Finite Group Databasebeta

← C2×#11737581 #14222028

Subgroups — C2×#11737581 #14222028

Order 1792.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90489C211yesmaximal, characteristic, complemented
2C2×#90334C211yesmaximal, characteristic, complemented
3C2×C7×#450C211yesmaximal, characteristic, complemented
4C2×#89989C211yesmaximal, characteristic
5C2×#89937C211yesmaximal, characteristic, complemented
6C2×#89937C211yesmaximal, characteristic, complemented
7C2×#89936C211yesmaximal, characteristic, complemented
8C2×SD16×Dic7C211yesmaximal, characteristic, complemented
9C2×#89817C211yesmaximal, characteristic, complemented
10#11737581C2116yesmaximal, direct product factor
11C2×#89533C211yesmaximal, characteristic, complemented
12C2×#89531C211yesmaximal, characteristic, complemented
13C2×#89557C211yesmaximal, characteristic, complemented
14C2×#89528C211yesmaximal, characteristic, complemented
15C2×#89509C211yesmaximal, characteristic, complemented
16C2×#89492C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Dic7—21no—
22C22×C22⋊Dic7—21no—
23C2×#6510C2211yescharacteristic, complemented
24C2×Q8×Dic7C2211yescharacteristic, complemented
25#90489—24no—
26#90489C2218yescomplemented
27C2×D4×Dic7—21no—
28C2×D4×Dic7—21no—
29C2×D4×Dic7C2211yescharacteristic
30C2×D4×Dic7C2211yescharacteristic
31C2×D4×Dic7C2211yescharacteristic
32C2×D4×Dic7C2211yescharacteristic
33C22×#1141C2211yescharacteristic
34C22×#1141C2211yescharacteristic
35C2×#6493C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C2×#6489C2211yescharacteristic
38#90334—24no—
39#90334C2218yescomplemented
40C2×#6461—21no—
41C2×#6460—21no—
42C2×#6456C2211yescharacteristic, complemented
43C2×#6451C2211yescharacteristic, complemented
44C2×#6448—21no—
45C2×#6446—21no—
46C7×#450C2218yescomplemented
47C2×C7×#102C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×#6409C2211yescharacteristic, complemented
51C2×#6409C2211yescharacteristic, complemented
52#89989C2218yes—
53C2×#6406C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×C22⋊(C7⋊C8)C2211yescharacteristic
56#89937C2218yescomplemented
57#89937C2218yescomplemented
58#89936C2218yescomplemented
59SD16×Dic7C2218yescomplemented
60C2×#6395C2211yescharacteristic, complemented
61C2×#6395C2211yescharacteristic, complemented
62C2×#6392C2211yescharacteristic, complemented
63C2×#6391C2211yescharacteristic, complemented
64C2×#6389C2211yescharacteristic, complemented
65C2×Dic7⋊C8C2211yescharacteristic, complemented
66C2×Dic7⋊C8C2211yescharacteristic, complemented
67C2×C8×Dic7C2211yescharacteristic, complemented
68#89817C2218yescomplemented
69C2×#6382C2211yescharacteristic, complemented
70C2×#6381C2211yescharacteristic, complemented
71#89557C2218yescomplemented
72#89533C2218yescomplemented
73#89531C2218yescomplemented
74#89528C2218yescomplemented
75#89509C2218yescomplemented
76#89492C2218yescomplemented
77C2×#3118—71nomaximal, Sylow
78C25×C7—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4—24no—
81C22×C7×D4—24no—
82C22×C7×D4—21no—
83C22×C7×D4—22no—
84C22×C7×D4C2314yes—
85C22×C7×D4C2311yescharacteristic
86C22×C7×D4C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—21no—
89C23×Dic7—21no—
90C23×Dic7—21no—
91C23×Dic7—21no—
92C23×Dic7—21no—
93C22×D28C2311yescharacteristic
94C22×C4×D7—21no—
95C22×Dic14—21no—
96C2×C7×SD16—24no—
97C2×C7×SD16—24no—
98C2×C7×SD16C2314yes—
99C2×C7×SD16C2314yes—
100C22×C7×C8C2311yescharacteristic
101C22×C7×C8C2311yescharacteristic
102C7×C22⋊Q8—22no—
103C7×C22⋊Q8C2314yes—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C22⋊C4—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109C2×C22⋊Dic7—21no—
110C2×C22⋊Dic7—21no—
111C2×C22⋊Dic7—21no—
112C2×C22⋊Dic7—28no—
113C2×C22⋊Dic7—28no—
114C2×C22⋊Dic7D411yescharacteristic
115C2×C22⋊Dic7D411yescharacteristic
116#6510—22no—
117#6510C2314yescomplemented
118Q8×Dic7—22no—
119Q8×Dic7C2314yescomplemented
120D4×Dic7—28no—
121D4×Dic7—28no—
122D4×Dic7—22no—
123D4×Dic7—22no—
124D4×Dic7—22no—
125D4×Dic7—22no—
126D4×Dic7C2314yes—
127D4×Dic7C2314yes—
128D4×Dic7C2314yes—
129D4×Dic7C2314yes—
130C2×#1141—24no—
131C2×#1141—24no—
132C2×#1141C2314yes—
133C2×#1141C2314yes—
134#6493—22no—
135#6493C2314yes—
136C2×(C2×D7)⋊C4—21no—
137C2×(C2×D7)⋊C4—21no—
138C2×(C2×D7)⋊C4—21no—
139C2×(C2×D7)⋊C4—21no—
140#6489—22no—
141#6489D414yes—
142#6489C2314yes—
143#6489C2314yes—
144C2×C4⋊Dic7—21no—
145C2×C4⋊Dic7D411yescharacteristic
146C2×C4⋊Dic7D411yescharacteristic
147C2×C4⋊Dic7C2311yescharacteristic
148C2×C4⋊Dic7C2311yescharacteristic
149C2×C4⋊Dic7C2311yescharacteristic
150C2×Dic7⋊C4—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#6456C2314yescomplemented
161#6451—22no—
162#6451C2314yescomplemented
163#6448—28no—
164#6446—28no—
165C7×#102C2314yes—
166C7×#102C2314yes—
167C7×C22⋊C8C2314yes—
168#6409C2314yescomplemented
169#6409C2314yescomplemented
170#6406C2314yes—
171#6406C2314yes—
172C22⋊(C7⋊C8)C2314yes—
173#6395C2314yescomplemented
174#6395C2314yescomplemented
175#6392C2314yescomplemented
176#6391C2314yescomplemented
177#6389C2314yescomplemented
178Dic7⋊C8C2314yescomplemented
179Dic7⋊C8C2314yescomplemented
180C8×Dic7C2314yescomplemented
181#6382C2314yescomplemented
182#6381C2314yescomplemented
183C2×#542—71no—
184C2×#518—71no—
185#3118—716no—
186C2×#485—71no—
187C2×#482—71no—
188C2×#476—71no—
189C2×#474—71no—
190C2×#463—71no—
191C2×#463—71no—
192C2×#450D711yescharacteristic, complemented
193C2×#447—71no—
194C2×#442—71no—
195C2×#440—71no—
196C2×C4×SD16—71no—
197C2×C4×D8—71no—
198C2×#433—71no—
199C24×C7—28no—
200C24×C7—21no—
201C24×C7—21no—
202C24×C7—24no—
203C24×C7—82no—
204C24×C7—82no—
205C24×C7C2×D411yescharacteristic
206C23×D7—21no—
207C2×C7×Q8—21no—
208C2×C7×Q8—22no—
209C2×C7×Q8—22no—
210C2×C7×Q8C2412yes—
211C2×C7×D4—28no—
212C2×C7×D4—216no—
213C2×C7×D4—28no—
214C2×C7×D4—28no—
215C2×C7×D4—24no—
216C2×C7×D4—21no—
217C2×C7×D4—21no—
218C2×C7×D4—22no—
219C2×C7×D4—22no—
220C2×C7×D4#4114yes—
221C2×C7×D4#4114yes—
222C2×C7×D4C2412yes—
223C2×C7×D4C2412yes—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2×D412yes—
230C22×C4×C7C2412yes—
231C22×C4×C7C2411yescharacteristic
232C2×C22⋊D7—24no—
233C2×C22⋊D7—82no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—24no—
238C22×Dic7—24no—
239C22×Dic7—24no—
240C22×Dic7—24no—
241C22×Dic7—82no—
242C22×Dic7—82no—
243C22×Dic7—82no—
244C22×Dic7—82no—
245C22×Dic7C2×D411yescharacteristic
246C22×Dic7C2×D411yescharacteristic
247C22×Dic7C2×D411yescharacteristic
248C22×Dic7C2×D411yescharacteristic
249C2×D28—22no—
250C2×D28—22no—
251C2×D28—21no—
252C2×D28C2412yes—
253C2×C4×D7—24no—
254C2×C4×D7—82no—
255C2×Dic14—24no—
256C2×Dic14—82no—
257C7×SD16—28no—
258C7×SD16—28no—
259C2×C7×C8—22no—
260C2×C7×C8—22no—
261C2×C7×C8C2412yes—
262C2×C7×C8C2412yes—
263C7×C4⋊C4—21no—
264C7×C4⋊C4—24no—
265C7×C4⋊C4C2412yes—
266C7×C22⋊C4—24no—
267C22⋊Dic7—24no—
268C22⋊Dic7—24no—
269C22⋊Dic7—24no—
270C22⋊Dic7—24no—
271C22⋊Dic7—24no—
272C22⋊Dic7C2×D414yes—
273C22⋊Dic7C2×D414yes—
274#1141—28no—
275#1141—28no—
276(C2×D7)⋊C4—24no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4—24no—
280C4⋊Dic7—21no—
281C4⋊Dic7—21no—
282C4⋊Dic7—21no—
283C4⋊Dic7—24no—
284C4⋊Dic7C2×D414yes—
285C4⋊Dic7C2×D414yes—
286C4⋊Dic7C2412yes—
287C4⋊Dic7C2412yes—
288C4⋊Dic7C2412yes—
289Dic7⋊C4—24no—
290C4×Dic7—24no—
291C4×Dic7—24no—
292C4×Dic7C2×D412yes—
293C4×Dic7C2×D412yes—
294C4×Dic7C2412yes—
295C4×Dic7C2412yes—
296C2×C7⋊C8—22no—
297C2×C7⋊C8—22no—
298C2×C7⋊C8C2412yes—
299C2×C7⋊C8C2412yes—
300C23×D4C2×D711yescharacteristic
301C22×SD16C2×D711yescharacteristic
302C22×SD16C2×D711yescharacteristic
303C22×D8—71no—
304C22×D8—71no—
305#542—78no—
306#542—144no—
307C2×C4⋊Q8—71no—
308C2×#126—141no—
309C2×#124—71no—
310C2×#124—141no—
311C2×#123—141no—
312C2×C22⋊Q8—141no—
313C2×C22⋊Q8C2×D711yescharacteristic
314C2×#121—71no—
315#518—78no—
316#518—144no—
317C2×C4×Q8—71no—
318C2×C4×D4—71no—
319C2×C4×D4—71no—
320C2×C4×D4—71no—
321C2×C4×D4—71no—
322C2×C4×D4—71no—
323C2×C4×D4—141no—
324C2×C4×D4—141no—
325C2×#117—71no—
326C2×#117—71no—
327C22×C22⋊C4—141no—
328C22×C22⋊C4—141no—
329#485—78no—
330#482—78no—
331#476—78no—
332#474—78no—
333#463—78no—
334#463—78no—
335#450C2×D718yescomplemented
336#447—78no—
337#442—78no—
338#440—78no—
339C4×SD16—78no—
340C4×D8—78no—
341#433—78no—
342C2×#107—71no—
343C2×#107—71no—
344C2×#106—71no—
345C2×#106—71no—
346C2×C4⋊C8—71no—
347C2×C4⋊C8—71no—
348C2×#103—71no—
349C2×#103—71no—
350C2×#102—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×#102—71no—
354C2×#102C2×D711yescharacteristic
355C2×#102C2×D711yescharacteristic
356C2×C22⋊C8—71no—
357C2×C22⋊C8C2×D711yescharacteristic
358C2×#97—71no—
359C2×C4×C8—71no—
360C23×C7—216no—
361C23×C7—22no—
362C23×C7—24no—
363C23×C7—24no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—42no—
369C23×C7—42no—
370C23×C7—42no—
371C23×C7—42no—
372C23×C7—84no—
373C23×C7—84no—
374C23×C7—816no—
375C23×C7C22×D412yes—
376C23×C7C22×D411yescharacteristic
377C22×D7—22no—
378C22×D7—42no—
379C22×D7—42no—
380C22×D7—42no—
381C7×Q8—22no—
382C7×Q8—22no—
383C7×Q8—42no—
384C7×D4—216no—
385C7×D4—24no—
386C7×D4—24no—
387C7×D4—22no—
388C7×D4—22no—
389C7×D4C2×#4114yes—
390C7×D4C2×#4114yes—
391C2×C4×C7—22no—
392C2×C4×C7—24no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—42no—
398C2×C4×C7—42no—
399C2×C4×C7C22×D412yes—
400C2×C4×C7C22×D411yescharacteristic
401C2×C4×C7C2×#4112yes—
402C2×C4×C7C2×#4112yes—
403C2×C4×C7C2511yescharacteristic
404C22⋊D7—84no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—42no—
413C2×Dic7—42no—
414C2×Dic7—42no—
415C2×Dic7—84no—
416C2×Dic7—84no—
417C2×Dic7—84no—
418C2×Dic7—84no—
419C2×Dic7C22×D412yes—
420C2×Dic7C22×D412yes—
421C2×Dic7C22×D412yes—
422C2×Dic7C22×D412yes—
423D28—22no—
424D28—22no—
425D28—42no—
426C4×D7—84no—
427Dic14—84no—
428C7×C8—22no—
429C7×C8—22no—
430C7⋊C8—22no—
431C7⋊C8—22no—
432C25—21no—
433C22×Q8—141no—
434C22×Q8C22×D711yescharacteristic
435C22×D4—24no—
436C22×D4—24no—
437C22×D4—21no—
438C22×D4—22no—
439C22×D4—71no—
440C22×D4—141no—
441C22×D4C22×D714yes—
442C22×D4C22×D711yescharacteristic
443C22×D4C22×D711yescharacteristic
444C23×C4—141no—
445C23×C4—141no—
446C23×C4—141no—
447C23×C4—141no—
448C23×C4—141no—
449C23×C4C22×D711yescharacteristic
450C2×SD16—24no—
451C2×SD16—24no—
452C2×SD16C22×D714yes—
453C2×SD16C22×D714yes—
454C2×D8—74no—
455C2×D8—74no—
456C2×D8—144no—
457C2×D8—144no—
458C22×C8—71no—
459C22×C8—71no—
460C22×C8C22×D711yescharacteristic
461C22×C8C22×D711yescharacteristic
462C4⋊Q8—74no—
463C4⋊Q8—142no—
464#126—148no—
465#124—74no—
466#124—142no—
467#124—148no—
468#123—148no—
469C22⋊Q8—22no—
470C22⋊Q8—148no—
471C22⋊Q8C22×D714yes—
472#121—74no—
473#121—142no—
474C4×Q8—74no—
475C4×Q8—142no—
476C4×D4—74no—
477C4×D4—74no—
478C4×D4—74no—
479C4×D4—74no—
480C4×D4—74no—
481C4×D4—142no—
482C4×D4—142no—
483C4×D4—142no—
484C4×D4—142no—
485C4×D4—142no—
486C4×D4—148no—
487C4×D4—148no—
488#117—74no—
489#117—74no—
490#117—74no—
491#117—142no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—71no—
495C2×C4⋊C4—71no—
496C2×C4⋊C4—71no—
497C2×C4⋊C4—71no—
498C2×C4⋊C4—141no—
499C2×C4⋊C4—141no—
500C2×C4⋊C4C22×D711yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—71no—
503C2×C22⋊C4—71no—
504C2×C22⋊C4—148no—
505C2×C22⋊C4—148no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4—141no—
508C2×C22⋊C4—141no—
509C2×C22⋊C4—141no—
510C2×C22⋊C4—141no—
511C2×C22⋊C4—141no—
512C2×C22⋊C4—141no—
513C2×C22⋊C4—141no—
514C2×C22⋊C4—141no—
515C2×C42—71no—
516C2×C42—71no—
517C2×C42—141no—
518C2×C42—141no—
519#107—74no—
520#107—74no—
521#106—74no—
522#106—74no—
523C4⋊C8—74no—
524C4⋊C8—74no—
525#103—74no—
526#103—74no—
527#102—74no—
528#102—74no—
529#102—74no—
530#102—74no—
531#102C22×D714yes—
532#102C22×D714yes—
533C22⋊C8—74no—
534C22⋊C8C22×D714yes—
535#97—74no—
536C4×C8—74no—
537C22×C7—22no—
538C22×C7—24no—
539C22×C7—24no—
540C22×C7—22no—
541C22×C7—22no—
542C22×C7—44no—
543C22×C7—48no—
544C22×C7—48no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—816no—
550C22×C7#52512yes—
551C22×C7#57612yes—
552C22×C7#57712yes—
553C22×C7C23×D411yescharacteristic
554C2×D7—42no—
555C2×D7—42no—
556C2×D7—42no—
557C2×D7—84no—
558C4×C7—22no—
559C4×C7—42no—
560C4×C7—42no—
561C4×C7#52512yes—
562C4×C7C22×#4111yescharacteristic
563C4×C7C22×#4111yescharacteristic
564Dic7—22no—
565Dic7—22no—
566Dic7—22no—
567Dic7—22no—
568Dic7—42no—
569Dic7—42no—
570Dic7—42no—
571C24—28no—
572C24—21no—
573C24—21no—
574C24—24no—
575C24—82no—
576C24—82no—
577C24—141no—
578C24D4×D711yescharacteristic
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—144no—
583C2×Q8—562no—
584C2×Q8C23×D712yes—
585C2×D4—28no—
586C2×D4—216no—
587C2×D4—28no—
588C2×D4—28no—
589C2×D4—24no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—72no—
595C2×D4—144no—
596C2×D4—141no—
597C2×D4—142no—
598C2×D4—142no—
599C2×D4—562no—
600C2×D4#115914yes—
601C2×D4#115914yes—
602C2×D4C23×D712yes—
603C2×D4C23×D712yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—71no—
609C22×C4—71no—
610C22×C4—71no—
611C22×C4—71no—
612C22×C4—144no—
613C22×C4—144no—
614C22×C4—144no—
615C22×C4—144no—
616C22×C4—144no—
617C22×C4—141no—
618C22×C4—141no—
619C22×C4—141no—
620C22×C4—562no—
621C22×C4—562no—
622C22×C4—562no—
623C22×C4—562no—
624C22×C4—562no—
625C22×C4D4×D712yes—
626C22×C4D4×D711yescharacteristic
627C22×C4C23×D712yes—
628C22×C4C23×D711yescharacteristic
629SD16—28no—
630SD16—28no—
631D8—148no—
632D8—148no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—72no—
636C2×C8—72no—
637C2×C8—142no—
638C2×C8—142no—
639C2×C8C23×D712yes—
640C2×C8C23×D712yes—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—74no—
644C4⋊C4—74no—
645C4⋊C4—72no—
646C4⋊C4—72no—
647C4⋊C4—72no—
648C4⋊C4—144no—
649C4⋊C4—144no—
650C4⋊C4—141no—
651C4⋊C4—141no—
652C4⋊C4—141no—
653C4⋊C4C23×D712yes—
654C22⋊C4—24no—
655C22⋊C4—74no—
656C22⋊C4—74no—
657C22⋊C4—144no—
658C22⋊C4—144no—
659C22⋊C4—144no—
660C22⋊C4—144no—
661C22⋊C4—144no—
662C22⋊C4—144no—
663C22⋊C4—144no—
664C22⋊C4—144no—
665C22⋊C4—144no—
666C42—72no—
667C42—72no—
668C42—72no—
669C42—72no—
670C42—144no—
671C42—144no—
672C2×C7—42no—
673C2×C7—44no—
674C2×C7—44no—
675C2×C7#311814yescomplemented
676C2×C7C2×#52511yescharacteristic
677C2×C7C2×#57611yescharacteristic
678C2×C7C2×#57711yescharacteristic
679D7—82no—
680C23—216no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—22no—
687C23—22no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—84no—
693C23—84no—
694C23—816no—
695C23—142no—
696C23—282no—
697C23—282no—
698C23—282no—
699C23C2×D4×D712yes—
700C23C2×D4×D711yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—564no—
705D4—216no—
706D4—24no—
707D4—24no—
708D4—22no—
709D4—22no—
710D4—142no—
711D4—142no—
712D4—282no—
713D4—564no—
714D4C2×#115914yes—
715D4C2×#115914yes—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—72no—
725C2×C4—72no—
726C2×C4—72no—
727C2×C4—72no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—282no—
736C2×C4—282no—
737C2×C4—282no—
738C2×C4—564no—
739C2×C4—564no—
740C2×C4—564no—
741C2×C4—564no—
742C2×C4—564no—
743C2×C4C2×D4×D712yes—
744C2×C4C2×D4×D711yescharacteristic
745C2×C4C2×#115912yes—
746C2×C4C2×#115912yes—
747C2×C4C24×D711yescharacteristic
748C8—22no—
749C8—22no—
750C8—142no—
751C8—142no—
752C7C2×#311811yescharacteristic, complemented, Sylow
753C22—22no—
754C22—24no—
755C22—24no—
756C22—22no—
757C22—22no—
758C22—42no—
759C22—42no—
760C22—44no—
761C22—48no—
762C22—48no—
763C22—42no—
764C22—42no—
765C22—816no—
766C22—282no—
767C22—282no—
768C22—282no—
769C22—564no—
770C22#9027712yes—
771C22#9045312yes—
772C22#9046512yes—
773C22C22×D4×D711yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—142no—
778C4—142no—
779C4—142no—
780C4—142no—
781C4—282no—
782C4—282no—
783C4—282no—
784C4#9027712yes—
785C4C22×#115911yescharacteristic
786C4C22×#115911yescharacteristic
787C2—42no—
788C2—44no—
789C2—44no—
790C2—562no—
791C2#1173758114yesdirect product factor
792C2C2×#9027711yescharacteristic
793C2C2×#9045311yescharacteristic
794C2C2×#9046511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#450C2
socleC23×C7C22×D4
prime radicalC2×#89989C2
hypercenterC2×#450D7
hypocenterC7C2×#3118
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#90489C2semidirect
2. C2×#90334C2semidirect
3. C2×C7×#450C2semidirect
5. C2×#89937C2semidirect
6. C2×#89937C2semidirect
7. C2×#89936C2semidirect
8. C2×SD16×Dic7C2semidirect
9. C2×#89817C2semidirect
10. #11737581C2direct (N × H)
11. C2×#89533C2semidirect
12. C2×#89531C2semidirect
13. C2×#89557C2semidirect
14. C2×#89528C2semidirect
15. C2×#89509C2semidirect
16. C2×#89492C2semidirect
23. C2×#6510C22semidirect
24. C2×Q8×Dic7C22semidirect
26. #90489C22semidirect
39. #90334C22semidirect
42. C2×#6456C22semidirect
43. C2×#6451C22semidirect
46. C7×#450C22semidirect
50. C2×#6409C22semidirect
51. C2×#6409C22semidirect
56. #89937C22semidirect
57. #89937C22semidirect
58. #89936C22semidirect
59. SD16×Dic7C22semidirect
60. C2×#6395C22semidirect
61. C2×#6395C22semidirect
62. C2×#6392C22semidirect
63. C2×#6391C22semidirect
64. C2×#6389C22semidirect
65. C2×Dic7⋊C8C22semidirect
66. C2×Dic7⋊C8C22semidirect
67. C2×C8×Dic7C22semidirect
68. #89817C22semidirect
69. C2×#6382C22semidirect
70. C2×#6381C22semidirect
71. #89557C22semidirect
72. #89533C22semidirect
73. #89531C22semidirect
74. #89528C22semidirect
75. #89509C22semidirect
76. #89492C22semidirect
117. #6510C23semidirect
119. Q8×Dic7C23semidirect
160. #6456C23semidirect
162. #6451C23semidirect
168. #6409C23semidirect
169. #6409C23semidirect
173. #6395C23semidirect
174. #6395C23semidirect
175. #6392C23semidirect
176. #6391C23semidirect
177. #6389C23semidirect
178. Dic7⋊C8C23semidirect
179. Dic7⋊C8C23semidirect
180. C8×Dic7C23semidirect
181. #6382C23semidirect
182. #6381C23semidirect
192. C2×#450D7semidirect
335. #450C2×D7semidirect
675. C2×C7#3118semidirect
752. C7C2×#3118semidirect
791. C2#11737581direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904892
C2×#903342
C2×C7×#4502
C2×#899892
C2×#899372
C2×#899362
C2×SD16×Dic72
C2×#898172
#117375812
C2×#895332
C2×#895312
C2×#895572
C2×#895282
C2×#895092
C2×#894922
C2×#31187