Finite Group Databasebeta

← C2×#11738640 #14232265

Subgroups — C2×#11738640 #14232265

Order 1792.

1994 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×#90386C211yesmaximal, characteristic, complemented
2C2×#90249C211yesmaximal, characteristic, complemented
3C2×C7×#478C211yesmaximal, characteristic, complemented
4C2×#89836C211yesmaximal, characteristic, complemented
5C2×C4×#1141C211yesmaximal, characteristic, complemented
6#11738640C2116yesmaximal, direct product factor
7C2×D7×#107C211yesmaximal, characteristic, complemented
8C2×#89657C211yesmaximal, characteristic, complemented
9C2×#89635C211yesmaximal, characteristic, complemented
10C2×#89632C211yesmaximal, characteristic, complemented
11C2×#89619C211yesmaximal, characteristic, complemented
12C2×#89606C211yesmaximal, characteristic, complemented
13C2×#89549C211yesmaximal, characteristic, complemented
14C2×#89556C211yesmaximal, characteristic, complemented
15C2×#89547C211yesmaximal, characteristic, complemented
16C2×#89547C211yesmaximal, characteristic, complemented
17C2×C7×#125C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C2×#6501C2211yescharacteristic
20C2×#6501C2211yescharacteristic
21C22×#1141C2211yescharacteristic
22C2×#6492—21no—
23C2×C4×C22⋊D7—21no—
24C22×C8×D7C2211yescharacteristic
25C22×C8×D7C2211yescharacteristic
26#90386—24no—
27#90386C2218yescomplemented
28#90249—24no—
29#90249C2218yescomplemented
30C2×#6461—21no—
31C2×#6458—21no—
32C2×#6458C2211yescharacteristic
33C2×#6458C2211yescharacteristic
34C2×#6457—21no—
35C2×#6456—21no—
36C2×#6455C2211yescharacteristic
37C2×#6455C2211yescharacteristic
38C2×D7×C4⋊C4C2211yescharacteristic
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×#6447—21no—
41C2×#6442—21no—
42C2×C4×D28C2211yescharacteristic
43C2×C4×D28C2211yescharacteristic
44C2×#6433C2211yescharacteristic
45C7×#478C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#106C2211yescharacteristic
48C2×C7×C4⋊C8C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×(C2×D7)⋊C8C2211yescharacteristic
56C2×#6392C2211yescharacteristic
57C2×#6391C2211yescharacteristic
58#89836C2218yescomplemented
59C4×#1141C2218yescomplemented
60C2×#6383C2211yescharacteristic
61C2×#6382C2211yescharacteristic
62C2×#6382C2211yescharacteristic
63C2×#6381C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×C4×C7⋊C8C2211yescharacteristic
67#89657C2218yescomplemented
68D7×#107C2218yescomplemented
69#89635C2218yescomplemented
70#89632C2218yescomplemented
71#89619C2218yescomplemented
72#89606C2218yescomplemented
73#89556C2218yescomplemented
74#89549C2218yescomplemented
75#89547C2218yescomplemented
76#89547C2218yescomplemented
77C2×#3339—71nomaximal, Sylow
78C22×C7×D4C2311yescharacteristic
79C23×C4×C7—21no—
80C22×C22⋊D7—21no—
81C22×C22⋊D7—21no—
82C22×D28—21no—
83C22×D28—21no—
84C22×D28D411yescharacteristic
85C22×D28C2311yescharacteristic
86C22×C4×D7—21no—
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×C4×D7C2311yescharacteristic
90C22×C4×D7C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C7×#125—22no—
94C7×#125C2314yes—
95C4×C7×D4—22no—
96C4×C7×D4C2314yes—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C22⋊C4—21no—
103C2×C42×C7C2311yescharacteristic
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106#6501—22no—
107#6501—22no—
108#6501C2314yes—
109#6501C2314yes—
110C2×#1141—24no—
111C2×#1141C2314yes—
112#6492—28no—
113C4×C22⋊D7—28no—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4D411yescharacteristic
120C2×(C2×D7)⋊C4D411yescharacteristic
121C2×C4⋊Dic7D411yescharacteristic
122C2×C4⋊Dic7C2311yescharacteristic
123C2×C4⋊Dic7C2311yescharacteristic
124C2×C4⋊Dic7C2311yescharacteristic
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×C4×Dic7—21no—
130C2×C4×Dic7—21no—
131C22×C7⋊C8C2311yescharacteristic
132C22×C7⋊C8C2311yescharacteristic
133C2×C8×D7—24no—
134C2×C8×D7—24no—
135C2×C8×D7C2314yes—
136C2×C8×D7C2314yes—
137#6461—28no—
138#6458—28no—
139#6458—22no—
140#6458—22no—
141#6458C2314yes—
142#6458C2314yes—
143#6457—28no—
144#6456—28no—
145#6455—22no—
146#6455—22no—
147#6455C2314yes—
148#6455C2314yes—
149D7×C4⋊C4—22no—
150D7×C4⋊C4—22no—
151D7×C4⋊C4C2314yes—
152D7×C4⋊C4C2314yes—
153#6447—28no—
154#6442—28no—
155C4×D28—22no—
156C4×D28D414yes—
157C4×D28C2314yes—
158C4×D28C2314yes—
159#6433—22no—
160#6433C2314yes—
161C7×#107C2314yes—
162C7×#106C2314yes—
163C7×C4⋊C8C2314yes—
164C7×#102C2314yes—
165C7×#102C2314yes—
166#6406C2314yes—
167#6395C2314yes—
168#6395C2314yes—
169(C2×D7)⋊C8C2314yes—
170(C2×D7)⋊C8C2314yes—
171#6392C2314yes—
172#6391C2314yes—
173#6383C2314yes—
174#6382C2314yes—
175#6382C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179C4×C7⋊C8C2314yes—
180C2×#553—71no—
181C2×#553—71no—
182#3339—716no—
183C2×#499—71no—
184C2×#481—71no—
185C2×#481—71no—
186C2×#482—71no—
187C2×#482—71no—
188C2×#478—71no—
189C2×#478D711yescharacteristic, complemented
190C2×#466—71no—
191C2×#466—71no—
192C2×C4×D8—71no—
193C2×C8×D4—71no—
194C2×#427—71no—
195C22×#107—71no—
196C24×C7—21no—
197C23×D7—21no—
198C23×D7C2×D411yescharacteristic
199C23×D7C2×D411yescharacteristic
200C2×C7×D4—21no—
201C2×C7×D4—22no—
202C2×C7×D4—22no—
203C2×C7×D4C2412yes—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—24no—
208C22×C4×C7—82no—
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2411yescharacteristic
212C2×C22⋊D7—24no—
213C2×C22⋊D7—24no—
214C2×C22⋊D7—44no—
215C2×C22⋊D7—82no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7C2×D411yescharacteristic
220C22×Dic7C2×D411yescharacteristic
221C2×D28—24no—
222C2×D28—22no—
223C2×D28—22no—
224C2×D28—24no—
225C2×D28—21no—
226C2×D28—24no—
227C2×D28—44no—
228C2×D28—82no—
229C2×D28C2×D414yes—
230C2×D28C2412yes—
231C2×C4×D7—22no—
232C2×C4×D7—22no—
233C2×C4×D7—22no—
234C2×C4×D7—22no—
235C2×C4×D7—24no—
236C2×C4×D7—24no—
237C2×C4×D7—24no—
238C2×C4×D7—82no—
239C2×C4×D7—82no—
240C2×C4×D7—82no—
241C2×C4×D7C2×D412yes—
242C2×C4×D7C2×D412yes—
243C2×C4×D7C2412yes—
244C2×C4×D7C2412yes—
245C2×C7×C8—22no—
246C2×C7×C8—22no—
247C2×C7×C8C2412yes—
248C2×C7×C8C2412yes—
249C7×C4⋊C4—21no—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—24no—
253C7×C4⋊C4—24no—
254C7×C4⋊C4C2412yes—
255C7×C4⋊C4C2412yes—
256C7×C4⋊C4C2412yes—
257C7×C22⋊C4—24no—
258C42×C7C2×D412yes—
259C42×C7C2412yes—
260C22⋊Dic7—24no—
261C22⋊Dic7—24no—
262#1141—28no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4C2×D414yes—
269(C2×D7)⋊C4C2×D414yes—
270C4⋊Dic7—21no—
271C4⋊Dic7—21no—
272C4⋊Dic7—21no—
273C4⋊Dic7C2×D414yes—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276C4⋊Dic7C2412yes—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281C4×Dic7—24no—
282C4×Dic7—24no—
283C2×C7⋊C8—22no—
284C2×C7⋊C8#4114yes—
285C2×C7⋊C8C2412yes—
286C2×C7⋊C8C2412yes—
287C8×D7—28no—
288C8×D7—28no—
289C22×D8—71no—
290C23×C8—71no—
291C23×C8—71no—
292#553—78no—
293#553—78no—
294#553—144no—
295#553—144no—
296C2×#126—141no—
297C2×#126—141no—
298C2×#125—71no—
299C2×#125C2×D711yescharacteristic
300C2×#123—141no—
301C2×#123—141no—
302C2×#121—71no—
303C2×#121—71no—
304C2×#121—71no—
305C2×#121—71no—
306C2×#121—141no—
307C2×#121—141no—
308C2×C4×D4—71no—
309C2×C4×D4—71no—
310C2×C4×D4—141no—
311C2×C4×D4—141no—
312C2×C4×D4C2×D711yescharacteristic
313C2×#117—71no—
314C2×#117—71no—
315C22×C4⋊C4—71no—
316C22×C4⋊C4—71no—
317#499—78no—
318#482—78no—
319#482—78no—
320#481—78no—
321#481—78no—
322#478—78no—
323#478C2×D718yescomplemented
324#466—78no—
325#466—78no—
326C4×D8—78no—
327C8×D4—78no—
328#427—78no—
329C2×#107—71no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#107—71no—
333C2×#107—78no—
334C2×#107C2×D711yescharacteristic
335C2×#106—71no—
336C2×#106—71no—
337C2×#106—71no—
338C2×#106C2×D711yescharacteristic
339C2×C4⋊C8C2×D711yescharacteristic
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—42no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7C22×D411yescharacteristic
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—42no—
361C22×D7—42no—
362C22×D7—42no—
363C22×D7#13514yes—
364C22×D7C22×D412yes—
365C22×D7C22×D412yes—
366C7×D4—22no—
367C7×D4—22no—
368C7×D4—42no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7—84no—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7C2×#4112yes—
382C2×C4×C72−1+412yes—
383C2×C4×C7C2511yescharacteristic
384C22⋊D7—48no—
385C22⋊D7—84no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7C22×D412yes—
395C2×Dic7C22×D412yes—
396D28—28no—
397D28—22no—
398D28—22no—
399D28—48no—
400D28—42no—
401D28—84no—
402C4×D7—24no—
403C4×D7—24no—
404C4×D7—22no—
405C4×D7—22no—
406C4×D7—22no—
407C4×D7—22no—
408C4×D7—84no—
409C4×D7—84no—
410C4×D7—84no—
411C7×C8—22no—
412C7×C8—22no—
413C7⋊C8—22no—
414C7⋊C8C2×#4114yes—
415C22×D4—71no—
416C22×D4—71no—
417C22×D4—141no—
418C22×D4—141no—
419C22×D4—141no—
420C22×D4—141no—
421C22×D4C22×D711yescharacteristic
422C23×C4—21no—
423C23×C4—71no—
424C23×C4—71no—
425C23×C4—141no—
426C23×C4—141no—
427C23×C4—141no—
428C2×D8—74no—
429C2×D8—144no—
430C22×C8—71no—
431C22×C8—71no—
432C22×C8—74no—
433C22×C8—74no—
434C22×C8—144no—
435C22×C8—144no—
436C22×C8C22×D711yescharacteristic
437C22×C8C22×D711yescharacteristic
438#126—148no—
439#126—148no—
440#125—22no—
441#125—74no—
442#125—142no—
443#125C22×D714yes—
444#123—148no—
445#123—148no—
446#121—74no—
447#121—74no—
448#121—74no—
449#121—74no—
450#121—148no—
451#121—142no—
452#121—142no—
453#121—148no—
454#121—142no—
455#121—142no—
456C4×D4—22no—
457C4×D4—74no—
458C4×D4—74no—
459C4×D4—74no—
460C4×D4—148no—
461C4×D4—148no—
462C4×D4—142no—
463C4×D4C22×D714yes—
464#117—74no—
465#117—74no—
466#117—142no—
467#117—142no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—74no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—142no—
477C2×C4⋊C4—142no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C4⋊C4C22×D711yescharacteristic
484C2×C4⋊C4C22×D711yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—71no—
487C2×C22⋊C4—71no—
488C2×C22⋊C4—141no—
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—141no—
496C2×C42—141no—
497C2×C42C22×D711yescharacteristic
498#107—74no—
499#107—74no—
500#107—74no—
501#107—74no—
502#107C22×D714yes—
503#106—74no—
504#106—74no—
505#106—74no—
506#106C22×D714yes—
507C4⋊C8C22×D714yes—
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—42no—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7—84no—
521C22×C7#54712yes—
522C22×C7C2×#13512yes—
523C22×C7#57612yes—
524C22×C7C23×D411yescharacteristic
525C2×D7—28no—
526C2×D7—22no—
527C2×D7—22no—
528C2×D7—22no—
529C2×D7—22no—
530C2×D7—22no—
531C2×D7—44no—
532C2×D7—42no—
533C2×D7—42no—
534C2×D7—42no—
535C2×D7—84no—
536C2×D7C2×#13514yes—
537C4×C7—22no—
538C4×C7—22no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7—42no—
542C4×C7#54712yes—
543C4×C7C22×#4111yescharacteristic
544C4×C7C2×2−1+411yescharacteristic
545Dic7—22no—
546Dic7—22no—
547Dic7—42no—
548Dic7—42no—
549Dic7—42no—
550C24—21no—
551C24—71no—
552C24—71no—
553C24—141no—
554C2×D4—21no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—74no—
558C2×D4—72no—
559C2×D4—144no—
560C2×D4—144no—
561C2×D4—144no—
562C2×D4—144no—
563C2×D4—144no—
564C2×D4—141no—
565C2×D4—142no—
566C2×D4—142no—
567C2×D4—284no—
568C2×D4—284no—
569C2×D4—562no—
570C2×D4—562no—
571C2×D4C23×D712yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—71no—
577C22×C4—71no—
578C22×C4—72no—
579C22×C4—72no—
580C22×C4—72no—
581C22×C4—72no—
582C22×C4—82no—
583C22×C4—144no—
584C22×C4—144no—
585C22×C4—142no—
586C22×C4—142no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—141no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—144no—
593C22×C4—562no—
594C22×C4—562no—
595C22×C4—562no—
596C22×C4D4×D711yescharacteristic
597C22×C4D4×D711yescharacteristic
598C22×C4C23×D711yescharacteristic
599D8—148no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—74no—
603C2×C8—72no—
604C2×C8—72no—
605C2×C8—148no—
606C2×C8—148no—
607C2×C8—142no—
608C2×C8C23×D712yes—
609C2×C8C23×D712yes—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—74no—
616C4⋊C4—72no—
617C4⋊C4—72no—
618C4⋊C4—72no—
619C4⋊C4—144no—
620C4⋊C4—144no—
621C4⋊C4—144no—
622C4⋊C4—144no—
623C4⋊C4—141no—
624C4⋊C4—141no—
625C4⋊C4—141no—
626C4⋊C4C23×D712yes—
627C4⋊C4C23×D712yes—
628C4⋊C4C23×D712yes—
629C22⋊C4—24no—
630C22⋊C4—74no—
631C22⋊C4—74no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4—144no—
637C22⋊C4—144no—
638C22⋊C4—144no—
639C42—144no—
640C42—144no—
641C42D4×D712yes—
642C42C23×D712yes—
643C2×C7—82no—
644C2×C7#333914yescomplemented
645C2×C7C2×#54711yescharacteristic
646C2×C7C22×#13511yescharacteristic
647C2×C7C2×#57611yescharacteristic
648D7—24no—
649D7—42no—
650D7—82no—
651C23—22no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—74no—
656C23—72no—
657C23—72no—
658C23—142no—
659C23—142no—
660C23—142no—
661C23—142no—
662C23—142no—
663C23—142no—
664C23—282no—
665C23—282no—
666C23—282no—
667C23C2×D4×D711yescharacteristic
668D4—22no—
669D4—22no—
670D4—42no—
671D4—148no—
672D4—142no—
673D4—142no—
674D4—288no—
675D4—288no—
676D4—282no—
677D4—564no—
678D4—564no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—72no—
688C2×C4—72no—
689C2×C4—84no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—144no—
693C2×C4—144no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—282no—
702C2×C4—282no—
703C2×C4—282no—
704C2×C4—564no—
705C2×C4—564no—
706C2×C4—564no—
707C2×C4C2×D4×D712yes—
708C2×C4C2×D4×D712yes—
709C2×C4C2×D4×D711yescharacteristic
710C2×C4#655112yes—
711C2×C4D7×#4112yes—
712C2×C4C24×D711yescharacteristic
713C8—22no—
714C8—22no—
715C8—74no—
716C8—142no—
717C7C2×#333911yescharacteristic, complemented, Sylow
718C22—42no—
719C22—42no—
720C22—42no—
721C22—74no—
722C22—84no—
723C22—142no—
724C22—148no—
725C22—142no—
726C22—142no—
727C22—142no—
728C22—142no—
729C22—284no—
730C22—282no—
731C22—282no—
732C22—282no—
733C22—564no—
734C22#9032212yes—
735C22D7×#13512yes—
736C22#9046512yes—
737C22C22×D4×D711yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—142no—
744C4—142no—
745C4—282no—
746C4—282no—
747C4—282no—
748C4#9032212yes—
749C4C2×#655111yescharacteristic
750C4C2×D7×#4111yescharacteristic
751C2—82no—
752C2—144no—
753C2—282no—
754C2—562no—
755C2#1173864014yesdirect product factor
756C2C2×#9032211yescharacteristic
757C2C2×D7×#13511yescharacteristic
758C2C2×#9046511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#478C2
socleC23×C7C22×D4
hypercenterC2×#478D7
hypocenterC7C2×#3339
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#90386C2semidirect
2. C2×#90249C2semidirect
3. C2×C7×#478C2semidirect
4. C2×#89836C2semidirect
5. C2×C4×#1141C2semidirect
6. #11738640C2direct (N × H)
7. C2×D7×#107C2semidirect
8. C2×#89657C2semidirect
9. C2×#89635C2semidirect
10. C2×#89632C2semidirect
11. C2×#89619C2semidirect
12. C2×#89606C2semidirect
13. C2×#89549C2semidirect
14. C2×#89556C2semidirect
15. C2×#89547C2semidirect
16. C2×#89547C2semidirect
27. #90386C22semidirect
29. #90249C22semidirect
45. C7×#478C22semidirect
58. #89836C22semidirect
59. C4×#1141C22semidirect
67. #89657C22semidirect
68. D7×#107C22semidirect
69. #89635C22semidirect
70. #89632C22semidirect
71. #89619C22semidirect
72. #89606C22semidirect
73. #89556C22semidirect
74. #89549C22semidirect
75. #89547C22semidirect
76. #89547C22semidirect
189. C2×#478D7semidirect
323. #478C2×D7semidirect
644. C2×C7#3339semidirect
717. C7C2×#3339semidirect
755. C2#11738640direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903862
C2×#902492
C2×C7×#4782
C2×#898362
C2×C4×#11412
#117386402
C2×D7×#1072
C2×#896572
C2×#896352
C2×#896322
C2×#896192
C2×#896062
C2×#895492
C2×#895562
C2×#895472
C2×#33397