Finite Group Databasebeta

← C2×#11738306 #14232519

Subgroups — C2×#11738306 #14232519

Order 1792.

1962 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×#90305C211yesmaximal, characteristic, complemented
2C2×#90309C211yesmaximal, characteristic, complemented
3C2×C7×#469C211yesmaximal, characteristic, complemented
4C2×#89931C211yesmaximal, characteristic, complemented
5C2×D8×Dic7C211yesmaximal, characteristic, complemented
6C2×#89900C211yesmaximal, characteristic, complemented
7C2×#89893C211yesmaximal, characteristic, complemented
8C2×#89807C211yesmaximal, characteristic, complemented
9C2×#89805C211yesmaximal, characteristic, complemented
10#11738306C2116yesmaximal, direct product factor
11C2×#89633C211yesmaximal, characteristic, complemented
12C2×#89630C211yesmaximal, characteristic, complemented
13C2×#89546C211yesmaximal, characteristic, complemented
14C2×#89551C211yesmaximal, characteristic, complemented
15C2×#89535C211yesmaximal, characteristic, complemented
16C2×#89538C211yesmaximal, characteristic, complemented
17C22×C7×D8C2211yescharacteristic
18C22×C7×M16C2211yescharacteristic
19C2×C7×#121C2211yescharacteristic
20C2×C7×#121C2211yescharacteristic
21C2×#6502—21no—
22C2×#6501—21no—
23C2×#6501C2211yescharacteristic
24C2×#6501C2211yescharacteristic
25C2×#6498—21no—
26C2×D4×Dic7—21no—
27C2×D4×Dic7C2211yescharacteristic
28C2×D4×Dic7C2211yescharacteristic
29C2×C4×C22⋊D7C2211yescharacteristic
30C2×#6489C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×#1131C2211yescharacteristic
33#90309—24no—
34#90309C2218yescomplemented
35#90305—24no—
36#90305C2218yescomplemented
37C2×#6455C2211yescharacteristic
38C2×D7×C4⋊C4C2211yescharacteristic
39C2×#6453C2211yescharacteristic
40C2×#6453C2211yescharacteristic
41C2×#6449—21no—
42C2×(C22⋊D7)⋊C4—21no—
43C2×#6442—21no—
44C2×#6442—21no—
45C7×#469C2218yescomplemented
46C2×C7×#106C2211yescharacteristic
47C2×C7×#102C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×#6406C2211yescharacteristic
50C2×#6406C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×C22⋊(C7⋊C8)C2211yescharacteristic
54#89931C2218yescomplemented
55D8×Dic7C2218yescomplemented
56#89900C2218yescomplemented
57#89893C2218yescomplemented
58C2×(C2×D7)⋊C8C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6391C2211yescharacteristic
63C2×Dic7⋊C8C2211yescharacteristic
64C2×C8×Dic7C2211yescharacteristic
65#89807C2218yescomplemented
66#89805C2218yescomplemented
67C2×#6382C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71#89633C2218yescomplemented
72#89630C2218yescomplemented
73#89551C2218yescomplemented
74#89546C2218yescomplemented
75#89538C2218yescomplemented
76#89535C2218yescomplemented
77C2×#3355—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4—21no—
80C22×C7×D4C2311yescharacteristic
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C22×C22⋊D7D411yescharacteristic
86C23×Dic7—21no—
87C23×Dic7—21no—
88C23×Dic7—21no—
89C22×C4×D7—21no—
90C22×C4×D7C2311yescharacteristic
91C2×C7×D8—24no—
92C2×C7×D8C2314yes—
93C2×C7×M16—24no—
94C2×C7×M16C2314yes—
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C7×#121—22no—
98C7×#121—22no—
99C7×#121C2314yes—
100C7×#121C2314yes—
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C22⋊C4—21no—
104C2×C7×C22⋊C4—21no—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109C2×C22⋊Dic7—21no—
110C2×C22⋊Dic7D411yescharacteristic
111#6502—28no—
112#6501—28no—
113#6501—22no—
114#6501—22no—
115#6501C2314yes—
116#6501C2314yes—
117#6498—28no—
118D4×Dic7—28no—
119D4×Dic7—22no—
120D4×Dic7—22no—
121D4×Dic7C2314yes—
122D4×Dic7C2314yes—
123C4×C22⋊D7D414yes—
124C4×C22⋊D7C2314yes—
125C2×(C2×D7)⋊C4—21no—
126C2×(C2×D7)⋊C4D411yescharacteristic
127#6489—22no—
128#6489C2314yes—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—22no—
131C2×C4⋊Dic7—21no—
132C2×C4⋊Dic7—21no—
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2311yescharacteristic
135C2×C4⋊Dic7C2311yescharacteristic
136C2×C4⋊Dic7C2311yescharacteristic
137C2×C4⋊Dic7C2314yes—
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4D411yescharacteristic
142C2×C4×Dic7—21no—
143C2×C4×Dic7—21no—
144C2×C4×Dic7C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146C22×C7⋊C8C2311yescharacteristic
147C2×#1131—24no—
148C2×#1131C2314yes—
149#6455—22no—
150#6455C2314yes—
151D7×C4⋊C4—22no—
152D7×C4⋊C4C2314yes—
153#6453—22no—
154#6453—22no—
155#6453C2314yes—
156#6453C2314yes—
157#6449—28no—
158(C22⋊D7)⋊C4—28no—
159#6442—28no—
160#6442—28no—
161C7×#106C2314yes—
162C7×#102C2314yes—
163C7×#102C2314yes—
164#6406C2314yes—
165#6406C2314yes—
166#6406C2314yes—
167#6406C2314yes—
168C22⋊(C7⋊C8)C2314yes—
169(C2×D7)⋊C8C2314yes—
170#6392C2314yes—
171#6392C2314yes—
172#6391C2314yes—
173#6391C2314yes—
174Dic7⋊C8C2314yes—
175C8×Dic7C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180C2×#553—71no—
181C2×#553—71no—
182#3355—716no—
183C2×#499—71no—
184C2×#482—71no—
185C2×#482—71no—
186C2×#480—71no—
187C2×#480—71no—
188C2×#478—71no—
189C2×#478—71no—
190C2×#469—71no—
191C2×#469D711yescharacteristic, complemented
192C2×C4×D8—71no—
193C2×#436—71no—
194C2×#428—71no—
195C2×#428—71no—
196C24×C7—21no—
197C24×C7—21no—
198C24×C7C2×D411yescharacteristic
199C23×D7C2×D411yescharacteristic
200C2×C7×D4—24no—
201C2×C7×D4—24no—
202C2×C7×D4—21no—
203C2×C7×D4—21no—
204C2×C7×D4—22no—
205C2×C7×D4—22no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4—44no—
209C2×C7×D4—82no—
210C2×C7×D4C2412yes—
211C2×C7×D4C2412yes—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2411yescharacteristic
220C2×C22⋊D7—24no—
221C2×C22⋊D7—24no—
222C2×C22⋊D7—42no—
223C2×C22⋊D7—44no—
224C2×C22⋊D7—82no—
225C2×C22⋊D7C2×D414yes—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—24no—
231C22×Dic7—24no—
232C22×Dic7—24no—
233C22×Dic7—82no—
234C22×Dic7—82no—
235C22×Dic7—82no—
236C22×Dic7C2×D411yescharacteristic
237C22×Dic7C2×D411yescharacteristic
238C22×Dic7C2×D411yescharacteristic
239C2×C4×D7—22no—
240C2×C4×D7—22no—
241C2×C4×D7—24no—
242C2×C4×D7—82no—
243C2×C4×D7C2×D412yes—
244C2×C4×D7C2412yes—
245C7×D8—28no—
246C7×M16—28no—
247C2×C7×C8—22no—
248C2×C7×C8#4114yes—
249C2×C7×C8C2412yes—
250C2×C7×C8C2412yes—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C22⋊C4—24no—
256C7×C22⋊C4—24no—
257C22⋊Dic7—24no—
258C22⋊Dic7—24no—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261C22⋊Dic7—24no—
262C22⋊Dic7C2×D414yes—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4C2×D414yes—
265C4⋊Dic7—24no—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—21no—
270C4⋊Dic7—24no—
271C4⋊Dic7—24no—
272C4⋊Dic7C2412yes—
273C4⋊Dic7C2412yes—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4C2×D414yes—
280C4×Dic7—24no—
281C4×Dic7—24no—
282C4×Dic7C2×D412yes—
283C4×Dic7C2412yes—
284C2×C7⋊C8—22no—
285C2×C7⋊C8—22no—
286C2×C7⋊C8C2412yes—
287C2×C7⋊C8C2412yes—
288#1131—28no—
289C22×D8C2×D711yescharacteristic
290C22×M16—71no—
291C22×M16C2×D711yescharacteristic
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—141no—
305C2×#121—141no—
306C2×#121C2×D711yescharacteristic
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⋊C4—71no—
317#499—78no—
318#482—78no—
319#482—78no—
320#480—78no—
321#480—78no—
322#478—78no—
323#478—78no—
324#469—78no—
325#469C2×D718yescomplemented
326C4×D8—78no—
327#436—78no—
328#428—78no—
329#428—78no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#107—71no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#106—71no—
336C2×#106—71no—
337C2×#106—71no—
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⋊C8—71no—
348C2×C4×C8—71no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7—42no—
359C23×C7—42no—
360C23×C7C22×D412yes—
361C23×C7C22×D411yescharacteristic
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7C22×D412yes—
366C7×D4—22no—
367C7×D4—22no—
368C7×D4—22no—
369C7×D4—22no—
370C7×D4—48no—
371C7×D4—42no—
372C7×D4—42no—
373C7×D4—84no—
374C2×C4×C7—22no—
375C2×C4×C7—24no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D411yescharacteristic
384C2×C4×C7C2×#4112yes—
385C2×C4×C72−1+412yes—
386C2×C4×C7C2511yescharacteristic
387C22⋊D7—44no—
388C22⋊D7—48no—
389C22⋊D7—84no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—42no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400C2×Dic7—42no—
401C2×Dic7—84no—
402C2×Dic7—84no—
403C2×Dic7—84no—
404C2×Dic7C22×D412yes—
405C2×Dic7C22×D412yes—
406C2×Dic7C22×D412yes—
407C4×D7—24no—
408C4×D7—22no—
409C4×D7—22no—
410C4×D7—84no—
411C7×C8—22no—
412C7×C8C2×#4114yes—
413C7⋊C8—22no—
414C7⋊C8—22no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—71no—
418C22×D4—141no—
419C22×D4—141no—
420C22×D4C22×D711yescharacteristic
421C22×D4C22×D711yescharacteristic
422C23×C4—71no—
423C23×C4—141no—
424C23×C4—141no—
425C23×C4—141no—
426C23×C4—141no—
427C23×C4C22×D711yescharacteristic
428C2×D8—24no—
429C2×D8C22×D714yes—
430C2×M16—24no—
431C2×M16—74no—
432C2×M16—144no—
433C2×M16C22×D714yes—
434C22×C8—71no—
435C22×C8—71no—
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—22no—
448#121—74no—
449#121—74no—
450#121—142no—
451#121—142no—
452#121—148no—
453#121—148no—
454#121C22×D714yes—
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—71no—
469C2×C4⋊C4—71no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—74no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—74no—
475C2×C4⋊C4—142no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—142no—
483C2×C4⋊C4C22×D711yescharacteristic
484C2×C4⋊C4C22×D711yescharacteristic
485C2×C22⋊C4—21no—
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×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#106—74no—
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⋊C8—74no—
516C4×C8—74no—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—22no—
520C22×C7—44no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—42no—
527C22×C7—84no—
528C22×C7—84no—
529C22×C7#54712yes—
530C22×C7#57512yes—
531C22×C7#57612yes—
532C22×C7C23×D411yescharacteristic
533C2×D7—22no—
534C2×D7—22no—
535C2×D7—22no—
536C2×D7—44no—
537C4×C7—22no—
538C4×C7—42no—
539C4×C7—42no—
540C4×C7#54712yes—
541C4×C7C22×#4111yescharacteristic
542C4×C7C2×2−1+411yescharacteristic
543Dic7—22no—
544Dic7—22no—
545Dic7—22no—
546Dic7—42no—
547Dic7—42no—
548Dic7—42no—
549Dic7—42no—
550C24—21no—
551C24—21no—
552C24—71no—
553C24D4×D711yescharacteristic
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—44no—
563C2×D4—74no—
564C2×D4—82no—
565C2×D4—144no—
566C2×D4—144no—
567C2×D4—282no—
568C2×D4—284no—
569C2×D4—562no—
570C2×D4C23×D712yes—
571C2×D4C23×D712yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—71no—
577C22×C4—71no—
578C22×C4—71no—
579C22×C4—72no—
580C22×C4—72no—
581C22×C4—144no—
582C22×C4—144no—
583C22×C4—144no—
584C22×C4—142no—
585C22×C4—142no—
586C22×C4—141no—
587C22×C4—141no—
588C22×C4—141no—
589C22×C4—141no—
590C22×C4—144no—
591C22×C4—562no—
592C22×C4—562no—
593C22×C4—562no—
594C22×C4—562no—
595C22×C4D4×D712yes—
596C22×C4D4×D711yescharacteristic
597C22×C4C23×D712yes—
598C22×C4C23×D711yescharacteristic
599D8—28no—
600M16—28no—
601M16—148no—
602C2×C8—22no—
603C2×C8—72no—
604C2×C8—72no—
605C2×C8—142no—
606C2×C8—142no—
607C2×C8#115914yes—
608C2×C8C23×D712yes—
609C2×C8C23×D712yes—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—74no—
613C4⋊C4—72no—
614C4⋊C4—72no—
615C4⋊C4—72no—
616C4⋊C4—72no—
617C4⋊C4—144no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—144no—
621C4⋊C4—144no—
622C4⋊C4—141no—
623C4⋊C4—141no—
624C4⋊C4—141no—
625C4⋊C4—144no—
626C4⋊C4—141no—
627C4⋊C4C23×D712yes—
628C4⋊C4C23×D712yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—74no—
632C22⋊C4—74no—
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—42no—
644C2×C7—82no—
645C2×C7—82no—
646C2×C7#335514yescomplemented
647C2×C7C2×#54711yescharacteristic
648C2×C7C2×#57511yescharacteristic
649C2×C7C2×#57611yescharacteristic
650D7—42no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—72no—
663C23—142no—
664C23—142no—
665C23—142no—
666C23C2×D4×D712yes—
667C23C2×D4×D711yescharacteristic
668D4—22no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4—48no—
673D4—42no—
674D4—42no—
675D4—84no—
676D4—284no—
677D4—288no—
678D4—564no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—72no—
688C2×C4—72no—
689C2×C4—72no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—144no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—282no—
701C2×C4—282no—
702C2×C4—282no—
703C2×C4—282no—
704C2×C4—564no—
705C2×C4—564no—
706C2×C4—564no—
707C2×C4—564no—
708C2×C4C2×D4×D712yes—
709C2×C4C2×D4×D711yescharacteristic
710C2×C4C2×#115912yes—
711C2×C4#655412yes—
712C2×C4C24×D711yescharacteristic
713C8—22no—
714C8—142no—
715C8—142no—
716C8C2×#115914yes—
717C7C2×#335511yescharacteristic, complemented, Sylow
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—84no—
729C22—84no—
730C22—142no—
731C22—142no—
732C22—142no—
733C22—284no—
734C22#9030212yes—
735C22#9046412yes—
736C22#9046512yes—
737C22C22×D4×D711yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—142no—
742C4—142no—
743C4—142no—
744C4—282no—
745C4—282no—
746C4—282no—
747C4—282no—
748C4#9030212yes—
749C4C22×#115911yescharacteristic
750C4C2×#655411yescharacteristic
751C2—42no—
752C2—82no—
753C2—82no—
754C2—282no—
755C2#1173830614yesdirect product factor
756C2C2×#9030211yescharacteristic
757C2C2×#9046411yescharacteristic
758C2C2×#9046511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#469C2
socleC23×C7C22×D4
hypercenterC2×#469D7
hypocenterC7C2×#3355
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#90305C2semidirect
2. C2×#90309C2semidirect
3. C2×C7×#469C2semidirect
4. C2×#89931C2semidirect
5. C2×D8×Dic7C2semidirect
6. C2×#89900C2semidirect
7. C2×#89893C2semidirect
8. C2×#89807C2semidirect
9. C2×#89805C2semidirect
10. #11738306C2direct (N × H)
11. C2×#89633C2semidirect
12. C2×#89630C2semidirect
13. C2×#89546C2semidirect
14. C2×#89551C2semidirect
15. C2×#89535C2semidirect
16. C2×#89538C2semidirect
34. #90309C22semidirect
36. #90305C22semidirect
45. C7×#469C22semidirect
54. #89931C22semidirect
55. D8×Dic7C22semidirect
56. #89900C22semidirect
57. #89893C22semidirect
65. #89807C22semidirect
66. #89805C22semidirect
71. #89633C22semidirect
72. #89630C22semidirect
73. #89551C22semidirect
74. #89546C22semidirect
75. #89538C22semidirect
76. #89535C22semidirect
191. C2×#469D7semidirect
325. #469C2×D7semidirect
646. C2×C7#3355semidirect
717. C7C2×#3355semidirect
755. C2#11738306direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903052
C2×#903092
C2×C7×#4692
C2×#899312
C2×D8×Dic72
C2×#899002
C2×#898932
C2×#898072
C2×#898052
#117383062
C2×#896332
C2×#896302
C2×#895462
C2×#895512
C2×#895352
C2×#895382
C2×#33557