Finite Group Databasebeta

← C2×#11736917 #14232377

Subgroups — C2×#11736917 #14232377

Order 1792.

1942 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×#90234C211yesmaximal, characteristic, complemented
2C2×#90256C211yesmaximal, characteristic
3C2×C7×#435C211yesmaximal, characteristic, complemented
4C2×#89906C211yesmaximal, characteristic, complemented
5C2×#89893C211yesmaximal, characteristic, complemented
6C2×#89886C211yesmaximal, characteristic, complemented
7C22×#6392C211yesmaximal, characteristic, complemented
8#11736917C2116yesmaximal, direct product factor
9C2×#89601C211yesmaximal, characteristic, complemented
10C2×#89618C211yesmaximal, characteristic, complemented
11C2×#89494C211yesmaximal, characteristic, complemented
12C2×#89507C211yesmaximal, characteristic, complemented
13C2×#89495C211yesmaximal, characteristic, complemented
14C2×#89508C211yesmaximal, characteristic, complemented
15C2×#89482C211yesmaximal, characteristic, complemented
16C2×#89474C211yesmaximal, characteristic, complemented
17C22×C7×M16C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×#6502—21no—
21C2×D4×Dic7—21no—
22C2×#6493C2211yescharacteristic
23C2×#6493C2211yescharacteristic
24C2×#6489C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C2×#6487C2211yescharacteristic
29C2×#6487C2211yescharacteristic
30C22×#1132C2211yescharacteristic
31#90256—24no—
32#90256C2218yes—
33#90234—24no—
34#90234C2218yescomplemented
35C2×#6461—21no—
36C2×#6453—21no—
37C2×#6446—21no—
38C2×(C22⋊D7)⋊C4—21no—
39C2×#6441—21no—
40C2×#6441—21no—
41C2×C4×D28C2211yescharacteristic
42C2×#6433C2211yescharacteristic
43C2×#6432C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×#435C2218yescomplemented
46C2×C7×C4⋊C8C2211yescharacteristic
47C2×C7×C22⋊C8C2211yescharacteristic
48C2×C7×C22⋊C8C2211yescharacteristic
49C2×C7×#97C2211yescharacteristic
50#89906C2218yescomplemented
51#89893C2218yescomplemented
52#89886C2218yescomplemented
53C2×#6395C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×#6395C2211yescharacteristic
56C2×#6392C2211yescharacteristic
57C2×#6392C2211yescharacteristic
58C2×#6392C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6392C2211yescharacteristic
62C2×#6392C2218yescomplemented
63C2×#6391C2211yescharacteristic
64C2×#6391C2211yescharacteristic
65C2×#6391C2211yescharacteristic
66C2×#6390C2211yescharacteristic
67C2×#6390C2211yescharacteristic
68C2×#6390C2211yescharacteristic
69#89618C2218yescomplemented
70#89601C2218yescomplemented
71#89508C2218yescomplemented
72#89507C2218yescomplemented
73#89495C2218yescomplemented
74#89494C2218yescomplemented
75#89482C2218yescomplemented
76#89474C2218yescomplemented
77C2×#3346—71nomaximal, Sylow
78C22×C7×D4D411yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C23×Dic7—21no—
84C23×Dic7—21no—
85C23×Dic7—21no—
86C22×D28C2311yescharacteristic
87C22×C4×D7—21no—
88C22×Dic14—21no—
89C22×Dic14C2311yescharacteristic
90C2×C7×M16—24no—
91C2×C7×M16C2314yes—
92C22×C7×C8—24no—
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2314yes—
97C22×C7×C8C2311yescharacteristic
98C4×C7×D4D414yes—
99C4×C7×D4C2314yes—
100C2×C7×C4⋊C4D411yescharacteristic
101C2×C7×C22⋊C4D411yescharacteristic
102C2×C7×C22⋊C4D411yescharacteristic
103C2×C42×C7C2311yescharacteristic
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107#6502—28no—
108D4×Dic7—28no—
109#6493—22no—
110#6493—22no—
111#6493C2314yes—
112#6493C2314yes—
113C2×(C2×D7)⋊C4—21no—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—21no—
116#6489—22no—
117#6489C2314yes—
118C2×C4⋊Dic7—21no—
119C2×C4⋊Dic7—21no—
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7—22no—
123C2×C4⋊Dic7—22no—
124C2×C4⋊Dic7—22no—
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129C2×C4⋊Dic7C2311yescharacteristic
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2314yes—
132C2×C4⋊Dic7C2314yes—
133C2×C4⋊Dic7C2314yes—
134#6487—22no—
135#6487—22no—
136#6487C2314yes—
137#6487C2314yes—
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×C4×Dic7—21no—
144C2×C4×Dic7—21no—
145C2×#1132—24no—
146C2×#1132C2314yes—
147#6461—28no—
148#6453—28no—
149#6446—28no—
150(C22⋊D7)⋊C4—28no—
151#6441—28no—
152#6441—28no—
153C4×D28—22no—
154C4×D28C2314yes—
155#6433—22no—
156#6433C2314yes—
157#6432—22no—
158#6432C2314yes—
159C4×Dic14—22no—
160C4×Dic14C2314yes—
161C7×C4⋊C8C2314yes—
162C7×C22⋊C8C2314yes—
163C7×C22⋊C8C2314yes—
164C7×#97C2314yes—
165#6395C2314yes—
166#6395C2314yes—
167#6395C2314yes—
168#6392C2314yes—
169#6392C2314yes—
170#6392C2314yes—
171#6392C2314yes—
172#6392C2314yes—
173#6392C2314yes—
174#6391C2314yes—
175#6391C2314yes—
176#6391C2314yes—
177#6390C2314yes—
178#6390C2314yes—
179#6390C2314yes—
180C2×#554—71no—
181C2×#553—71no—
182#3346—716no—
183C2×#501—71no—
184C2×#484—71no—
185C2×#481—71no—
186C2×#485—71no—
187C2×#480—71no—
188C2×#479—71no—
189C2×#474—71no—
190C2×#468—71no—
191C2×#465—71no—
192C2×#440—71no—
193C2×#435D711yescharacteristic, complemented
194C2×#428—71no—
195C22×#107—71no—
196C24×C7C2×D411yescharacteristic
197C24×C7C2×D411yescharacteristic
198C23×D7—21no—
199C2×C7×D4—24no—
200C2×C7×D4C2×D414yes—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D412yes—
210C22×C4×C7C2×D412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2411yescharacteristic
214C2×C22⋊D7—24no—
215C2×C22⋊D7—24no—
216C2×C22⋊D7—44no—
217C2×C22⋊D7—82no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—24no—
226C22×Dic7—24no—
227C22×Dic7—24no—
228C22×Dic7—82no—
229C22×Dic7—82no—
230C22×Dic7—82no—
231C2×D28—22no—
232C2×D28—22no—
233C2×D28—21no—
234C2×D28C2412yes—
235C2×C4×D7—24no—
236C2×C4×D7—82no—
237C2×Dic14—22no—
238C2×Dic14—22no—
239C2×Dic14—21no—
240C2×Dic14—24no—
241C2×Dic14—82no—
242C2×Dic14C2412yes—
243C7×M16—28no—
244C2×C7×C8—22no—
245C2×C7×C8—22no—
246C2×C7×C8—22no—
247C2×C7×C8—28no—
248C2×C7×C8#4114yes—
249C2×C7×C8C2412yes—
250C2×C7×C8C2412yes—
251C2×C7×C8C2412yes—
252C2×C7×C8C2412yes—
253C7×C4⋊C4C2×D414yes—
254C7×C22⋊C4C2×D414yes—
255C7×C22⋊C4C2×D414yes—
256C42×C7C2×D412yes—
257C42×C7C2412yes—
258C22⋊Dic7—24no—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261(C2×D7)⋊C4—24no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264C4⋊Dic7—21no—
265C4⋊Dic7—21no—
266C4⋊Dic7—21no—
267C4⋊Dic7—24no—
268C4⋊Dic7—21no—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7—24no—
272C4⋊Dic7—24no—
273C4⋊Dic7—24no—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276C4⋊Dic7C2412yes—
277C4⋊Dic7C2412yes—
278C4⋊Dic7C2412yes—
279C4⋊Dic7C2412yes—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285C4×Dic7—24no—
286C4×Dic7—24no—
287#1132—28no—
288C22×SD16—71no—
289C22×M16C2×D711yescharacteristic
290C23×C8C2×D711yescharacteristic
291#554—78no—
292#554—144no—
293#553—78no—
294#553—144no—
295C2×C4⋊Q8—71no—
296C2×#126—141no—
297C2×#125—71no—
298C2×#125—141no—
299C2×#123—141no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8—71no—
302C2×C22⋊Q8—141no—
303C2×C22⋊Q8—141no—
304C2×#121—71no—
305C2×#121—71no—
306C2×#121—141no—
307C2×C4×Q8—71no—
308C2×C4×D4—71no—
309C2×C4×D4—141no—
310C2×C4×D4—141no—
311C2×C4×D4C2×D711yescharacteristic
312C2×#117—71no—
313C22×C4⋊C4—71no—
314C22×C4⋊C4—71no—
315C22×C4⋊C4—71no—
316#501—78no—
317#485—78no—
318#484—78no—
319#481—78no—
320#480—78no—
321#479—78no—
322#474—78no—
323#468—78no—
324#465—78no—
325#440—78no—
326#435C2×D718yescomplemented
327#428—78no—
328C2×#107—71no—
329C2×#107—71no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#107—78no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#106—71no—
336C2×#106—71no—
337C2×#106—71no—
338C2×C4⋊C8C2×D711yescharacteristic
339C2×#103—71no—
340C2×#103—71no—
341C2×#103—71no—
342C2×#102—71no—
343C2×#102—71no—
344C2×#102—71no—
345C2×C22⋊C8C2×D711yescharacteristic
346C2×C22⋊C8C2×D711yescharacteristic
347C2×#97C2×D711yescharacteristic
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7#13714yes—
354C23×C7C22×D412yes—
355C23×C7C22×D412yes—
356C23×C7C22×D411yescharacteristic
357C22×D7—22no—
358C22×D7—42no—
359C22×D7—42no—
360C22×D7—42no—
361C7×D4—28no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—24no—
367C2×C4×C7—24no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7C22×D412yes—
373C2×C4×C7C22×D412yes—
374C2×C4×C7C22×D412yes—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D411yescharacteristic
377C2×C4×C7C2×#4112yes—
378C2×C4×C72−1+412yes—
379C2×C4×C7C2511yescharacteristic
380C22⋊D7—48no—
381C22⋊D7—84no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7—84no—
397C2×Dic7—84no—
398C2×Dic7—84no—
399D28—22no—
400D28—22no—
401D28—42no—
402C4×D7—84no—
403Dic14—22no—
404Dic14—22no—
405Dic14—42no—
406Dic14—84no—
407C7×C8—22no—
408C7×C8—22no—
409C7×C8—22no—
410C7×C8C2×#4114yes—
411C22×Q8—71no—
412C22×Q8—141no—
413C22×D4—71no—
414C22×D4—141no—
415C22×D4—141no—
416C22×D4D2811yescharacteristic
417C23×C4—141no—
418C23×C4—141no—
419C23×C4—141no—
420C23×C4—141no—
421C23×C4C22×D711yescharacteristic
422C23×C4C22×D711yescharacteristic
423C2×SD16—74no—
424C2×SD16—144no—
425C2×M16—24no—
426C2×M16C22×D714yes—
427C22×C8—24no—
428C22×C8C22×D711yescharacteristic
429C22×C8C22×D714yes—
430C22×C8C22×D711yescharacteristic
431C22×C8C22×D711yescharacteristic
432C22×C8C22×D711yescharacteristic
433C4⋊Q8—74no—
434C4⋊Q8—142no—
435#126—148no—
436#125—74no—
437#125—148no—
438#125—142no—
439#123—148no—
440C22⋊Q8—74no—
441C22⋊Q8—74no—
442C22⋊Q8—142no—
443C22⋊Q8—142no—
444C22⋊Q8—148no—
445C22⋊Q8—148no—
446#121—74no—
447#121—74no—
448#121—148no—
449#121—142no—
450#121—142no—
451C4×Q8—74no—
452C4×Q8—142no—
453C4×D4—74no—
454C4×D4—148no—
455C4×D4—148no—
456C4×D4—142no—
457C4×D4D2814yes—
458C4×D4C22×D714yes—
459#117—74no—
460#117—142no—
461C2×C4⋊C4—71no—
462C2×C4⋊C4—71no—
463C2×C4⋊C4—71no—
464C2×C4⋊C4—71no—
465C2×C4⋊C4—71no—
466C2×C4⋊C4—74no—
467C2×C4⋊C4—74no—
468C2×C4⋊C4—74no—
469C2×C4⋊C4—71no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4—141no—
473C2×C4⋊C4—142no—
474C2×C4⋊C4—142no—
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⋊C4D2811yescharacteristic
483C2×C22⋊C4—141no—
484C2×C22⋊C4—141no—
485C2×C22⋊C4—141no—
486C2×C22⋊C4—141no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4D2811yescharacteristic
490C2×C22⋊C4D2811yescharacteristic
491C2×C42—141no—
492C2×C42—141no—
493C2×C42C22×D711yescharacteristic
494#107—74no—
495#107—74no—
496#107—74no—
497#107—74no—
498#107—74no—
499#107—74no—
500#106—74no—
501#106—74no—
502#106—74no—
503C4⋊C8C22×D714yes—
504#103—74no—
505#103—74no—
506#103—74no—
507#102—74no—
508#102—74no—
509#102—74no—
510C22⋊C8C22×D714yes—
511C22⋊C8C22×D714yes—
512#97C22×D714yes—
513C22×C7—28no—
514C22×C7—22no—
515C22×C7—22no—
516C22×C7—22no—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—44no—
520C22×C7#54712yes—
521C22×C7C2×#13714yes—
522C22×C7C2×#13712yes—
523C22×C7#57612yes—
524C22×C7C23×D411yescharacteristic
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—42no—
528C2×D7—84no—
529C4×C7—22no—
530C4×C7—22no—
531C4×C7—22no—
532C4×C7—22no—
533C4×C7#54712yes—
534C4×C7C22×#4111yescharacteristic
535C4×C7C2×2−1+411yescharacteristic
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543C24—141no—
544C24C2×D2811yescharacteristic
545C24C2×D2811yescharacteristic
546C2×Q8—72no—
547C2×Q8—141no—
548C2×Q8—144no—
549C2×Q8—142no—
550C2×Q8—142no—
551C2×Q8—562no—
552C2×D4—24no—
553C2×D4—72no—
554C2×D4—144no—
555C2×D4—144no—
556C2×D4—141no—
557C2×D4—142no—
558C2×D4—142no—
559C2×D4—284no—
560C2×D4—562no—
561C2×D4C2×D2814yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—141no—
567C22×C4—141no—
568C22×C4—141no—
569C22×C4—141no—
570C22×C4—141no—
571C22×C4—141no—
572C22×C4—141no—
573C22×C4—144no—
574C22×C4—144no—
575C22×C4—144no—
576C22×C4—144no—
577C22×C4—562no—
578C22×C4—562no—
579C22×C4—562no—
580C22×C4—562no—
581C22×C4C2×D2812yes—
582C22×C4C2×D2812yes—
583C22×C4C2×D2811yescharacteristic
584C22×C4C2×D2811yescharacteristic
585C22×C4C2×D2811yescharacteristic
586C22×C4C2×D2811yescharacteristic
587C22×C4C23×D712yes—
588C22×C4C23×D712yes—
589C22×C4C23×D711yescharacteristic
590SD16—148no—
591M16—28no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—28no—
596C2×C8#115914yes—
597C2×C8C23×D712yes—
598C2×C8C23×D712yes—
599C2×C8C23×D712yes—
600C2×C8C23×D712yes—
601C4⋊C4—72no—
602C4⋊C4—72no—
603C4⋊C4—72no—
604C4⋊C4—72no—
605C4⋊C4—72no—
606C4⋊C4—72no—
607C4⋊C4—144no—
608C4⋊C4—144no—
609C4⋊C4—144no—
610C4⋊C4—144no—
611C4⋊C4—144no—
612C4⋊C4—141no—
613C4⋊C4—141no—
614C4⋊C4—141no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—141no—
618C4⋊C4—141no—
619C4⋊C4—144no—
620C4⋊C4—141no—
621C4⋊C4—144no—
622C4⋊C4C2×D2814yes—
623C22⋊C4—144no—
624C22⋊C4—144no—
625C22⋊C4—144no—
626C22⋊C4—144no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4C2×D2814yes—
630C22⋊C4C2×D2814yes—
631C42—144no—
632C42—144no—
633C42C2×D2812yes—
634C42C23×D712yes—
635C2×C7—24no—
636C2×C7—42no—
637C2×C7#334614yescomplemented
638C2×C7C2×#54711yescharacteristic
639C2×C7C22×#13711yescharacteristic
640C2×C7C2×#57611yescharacteristic
641D7—82no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—142no—
648C23—282no—
649C23—282no—
650C23—282no—
651C23#647214yes—
652C23C22×D2812yes—
653C23C22×D2812yes—
654C23C22×D2811yescharacteristic
655Q8—142no—
656Q8—142no—
657Q8—282no—
658Q8—564no—
659D4—28no—
660D4—142no—
661D4—142no—
662D4—288no—
663D4—282no—
664D4—564no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—142no—
676C2×C4—142no—
677C2×C4—142no—
678C2×C4—142no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—282no—
683C2×C4—282no—
684C2×C4—282no—
685C2×C4—282no—
686C2×C4—282no—
687C2×C4—282no—
688C2×C4—282no—
689C2×C4—564no—
690C2×C4—564no—
691C2×C4—564no—
692C2×C4—564no—
693C2×C4C22×D2812yes—
694C2×C4C22×D2812yes—
695C2×C4C22×D2812yes—
696C2×C4C22×D2812yes—
697C2×C4C22×D2811yescharacteristic
698C2×C4C2×#115912yes—
699C2×C4#655412yes—
700C2×C4C24×D711yescharacteristic
701C8—22no—
702C8—22no—
703C8—22no—
704C8C2×#115914yes—
705C7C2×#334611yescharacteristic, complemented, Sylow
706C22—28no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—282no—
714C22—282no—
715C22—282no—
716C22—564no—
717C22#9024612yes—
718C22C2×#647214yes—
719C22C2×#647212yes—
720C22#9044312yes—
721C22C23×D2811yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—282no—
727C4—282no—
728C4—282no—
729C4—282no—
730C4—282no—
731C4—282no—
732C4—282no—
733C4#9024612yes—
734C4C22×#115911yescharacteristic
735C4C2×#655411yescharacteristic
736C2—24no—
737C2—42no—
738C2—562no—
739C2#1173691714yesdirect product factor
740C2C2×#9024611yescharacteristic
741C2C22×#647211yescharacteristic
742C2C2×#9044311yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#435C2
socleC23×C7C22×D4
prime radicalC2×#90256C2
hypercenterC2×#435D7
hypocenterC7C2×#3346
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#90234C2semidirect
3. C2×C7×#435C2semidirect
4. C2×#89906C2semidirect
5. C2×#89893C2semidirect
6. C2×#89886C2semidirect
7. C22×#6392C2semidirect
8. #11736917C2direct (N × H)
9. C2×#89601C2semidirect
10. C2×#89618C2semidirect
11. C2×#89494C2semidirect
12. C2×#89507C2semidirect
13. C2×#89495C2semidirect
14. C2×#89508C2semidirect
15. C2×#89482C2semidirect
16. C2×#89474C2semidirect
34. #90234C22semidirect
45. C7×#435C22semidirect
50. #89906C22semidirect
51. #89893C22semidirect
52. #89886C22semidirect
62. C2×#6392C22semidirect
69. #89618C22semidirect
70. #89601C22semidirect
71. #89508C22semidirect
72. #89507C22semidirect
73. #89495C22semidirect
74. #89494C22semidirect
75. #89482C22semidirect
76. #89474C22semidirect
193. C2×#435D7semidirect
326. #435C2×D7semidirect
637. C2×C7#3346semidirect
705. C7C2×#3346semidirect
739. C2#11736917direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902342
C2×#902562
C2×C7×#4352
C2×#899062
C2×#898932
C2×#898862
C22×#63922
#117369172
C2×#896012
C2×#896182
C2×#894942
C2×#895072
C2×#894952
C2×#895082
C2×#894822
C2×#894742
C2×#33467