Finite Group Databasebeta

← C2×#11738094 #14232249

Subgroups — C2×#11738094 #14232249

Order 1792.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90333C211yesmaximal, characteristic, complemented
2C2×#90309C211yesmaximal, characteristic
3C2×C7×#465C211yesmaximal, characteristic, complemented
4C2×#89943C211yesmaximal, characteristic, complemented
5C2×SD16×Dic7C211yesmaximal, characteristic, complemented
6C2×C8×C22⋊D7C211yesmaximal, characteristic, complemented
7C22×#6391C211yesmaximal, characteristic, complemented
8C2×#89816C211yesmaximal, characteristic, complemented
9C2×#89805C211yesmaximal, characteristic, complemented
10#11738094C2116yesmaximal, direct product factor
11C2×#89632C211yesmaximal, characteristic, complemented
12C2×#89630C211yesmaximal, characteristic, complemented
13C2×#89587C211yesmaximal, characteristic, complemented
14C2×#89571C211yesmaximal, characteristic, complemented
15C2×#89551C211yesmaximal, characteristic, complemented
16C2×#89535C211yesmaximal, characteristic, complemented
17C22×C7×SD16C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×#121C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×#6502—21no—
24C2×#6501C2211yescharacteristic
25C2×D4×Dic7—21no—
26C2×D4×Dic7C2211yescharacteristic
27C2×C4×C22⋊D7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C8×D7C2211yescharacteristic
31#90333—24no—
32#90333C2218yescomplemented
33#90309—24no—
34#90309C2218yes—
35C2×#6461—21no—
36C2×#6455C2211yescharacteristic
37C2×#6455C2211yescharacteristic
38C2×#6453—21no—
39C2×#6453C2211yescharacteristic
40C2×#6453C2211yescharacteristic
41C2×#6449—21no—
42C2×#6449—21no—
43C2×#6442—21no—
44C2×#6440—21no—
45C7×#465C2218yescomplemented
46C2×C7×#106C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×#6409C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×C22⋊(C7⋊C8)C2211yescharacteristic
54#89943C2218yescomplemented
55SD16×Dic7C2218yescomplemented
56C8×C22⋊D7C2218yescomplemented
57C2×(C2×D7)⋊C8C2211yescharacteristic
58C2×#6391C2211yescharacteristic
59C2×#6391C2211yescharacteristic
60C2×#6391C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6391C2218yescomplemented
63C2×Dic7⋊C8C2211yescharacteristic
64C2×C8×Dic7C2211yescharacteristic
65#89816C2218yescomplemented
66#89805C2218yescomplemented
67C2×#6381C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71#89632C2218yescomplemented
72#89630C2218yescomplemented
73#89587C2218yescomplemented
74#89571C2218yescomplemented
75#89551C2218yescomplemented
76#89535C2218yescomplemented
77C2×#3337—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4—21no—
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—21no—
83C22×C22⋊D7D411yescharacteristic
84C23×Dic7—21no—
85C23×Dic7—21no—
86C23×Dic7—21no—
87C22×C4×D7C2311yescharacteristic
88C2×C7×SD16—24no—
89C2×C7×SD16C2314yes—
90C22×C7×C8—24no—
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2314yes—
93C22×C7×C8C2311yescharacteristic
94C7×C22⋊Q8—22no—
95C7×C22⋊Q8C2314yes—
96C7×#121—22no—
97C7×#121C2314yes—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C22⋊C4—21no—
102C2×C7×C22⋊C4—21no—
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7D411yescharacteristic
106#6509—22no—
107#6509C2314yes—
108Q8×Dic7—22no—
109Q8×Dic7C2314yes—
110#6502—28no—
111#6501—22no—
112#6501C2314yes—
113D4×Dic7—28no—
114D4×Dic7—22no—
115D4×Dic7C2314yes—
116C4×C22⋊D7D414yes—
117C4×C22⋊D7C2314yes—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4D411yescharacteristic
122C2×C4⋊Dic7—21no—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7—22no—
125C2×C4⋊Dic7—22no—
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7C2311yescharacteristic
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133C2×C4⋊Dic7C2314yes—
134C2×C4⋊Dic7C2314yes—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4D411yescharacteristic
139C2×C4×Dic7—21no—
140C2×C4×Dic7—21no—
141C2×C4×Dic7—21no—
142C2×C4×Dic7C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C2×C8×D7—24no—
146C2×C8×D7C2314yes—
147#6461—28no—
148#6455—22no—
149#6455—22no—
150#6455C2314yes—
151#6455C2314yes—
152#6453—28no—
153#6453—22no—
154#6453—22no—
155#6453C2314yes—
156#6453C2314yes—
157#6449—28no—
158#6449—28no—
159#6442—28no—
160#6440—28no—
161C7×#106C2314yes—
162C7×#103C2314yes—
163C7×#102C2314yes—
164#6409C2314yes—
165#6409C2314yes—
166#6406C2314yes—
167#6406C2314yes—
168C22⋊(C7⋊C8)C2314yes—
169(C2×D7)⋊C8C2314yes—
170#6391C2314yes—
171#6391C2314yes—
172#6391C2314yes—
173#6391C2314yes—
174Dic7⋊C8C2314yes—
175C8×Dic7C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180C2×#553—71no—
181C2×#552—71no—
182#3337—716no—
183C2×#499—71no—
184C2×#484—71no—
185C2×#485—71no—
186C2×#482—71no—
187C2×#480—71no—
188C2×#479—71no—
189C2×#478—71no—
190C2×#465—71no—
191C2×#465D711yescharacteristic, complemented
192C2×C4×SD16—71no—
193C2×C8×D4—71no—
194C2×#427—71no—
195C22×#106—71no—
196C24×C7—21no—
197C24×C7C2×D411yescharacteristic
198C23×D7C2×D411yescharacteristic
199C2×C7×Q8—21no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8C2412yes—
203C2×C7×D4—24no—
204C2×C7×D4—21no—
205C2×C7×D4—22no—
206C2×C7×D4—22no—
207C2×C7×D4—44no—
208C2×C7×D4C2412yes—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2411yescharacteristic
218C2×C22⋊D7—24no—
219C2×C22⋊D7—24no—
220C2×C22⋊D7—82no—
221C2×C22⋊D7C2×D414yes—
222C22×Dic7—24no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—24no—
228C22×Dic7—24no—
229C22×Dic7—44no—
230C22×Dic7—82no—
231C22×Dic7—82no—
232C22×Dic7C2×D411yescharacteristic
233C22×Dic7C2×D411yescharacteristic
234C22×Dic7C2×D411yescharacteristic
235C2×C4×D7—22no—
236C2×C4×D7—22no—
237C2×C4×D7C2×D412yes—
238C2×C4×D7C2412yes—
239C7×SD16—28no—
240C2×C7×C8—22no—
241C2×C7×C8—28no—
242C2×C7×C8#4114yes—
243C2×C7×C8C2412yes—
244C2×C7×C8C2412yes—
245C7×C4⋊C4—21no—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—24no—
248C7×C4⋊C4C2412yes—
249C7×C4⋊C4C2412yes—
250C7×C22⋊C4—24no—
251C7×C22⋊C4—24no—
252C22⋊Dic7—24no—
253C22⋊Dic7—24no—
254C22⋊Dic7C2×D414yes—
255(C2×D7)⋊C4—24no—
256(C2×D7)⋊C4—24no—
257(C2×D7)⋊C4—24no—
258(C2×D7)⋊C4C2×D414yes—
259C4⋊Dic7—24no—
260C4⋊Dic7—24no—
261C4⋊Dic7—21no—
262C4⋊Dic7—21no—
263C4⋊Dic7—21no—
264C4⋊Dic7—21no—
265C4⋊Dic7—24no—
266C4⋊Dic7—24no—
267C4⋊Dic7—24no—
268C4⋊Dic7C2412yes—
269C4⋊Dic7C2412yes—
270C4⋊Dic7C2412yes—
271C4⋊Dic7C2412yes—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4C2×D414yes—
276C4×Dic7—24no—
277C4×Dic7—24no—
278C4×Dic7—24no—
279C4×Dic7C2×D412yes—
280C4×Dic7C2412yes—
281C2×C7⋊C8—22no—
282C2×C7⋊C8—22no—
283C2×C7⋊C8C2412yes—
284C2×C7⋊C8C2412yes—
285C8×D7—28no—
286C22×SD16C2×D711yescharacteristic
287C23×C8—71no—
288C23×C8C2×D711yescharacteristic
289#553—78no—
290#553—144no—
291#552—78no—
292#552—144no—
293C2×#126—141no—
294C2×#126—141no—
295C2×#125—71no—
296C2×#125—71no—
297C2×#125—141no—
298C2×#123—141no—
299C2×#123—141no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8C2×D711yescharacteristic
302C2×#121—71no—
303C2×#121—141no—
304C2×#121C2×D711yescharacteristic
305C2×C4×Q8—71no—
306C2×C4×D4—71no—
307C2×C4×D4—71no—
308C2×C4×D4—141no—
309C2×#117—71no—
310C2×#117—71no—
311C2×#117—141no—
312C22×C4⋊C4—71no—
313C22×C4⋊C4—71no—
314#499—78no—
315#485—78no—
316#484—78no—
317#482—78no—
318#480—78no—
319#479—78no—
320#478—78no—
321#465—78no—
322#465C2×D718yescomplemented
323C4×SD16—78no—
324C8×D4—78no—
325#427—78no—
326C2×#107—71no—
327C2×#107—71no—
328C2×#107—71no—
329C2×#107—71no—
330C2×#106—71no—
331C2×#106—71no—
332C2×#106—78no—
333C2×#106—71no—
334C2×#106—71no—
335C2×#106C2×D711yescharacteristic
336C2×C4⋊C8—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#103C2×D711yescharacteristic
340C2×#102—71no—
341C2×#102—71no—
342C2×#102C2×D711yescharacteristic
343C2×C22⋊C8—71no—
344C2×C22⋊C8—71no—
345C2×C4×C8—71no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—42no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7#13514yes—
353C23×C7C22×D412yes—
354C23×C7C22×D411yescharacteristic
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7C22×D412yes—
359C7×Q8—22no—
360C7×Q8—22no—
361C7×Q8—42no—
362C7×D4—22no—
363C7×D4—22no—
364C7×D4—48no—
365C7×D4—42no—
366C2×C4×C7—22no—
367C2×C4×C7—24no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—42no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7C22×D412yes—
377C2×C4×C7C22×D411yescharacteristic
378C2×C4×C7C2×#4112yes—
379C2×C4×C72−1+412yes—
380C2×C4×C7C2511yescharacteristic
381C22⋊D7—28no—
382C22⋊D7—84no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—48no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—84no—
396C2×Dic7—84no—
397C2×Dic7C22×D412yes—
398C2×Dic7C22×D412yes—
399C2×Dic7C22×D412yes—
400C4×D7—24no—
401C4×D7—22no—
402C4×D7—22no—
403C7×C8—22no—
404C7×C8C2×#4114yes—
405C7⋊C8—22no—
406C7⋊C8—22no—
407C22×Q8C22×D711yescharacteristic
408C22×D4—21no—
409C22×D4—71no—
410C22×D4—141no—
411C22×D4C22×D711yescharacteristic
412C23×C4—71no—
413C23×C4—141no—
414C23×C4—141no—
415C23×C4—141no—
416C23×C4C22×D711yescharacteristic
417C2×SD16—24no—
418C2×SD16C22×D714yes—
419C22×C8—24no—
420C22×C8—71no—
421C22×C8—71no—
422C22×C8—74no—
423C22×C8—144no—
424C22×C8C22×D711yescharacteristic
425C22×C8C22×D714yes—
426C22×C8C22×D711yescharacteristic
427#126—148no—
428#126—148no—
429#125—74no—
430#125—74no—
431#125—142no—
432#125—142no—
433#125—148no—
434#123—148no—
435#123—148no—
436C22⋊Q8—22no—
437C22⋊Q8—74no—
438C22⋊Q8—142no—
439C22⋊Q8C22×D714yes—
440#121—22no—
441#121—74no—
442#121—142no—
443#121—148no—
444#121C22×D714yes—
445C4×Q8—74no—
446C4×Q8—142no—
447C4×D4—74no—
448C4×D4—74no—
449C4×D4—74no—
450C4×D4—142no—
451C4×D4—148no—
452#117—74no—
453#117—74no—
454#117—148no—
455#117—142no—
456#117—142no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—71no—
459C2×C4⋊C4—71no—
460C2×C4⋊C4—71no—
461C2×C4⋊C4—71no—
462C2×C4⋊C4—71no—
463C2×C4⋊C4—74no—
464C2×C4⋊C4—74no—
465C2×C4⋊C4—141no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4—141no—
473C2×C4⋊C4—142no—
474C2×C4⋊C4—142no—
475C2×C4⋊C4C22×D711yescharacteristic
476C2×C4⋊C4C22×D711yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—71no—
480C2×C22⋊C4—71no—
481C2×C22⋊C4—141no—
482C2×C22⋊C4—141no—
483C2×C22⋊C4—141no—
484C2×C22⋊C4—141no—
485C2×C22⋊C4—141no—
486C2×C42—71no—
487C2×C42—141no—
488C2×C42—141no—
489C2×C42—141no—
490#107—74no—
491#107—74no—
492#107—74no—
493#107—74no—
494#106—74no—
495#106—74no—
496#106—74no—
497#106—74no—
498#106C22×D714yes—
499C4⋊C8—74no—
500#103—74no—
501#103—74no—
502#103C22×D714yes—
503#102—74no—
504#102—74no—
505#102C22×D714yes—
506C22⋊C8—74no—
507C22⋊C8—74no—
508C4×C8—74no—
509C22×C7—28no—
510C22×C7—22no—
511C22×C7—22no—
512C22×C7—42no—
513C22×C7—42no—
514C22×C7—42no—
515C22×C7—84no—
516C22×C7#54712yes—
517C22×C7C2×#13514yes—
518C22×C7C2×#13512yes—
519C22×C7#57712yes—
520C22×C7C23×D411yescharacteristic
521C2×D7—22no—
522C2×D7—22no—
523C2×D7—22no—
524C2×D7—44no—
525C4×C7—22no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7—42no—
529C4×C7#54712yes—
530C4×C7C22×#4111yescharacteristic
531C4×C7C2×2−1+411yescharacteristic
532Dic7—22no—
533Dic7—22no—
534Dic7—22no—
535Dic7—42no—
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539C24—21no—
540C24—71no—
541C24D4×D711yescharacteristic
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8C23×D712yes—
546C2×D4—24no—
547C2×D4—21no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—44no—
551C2×D4—74no—
552C2×D4—144no—
553C2×D4—144no—
554C2×D4—562no—
555C2×D4C23×D712yes—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—71no—
562C22×C4—71no—
563C22×C4—71no—
564C22×C4—72no—
565C22×C4—72no—
566C22×C4—144no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—144no—
570C22×C4—141no—
571C22×C4—141no—
572C22×C4—141no—
573C22×C4—141no—
574C22×C4—144no—
575C22×C4—284no—
576C22×C4—562no—
577C22×C4—562no—
578C22×C4D4×D712yes—
579C22×C4D4×D711yescharacteristic
580C22×C4C23×D712yes—
581C22×C4C23×D711yescharacteristic
582SD16—28no—
583C2×C8—22no—
584C2×C8—28no—
585C2×C8—72no—
586C2×C8—72no—
587C2×C8—142no—
588C2×C8—142no—
589C2×C8—148no—
590C2×C8#115914yes—
591C2×C8C23×D712yes—
592C2×C8C23×D712yes—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—74no—
597C4⋊C4—72no—
598C4⋊C4—72no—
599C4⋊C4—72no—
600C4⋊C4—72no—
601C4⋊C4—144no—
602C4⋊C4—144no—
603C4⋊C4—144no—
604C4⋊C4—144no—
605C4⋊C4—144no—
606C4⋊C4—144no—
607C4⋊C4—141no—
608C4⋊C4—141no—
609C4⋊C4—141no—
610C4⋊C4—141no—
611C4⋊C4—144no—
612C4⋊C4—144no—
613C4⋊C4C23×D712yes—
614C4⋊C4C23×D712yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—74no—
618C22⋊C4—74no—
619C22⋊C4—144no—
620C22⋊C4—144no—
621C22⋊C4—144no—
622C22⋊C4—144no—
623C22⋊C4—144no—
624C42—72no—
625C42—72no—
626C42—144no—
627C42—144no—
628C42—144no—
629C2×C7—24no—
630C2×C7—82no—
631C2×C7#333714yescomplemented
632C2×C7C2×#54711yescharacteristic
633C2×C7C22×#13511yescharacteristic
634C2×C7C2×#57711yescharacteristic
635D7—42no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—72no—
643C23—142no—
644C23—142no—
645C23—142no—
646C23#647914yes—
647C23C2×D4×D712yes—
648C23C2×D4×D711yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—42no—
652D4—22no—
653D4—22no—
654D4—48no—
655D4—42no—
656D4—148no—
657D4—564no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—72no—
669C2×C4—72no—
670C2×C4—72no—
671C2×C4—142no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—144no—
675C2×C4—142no—
676C2×C4—142no—
677C2×C4—142no—
678C2×C4—142no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—288no—
682C2×C4—282no—
683C2×C4—282no—
684C2×C4—282no—
685C2×C4—282no—
686C2×C4—564no—
687C2×C4—564no—
688C2×C4C2×D4×D712yes—
689C2×C4C2×D4×D711yescharacteristic
690C2×C4C2×#115912yes—
691C2×C4#655412yes—
692C2×C4C24×D711yescharacteristic
693C8—22no—
694C8—142no—
695C8—142no—
696C8C2×#115914yes—
697C7C2×#333711yescharacteristic, complemented, Sylow
698C22—22no—
699C22—28no—
700C22—22no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—84no—
705C22—142no—
706C22—142no—
707C22—142no—
708C22—284no—
709C22#9030212yes—
710C22C2×#647914yes—
711C22C2×#647912yes—
712C22#9046112yes—
713C22C22×D4×D711yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—142no—
719C4—142no—
720C4—142no—
721C4—282no—
722C4—282no—
723C4—282no—
724C4—282no—
725C4#9030212yes—
726C4C22×#115911yescharacteristic
727C4C2×#655411yescharacteristic
728C2—24no—
729C2—82no—
730C2—282no—
731C2#1173809414yesdirect product factor
732C2C2×#9030211yescharacteristic
733C2C22×#647911yescharacteristic
734C2C2×#9046111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#465C2
socleC23×C7C22×D4
prime radicalC2×#90309C2
hypercenterC2×#465D7
hypocenterC7C2×#3337
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#90333C2semidirect
3. C2×C7×#465C2semidirect
4. C2×#89943C2semidirect
5. C2×SD16×Dic7C2semidirect
6. C2×C8×C22⋊D7C2semidirect
7. C22×#6391C2semidirect
8. C2×#89816C2semidirect
9. C2×#89805C2semidirect
10. #11738094C2direct (N × H)
11. C2×#89632C2semidirect
12. C2×#89630C2semidirect
13. C2×#89587C2semidirect
14. C2×#89571C2semidirect
15. C2×#89551C2semidirect
16. C2×#89535C2semidirect
32. #90333C22semidirect
45. C7×#465C22semidirect
54. #89943C22semidirect
55. SD16×Dic7C22semidirect
56. C8×C22⋊D7C22semidirect
62. C2×#6391C22semidirect
65. #89816C22semidirect
66. #89805C22semidirect
71. #89632C22semidirect
72. #89630C22semidirect
73. #89587C22semidirect
74. #89571C22semidirect
75. #89551C22semidirect
76. #89535C22semidirect
191. C2×#465D7semidirect
322. #465C2×D7semidirect
631. C2×C7#3337semidirect
697. C7C2×#3337semidirect
731. C2#11738094direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903332
C2×#903092
C2×C7×#4652
C2×#899432
C2×SD16×Dic72
C2×C8×C22⋊D72
C22×#63912
C2×#898162
C2×#898052
#117380942
C2×#896322
C2×#896302
C2×#895872
C2×#895712
C2×#895512
C2×#895352
C2×#33377