Finite Group Databasebeta

← C2×#11741070 #14232369

Subgroups — C2×#11741070 #14232369

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×C7×#554C211yesmaximal, characteristic, complemented
2C2×#90256C211yesmaximal, characteristic
3#11741070C2116yesmaximal, direct product factor
4C2×#89859C211yesmaximal, characteristic, complemented
5C2×#89852C211yesmaximal, characteristic, complemented
6C2×#89821C211yesmaximal, characteristic, complemented
7C2×#89820C211yesmaximal, characteristic, complemented
8C2×#89816C211yesmaximal, characteristic, complemented
9C2×#89817C211yesmaximal, characteristic, complemented
10C2×#89798C211yesmaximal, characteristic, complemented
11C2×#89794C211yesmaximal, characteristic, complemented
12C2×#89783C211yesmaximal, characteristic, complemented
13C2×#89740C211yesmaximal, characteristic, complemented
14C2×#89739C211yesmaximal, characteristic, complemented
15C2×#89736C211yesmaximal, characteristic, complemented
16C22×#6381C211yesmaximal, characteristic, complemented
17C7×#554—24no—
18C7×#554C2218yescomplemented
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#125—21no—
21C2×C7×C22⋊Q8—21no—
22C2×C7×C22⋊Q8—21no—
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C4×C7×Q8C2211yescharacteristic
26C2×C4×C7×D4—21no—
27C2×C4×C7×D4C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C22×C7×C4⋊C4C2211yescharacteristic
30C22×#1143C2211yescharacteristic
31C2×#6502—21no—
32C2×#6493C2211yescharacteristic
33C2×#6493C2211yescharacteristic
34C2×#6489C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×#1136C2211yescharacteristic
37C23×C7⋊C8C2211yescharacteristic
38#90256—24no—
39#90256C2218yes—
40C2×#6461—21no—
41C2×#6446—21no—
42C2×(C22⋊D7)⋊C4—21no—
43C2×C4×D28C2211yescharacteristic
44C2×#6433C2211yescharacteristic
45C2×#6409C2211yescharacteristic
46C2×#6409C2211yescharacteristic
47C2×#6409C2211yescharacteristic
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49C2×C22⋊(C7⋊C8)C2211yescharacteristic
50#89859C2218yescomplemented
51#89852C2218yescomplemented
52#89821C2218yescomplemented
53#89820C2218yescomplemented
54#89817C2218yescomplemented
55#89816C2218yescomplemented
56#89798C2218yescomplemented
57#89794C2218yescomplemented
58#89783C2218yescomplemented
59#89740C2218yescomplemented
60#89739C2218yescomplemented
61C2×#6383C2211yescharacteristic
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64#89736C2218yescomplemented
65C2×#6382C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71C2×#6381C2211yescharacteristic
72C2×#6381C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2218yescomplemented
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3346—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4D411yescharacteristic
81C23×C4×C7—21no—
82C23×C4×C7—21no—
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C22×C22⋊D7—21no—
86C22×C22⋊D7—21no—
87C23×Dic7—21no—
88C22×D28C2311yescharacteristic
89C22×C4×D7—21no—
90C7×C4⋊Q8—22no—
91C7×C4⋊Q8C2314yes—
92C7×#125—28no—
93C7×C22⋊Q8—22no—
94C7×C22⋊Q8—22no—
95C7×C22⋊Q8—28no—
96C7×C22⋊Q8—28no—
97C7×C22⋊Q8C2314yes—
98C7×C22⋊Q8C2314yes—
99C4×C7×Q8—22no—
100C4×C7×Q8C2314yes—
101C4×C7×D4—28no—
102C4×C7×D4D414yes—
103C4×C7×D4C2314yes—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—22no—
107C2×C7×C4⋊C4—22no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4D411yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C4⋊C4C2311yescharacteristic
116C2×C7×C4⋊C4C2314yes—
117C2×C7×C4⋊C4C2314yes—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4D411yescharacteristic
121C2×C7×C22⋊C4D411yescharacteristic
122C2×C42×C7—21no—
123C2×C42×C7C2311yescharacteristic
124C2×C22⋊Dic7—21no—
125C2×#1143—24no—
126C2×#1143C2314yes—
127#6502—28no—
128#6493—22no—
129#6493—22no—
130#6493C2314yes—
131#6493C2314yes—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135#6489—22no—
136#6489C2314yes—
137C2×C4⋊Dic7—21no—
138C2×C4⋊Dic7—22no—
139C2×C4⋊Dic7C2311yescharacteristic
140C2×C4⋊Dic7C2311yescharacteristic
141C2×C4⋊Dic7C2311yescharacteristic
142C2×C4⋊Dic7C2314yes—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×C4×Dic7—21no—
146C2×#1136—24no—
147C2×#1136C2314yes—
148C22×C7⋊C8—24no—
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2314yes—
153C22×C7⋊C8C2311yescharacteristic
154#6461—28no—
155#6446—28no—
156(C22⋊D7)⋊C4—28no—
157C4×D28—22no—
158C4×D28C2314yes—
159#6433—22no—
160#6433C2314yes—
161#6409C2314yes—
162#6409C2314yes—
163#6409C2314yes—
164C22⋊(C7⋊C8)C2314yes—
165C22⋊(C7⋊C8)C2314yes—
166#6383C2314yes—
167#6383C2314yes—
168#6383C2314yes—
169#6382C2314yes—
170#6382C2314yes—
171#6382C2314yes—
172#6381C2314yes—
173#6381C2314yes—
174#6381C2314yes—
175#6381C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178C4⋊(C7⋊C8)C2314yes—
179#6377C2314yes—
180C2×#554D711yescharacteristic, complemented
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×#435—71no—
194C2×#428—71no—
195C22×#107—71no—
196C24×C7C2×D411yescharacteristic
197C24×C7C2×D411yescharacteristic
198C23×D7—21no—
199C2×C7×Q8—21no—
200C2×C7×Q8—24no—
201C2×C7×Q8—22no—
202C2×C7×Q8—22no—
203C2×C7×Q8—82no—
204C2×C7×Q8C2412yes—
205C2×C7×D4—24no—
206C2×C7×D4C2×D414yes—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—24no—
216C22×C4×C7—24no—
217C22×C4×C7—82no—
218C22×C4×C7—82no—
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D412yes—
224C22×C4×C7C2×D412yes—
225C22×C4×C7C2412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2411yescharacteristic
228C2×C22⋊D7—24no—
229C2×C22⋊D7—24no—
230C2×C22⋊D7—44no—
231C2×C22⋊D7—82no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—24no—
236C22×Dic7—82no—
237C2×D28—22no—
238C2×D28—22no—
239C2×D28—21no—
240C2×D28C2412yes—
241C2×C4×D7—24no—
242C2×C4×D7—82no—
243C7×C4⋊C4—21no—
244C7×C4⋊C4—24no—
245C7×C4⋊C4—24no—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—24no—
252C7×C4⋊C4C2×D414yes—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C4⋊C4C2412yes—
256C7×C22⋊C4—24no—
257C7×C22⋊C4—24no—
258C7×C22⋊C4C2×D414yes—
259C7×C22⋊C4C2×D414yes—
260C42×C7—24no—
261C42×C7C2×D412yes—
262C42×C7C2412yes—
263C22⋊Dic7—24no—
264#1143—28no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268C4⋊Dic7—21no—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7—24no—
272C4⋊Dic7C2412yes—
273C4⋊Dic7C2412yes—
274C4⋊Dic7C2412yes—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277C4×Dic7—24no—
278#1136—28no—
279C2×C7⋊C8—22no—
280C2×C7⋊C8—22no—
281C2×C7⋊C8—22no—
282C2×C7⋊C8—28no—
283C2×C7⋊C8#4114yes—
284C2×C7⋊C8C2412yes—
285C2×C7⋊C8C2412yes—
286C2×C7⋊C8C2412yes—
287C2×C7⋊C8C2412yes—
288C22×SD16—71no—
289C22×M16—71no—
290C23×C8—71no—
291#554—24no—
292#554C2×D718yescomplemented
293#553—78no—
294#553—144no—
295C2×C4⋊Q8C2×D711yescharacteristic
296C2×#126—141no—
297C2×#125—21no—
298C2×#125—71no—
299C2×#123—141no—
300C2×C22⋊Q8—21no—
301C2×C22⋊Q8—21no—
302C2×C22⋊Q8C2×D711yescharacteristic
303C2×C22⋊Q8C2×D711yescharacteristic
304C2×#121—71no—
305C2×#121—71no—
306C2×#121—141no—
307C2×C4×Q8C2×D711yescharacteristic
308C2×C4×D4—21no—
309C2×C4×D4—71no—
310C2×C4×D4—141no—
311C2×C4×D4C2×D711yescharacteristic
312C2×#117—71no—
313C22×C4⋊C4—71no—
314C22×C4⋊C4C2×D711yescharacteristic
315C22×C4⋊C4C2×D711yescharacteristic
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#435—78no—
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⋊C8—71no—
339C2×#103—71no—
340C2×#103—71no—
341C2×#103—71no—
342C2×#102—71no—
343C2×#102—71no—
344C2×#102—71no—
345C2×C22⋊C8—71no—
346C2×C22⋊C8—71no—
347C2×#97—71no—
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×Q8—22no—
362C7×Q8—22no—
363C7×Q8—42no—
364C7×Q8—84no—
365C7×D4—28no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—24no—
371C2×C4×C7—24no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7—84no—
385C2×C4×C7—84no—
386C2×C4×C7C22×D412yes—
387C2×C4×C7C22×D412yes—
388C2×C4×C7C22×D412yes—
389C2×C4×C7C22×D412yes—
390C2×C4×C7C22×D411yescharacteristic
391C2×C4×C7C2×#4112yes—
392C2×C4×C72−1+412yes—
393C2×C4×C7C2511yescharacteristic
394C22⋊D7—48no—
395C22⋊D7—84no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—42no—
400C2×Dic7—42no—
401C2×Dic7—42no—
402C2×Dic7—84no—
403D28—22no—
404D28—22no—
405D28—42no—
406C4×D7—84no—
407C7⋊C8—22no—
408C7⋊C8—22no—
409C7⋊C8—22no—
410C7⋊C8C2×#4114yes—
411C22×Q8—21no—
412C22×Q8C22×D711yescharacteristic
413C22×D4—71no—
414C22×D4—141no—
415C22×D4—141no—
416C22×D4C22⋊D711yescharacteristic
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—141no—
420C23×C4—141no—
421C23×C4C22×D711yescharacteristic
422C23×C4C22×D711yescharacteristic
423C2×SD16—74no—
424C2×SD16—144no—
425C2×M16—74no—
426C2×M16—144no—
427C22×C8—71no—
428C22×C8—71no—
429C22×C8—74no—
430C22×C8—71no—
431C22×C8—71no—
432C22×C8—144no—
433C4⋊Q8—22no—
434C4⋊Q8C22×D714yes—
435#126—148no—
436#125—28no—
437#125—74no—
438#125—142no—
439#123—148no—
440C22⋊Q8—22no—
441C22⋊Q8—22no—
442C22⋊Q8—28no—
443C22⋊Q8—28no—
444C22⋊Q8C22×D714yes—
445C22⋊Q8C22×D714yes—
446#121—74no—
447#121—74no—
448#121—148no—
449#121—142no—
450#121—142no—
451C4×Q8—22no—
452C4×Q8C22×D714yes—
453C4×D4—28no—
454C4×D4—74no—
455C4×D4—148no—
456C4×D4—142no—
457C4×D4C22⋊D714yes—
458C4×D4C22×D714yes—
459#117—74no—
460#117—142no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—71no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—74no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4—142no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4C22⋊D711yescharacteristic
478C2×C4⋊C4C22×D711yescharacteristic
479C2×C4⋊C4C22×D711yescharacteristic
480C2×C4⋊C4C22×D711yescharacteristic
481C2×C4⋊C4C22×D714yes—
482C2×C4⋊C4C22×D714yes—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—141no—
486C2×C22⋊C4—141no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4C22⋊D711yescharacteristic
490C2×C22⋊C4C22⋊D711yescharacteristic
491C2×C42—21no—
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⋊C8—74no—
504#103—74no—
505#103—74no—
506#103—74no—
507#102—74no—
508#102—74no—
509#102—74no—
510C22⋊C8—74no—
511C22⋊C8—74no—
512#97—74no—
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—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7—42no—
537C4×C7#54712yes—
538C4×C7C22×#4111yescharacteristic
539C4×C7C2×2−1+411yescharacteristic
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543C24—141no—
544C24C2×C22⋊D711yescharacteristic
545C24C2×C22⋊D711yescharacteristic
546C2×Q8—21no—
547C2×Q8—24no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—82no—
551C2×Q8C23×D712yes—
552C2×D4—24no—
553C2×D4—72no—
554C2×D4—144no—
555C2×D4—144no—
556C2×D4—142no—
557C2×D4—142no—
558C2×D4—141no—
559C2×D4—284no—
560C2×D4—562no—
561C2×D4C2×C22⋊D714yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—82no—
573C22×C4—82no—
574C22×C4—141no—
575C22×C4—141no—
576C22×C4—141no—
577C22×C4—144no—
578C22×C4—144no—
579C22×C4—562no—
580C22×C4—562no—
581C22×C4C2×C22⋊D712yes—
582C22×C4C2×C22⋊D712yes—
583C22×C4C2×C22⋊D711yescharacteristic
584C22×C4C2×C22⋊D711yescharacteristic
585C22×C4C2×C22⋊D711yescharacteristic
586C22×C4C2×C22⋊D711yescharacteristic
587C22×C4C23×D712yes—
588C22×C4C23×D712yes—
589C22×C4C23×D711yescharacteristic
590SD16—148no—
591M16—148no—
592C2×C8—74no—
593C2×C8—72no—
594C2×C8—72no—
595C2×C8—72no—
596C2×C8—72no—
597C2×C8—148no—
598C2×C8—142no—
599C2×C8—142no—
600C2×C8—142no—
601C4⋊C4—21no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—72no—
611C4⋊C4—72no—
612C4⋊C4—72no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—141no—
616C4⋊C4—141no—
617C4⋊C4—144no—
618C4⋊C4—141no—
619C4⋊C4C2×C22⋊D714yes—
620C4⋊C4C23×D712yes—
621C4⋊C4C23×D712yes—
622C4⋊C4C23×D712yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—144no—
626C22⋊C4—144no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4C2×C22⋊D714yes—
630C22⋊C4C2×C22⋊D714yes—
631C42—24no—
632C42—144no—
633C42C2×C22⋊D712yes—
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#650514yes—
652C23C22×C22⋊D712yes—
653C23C22×C22⋊D712yes—
654C23C22×C22⋊D711yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—42no—
658Q8—84no—
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—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—84no—
684C2×C4—84no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—282no—
689C2×C4—282no—
690C2×C4—282no—
691C2×C4—564no—
692C2×C4—564no—
693C2×C4D7×#4112yes—
694C2×C4#655412yes—
695C2×C4C22×C22⋊D712yes—
696C2×C4C22×C22⋊D712yes—
697C2×C4C22×C22⋊D712yes—
698C2×C4C22×C22⋊D712yes—
699C2×C4C22×C22⋊D711yescharacteristic
700C2×C4C24×D711yescharacteristic
701C8—74no—
702C8—142no—
703C8—142no—
704C8—142no—
705C7C2×#334611yescharacteristic, complemented, Sylow
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—282no—
714C22—282no—
715C22—282no—
716C22—564no—
717C22C2×#650514yes—
718C22C2×#650512yes—
719C22#9051512yes—
720C22#9052612yes—
721C22C23×C22⋊D711yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—282no—
731C4—282no—
732C4—282no—
733C4#9051512yes—
734C4C2×D7×#4111yescharacteristic
735C4C2×#655411yescharacteristic
736C2—24no—
737C2—42no—
738C2—562no—
739C2#1174107014yesdirect product factor
740C2C22×#650511yescharacteristic
741C2C2×#9051511yescharacteristic
742C2C2×#9052611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#554C2
socleC23×C7C22×D4
prime radicalC2×#90256C2
hypercenterC2×#554D7
hypocenterC7C2×#3346
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×C7×#554C2semidirect
3. #11741070C2direct (N × H)
4. C2×#89859C2semidirect
5. C2×#89852C2semidirect
6. C2×#89821C2semidirect
7. C2×#89820C2semidirect
8. C2×#89816C2semidirect
9. C2×#89817C2semidirect
10. C2×#89798C2semidirect
11. C2×#89794C2semidirect
12. C2×#89783C2semidirect
13. C2×#89740C2semidirect
14. C2×#89739C2semidirect
15. C2×#89736C2semidirect
16. C22×#6381C2semidirect
18. C7×#554C22semidirect
50. #89859C22semidirect
51. #89852C22semidirect
52. #89821C22semidirect
53. #89820C22semidirect
54. #89817C22semidirect
55. #89816C22semidirect
56. #89798C22semidirect
57. #89794C22semidirect
58. #89783C22semidirect
59. #89740C22semidirect
60. #89739C22semidirect
64. #89736C22semidirect
74. C2×#6381C22semidirect
180. C2×#554D7semidirect
292. #554C2×D7semidirect
637. C2×C7#3346semidirect
705. C7C2×#3346semidirect
739. C2#11741070direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5542
C2×#902562
#117410702
C2×#898592
C2×#898522
C2×#898212
C2×#898202
C2×#898162
C2×#898172
C2×#897982
C2×#897942
C2×#897832
C2×#897402
C2×#897392
C2×#897362
C22×#63812
C2×#33467