Finite Group Databasebeta

← C2×#11741065 #14230412

Subgroups — C2×#11741065 #14230412

Order 1792.

2158 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×C7×#553C211yesmaximal, characteristic
2C2×D4×Dic14C211yesmaximal, characteristic, complemented
3#11741065C2116yesmaximal, direct product factor
4C2×#89835C211yesmaximal, characteristic, complemented
5C2×#89841C211yesmaximal, characteristic, complemented
6C2×#89812C211yesmaximal, characteristic, complemented
7C2×#89812C211yesmaximal, characteristic, complemented
8C2×#89814C211yesmaximal, characteristic, complemented
9C2×#89813C211yesmaximal, characteristic, complemented
10C2×#89791C211yesmaximal, characteristic, complemented
11C2×#89783C211yesmaximal, characteristic, complemented
12C2×#89790C211yesmaximal, characteristic, complemented
13C2×#89768C211yesmaximal, characteristic, complemented
14C2×#89776C211yesmaximal, characteristic, complemented
15C2×#89742C211yesmaximal, characteristic, complemented
16C22×#6384C211yesmaximal, characteristic, complemented
17C23×Dic14C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C7×#553—24no—
20C7×#553C2218yes—
21C2×C7×#126—21no—
22C2×C7×#125C2211yescharacteristic
23C2×C7×#123—21no—
24C2×C7×#121—21no—
25C2×C7×#121C2211yescharacteristic
26C2×C7×#121C2211yescharacteristic
27C2×C4×C7×D4—21no—
28C2×C4×C7×D4C2211yescharacteristic
29C2×C4×C7×D4C2211yescharacteristic
30C2×C7×#117C2211yescharacteristic
31C22×C7×C4⋊C4C2211yescharacteristic
32C2×D4×Dic7—21no—
33C22×#1142C2211yescharacteristic
34C22×#1142C2211yescharacteristic
35C22×#1142C2211yescharacteristic
36C2×#6487C2211yescharacteristic
37C2×#6487C2211yescharacteristic
38C22×#1136C2211yescharacteristic
39C23×C7⋊C8C2211yescharacteristic
40D4×Dic14—24no—
41D4×Dic14C2218yescomplemented
42C2×#6451—21no—
43C2×#6441—21no—
44C2×#6441—21no—
45C2×#6432C2211yescharacteristic
46C2×C4×Dic14C2211yescharacteristic
47C2×#6406C2211yescharacteristic
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49C2×C22⋊(C7⋊C8)C2211yescharacteristic
50#89841C2218yescomplemented
51#89835C2218yescomplemented
52#89814C2218yescomplemented
53#89813C2218yescomplemented
54#89812C2218yescomplemented
55#89812C2218yescomplemented
56#89791C2218yescomplemented
57#89790C2218yescomplemented
58#89783C2218yescomplemented
59#89776C2218yescomplemented
60#89768C2218yescomplemented
61#89742C2218yescomplemented
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64C2×#6384C2211yescharacteristic
65C2×#6384C2211yescharacteristic
66C2×#6384C2211yescharacteristic
67C2×#6384C2211yescharacteristic
68C2×#6384C2211yescharacteristic
69C2×#6384C2211yescharacteristic
70C2×#6384C2211yescharacteristic
71C2×#6384C2218yescomplemented
72C2×#6382C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3320—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4—21no—
80C22×C7×D4D411yescharacteristic
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C23×C4×C7—21no—
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×Dic7—21no—
87C23×Dic7—21no—
88C22×Dic14—24no—
89C22×Dic14—24no—
90C22×Dic14—21no—
91C22×Dic14—21no—
92C22×Dic14—22no—
93C22×Dic14—22no—
94C22×Dic14—42no—
95C22×Dic14—42no—
96C22×Dic14C2311yescharacteristic
97C22×Dic14C2311yescharacteristic
98C22×Dic14C2314yes—
99C22×Dic14C2314yes—
100C22×Dic14C2311yescharacteristic
101C7×#126—28no—
102C7×#125—22no—
103C7×#125C2314yes—
104C7×#123—28no—
105C7×#121—28no—
106C7×#121—22no—
107C7×#121—22no—
108C7×#121C2314yes—
109C7×#121C2314yes—
110C4×C7×D4—28no—
111C4×C7×D4—22no—
112C4×C7×D4D414yes—
113C4×C7×D4C2314yes—
114C4×C7×D4C2314yes—
115C7×#117—22no—
116C7×#117C2314yes—
117C2×C7×C4⋊C4—21no—
118C2×C7×C4⋊C4—22no—
119C2×C7×C4⋊C4—21no—
120C2×C7×C4⋊C4—21no—
121C2×C7×C4⋊C4D411yescharacteristic
122C2×C7×C4⋊C4C2311yescharacteristic
123C2×C7×C4⋊C4C2311yescharacteristic
124C2×C7×C4⋊C4C2311yescharacteristic
125C2×C7×C4⋊C4C2314yes—
126C2×C7×C22⋊C4—21no—
127C2×C7×C22⋊C4—21no—
128C2×C7×C22⋊C4—21no—
129C2×C7×C22⋊C4—21no—
130C2×C7×C22⋊C4D411yescharacteristic
131C2×C7×C22⋊C4D411yescharacteristic
132C2×C42×C7—21no—
133C2×C42×C7C2311yescharacteristic
134C2×C22⋊Dic7—21no—
135C2×C22⋊Dic7—21no—
136D4×Dic7—28no—
137C2×#1142—24no—
138C2×#1142—42no—
139C2×#1142—42no—
140C2×#1142C2314yes—
141C2×#1142C2314yes—
142C2×#1142C2314yes—
143C2×C4⋊Dic7—21no—
144C2×C4⋊Dic7—21no—
145C2×C4⋊Dic7C2311yescharacteristic
146#6487—22no—
147#6487—22no—
148#6487C2314yes—
149#6487C2314yes—
150C2×Dic7⋊C4—21no—
151C2×Dic7⋊C4—21no—
152C2×Dic7⋊C4—21no—
153C2×C4×Dic7—21no—
154C2×#1136—42no—
155C2×#1136C2314yes—
156C22×C7⋊C8—42no—
157C22×C7⋊C8C2311yescharacteristic
158C22×C7⋊C8C2311yescharacteristic
159C22×C7⋊C8C2311yescharacteristic
160C22×C7⋊C8C2311yescharacteristic
161C22×C7⋊C8C2314yes—
162#6451—28no—
163#6441—28no—
164#6441—28no—
165#6432—22no—
166#6432C2314yes—
167C4×Dic14—22no—
168C4×Dic14C2314yes—
169#6406C2314yes—
170C22⋊(C7⋊C8)C2314yes—
171C22⋊(C7⋊C8)C2314yes—
172#6384C2314yes—
173#6384C2314yes—
174#6384C2314yes—
175#6384C2314yes—
176#6384C2314yes—
177#6384C2314yes—
178#6384C2314yes—
179#6384C2314yes—
180#6384C2314yes—
181#6382C2314yes—
182#6381C2314yes—
183#6381C2314yes—
184C4⋊(C7⋊C8)C2314yes—
185#6377C2314yes—
186C2×#553D711yescharacteristic
187C2×D4×Q8—71no—
188#3320—716no—
189C2×#491—71no—
190C2×#484—71no—
191C2×#485—71no—
192C2×#479—71no—
193C2×#468—71no—
194C2×#465—71no—
195C2×#461—71no—
196C2×#448—71no—
197C2×#448—71no—
198C2×#440—71no—
199C2×#435—71no—
200C2×#419—71no—
201C22×#103—71no—
202C24×C7—21no—
203C24×C7C2×D411yescharacteristic
204C24×C7C2×D411yescharacteristic
205C2×C7×D4—24no—
206C2×C7×D4—24no—
207C2×C7×D4—24no—
208C2×C7×D4—21no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4—44no—
212C2×C7×D4—82no—
213C2×C7×D4C2×D414yes—
214C2×C7×D4C2412yes—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—24no—
223C22×C4×C7—24no—
224C22×C4×C7—82no—
225C22×C4×C7—82no—
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2×D412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2411yescharacteristic
235C22×Dic7—21no—
236C22×Dic7—24no—
237C22×Dic7—24no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—44no—
242C22×Dic7—44no—
243C2×Dic14—21no—
244C2×Dic14—22no—
245C2×Dic14—22no—
246C2×Dic14—22no—
247C2×Dic14—22no—
248C2×Dic14—22no—
249C2×Dic14—28no—
250C2×Dic14—28no—
251C2×Dic14—21no—
252C2×Dic14—21no—
253C2×Dic14—24no—
254C2×Dic14—24no—
255C2×Dic14—44no—
256C2×Dic14—44no—
257C2×Dic14—48no—
258C2×Dic14—48no—
259C2×Dic14—44no—
260C2×Dic14—44no—
261C2×Dic14#4114yes—
262C2×Dic14C2412yes—
263C2×Dic14C2412yes—
264C2×Dic14C2412yes—
265C7×C4⋊C4—21no—
266C7×C4⋊C4—21no—
267C7×C4⋊C4—24no—
268C7×C4⋊C4—24no—
269C7×C4⋊C4—24no—
270C7×C4⋊C4—21no—
271C7×C4⋊C4C2×D414yes—
272C7×C4⋊C4C2412yes—
273C7×C4⋊C4C2412yes—
274C7×C4⋊C4C2412yes—
275C7×C22⋊C4—24no—
276C7×C22⋊C4—24no—
277C7×C22⋊C4—24no—
278C7×C22⋊C4—24no—
279C7×C22⋊C4C2×D414yes—
280C7×C22⋊C4C2×D414yes—
281C42×C7—24no—
282C42×C7C2×D412yes—
283C42×C7C2412yes—
284C22⋊Dic7—24no—
285C22⋊Dic7—24no—
286#1142—28no—
287#1142—44no—
288#1142—44no—
289C4⋊Dic7—21no—
290C4⋊Dic7—24no—
291C4⋊Dic7—24no—
292C4⋊Dic7C2412yes—
293Dic7⋊C4—24no—
294Dic7⋊C4—24no—
295Dic7⋊C4—24no—
296C4×Dic7—24no—
297#1136—44no—
298C2×C7⋊C8—22no—
299C2×C7⋊C8—22no—
300C2×C7⋊C8—22no—
301C2×C7⋊C8—22no—
302C2×C7⋊C8—44no—
303C2×C7⋊C8C2412yes—
304C2×C7⋊C8C2412yes—
305C2×C7⋊C8C2412yes—
306C2×C7⋊C8C2412yes—
307C23×Q8—71no—
308C23×Q8—71no—
309C22×SD16—71no—
310C22×SD16—71no—
311C22×SD16—71no—
312C22×M16—71no—
313C23×C8—71no—
314#553—24no—
315#553C2×D718yes—
316D4×Q8—78no—
317D4×Q8—144no—
318C2×C4⋊Q8—71no—
319C2×C4⋊Q8—141no—
320C2×#126—21no—
321C2×#125C2×D711yescharacteristic
322C2×#123—21no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—71no—
325C2×C22⋊Q8—141no—
326C2×C22⋊Q8—141no—
327C2×#121—21no—
328C2×#121C2×D711yescharacteristic
329C2×#121C2×D711yescharacteristic
330C2×C4×Q8—71no—
331C2×C4×D4—21no—
332C2×C4×D4—141no—
333C2×C4×D4C2×D711yescharacteristic
334C2×C4×D4C2×D711yescharacteristic
335C2×#117C2×D711yescharacteristic
336C22×C4⋊C4C2×D711yescharacteristic
337#491—78no—
338#485—78no—
339#484—78no—
340#479—78no—
341#468—78no—
342#465—78no—
343#461—78no—
344#448—78no—
345#448—78no—
346#440—78no—
347#435—78no—
348C2×#107—71no—
349C2×#107—71no—
350C2×#106—71no—
351C2×C4⋊C8—71no—
352#419—78no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—71no—
361C2×#103—71no—
362C2×#103—78no—
363C2×#102—71no—
364C2×C22⋊C8—71no—
365C2×C22⋊C8—71no—
366C2×#97—71no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—42no—
374C23×C7—42no—
375C23×C7—42no—
376C23×C7#13714yes—
377C23×C7C22×D412yes—
378C23×C7C22×D412yes—
379C23×C7C22×D411yescharacteristic
380C7×D4—28no—
381C7×D4—22no—
382C7×D4—22no—
383C7×D4—48no—
384C7×D4—42no—
385C7×D4—84no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—24no—
391C2×C4×C7—24no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—42no—
400C2×C4×C7—42no—
401C2×C4×C7—42no—
402C2×C4×C7—84no—
403C2×C4×C7—84no—
404C2×C4×C7C22×D412yes—
405C2×C4×C7C22×D412yes—
406C2×C4×C7C22×D412yes—
407C2×C4×C7C22×D412yes—
408C2×C4×C7C22×D411yescharacteristic
409C2×C4×C7C2×#4112yes—
410C2×C4×C7H(5,𝔽2)12yes—
411C2×C4×C7C2511yescharacteristic
412C2×Dic7—24no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—48no—
418C2×Dic7—48no—
419C2×Dic7—42no—
420C2×Dic7—42no—
421C2×Dic7—42no—
422Dic14—24no—
423Dic14—22no—
424Dic14—22no—
425Dic14—22no—
426Dic14—22no—
427Dic14—22no—
428Dic14—48no—
429Dic14—48no—
430Dic14—42no—
431Dic14—42no—
432Dic14C2×#4114yes—
433C7⋊C8—22no—
434C7⋊C8—22no—
435C7⋊C8—22no—
436C7⋊C8—22no—
437C22×Q8—71no—
438C22×Q8—71no—
439C22×Q8—71no—
440C22×Q8—74no—
441C22×Q8—74no—
442C22×Q8—144no—
443C22×Q8—144no—
444C22×Q8—141no—
445C22×Q8—141no—
446C22×Q8—142no—
447C22×Q8—142no—
448C22×Q8—282no—
449C22×Q8—282no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4C22⋊D711yescharacteristic
453C22×D4C22×D711yescharacteristic
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—141no—
457C23×C4—141no—
458C23×C4C22×D711yescharacteristic
459C23×C4C22×D711yescharacteristic
460C2×SD16—74no—
461C2×SD16—74no—
462C2×SD16—74no—
463C2×SD16—144no—
464C2×SD16—282no—
465C2×SD16—282no—
466C2×M16—74no—
467C2×M16—282no—
468C22×C8—71no—
469C22×C8—71no—
470C22×C8—71no—
471C22×C8—71no—
472C22×C8—74no—
473C22×C8—282no—
474C4⋊Q8—74no—
475C4⋊Q8—148no—
476C4⋊Q8—142no—
477#126—28no—
478#125—22no—
479#125C22×D714yes—
480#123—28no—
481C22⋊Q8—74no—
482C22⋊Q8—74no—
483C22⋊Q8—142no—
484C22⋊Q8—142no—
485C22⋊Q8—148no—
486C22⋊Q8—148no—
487#121—28no—
488#121—22no—
489#121—22no—
490#121C22×D714yes—
491#121C22×D714yes—
492C4×Q8—74no—
493C4×Q8—142no—
494C4×D4—28no—
495C4×D4—22no—
496C4×D4—148no—
497C4×D4C22⋊D714yes—
498C4×D4C22×D714yes—
499C4×D4C22×D714yes—
500#117—22no—
501#117C22×D714yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—71no—
507C2×C4⋊C4—141no—
508C2×C4⋊C4—141no—
509C2×C4⋊C4—141no—
510C2×C4⋊C4—141no—
511C2×C4⋊C4—141no—
512C2×C4⋊C4C22⋊D711yescharacteristic
513C2×C4⋊C4C22×D711yescharacteristic
514C2×C4⋊C4C22×D711yescharacteristic
515C2×C4⋊C4C22×D714yes—
516C2×C4⋊C4C22×D711yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—141no—
522C2×C22⋊C4—141no—
523C2×C22⋊C4C22⋊D711yescharacteristic
524C2×C22⋊C4C22⋊D711yescharacteristic
525C2×C42—21no—
526C2×C42—141no—
527C2×C42C22×D711yescharacteristic
528#107—74no—
529#107—74no—
530#106—74no—
531C4⋊C8—74no—
532#103—74no—
533#103—74no—
534#103—74no—
535#103—74no—
536#103—74no—
537#103—74no—
538#103—74no—
539#103—74no—
540#103—74no—
541#102—74no—
542C22⋊C8—74no—
543C22⋊C8—74no—
544#97—74no—
545C22×C7—22no—
546C22×C7—28no—
547C22×C7—22no—
548C22×C7—22no—
549C22×C7—22no—
550C22×C7—22no—
551C22×C7—44no—
552C22×C7—42no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—84no—
556C22×C7#54612yes—
557C22×C7C2×#13714yes—
558C22×C7C2×#13712yes—
559C22×C7#57712yes—
560C22×C7C23×D411yescharacteristic
561C4×C7—22no—
562C4×C7—22no—
563C4×C7—22no—
564C4×C7—22no—
565C4×C7—42no—
566C4×C7—42no—
567C4×C7—42no—
568C4×C7#54612yes—
569C4×C7C22×#4111yescharacteristic
570C4×C7C2×H(5,𝔽2)11yescharacteristic
571Dic7—24no—
572Dic7—42no—
573Dic7—42no—
574Dic7—42no—
575C24—21no—
576C24C2×C22⋊D711yescharacteristic
577C24C2×C22⋊D711yescharacteristic
578C2×Q8—74no—
579C2×Q8—72no—
580C2×Q8—72no—
581C2×Q8—72no—
582C2×Q8—148no—
583C2×Q8—148no—
584C2×Q8—142no—
585C2×Q8—141no—
586C2×Q8—144no—
587C2×Q8—144no—
588C2×Q8—141no—
589C2×Q8—141no—
590C2×Q8—142no—
591C2×Q8—142no—
592C2×Q8—142no—
593C2×Q8—142no—
594C2×Q8—284no—
595C2×Q8—284no—
596C2×Q8—284no—
597C2×Q8—284no—
598C2×Q8—288no—
599C2×Q8—288no—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—21no—
606C2×D4—44no—
607C2×D4—82no—
608C2×D4C2×C22⋊D714yes—
609C2×D4C23×D712yes—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—82no—
620C22×C4—82no—
621C22×C4—141no—
622C22×C4—144no—
623C22×C4—144no—
624C22×C4—141no—
625C22×C4—141no—
626C22×C4—141no—
627C22×C4—284no—
628C22×C4—284no—
629C22×C4C2×C22⋊D712yes—
630C22×C4C2×C22⋊D712yes—
631C22×C4C2×C22⋊D711yescharacteristic
632C22×C4C2×C22⋊D711yescharacteristic
633C22×C4C2×C22⋊D711yescharacteristic
634C22×C4C2×C22⋊D711yescharacteristic
635C22×C4C23×D712yes—
636C22×C4C23×D712yes—
637C22×C4C23×D711yescharacteristic
638SD16—148no—
639SD16—284no—
640SD16—284no—
641M16—284no—
642C2×C8—72no—
643C2×C8—72no—
644C2×C8—72no—
645C2×C8—72no—
646C2×C8—142no—
647C2×C8—142no—
648C2×C8—142no—
649C2×C8—142no—
650C2×C8—284no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—21no—
657C4⋊C4—72no—
658C4⋊C4—144no—
659C4⋊C4—144no—
660C4⋊C4—144no—
661C4⋊C4—141no—
662C4⋊C4—144no—
663C4⋊C4—144no—
664C4⋊C4C2×C22⋊D714yes—
665C4⋊C4C23×D712yes—
666C4⋊C4C23×D712yes—
667C4⋊C4C23×D712yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—144no—
673C22⋊C4—144no—
674C22⋊C4C2×C22⋊D714yes—
675C22⋊C4C2×C22⋊D714yes—
676C42—24no—
677C42—144no—
678C42C2×C22⋊D712yes—
679C42C23×D712yes—
680C2×C7—24no—
681C2×C7—42no—
682C2×C7—82no—
683C2×C7#332014yescomplemented
684C2×C7C2×#54611yescharacteristic
685C2×C7C22×#13711yescharacteristic
686C2×C7C2×#57711yescharacteristic
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23#651414yes—
697C23C22×C22⋊D712yes—
698C23C22×C22⋊D712yes—
699C23C22×C22⋊D711yescharacteristic
700Q8—74no—
701Q8—144no—
702Q8—142no—
703Q8—142no—
704Q8—142no—
705Q8—142no—
706Q8—142no—
707Q8—288no—
708Q8—288no—
709Q8—282no—
710Q8—282no—
711D4—28no—
712D4—22no—
713D4—22no—
714D4—48no—
715D4—42no—
716D4—84no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—84no—
734C2×C4—84no—
735C2×C4—144no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—288no—
741C2×C4—288no—
742C2×C4—282no—
743C2×C4—282no—
744C2×C4—282no—
745C2×C4D7×#4112yes—
746C2×C4#655312yes—
747C2×C4C22×C22⋊D712yes—
748C2×C4C22×C22⋊D712yes—
749C2×C4C22×C22⋊D712yes—
750C2×C4C22×C22⋊D712yes—
751C2×C4C22×C22⋊D711yescharacteristic
752C2×C4C24×D711yescharacteristic
753C8—142no—
754C8—142no—
755C8—142no—
756C8—142no—
757C7C2×#332011yescharacteristic, complemented, Sylow
758C22—22no—
759C22—22no—
760C22—28no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22C2×#651414yes—
770C22C2×#651412yes—
771C22#9052012yes—
772C22#9052712yes—
773C22C23×C22⋊D711yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—144no—
782C4—282no—
783C4—282no—
784C4—282no—
785C4#9052012yes—
786C4C2×D7×#4111yescharacteristic
787C4C2×#655311yescharacteristic
788C2—24no—
789C2—42no—
790C2—82no—
791C2#1174106514yesdirect product factor
792C2C22×#651411yescharacteristic
793C2C2×#9052011yescharacteristic
794C2C2×#9052711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
Fitting, prime radicalC2×C7×#553C2
socleC23×C7C22×D4
hypercenterC2×#553D7
hypocenterC7C2×#3320
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic14C2semidirect
3. #11741065C2direct (N × H)
4. C2×#89835C2semidirect
5. C2×#89841C2semidirect
6. C2×#89812C2semidirect
7. C2×#89812C2semidirect
8. C2×#89814C2semidirect
9. C2×#89813C2semidirect
10. C2×#89791C2semidirect
11. C2×#89783C2semidirect
12. C2×#89790C2semidirect
13. C2×#89768C2semidirect
14. C2×#89776C2semidirect
15. C2×#89742C2semidirect
16. C22×#6384C2semidirect
41. D4×Dic14C22semidirect
50. #89841C22semidirect
51. #89835C22semidirect
52. #89814C22semidirect
53. #89813C22semidirect
54. #89812C22semidirect
55. #89812C22semidirect
56. #89791C22semidirect
57. #89790C22semidirect
58. #89783C22semidirect
59. #89776C22semidirect
60. #89768C22semidirect
61. #89742C22semidirect
71. C2×#6384C22semidirect
683. C2×C7#3320semidirect
757. C7C2×#3320semidirect
791. C2#11741065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5532
C2×D4×Dic142
#117410652
C2×#898352
C2×#898412
C2×#898122
C2×#898142
C2×#898132
C2×#897912
C2×#897832
C2×#897902
C2×#897682
C2×#897762
C2×#897422
C22×#63842
C2×#33207