142no—
470C4×D4—74no—
471C4×D4—74no—
472C4×D4—74no—
473C4×D4—142no—
474C4×D4—142no—
475C4×D4—142no—
476C4×D4—148no—
477C4×D4—148no—
478#117—74no—
479#117—74no—
480#117—148no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—71no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—71no—
485C2×C4⋊C4—71no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—71no—
488C2×C4⋊C4—148no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4—141no—
494C2×C4⋊C4—142no—
495C2×C4⋊C4C22×D711yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—71no—
498C2×C22⋊C4—71no—
499C2×C22⋊C4—141no—
500C2×C22⋊C4—141no—
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C22⋊C4—141no—
504C2×C22⋊C4—141no—
505C2×C42—71no—
506C2×C42—71no—
507C2×C42—141no—
508C2×C42—141no—
509C2×C42—141no—
510#107—74no—
511#107—74no—
512#107—74no—
513#107—74no—
514C4⋊C8—74no—
515C4⋊C8—74no—
516#103—74no—
517#103—74no—
518#103—74no—
519#103C22×D714yes—
520#102—74no—
521#102—74no—
522#102—74no—
523#102C22×D714yes—
524C22⋊C8—74no—
525C22⋊C8C22×D714yes—
526#97—74no—
527C4×C8—74no—
528C22×C7—22no—
529C22×C7—24no—
530C22×C7—22no—
531C22×C7—22no—
532C22×C7—44no—
533C22×C7—48no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7#52512yes—
537C22×C7#57612yes—
538C22×C7#57812yes—
539C22×C7C23×D411yescharacteristic
540C2×D7—42no—
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—84no—
544C4×C7—22no—
545C4×C7—24no—
546C4×C7—42no—
547C4×C7—42no—
548C4×C7#52512yes—
549C4×C7C22×#4111yescharacteristic
550C4×C7C22×#4111yescharacteristic
551Dic7—22no—
552Dic7—22no—
553Dic7—22no—
554Dic7—22no—
555Dic7—42no—
556Dic7—42no—
557Dic7—42no—
558C24—21no—
559C24—141no—
560C24D4×D711yescharacteristic
561#41—216no—
562#41—28no—
563#41—28no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—144no—
570C2×Q8—562no—
571C2×Q8#115914yes—
572C2×Q8C23×D712yes—
573C2×Q8C23×D712yes—
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—72no—
579C2×D4—144no—
580C2×D4—141no—
581C2×D4—142no—
582C2×D4—142no—
583C2×D4—562no—
584C2×D4#115914yes—
585C2×D4C23×D712yes—
586C22×C4—28no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—71no—
594C22×C4—71no—
595C22×C4—71no—
596C22×C4—71no—
597C22×C4—144no—
598C22×C4—144no—
599C22×C4—144no—
600C22×C4—141no—
601C22×C4—141no—
602C22×C4—141no—
603C22×C4—144no—
604C22×C4—562no—
605C22×C4—562no—
606C22×C4—562no—
607C22×C4—562no—
608C22×C4D4×D712yes—
609C22×C4D4×D711yescharacteristic
610C22×C4C23×D712yes—
611C22×C4C23×D711yescharacteristic
612Q16—28no—
613SD16—28no—
614SD16—148no—
615D8—148no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—72no—
619C2×C8—72no—
620C2×C8—142no—
621C2×C8—142no—
622C2×C8C23×D712yes—
623C2×C8C23×D712yes—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—74no—
627C4⋊C4—74no—
628C4⋊C4—72no—
629C4⋊C4—72no—
630C4⋊C4—72no—
631C4⋊C4—144no—
632C4⋊C4—144no—
633C4⋊C4—144no—
634C4⋊C4—144no—
635C4⋊C4—144no—
636C4⋊C4—141no—
637C4⋊C4—141no—
638C4⋊C4—141no—
639C4⋊C4C23×D712yes—
640C22⋊C4—24no—
641C22⋊C4—74no—
642C22⋊C4—74no—
643C22⋊C4—144no—
644C22⋊C4—144no—
645C22⋊C4—144no—
646C22⋊C4—144no—
647C22⋊C4—144no—
648C22⋊C4—144no—
649C42—72no—
650C42—72no—
651C42—72no—
652C42—72no—
653C42—144no—
654C42—144no—
655C42—144no—
656C2×C7—42no—
657C2×C7—44no—
658C2×C7#312414yescomplemented
659C2×C7C2×#52511yescharacteristic
660C2×C7C2×#57611yescharacteristic
661C2×C7C2×#57811yescharacteristic
662D7—82no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—142no—
671C23—282no—
672C23—282no—
673C23—282no—
674C23C2×D4×D712yes—
675C23C2×D4×D711yescharacteristic
676Q8—24no—
677Q8—22no—
678Q8—22no—
679Q8—22no—
680Q8—42no—
681Q8—564no—
682Q8C2×#115914yes—
683D4—216no—
684D4—24no—
685D4—22no—
686D4—142no—
687D4—142no—
688D4—282no—
689D4—564no—
690D4C2×#115914yes—
691C2×C4—216no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—72no—
703C2×C4—72no—
704C2×C4—72no—
705C2×C4—72no—
706C2×C4—142no—
707C2×C4—142no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—282no—
714C2×C4—282no—
715C2×C4—282no—
716C2×C4—564no—
717C2×C4—564no—
718C2×C4—564no—
719C2×C4—564no—
720C2×C4C2×D4×D712yes—
721C2×C4C2×D4×D711yescharacteristic
722C2×C4C2×#115912yes—
723C2×C4C2×#115912yes—
724C2×C4C24×D711yescharacteristic
725C8—22no—
726C8—22no—
727C8—142no—
728C8—142no—
729C7C2×#312411yescharacteristic, complemented, Sylow
730C22—22no—
731C22—24no—
732C22—22no—
733C22—22no—
734C22—42no—
735C22—44no—
736C22—48no—
737C22—42no—
738C22—282no—
739C22—282no—
740C22—282no—
741C22—564no—
742C22#9027712yes—
743C22#9046012yes—
744C22#9047012yes—
745C22C22×D4×D711yescharacteristic
746C4—22no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—142no—
751C4—142no—
752C4—142no—
753C4—142no—
754C4—282no—
755C4—282no—
756C4—282no—
757C4#9027712yes—
758C4C22×#115911yescharacteristic
759C4C22×#115911yescharacteristic
760C2—42no—
761C2—44no—
762C2—562no—
763C2#1173766314yesdirect product factor
764C2C2×#9027711yescharacteristic
765C2C2×#9046011yescharacteristic
766C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#452C2
socleC23×C7C22×D4
prime radicalC2×#90010C2
hypercenterC2×#452D7
hypocenterC7C2×#3124
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#90518C2semidirect
2. C2×#90334C2semidirect
3. C2×C7×#452C2semidirect
5. C2×#89957C2semidirect
6. C2×Q16×Dic7C2semidirect
7. C2×#89937C2semidirect
8. C2×#89936C2semidirect
9. C2×#89816C2semidirect
10. #11737663C2direct (N × H)
11. C2×#89566C2semidirect
12. C2×#89589C2semidirect
13. C2×#89531C2semidirect
14. C2×#89528C2semidirect
15. C2×#89508C2semidirect
16. C2×#89492C2semidirect
22. #90518C22semidirect
39. #90334C22semidirect
46. C7×#452C22semidirect
56. #89957C22semidirect
57. Q16×Dic7C22semidirect
58. #89937C22semidirect
59. #89936C22semidirect
68. #89816C22semidirect
71. #89589C22semidirect
72. #89566C22semidirect
73. #89531C22semidirect
74. #89528C22semidirect
75. #89508C22semidirect
76. #89492C22semidirect
192. C2×#452D7semidirect
332. #452C2×D7semidirect
658. C2×C7#3124semidirect
729. C7C2×#3124semidirect
763. C2#11737663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#905182
C2×#903342
C2×C7×#4522
C2×#900102
C2×#899572
C2×Q16×Dic72
C2×#899372
C2×#899362
C2×#898162
#117376632
C2×#895662
C2×#895892
C2×#895312
C2×#895282
C2×#895082
C2×#894922
C2×#31247